Study Guide
by
Matthew C.
for
Dancing with the Muses:
A Historical Approach to Basic Concepts of Music
by
M. Zachary Johnson
About this Study Guide
There are two types of questions in this study guide: Exercises and Questions for Thinking and
Discussion.
Exercises sequentially highlight the main progression of ideas in the book, and generally have short,
clear answers. All exercise answers can be found in the book itself, although they are also included at the end
of the study guide. Exercises often use key words or phrases from the corresponding answers in the book.
Questions for Thinking and Discussion are constellations of questions for stimulating thought on
particular topics, and they sometimes extend beyond the scope of the book. These questions can be thought
about; they can be discussed in a classroom setting; they can be addressed in short answers or paragraphs; or
they can be distilled into a thesis and explored in depth with a full length essay.
All page references pertain to the second edition of the book. (It has the author’s photo on the back
cover.)
This guide is also designed so that individual chapters can be printed as separate individual
worksheets if needed.
Table of Contents
Exercises
Questions for
Answers to
Thinking
Exercises
Preface
1
2
39
1. Melodic Shape
3
5
40
2. Interval
6
8
42
3. Scale
9
13
45
4. Time
14
16
49
5. Polyphony
17
19
51
6. Tonality
20
23
53
7. Counterpoint
24
29
56
8. Harmony
30
32
60
9. Primacy of Line vs. Primacy of Chord
33
37
62
Preface
Exercises
1. What four categories does the book teach?
2. How are these four categories ordered?
3. What method of presentation does this book adopt?
4. What method of presentation does this book not resort to?
5. What is one advantage to studying music historically?
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Preface
Questions for Thinking and Discussion
A. What is the “proper order” of concepts? Is it equivalent to the order by which mankind discovers
concepts, and why or why not? How might the historical order of learning reveal a logical progression to
concepts in music? How might history improve your understanding of music? How might a historical
approach to other subjects improve your understanding of them? [IX to XI]
B. What are the connections between music theory, music history, the philosophy of music, and other
usually separated fields in music? How would you connect music to other subjects, such as math, physics,
chemistry, biology, literature, or art? What do these subjects share, and to what degree are they similar?
What makes them different, and why might people have separated them in the first place? What are the
results of separating or integrating them? [X]
C. Reason and emotion are often viewed as opposites or as mutually exclusive. How does music refute this
view? How are logic in structure and feeling in expression both necessary to music? [X to XI]
D. How might composers, performers, listeners, critics, and teachers have different understandings of
music? How is music approached in each of these positions? [XI]
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Chapter 1: Melodic Shape
Exercises
1. What is the essential substance of music?
2. What is a musical line?
3. What kind of line is a cantus firmus—what elements does it abstract away from, what elements
does it isolate, and to what purpose?
4. Is the process of creating a cantus firmus only analytical? Is it only creative?
5. What degree of the scale should a cantus firmus always begin and end on?
6. How should the final note of a cantus firmus be approached?
7. How many notes should a cantus firmus be, and why?
8. Why shouldn’t one repeat two notes in succession in a cantus firmus?
9. What span of notes should a cantus firmus range within?
10. Why and how should a cantus firmus change direction and incorporate leaps?
11. How do these rules facilitate the purpose of a cantus firmus?
12. What is the strictest form of the rule for using leaps in a cantus firmus?
13. How can one include “hanging notes” in a cantus firmus?
14. What is the overall feature of a cantus firmus?
15. Write your own cantus firmus: plan an overall shape for the line, choose a specific note for its
beginning and end, decide upon the highest/lowest note, and begin writing a line backwards from
the end note. Add variety with several leaps or changes of direction, but remember to maintain
unity—refer to the guidelines listed on pages 2 and 3 for help.
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16. Define monophony and polyphony.
17. Define heterophonic and homophonic.
18. How is heterophony a special kind of monophony, and how is homophony a special kind of
polyphony?
Aristoxenus
19. Who was Aristoxenus? What particular aspect of melody did he address?
20. What two faculties does Aristoxenus assert we must judge music by?
21. What new concept did Aristoxenus originate?
Further Developments on Melodic Synthesis
22. What four great innovators advanced our knowledge of melodic shape and pitch connections?
23. When did Aristoxenus live, and what did he do?
24. When did Guido d’Arezzo live, and what did he do?
25. When did Zarlino live, and what did he do?
26. When did Rameau live, and what did he do?
27. When did Fux live, and what did he do?
28. When did Schenker live, and what did he do?
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Chapter 1: Melodic Shape
Questions for Thinking and Discussion
A. Why is melody, rather than rhythm by itself, the essential substance of music? Why does a cantus firmus
exercise isolate pitch but not rhythm? Would you recognize a melody if the notes were the same but the
rhythm altered? What about if the notes were altered but the rhythm was the same? What if only the
rhythm of the tune was clapped—could you identify the tune? [1] Note that rhythm is further covered in
chapter 4.
B. Revisit the two lists of rules for composing a cantus firmus—imagine a cantus firmus that intentionally
contravened one of the rules. What problems arise? Can any of the rules be removed? Could any be added?
Are these rules absolutes, or is there an underlying purpose or spirit to them? Is it perhaps impossible to
completely understand the purpose without having tried the rules beforehand? What reasons does the book
provide to explain their origin? Do the rules define the purpose, or does the purpose define the rules? [2 to
3]
C. Why might one defend the idea that the scale ought to be divided into equal (or unequal) intervals?
What assumptions are behind such an approach? Why does Aristoxenus assert that one must apprehend
music by hearing, and remembering and thinking about what we hear? What does he assume in asserting
this? [7]
D. Revisit the four great innovators listed on page 9. What progression do you see underlying their
discoveries? Could their discoveries have come in a different order—could Johann Fux have established
polyphonic composition methods before Guido d’Arezzo had developed a system of notating single lines? [9
and 11]
E. Revisit the chart on page 11. Several non-musical facts are included in this chart: what perspective and
orientation do they provide on the musical facts? Do similar kinds of events occur during the same period,
inside the music field and outside? How do advances in science or philosophy influence advances in music?
From this chart, what connections can you draw between fields? (Also, see question B from the preface.)
Briefly narrate the progression of successive facts. [11]
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Chapter 2: Interval
Exercises
1. What is an interval?
2. What two aspects do intervals have?
3. What might have been the first prehistoric knowledge of musical distances?
4. What is a step and what is a skip?
5. What is the general definition of the word scale and what is a musical scale?
6. How did the construction of musical instruments facilitate man’s understanding of the musical
scale?
7. How did the musical scale enable men to define a musical interval?
8. After the conceptualization of the interval, what two observations are likely to follow?
9. What particular three elements enabled these advances in music?
Pythagoras
10. Who was Pythagoras, and when did he live?
11. If the story about Pythagoras’ discovery of musical intervals is not literally possible, then what
overall meaning can still be learned from it?
Consonance, Dissonance, & Other Interval Qualities
12. What is the most obvious and basic distinction that can be made about intervals?
13. What is consonance and what is a dissonance?
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14. What is the difference between a perfect and an imperfect consonance?
15. What are the different interval qualities for perfect intervals? For imperfect intervals?
16. What are enharmonic notes or intervals?
17. When and why would the same interval be spelled differently?
18. In addition to enharmonic intervals, what is another way that intervals can be equivalent?
Dueling Worldviews: “Harmony of the Spheres” vs. Humanistic Science
19. Which two Ancient Greek philosophers originated opposing views on music theory; and what
were these opposing views?
20. What two different Ancient Greek philosophers originated opposing views on metaphysics; and
how are the views of all four Greek philosophers related?
Helmholtz
21. Who was Hermann von Helmholtz, and what law is he particularly known for?
22. What was Helmholtz’s view of reason and expression?
23. What is the difference between musical tones and noises?
24. What are the four attributes of an individual musical tone?
(Summary)
25. Describe the difference between a consonant interval and a dissonant interval in terms of frequency
ratio size.
26. What are the three perfect intervals, and what impression do they give?
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27. What are the two imperfect intervals, and what impression do they give? (What impression do
major and minor intervals each give?)
28. What are the dissonant intervals, and what impression do they give?
29. What did Helmholtz’s studies confirm about our experience of music?
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Chapter 2: Interval
Questions for Thinking and Discussion
A. Briefly narrate how the musical intervals probably would have been conceptualized in prehistory;
include how prehistoric men first must have made basic observations, then made a distinction between
steps and skips, then conceptualized the musical scale alongside musical instrument construction, and with
the help of the musical scale further studied the nature of intervals to arrive at our present understanding.
What connections did men make to progress from one step to another? What scientific measurements were
involved? Could these steps have occurred in another order, and why or why not? What is the point of
understanding the origin of the musical scale and the intervals that comprise it—does knowing their history
change their meaning to you in any way? [13 to 15]
B. How is music connected to mathematics, as shown in Pythagoras’ story? How is music connected to
science, as shown in Helmholtz’s studies? To what extent do mathematics and science connect to music? Do
they affect how you listen to music? When listening to music, do you naturally connect what you hear to
mathematics and science? [16 to 18; 25 to 30]
C. Why is melody integrated by means of stepwise intervals (C to D, for example), the very intervals
which, when sounded simultaneously, clash as a dissonance? The movement from C to D appears simple;
why then does it form a dissonant interval, which implies it has a complex frequency ratio? In fact, the
frequency ratio for the major second is 8:9 and for the minor second is 15:16. How can the simple interval
that connects melodies be complex in this way? The frequency ratio for the octave is 1:2 and for the fifth is
2:3. Why do these large, consonant intervals have such simple frequency ratios? [19; 29 to 30]
D. What is the connection between Aristoxenus’ view of music theory and Aristotle’s view of reality? What
is the connection between Pythagoras’ view of music theory and Plato’s view of reality? What is the
Aristotelian-Aristoxenian approach, and what is the Platonic-Pythagorean approach? Why are they
opposites? [22 to 25]
E. If both pitch and rhythm derive from the frequency of a vibration, then why do they sound different to
us? Why has the human hearing system evolved to perceive pitch-frequency and rhythmic beats in
different forms? What is the status of this difference—is it a subjective illusion or is it natural and inherent
in human hearing? Listen to a piece of music and try to think of rhythm and pitch as the same thing; can
you conceive music purely as frequencies? [28 to 29]
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Chapter 3: Scale
Exercises
1. What is the basis of all aspects of the notes used in music—what is the integrating framework of
music?
2. What are the three stages this chapter proceeds in?
I - Anthropological and Historical Data on the Scale
3. What type of scale is sounded by the two prehistoric bone flutes discovered in Germany?
4. What are some of the features of these flutes that confirm that the notes were intentionally chosen
to form a scale, that they were not random or haphazard?
5. What is another example of the scale in ancient history, in a musical tradition that still continues
today?
6. What is yet another example of the scale in ancient history, found on cuneiform tablets?
7. What is a tetrachord?
8. What is an enharmonic tetrachord?
9. What is a chromatic tetrachord?
10. What is a diatonic tetrachord, and where does the word diatonic come from?
11. How do tetrachords relate to scales? How did the ancient Greeks originate the diatonic scale from
tetrachords?
Scalar Mathematics
12. Summarize the two basic facts about music perception.
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13. Explain the mathematical patterns behind the three types of tetrachord. Create a chart showing the
three tetrachords’ frequency ratios and lowest common denominators.
14. How is the diatonic scale constructed out of diatonic tetrachords?
15. Explain the mathematical patterns behind the major and minor scale. Create a chart showing each
note’s frequency ratios and lowest common denominators.
16. What is a musical key?
Drawing on Our Ordinary Experience; Conclusion
17. What are several examples of the fundamentality of the diatonic scale?
II - Mode
18. What is a musical mode? How are modes related to and derived from the diatonic scale?
19. Choose one major mode and one minor mode and describe each; mention the impressions they give,
and examples of where they are used.
20. Describe how the diatonic scale is different from constructed, “symmetrical” scales.
Unique Numbers of Intervals in the Scale
21. Explain how the diatonic scale has a unique numbers of intervals, and describe other patterns that
arise from this fact.
The Tendency of Correcting Inflections
22. What is another fact that confirms that the diatonic scale is the fundamental basis of human
musical cognition?
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III - Solfege
23. What is solfege, and in what musical was it famously used?
Guido d’Arezzo
24. Who was Guido d’Arezzo?
25. What was one of his new devices?
26. What was the earliest form of notation succeeding the Greeks, that appeared in the 9th century
during the time of Charlemagne’s influence? What was special about this form of notation, that
even the Greeks had never done?
27. What was an even more comprehensive form of notation, found in the Musica Enchiriadis?
28. How did Guido d’Arezzo invent a new form of notation out of the two previous 9th century forms?
29. Why did the monks throw him out of his original monastery?
30. What topics did he cover in his Micrologus?
31. What formulaic method did he first devise, that would later evolve into solmisation?
32. What melody did he choose for the mnemonic solfege syllables? What were the original syllables?
33. What were some of the results of Guido’s solfege system?
34. Why are notes lettered beginning with A, on the minor scale? Why do we actually begin with C,
on the major scale; what does this signify?
35. What was the true source of the melody Guido used for the solfege, and why did he hide it?
The Transition to Modern Solfege
36. How did Gutenberg’s printing press influence music and the solfege system?
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Glover & Curwen
37. Who was Sarah Anne Glover, and what changes to Guido’s solfege system did she make?
38. Who was John Curwen, and what contribution is he best known for?
39. What are several examples of solfege-like systems in other cultures?
Note Names in the Romance Languages
40. How did advances in instrument construction during the Renaissance change people’s
understanding of musical notes?
41. What is fixed-do solfege and what is movable-do solfege?
42. Which method is more advanced and easier to use in real-time?
Summary
43. What is the essential overall importance of the scale?
44. What is a simple way of defining the diatonic scale?
45. What are examples of artificially constructed, non-diatonic scales?
46. What is the scientific or mathematical definition of the diatonic scale?
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Chapter 3: Scale
Questions for Thinking and Discussion
A. What is the significance of early flutes discovered by archaeologists? What information do flutes tell us
that the remains of other instruments could not? Could prehistoric men have had some sort of inspiration
to place holes and marks at certain places, or would they have experimented and judged sounds by ear to
create the flutes? Why did they try to make such instruments in the first place? Why did they arrange the
holes as they did? Why a diatonic scale rather than a chord or some other assortment of notes? [31 to 34]
B. In addition to musical modes, what other kinds of “modes” are there in other subjects (for example,
literature, science, mathematics, and computing)? Are any of those modes related to musical modes? How
do we know that modes are inflections of the diatonic scale and not the other way around; is the diatonic
scale simply another mode? Why must music in a certain mode necessarily convey the impression that the
mode itself conveys? What does diatonic music sound like in different modes? Choose any melody or
musical composition based on the diatonic scale, and translate it into a new mode (for example, Bach’s
Violin Concerto in D minor Movement 1 translated into a major or Dorian mode). What is the result? [41
to 48]
C. Why is Guido d’Arezzo’s form of notation significant? In what way is it an improvement on older
methods? Guido’s invention was from the 11th century, but it is still used today: will it become outdated?
What other forms of notation have been invented (in other cultures, for example)? What new forms of
notation are arising nowadays, from technological and computational advances? Are they based on Guido’s
notation or have they developed separately? What or whom are they intended for? What do all these forms
of notation share in common? [52 to 56]
D. As the book observes, Guido’s notation is essentially a scientific graph with a vertical axis for pitch and
horizontal axis for time. What similar graphs are there in mathematics, physics, chemistry, biology, and
the other sciences? Recall the four attributes of a musical tone (see Chapter 2, page 40). In what ways does
our modern, Guido-derived music notation system communicate all four attributes? Must all methods of
comprehensive music notation communicate information about these four attributes? [54]
E. Summarize the progression of thought proving the cognitive validity and necessity of the diatonic scale.
What is the diatonic scale? What evidence is there showing that the diatonic scale is inherent in man’s
nature? Compared to other possible note progressions, why does the diatonic scale stand out as special?
What scientific and mathematical basis is there for the diatonic scale? Overall, what proof is there that the
diatonic scale ought to be acknowledged as singular in importance? [69 to 70]
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Chapter 4: Time
Exercises
Rhythm and Life
1. What was the first and simplest form of locomotion?
2. What are examples of rhythm in life, biology, or nature?
3. What aspect of man brings a new dimension to bodily movements and rhythm?
4. What is rhythm?
Rhythm as a Measurement
5. How is rhythm something more for a man than it is for an animal?
6. By what central means does the mind integrate action?
7. What does measurement require?
8. What is a beat?
9. What kind of measurement of time is rhythm?
10. Is absolutely unwavering, scientifically, or mechanically precise regularity needed for rhythm? Is
this found in nature?
11. What is hierarchical about the measurement of rhythm?
12. What is a meter, and what is one instance of a metrical pattern?
13. What is duple meter? What is an example of duple meter, and what impression does it give?
14. What is triple meter? What is an example of triple meter, and what impression does it give?
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15. What is the difference between rhythm and meter?
16. What are the two basic subdivisions of a beat?
17. Choose and describe two types of meter (for example, duple meter duple subdivision).
Poetic Rhythm
18. How can poetry be a helpful way of considering abstract rhythmic patterns in music?
19. In Emily Dickinson’s “A Charm Invests a Face,” how does meter contribute to the poem’s meaning?
The Metronome
20. Who invented the metronome? When was it invented, and what is the origin of its name?
21. How is the metronome a helpful tool?
22. How did the metronome also lead to problematic ways of thinking?
23. What was one of the effects of this way of thinking?
Concluding Summary
24. What is the connection between rhythm and life?
25. What is the essence of rhythm?
26. What is a beat? What is a meter?
27. How is metrical organization hierarchical?
28. How is rhythm not the same for a man as it is for an animal?
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Chapter 4: Time
Questions for Thinking and Discussion
A. In what way does rhythm have meaning? In what way does rhythm express one’s self-concept? Think of
a variety of examples of rhythmic movement and describe the self-concept they express. How can one use
rhythm to infuse one’s own intended meaning to a piece of music? What is the point of deeper meaning—is
it necessary to humans in any way, is it simply a by-product of the human mind, or is it artificial and
unnecessary? What would music be like without meaning? [72 to 74]
B. What units do men use to measure intensity (volume) and pitch? How are they similar to the units we
use to measure rhythm? Are all forms of measurement hierarchical, and why or why not? What reason is
there for subdividing a unit? Are there any necessary properties that all units should have? [75 to 76]
C. Why don’t humans live by absolute, mechanically precise rhythms? What does this view assume or
oversimplify? What rhythms do humans naturally live by, and what rhythms do humans enjoy in music?
When performing a musical piece, what can an artist express with variances in tempo and rhythm? What
expression is lost when the rhythm is unvaried and mechanical? [75 to 76; 81 to 82]
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Chapter 5: Polyphony
Exercises
1. What is the distinctive achievement of Western Music?
2. What formed the starting point for polyphonic music?
Plato & Gregorian Chant
3. Briefly describe Plato’s philosophy.
4. How does Plato’s philosophy relate to Christianity?
5. Who was St. Augustine?
6. What music resulted from St. Augustine’s ideals?
7. Who was Pope Gregory the Great? What music is attributed to him and why?
8. What is Gregorian Chant?
9. What impression does Gregorian Chant give? How does it fulfill the Platonic and Augustine ideals?
The Birth of Polyphony
10. Who was Charlemagne?
11. How did the Carolingian Renaissance influence music in the Middle Ages?
12. What was musical life like in the Middle Ages?
13. What musical document resulted from the Carolingian Renaissance?
14. What was the first stage of polyphony?
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15. What problem arose from this first stage, and what rule was created to resolve it?
16. What was the idea behind this first rule of composition?
17. After Charlemagne, what three musical elements began to develop together in a continuous spiral?
18. How did polyphony rely on and enable the other two elements?
19. How did notation rely on and enable the other two elements?
20. How did rules rely on and enable the other two elements?
21. What principles led to this new progress?
22. Who was Palestrina, and why is his music remarkable?
23. In what way did music change during the Renaissance, and what was its underlying cause?
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Chapter 5: Polyphony
Questions for Thinking and Discussion
A. Why is Western Music distinguished by polyphony in particular? What enabled the development of
polyphony in the Renaissance, that cultures with monophonic music may not have had? Why did music
remain monophonic under the historical time dominated by St. Augustine's and Plato's views, and why did
music become polyphonic under the influence of Aristotle's views? Describe the progression of ideas that
lead from each philosophy to its resulting music—how specifically do these opposite philosophies manifest in
music? Listen to examples of Gregorian chant and Renaissance polyphony. What is “Platonic” about
Gregorian chant and what is “Aristotelian” about Renaissance polyphonic music? [85 to 88]
B. Discuss how polyphony, notation, and rules developed simultaneously in the post-Charlemagne period.
How did each enable the others? If one of these elements were to be removed, how would it limit the
development of the other two? What are instances of such spiral-development of elements within other
subjects (within science, literature, or the visual arts)? Can you think of any instances of a
spiral-development of elements between different subjects (interdisciplinary spiral-development)? [91 to 92]
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Chapter 6: Tonality
Exercises
1. What crucial principle animated Renaissance art? How did it manifest in the visual arts, literature,
and music?
2. What was the motion of polyphonic music like?
3. Why can polyphony give a feeling of direction over a longer period of time than monophony?
4. What is a cadence?
5. In addition to the cadence, what was another means of creating a feeling of goal-direction?
Zarlino
6. Generally describe tonality in its historical context. Who formulated this principle?
7. What is Zarlino’s view of consonances and dissonances, as stated in his treatise The Institution of
Harmony? What law did he begin with?
8. What did this law imply about a composition as a whole? How did Zarlino apply the law to longer
time spans?
9. What is Zarlino’s definition of tonality?
10. What Greek word does tonality derive from? Why does it accurately describe tonality?
11. If dissonances must resolve, as Zarlino taught, what is the most complex consonance (i.e. that does
not itself need to resolve, and that other dissonances resolve to)? What scale-steps does it typically
consist of?
12. What three crucial identifications did Zarlino indicate about triads?
13. What inconsistency or inadvertent error does the “unity of mode” solve?
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14. How does the principle of tonality require one to consider sonorities within the context of the
entire composition, and likewise prevent one from considering sonorities individually/separately
(out of context)?
15. What local rule of counterpoint did Zarlino start with?
16. What is the most powerful dissonance of all, and what unique effect distinguishes it from all other
dissonances?
Scale-step
17. What is the first factor determining the quality of a scale-note?
18. What is the second factor determining the quality of a scale-note?
19. Briefly characterize the tonic note.
20. Briefly characterize the supertonic.
21. Briefly characterize the mediant.
22. Briefly characterize the subdominant.
23. Briefly characterize the dominant.
24. Briefly characterize the submediant.
25. Briefly characterize the leading tone or subtonic.
Modulation
26. What is modulation?
27. What are the two possible functions of a chromatic tone in the context of the diatonic scale?
28. What is a key?
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29. In a scale, what happens when an established tone is replaced by a new inflection?
30. How did the flat accidental “soften” an interval?
31. What was the original purpose of the sharp accidental?
32. Is a change from C major to C minor a modulation? Why or why not?
33. What is the basic pattern of tonal music? How broadly can this principle be implemented?
Key Relation
34. What is the relationship between relative major and minor keys?
35. What is the relationship between parallel major and minor keys?
The Rise and Fall of Tonal Integrity
36. How did composers create a sense of drive towards the cadence?
37. How did composers incorporate dissonances?
38. How did composers use scale notes?
39. How did composers create expressive effects and the feeling of departure and return?
40. How did composers use chords?
41. Overall, what were the results of tonality?
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Chapter 6: Tonality
Questions for Thinking and Discussion
A. How does the principle of volition reveal fundamental differences between the philosophies of Plato and
Aristotle? Does the principle of volition flourish under Plato's philosophy or Aristotle's, and why?
Highlight the progression of ideas from “this worldliness” to “expression of volition.” How does volition
manifest in the art forms (for example, tonality in music, and perspective in the visual arts)? [95 to 97]
B. Recall the three elements that developed together in a continuous spiral during the post-Carolingian
Renaissance: polyphony, notation, and rules. How exactly do each of these three elements enable a clear
expression of volition? How do each of these three elements connect to tonality? Why specifically does
polyphonic music give a stronger impression of directionality than monophonic music? What specifically
about the interaction of multiple lines gives rise to the feeling of direction towards a goal? How do multiple
lines clarify tonality—how do they help recall the listener to, and help him orient mentally around the tonic
note? [96 to 99]
C. In what way is the tritone the most dissonant interval of all? How was the tritone viewed throughout
history? What does the tritone sound like when it resolves in proper musical context (for example, in the
exposition of a Baroque concerto or a Classical sonata)? What does the tritone sound like without proper
resolution or context? Describe how the musical context affects the mental effect this interval produces.
[100 to 105; 110 to 111]
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Chapter 7: Counterpoint
Questions for Thinking and Discussion
1. What is counterpoint and where does the term come from?
2. How did the first rules of counterpoint come about?
3. What three people helped to form early rules of combining lines?
Fux
4. Who was Johann Josef Fux?
5. What is the Gradus ad Parnassum?
6. In what way is the Gradus ad Parnassum an important achievement?
7. Who are some of the composers that practiced Fux’s theories?
Types of Relative Motion
8. Describe the four types of relative motion.
1st Species Counterpoint: Consonance
9. Briefly describe first species counterpoint.
10. What is the aim in first species counterpoint, and what should one thus avoid?
11. What is the positively stated rule summarizing this idea?
12. In order to keep variety and independence of the lines, how should parallel intervals be used?
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13. How can one keep track of the intervals between the two lines?
14. What intervals are available for first species counterpoint?
15. Choose or write a cantus firmus (see Chapter 1 for cantus firmi) and write a first species
counter-line for it, following the guidelines outlined in pages 118 to 120.
Iterative Method
16. What is the Iterative Method?
17. What is helpful about the Iterative Method—what are its advantages over attempting to create a
perfect, final version from the start?
2nd Species: Passing & Neighboring Tones
18. Briefly describe second species counterpoint.
19. How are dissonances introduced in second species?
20. How should dissonances be approached into and departed from, in order to be integrated with the
rest of the piece?
21. What is a passing tone and what is a neighboring tone?
22. How should leaps be used?
23. Choose or write a cantus firmus (see Chapter 1 for cantus firmi) and write a second species
counter-line for it, following the guidelines outlined in pages 122 to 123.
Rational vs. Irrational Creativity
24. What is the authoritarian view on the status of rules?
25. What is the rebel’s view on the status of rules?
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26. What is the rational view on the status of rules?
27. What is rational creativity?
28. What is irrational creativity?
29. What is sensationalism?
3rd Species: Scalar Motion
30. Briefly describe third species counterpoint.
31. What note must the counter-line end on?
32. How should the counter-line begin to offset it from the cantus firmus?
33. For each measure, what tones must be consonant and what notes can be dissonant?
34. Are changes of direction within the line appropriate, and why or why not?
35. Specifically describe the double-neighbor figure and the “nota cambiata” figure. What stepwise
motions or intervals are in each figure? See Figure 7.4 for examples.
36. Choose or write a cantus firmus (see Chapter 1 for cantus firmi) and write a third species
counter-line for it, following the guidelines outlined in pages 126 to 127.
4th Species: Syncopation
37. Briefly describe fourth species counterpoint.
38. What is syncopation, and what is its etymology?
39. In what way is fourth species particularly similar to first species?
40. What kind of syncopation is suspension, and what does it cause?
41. What is the simplest and most complete pattern for the suspension?
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42. How must the suspended note resolve (to allow the brain to integrate the dissonance)?
43. What is the etymology of the term resolution?
44. What is a chain of suspensions and how can they be used?
45. What is “breaking the species” and why is it sometimes useful?
46. Choose or write a cantus firmus (see Chapter 1 for cantus firmi) and write a fourth species
counter-line for it, following the guidelines outlined in pages 127 to 129.
Ornamented 4th Species
47. What are the five types of ornaments we can apply to suspensions to accentuate the syncopation?
48. Choose or write a cantus firmus (see Chapter 1 for cantus firmi) and write an ornamented fourth
species counter-line for it, following the guidelines outlined in pages 129 to 130. Alternatively,
choose and add ornaments to a preexisting fourth species counter-line (from the book, or from
Exercise 46).
5th Species: Organic Melody
49. Briefly describe fifth species counterpoint.
50. How should the counter-line begin, to offset it from the cantus firmus?
51. How long can one use a single note value, and why?
52. How does music flow well?
53. What events can break continuity?
54. Choose or write a cantus firmus (see Chapter 1 for cantus firmi) and write a fifth species
counter-line for it, following the guidelines outlined in pages 130 to 131.
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An Example by Brahms
55. How is this piece an example of counterpoint—what “species” is it?
1st Species in 3 Parts: Richer Sonorities
56. Briefly describe the first species of three part counterpoint.
57. What new relations must we contend with in three-part writing? Specifically, what do we
consider for each line?
58. What possible sonorities are there? In particular, what are the two possible full sonorities?
59. What is the status of the middle voice—is it solely for harmonizing the top and bass lines as “filler,”
is it as prominent as the other two lines, or is it somewhere in between?
60. Choose or write a cantus firmus (see Chapter 1 for cantus firmi) and write two first species,
three-part counter-lines for it, following the guidelines outlined in pages 133 to 134.
Conclusion
61. Briefly summarize the rules and considerations for line shape.
62. Describe the overall method for writing species counterpoint.
63. Briefly summarize the rules and considerations for first species.
64. Briefly summarize the rules and considerations for second species.
65. Briefly summarize the rules and considerations for third species.
66. Briefly summarize the rules and considerations for fourth species and ornamented fourth species.
67. Briefly summarize the rules and considerations for fifth species.
68. Briefly summarize the rules and considerations for first species in three parts.
69. Choose or write a cantus firmus (see Chapter 1 for cantus firmi). After completing the previous
counterpoint exercises, choose a species and write a counter-line to the cantus firmus, following
the guidelines outlined on page 135.
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Chapter 7: Counterpoint
Questions for Thinking and Discussion
A. In what ways does Fux’s Gradus ad Parnassum build upon and summarize the work of prior thinkers? How
does it rely upon Guido d’Arezzo’s notational innovations, Zarlino’s theories on tonality, and Palestrina’s
music? Why did Fux’s theories enable such a large number of great composers? Are there great composers
who did not apply his theories? Bach and Vivaldi were composing before the Gradus ad Parnassum was
published, for example—do they use the same principles as those who did learn Fux’s theories? [114 to 118]
B. Is it actually possible to begin with a whole draft of a composition or other work and then refine it in
progressive versions? Does one fundamentally develop works linearly (at points) or holistically (as a whole),
and why? Is it necessarily one or the other (are they mutually exclusive) or can a work develop in both
senses? Does one begin a work of art with fragments and details, or with a complete work in mind? Is the
iterative version more helpful for starting a creation, or finishing one? [120 to 122]
C. What are examples of the three views of rules and creativity (the authoritarian, rebel, and rational
views)? What are examples of these essential views in other subjects, such as in history, art, or science? Are
these three views connected to deeper philosophical viewpoints? How do these three views relate to creation
and creativity—how does each enable or disable certain aspects of creation and creativity? When one
“creates” a work of art, is one actually creating matter ex nihilo; or is it creation in another sense? Defend the
use of the term “create”; or reject it and propose a more accurate term, explaining why. What exactly is
creativity, and where does it come from? Why might it be helpful to one’s creativity to learn about what
others have discovered (as Goethe said in his quote)? [123 to 126]
D. Are Fux’s rules helpful and meaningful before (or without) trying them for oneself? If Fux’s rules were
presented without any justification or reasoning, would they still be helpful and meaningful? Without any
explanation of their purpose and advantages, would there be any reason to try them in the first place? Is it
possible to find the purpose and underlying reasoning of a rule just from looking at it as a final result? Does
the application of a rule necessarily reveal its underlying reasoning and justification? [125 to 126]
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Chapter 8: Harmony
Exercises
1. What is a musical chord, and where does the term come from?
2. What is a triad?
Voice-leading
3. What is voice-leading?
4. What is the difference between counterpoint and voice-leading?
Chord Function
5. What is harmonic progression?
6. What is the primary fact about a chord?
7. What is indicated by the Roman numerals assigned to chords?
8. What is the controlling element of harmony?
9. What is the characteristic difference between melody and bass line?
10. What intervals do bass lines primarily leap by?
11. What is the simplest, most elementary harmonic progression?
12. Explain the role of the dominant preparation chord.
13. What was the first aspect by which Weber designated chords?
14. What was the second aspect by which Weber designated chords?
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15. How did Weber signify the quality of a chord?
Cadence
16. What is the expressive effect of both forms of authentic cadence?
17. What is the imperfect authentic cadence, and what impression does it give?
18. What is the perfect authentic cadence, and what impression does it give?
19. What is the half cadence, and what impression does it give?
20. What is the plagal cadence, and what impression does it give?
21. What is the deceptive cadence, and what impression does it give?
Figured Bass
22. What is “basso continuo”?
Homophony
23. What does the word homophony derive from?
24. What is the principle structure of homophonic style?
25. How was opera created?
Chorale
26. How did the Protestant Reformation participate in the transition from polyphony to homophony?
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Concluding Summary
27. How does the chord facilitate composition?
28. How does the chord save time and effort for keyboardists?
29. What is homophony?
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Chapter 8: Harmony
Questions for Thinking and Discussion
A. Make a chart defining and comparing homophony, heterophony, polyphony, and monophony. What
connections can you draw between them? Why did homophony develop so late in history? How does
homophony build upon previous ideas; in what way is the chord a summary or product of previous musical
knowledge? [144 to 148]
B. Narrate the history of the chord. When and where did the concept of chord emerge? How did historical
events (in the Reformation, for example) shape the use of the chord? What are other examples of history
shaping music’s development—has music ever shaped history’s development? [146 to 148]
C. List some of your own questions regarding what harmony is, what the chord is, and what they do for us
as part of musical art.
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Chapter 9: Primacy of Line vs. Primacy of Chord
Exercises
1. What did music expressing the greatness of man require?
The Rise of the Primacy of Chord
2. What was the original meaning of the Greek concept harmoniai?
3. What is harmony now primarily associated with?
4. How was the invention of the chord useful?
5. What is neglected in explaining emotional content only by simultaneous sounds?
6. What larger shift was the transition from counterpoint to voice-leading a part of?
7. Does the overtone series exhibit the same structure as our harmonies?
Rameau
8. What is Rationalism? What definition of rationality do Rationalists uphold?
9. As a Rationalist, how did Rameau approach music in his Treatise on Harmony?
10. What was Rameau’s central model and starting point?
11. How does Rameau treat lines?
12. What is Rameau’s solitary positive contribution to musical thought?
13. What is the difference between Fux’s and Rameau’s approach to beginning composition?
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Causes and Consequences
14. What is the motivation for the chord-centered approach?
15. What is the result of the chord-centered approach?
16. What has happened to the concept of harmoniai?
17. What happened to the prestige of past knowledge in science, mathematics, and philosophy?
Au Contraire: Melody Comes First
18. How recent is the invention of the chord, in the context of human history?
19. What was the chord a product of?
20. When listening to music, what does one attend to, follow and remember?
21. Can single melodies, or single chords constitute music?
22. In what way does a chord need to be broken down to be taught or understood?
Melody Precedes Harmony
23. Briefly summarize how melody precedes harmony.
Isn’t it Both?
24. Can one logically uphold both the “primacy of line” and the “primacy of chord” at the same time?
Schenker
25. Who was Heinrich Schenker?
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26. What was Schenker’s position in terms of line and chord?
27. What is the fundamental basis and integrating framework of music according to Schenker?
Breaking the Rules
28. With the new instrumental style, how did some people view the old system?
29. How did Schenker solve the problem of instrumental technique?
30. How did the new innovations relate to the prior laws of order?
Levels of Structure
31. How did Schenker view the various notes and chords in a piece?
32. What levels of music did Schenker conceptualize?
33. By what principle did Schenker discover and systematically develop a theory of music?
34. What is Schenker’s “Urzatz”?
35. What is the “Urlinie”?
36. What are the most common Urlinie progressions?
37. What is the one significant shortcoming in Schenker’s theory?
38. What was Schenker’s mindset, in contrast to Rameau?
39. In what way was Schenker’s theory a tremendous advance upon and completion of Zarlino’s
original sentiment of “unity of mode”?
Concluding Summary
40. What is the fundamental of music?
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41. How does a musical line or melody become coherent?
42. How does a melody move, and what is essential to it?
43. What are the three categories of intervals?
44. What is a dissonance?
45. What is a fundamental tenet of counterpoint?
46. What is polyphony?
47. What is homophony?
48. What are chord progressions?
49. What is the correct conception of “harmony”?
50. What is the basic and controlling form of musical context?
51. What is rhythm?
52. What is meter and what does it provide?
53. How is the diatonic scale able to provide the mind with an orienting framework?
54. What two general impressions can modulation give?
55. What is tonality?
56. What same basic principle is expressed by melody, its intervals, the scale, rhythm, polyphony,
counterpoint, harmony, and tonality?
A Symphony by Beethoven
57. How does Beethoven’s Fourth Symphony have integrity?
58. What is the result of Beethoven’s masterful integration?
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Chapter 9: Primacy of Line vs. Primacy of Chord
Questions for Thinking and Discussion
A. Briefly narrate the history of melody and the history of the chord. How do the two histories compare?
Why does a historical outlook reveal a problem with the “primacy of chord” opinion? Can a historical
outlook be used to help solve other problems (for example, the particle-wave conflict in physics?), and why
or why not? What are analogous conflicts between fundamentally opposite viewpoints in other subjects?
For example, is there a parallelism between the Aristotelian/Platonic opposition in philosophy and the
line/chord opposition? [158 to 159]
B. In what way is the chord a summary or final product of previous musical knowledge? What exactly is the
problem with taking a later product as the starting place? Why is the conflict between the “primacy of line”
and “primacy of chord”; are there any other concepts that subvert the primacy of line (for example, a
“primacy of rhythm”)? Would you expect a new conflict with the “primacy of line” in the future, when
people take some later product at that point and use it as the starting place? [158 to 161]
C. How does the “primacy of chord” view, as most especially expressed in Rameau’s theory, affect how music
theory is taught? How would affect the kind of music produced by composers who learned musical
techniques and concepts on the premise that chords come first? How might it affect how a performer would
interpret and shape a piece he is performing? How does the “primacy of chord” idea block people from
understanding the substance and meaning of music?
D. In what way does the centrality and primacy of melody integrate and summarize all the content covered
in Dancing with the Muses? Review the main ideas of each chapter and connect them to this underlying
theme. Refer to the painting on the book’s cover and analyze it in relation to the theme of the importance of
line to the human mind.
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Supplemental Exercises for the Timeline of the Development of Music Theory
1. Who was Aristoxenus, and what did he accomplish? How did he build on past Greek philosophies?
2. Who was Guido de Arezzo, and what did he accomplish? How did he build on past knowledge in his
work?
3. Who was Zarlino, and what did he accomplish? How did he build on past knowledge in his work?
4. Who was Rameau, and what did he accomplish? How did he implement past knowledge in his
work?
5. Who was Fux, and what did he accomplish? How did he implement past knowledge in his work?
6. Who was Schenker, and what did he accomplish? How did his work build upon all the
achievements up to the Enlightenment?
7. Write a brief narration that connects the work of these six people in a coherent progression.
For answers to these exercises, please see the Timeline of the Development of Music Theory on page 176.
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Preface
Answers
1. It teaches melodic shape, the elements and basis of melody, polyphony, development of harmony.
[IX]
2. The topic are ordered by increasing complexity. [IX]
3. “The method of this book is historical. [...] It seeks to present the essentials of music, the basic
concepts, in their proper order [...] .” [IX]
4. The book does not resort to justifying facts by the phrase “because I said so”; it does not present facts
dogmatically. [X]
5. “Staying power and practical usefulness are signs of an idea being true and clear. [...] Using history
teaches the student not just the content, but its full meaning and context, including the answers to
the questions: Where do these concepts come from? How did they come to be? Why are they what
they are? Why are they worth knowing? [...] A further advantage of the historical approach is that
it enables the presentation of knowledge as much as possible in the form of stories.” [X]
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Chapter 1: Melodic Shape
Answers
1. “Emotion is an aspect or consequence of hearing the music, and the essential substance of the music
is its melody. [...] Whatever the complexities or richness of the music we are struck by, and
whatever emotion it arouses, its essential substance is a stringing-together of notes [...] . The first,
most basic thing to study is the musical line.” [1]
2. “A line is a succession of pitches that fit together.” [1]
3. “The best way to study line shape is to write short, simple examples using notes of uniform
duration. [...] In composing a cantus firmus we deliberately abstract away from the element of
rhythm to isolate and study how the pitches interconnect.” [1]
A cantus firmus is a simple line/melody that avoids the element of rhythm for the sake of isolating and
studying pitch.
4. “The process of composing a cantus firmus should be looked at as both analytical and creative; it is a
process of honing a malleable string of notes to bring it into an ideal form, like forming a shape
from a mass of soft clay.” [1]
5. A cantus firmus always begins and ends on the tonic/first scale degree/main note of the scale. [2]
6. “For satisfying closure, approach the final note by step.” [2]
7. “The line should be 8-12 notes long. Shorter than that is insubstantial, longer becomes blathering.”
[2]
8. Repeated notes are rhythmic in nature, and cantus firmi are specifically for studying pitch. [2]
9. It should range within an octave. [2]
10. For variety a cantus firmus should change direction 3-5 times, and have some leaps.
“However, we don’t want a simple scale going up and then down again. We want our proto-tune to
have unity in variety, not just unity. Therefore we must introduce some leaps and changes of
direction.” [3]
11. These rules purposefully delimit the study of simple melodies, so that one can focus on the interaction of
pitches without needing to consider other elements such as modulation or rhythm.
12. “The strictest form of the rule for using leaps is: compensate for a leap by an immediate motion by
step in the opposite direction.” [4]
13. See Figure 1.5 for an example of how hanging notes might actually be part of sub-lines, with a delayed stepwise
connection.
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“In the first example, the leap to A creates a new component sub-line, and the two line components
proceed independently until they fuse by stepwise connection for the last three notes; this
progression represents unity in variety.” [4]
14. The overall feature of a cantus firmus is its shape, which is typically a concave down arch.
15. (Answers vary. Cantus firmi can be checked against the guidelines listed on pages 2 and 3.)
16. Monophonic means having one line, and polyphonic means having multiple lines sounding at the same time.
“The basic form of music throughout history has been the single melody, the monophonic or
‘one-voiced’ style. [...] It was only late in history that men began to experiment with combining
lines at the same time in the form of polyphony or ‘many-voices.’” [5]
17. Heterophonic means having one line that is varied and embellished, and homophonic means having multiple
lines sounding at the same time, in the form of chords.
“Ancient written reports describe a practice of singing one version of a melody while
simultaneously playing an ornamented version of the same tune on an instrument, which practice
we call heterophonic or characterized by ‘diverse voices.’ [...] This style of music is called
homophonic or ‘same-voiced’ meaning that multiple voices move together in the form of changes of
chord.” [5]
18. Heterophony is using the multiple instances of the same line with embellishments, whereas monophy is only
one single line; homophony coordinates the multiple lines, whereas polyphony merely has multiple lines
playing at the same time with no rhythmic coordination.
19. The Ancient Greek philosopher Aristoxenus made the most important study of music. He particularly
addressed melodic coherence. [6]
20. “‘Our method rests in the last resort on an appeal to the two faculties of hearing and intellect. [...]
For the apprehension of music depends on these two faculties, sense-perception and memory; for
we must perceive the sound that is present, and remember that which is past. In no other way can
we follow the phenomena of music.’” [7]
21. “For now, we must emphasize the beginning in Western thought of the idea of melodic synthesis.
[...] The idea of synthesis or coherence of line is the broad new basic concept that enabled the
further development of music.” [8]
22. Aristoxenus, Guido d’Arezzo, Johann Fux, and Heinrich Schenker advanced our knowledge of melodic shape
and pitch connections. [9]
23. Aristoxenus lived at 300 BC, and summarized Greek music theory, including scales and melodic synthesis.
[11]
24. Guido d’Arezzo lived at ca. 1000 AD, and developed a staff notation and solfege system. [11]
25. Zarlino lived at 1558 AD, and wrote on the principle of tonality and principles of counterpoint. [11]
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26. Rameau lived in 1722 AD, and originated a system asserting the primacy of chord. [11]
27. Fux lived in 1725 AD, and originated a system of counterpoint. [11]
28. Schenker lived in the 1920’s, established the levels of musical structure, discovered the concept of organic
coherence, developed a method of graphical analysis, and re-asserted the primacy of line. [11]
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Chapter 2: Interval
Answers
1. An interval is the definite distance between two tones/pitches.
“It consists of motion from one discrete point of pitch to another, from one tone to the next by a
definite distance or interval. [...] Intervals differ in size, and each size produces in the mind a unique
affective or emotional impression.” [13]
2. “In other words, each interval has a cognitive aspect (perception of a certain distance) and an
emotional aspect (a certain sense quality)." [13]
3. “The beginning of our knowledge of musical distances must have been in prehistory when some
intelligent early men sang, and paused to reflect on the distances between notes, noticing
differences in the amount of tension they could feel in the voice when singing—differences which
related to the audible change in a systematic way.” [13]
4. “A fairly easy and gentle, incremental change of vocal tension makes a musical step. A greater
movement of the throat, which has a subtly different feeling because of the activation of more
tension in the vocal muscles, is a skip or a leap.” [13]
5. “The purpose of any scale is to measure something using a graduated series of uniform increments,
thereby enabling man to do something with it. [...] The musical scale makes the intervals
intelligible by putting them in a structured context or framework, and enables us to create pleasing
and expressive melody.” [14]
6. “The settled development and conceptualization of the musical scale was possible only with the
construction and playing of musical instruments.” [14]
Musical instruments provide a tangible means of understanding and constructing musical scales.
7. “It was the construction and playing of instruments, beginning in ancient prehistory and
continuing through high civilization, which enabled men to measure musical distances more
precisely and to make finer conceptual distinctions. [...] In order to identify an interval, one simply
counted the scale-steps.” [15]
8. “Next would have come an awareness that certain notes of the scale could be inflected; certain notes
could be sung in a slightly lower version which still had the same place in the scale. [...] It is also
readily apparent upon hearing that the lowered forms of the notes, the minor notes, produce a
darker emotional impression.” [15]
9. “Thus the growth of our understanding of music was made possible by the interaction of three
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elements: auditory perception, singing, and making and playing instruments.” [15]
10. Pythagoras (b. circa 570 BC) was a Greek mathematician and philosopher. [16]
11. “The story of Pythagoras is important not as a literal historical report, but for its overall meaning:
the discovery that physically measurable principles of ratio operate in music; music is
mathematical.” [18]
12. “The most obvious and basic distinction is between those intervals that blend versus those that
clash.” [19]
13. “The brain is able to unify the tones and we experience the result in the form of an experience of
this quality which men named consonance. The term comes from ‘con-’ plus ‘sonare’ meaning ‘to
sound with.’ [...] The brain works to complete its processing of the sensations, but it fails, and we
experience the result in the form of this sound-experience which men named dissonance. The term
comes from ‘dis-’ plus ‘sonare’ meaning ‘to sound against.’”[19]
“Consonance is a sensory union of elements. Dissonance, outside of a musical context that makes
sense of it, is a broken or fractured array of sense elements.” [20]
14. “The perfect intervals—the fourth, fifth and octave—have a very pure, strong, stark sound to them;
their notes fuse as completely as possible. The imperfect consonances—the third and sixth—make a
richer, more euphonious sound. The perfect consonances are rather cold, while the imperfect ones
are warmer and more sensuous.” [20]
15. “Perfect intervals made larger become augmented; made smaller, diminished. Major intervals made
larger become augmented; made smaller, minor and smaller again, diminished.” [20]
16. “Enharmonic notes or intervals sound the same but are spelled differently.” [21]
17. “These differences in spelling arise from different musical functions and therefore different mental
impressions in context. [Enharmonic intervals or notes] differ musically and psychologically because
the underlying scale differs.” [21]
18. “There is another sense in which intervals can be equivalent: when they have the same notes, but
relate by inversion. Just as to invert a fraction is to flip the numerator and denominator, to invert
an interval is to flip which note is lower and which is higher. To invert an interval, move the lower
note by octave so it is above, or move the upper note by octave so it is below. The inversion of E
over C is C over E.” [21]
“There is a pattern to the qualities too: Perfect inverts to perfect. Major inverts to minor and vice
versa. Augmented inverts to diminished and vice versa.” [22]
19. “One school, flowing from Pythagorean number mysticism, spurned listening and studied ratios in
and of themselves. The other school, expressing Aristoxenus’s insistence that the ear is the judge of
things musical, made concepts and rules follow from what we hear, not from self-contained
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mathematical deductions. The Pythagoreans cared about theory in a purely abstract way.
Aristoxenus regarded theory as derivative from what we hear, and as a means to singing, playing,
and enjoying music.” [22]
20. “Recall that Aristoxenus had been a leading pupil of Aristotle, the father of logic, the man who
rejected the notion of any dimension of reality beyond this earth.... In contrast, one of the major
voices in the Pythagorean line was Plato, who held that a world of perfect Ideas exists in a higher
dimension which represents true reality—and that the world around us is merely a shadowy
reflection of the superior world, the World of the Forms.” [23]
21. “And the body of scientific knowledge of sound came to a culmination in the work of a great
German scientist of the 19th century—a scientist who is a preeminent example of Aristotle’s kind of
robust, blazingly clear, heroic, this-worldly rationality. [...] Helmholtz is particularly known for
discovering the law of conservation of energy.” [26]
22. “Quite the opposite, in fact: the means to artistic expression, he held, was knowledge. Reason did
not kill expression, it served and enhanced it.” [27]
23. “A tone is a clear, simple sensation—a sound with a definite, constant pitch. A noise, such as the
sound of running water or the crumpling of paper, is a jumble of sound. A tone is the elementary
type of sound. Noises are more complicated and can be compounded out of tones, as when you strike
a bunch of adjacent keys on the piano.” [28]
24. “There are four, and only four, attributes of an individual musical tone: pitch, timbre, duration,
and loudness.” [28]
25. “The frequencies of a consonance stand in a ratio made up of the smallest whole numbers, such as
1:2 (the octave) or 2:3 (the fifth), while the frequencies of a dissonance stand in a ratio made up of
larger numbers, such as 8:9 (the whole step) or 8:15 (the Major seventh).” [29]
26. “Some consonances are perfect in that their tones blend so completely and thoroughly that they
produce a clear, strong, stark psychological impression. These are the octave (1:2), the fifth (2:3)
and the fourth (3:4). Among these, the perfect fourth has a biting quality to it.” [29]
27. “Other consonances are imperfect in that their tones are not so completely and thoroughly fused,
such that they produce a warm, rich, euphonious sound. These are the thirds and sixths.” [29]
“All imperfect consonances are warm and rich, but the major third (4:5) and sixth (3:5) give a
bright and sunny psychological impression while the minor third (5:6) and sixth (5:8) give a dark
and sultry one.” [30]
28. “The minor second (15:16) and major seventh (8:15) produce a more harshly discordant, more
bitingly painful sensation in the mind. Their ratios are the most complex of all. In contrast, the
major second (8:9) and the minor seventh (9:16) produce a still clashing but much mellower and
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less painful quality. The tritone (5:7) produces a very unusual, peculiar honking or pinching
discord.” [30]
29. “Helmholtz’s study and summary of pitch relationships affirmed, clarified and fully grounded what
had been indicated in the ancient story of Pythagoras and the blacksmith: an important basis of our
perception of interval qualities lies in the physical pitch-ratios between the notes. Measurable
quantitative relationships underlie and give rise to our affective, qualitative experience.” [30]
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Chapter 3: Scale
Answers
1. “[The musical scale] is the basis of all aspects of the notes used in music. It is the controlling factor,
the starting point, the integrating framework of music, and a crucial determining factor of music’s
emotional content.” [31]
2. The chapter covers the diatonic scale, the different modes, and solfege. [31]
3. The two flutes sound the pentatonic scale. [32]
4. “The bone flute, along with many others like it in the area, has cut marks on it which the maker
used to measure the position of the holes. The spacing of the notes was not random or haphazard,
but a result of conscious calculation. [...] There is also a tiny extra hole used to correct the pitch of
the upper A to make it better in tune, further confirming the fact that the pattern of pitches was
not random but a result of measured intention.” [32]
5. “The Hindu practices are another musical tradition—involving billions of people over millennia—in
which the diatonic scale plays a central role.” [33, also see 32]
6. “The instructions [on the Babylonian cuneiform tablets] thus produce the notes of the diatonic scale
exactly as we know it today.” [33]
7. “The Greeks conceived of music basically in terms of tetrachords, four-note groups bounded by the
interval of the perfect fourth (frequency ratio 4:3).” [33]
8. The enharmonic tetrachord uses micro-intervals, bunched together at the bottom of the fourth in the pattern
B-B#(here meaning the quarter tone between B and C)-C-E, and gives a hypnotic or lustful sound. [33]
9. “The chromatic type of tetrachord, which gets its name from ‘chroma’ meaning ‘color,’ used
half-steps bunched together at the bottom of the fourth in the pattern B-C-Db-E.” [34]
10. “The diatonic type of tetrachord, however, spread the notes across the 4th in a more even way,
using only stepwise motion with no gaps. [...] The word ‘diatonic’ comes from ‘dia’ meaning ‘across’
and ‘tonos’ meaning ‘to stretch.’” [34]
11. “Because of the proportions among its parts, because of its rational structure, the diatonic
tetrachord alone can serve as a building block for constructing a scale system—which is what the
Greeks did with it. The full diatonic scale is simply a combination of diatonic tetrachords.” [34]
12. “As a brief summary: The brain integrates music based on frequency relationships that are
reducible to small whole-number ratios; interrelated tones have a lowest common denominator
(which, in hearing music, the brain automatically processes).” [35]
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13. (See Figure 3.1, on page 36.)
14. “For instance, B-C-D-E can be extended by attaching another four-note group in the same pattern
(half-step, whole- step, whole-step) to the top note: E-F-G-A. This combination gives all the notes
of the C scale: C-D-E-F-G-A-B-C.” [36]
15. (See Figures 3.2, 3.3, and 3.4 on page 37)
16. “A ‘key’ is a central-note with its surrounding scale.” [38]
17. Young children’s songs, ability to discern wrong notes, ease of grasping the scale, success of the solfege,
incorporation into music notation and keyboard instruments, archaeological records. [39, 40]
18. “[Modes] are the various segments or inflections of the diatonic scale. [...] [One can] identify the
modes using the starting note of the pattern on the white keys of the keyboard.” [41]
19. Answers vary. See pages 46 to 48.
20. “The diatonic scale has a distinctive structure giving each note a unique and recognizable position,
thus helping orient the ear and mind. The ‘symmetrical’ scales do not provide such a framework,
and their effect is disorienting; their sound produces an experience of bewilderment or
uncertainty—in harsher or more frenzied cases, of actual chaos.” [49]
21. See page 50 and 51.
“You will find that in the diatonic 7-note collection there is a unique number of each type of
interval. [...] Comparing these two, notice that the diatonic set has a maximal number of perfect
consonances; the largest presence is the perfect fourth (3:4) or perfect fifth (2:3).” [50]
22. “If you improvise a bit using these sorts of alterations, you will find your ear drawn to notes that
correct the inflection sometime after it happens, to restore the scale to its normal form.” [51]
23. “Each syllable [of “Do-Re-Mi-Fa-So-La-Ti-Do”] is a mnemonic for a single step of the major scale, and
they are arranged in memorized series.” [52]
The solfege appeared in the Rodgers and Hammerstein musical The Sound of Music.
24. “Guido d’Arezzo, born around 991 AD in Italy, began his career as a Benedictine monk at the
monastery of Pomposa.” [52]
“Early on, Guido began to challenge the existing methods, devising new, more efficient approaches
and techniques—all of which related to the nature and use of the musical scale.” [53]
25. “One of Guido’s new devices was a more precise and more easily readable form of music notation.”
[53]
26. “These squiggles are called “neumes” from the ancient Greek “pneuma” meaning breath or spirit;
the method is called neumatic notation. [...] But this was actually quite a revolutionary means of
notation; it was the first time in history that height of pitch was shown positionally on the page.” [53]
27. “This form of notation is called ‘Dasian’ (or ‘Daseian’) notation; the word comes from the Greek
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‘daseia,’ which means ‘rough breathing’ at the start of a spoken word.” [53]
28. “Guido’s innovation was to combine the marks from neumatic notation with the defined lines from
Dasian notation, thus gaining the advantages of each: the separation of text-markings from
pitch-markings from neumatic notation, plus the precision of the horizontal lines from Dasian
notation.” [54]
29. “ [...] ‘To tamper with the time-honoured methods of teaching Gregorian chant was sacrilegious
and to persist in changing them put individual pride above community commitment. They accused
Guido of heterodoxy and pride. [...] ’” [55]
30. He laid out the notes of the scale, explained how to tune notes on the monochord, classified modes, wrote on
musical character types, gives instructions on how to compose new melodies, suggested parallel melodic
phrases, begins dealing with polyphonic singing, and invented solfege. [55, 56]
31. “He simply assigned each vowel to a particular note, and whatever vowel a syllable used, that
determined what pitch to sing.” [57]
32. “According to the letter, Guido used a melody familiar to all his singers, the melody of a ‘Hymn to
St. John’ in which each line of verse, each phrase of the melody, began on a unique note of the scale:
the first phrase began on the first step, the second on the second, the third on the third, and so on.
He took the starting syllable of each line, and adopted it as the mnemonic for that step of the scale:
Ut-Re-Mi-Fa-Sol-La.” [58]
33. “Guido reported to Michael that after learning his method choirboys ‘were able before the third day
to sing an unknown melody with ease, which by other methods would not have been possible in
many weeks.’ And as for training a singer, with the older methods singers ‘have succeeded in
gaining only an imperfect knowledge of singing in ten years of study’ but his methods ‘produce a
perfect singer in the space of one year, or at the most in two.’” [59]
34. “All prior musical theory [...] had been oriented primarily around the darker sound of the various
minor modes. This is why our notes are lettered beginning with A on the first note of the natural
minor scale. But Guido used for his system the first six notes of the major scale. This was a profound
shift in approach and reflected progress toward greater enlightenment.” [59]
35. “The actual melody was a worldly tune, a setting of a love-poem by the Roman poet Horace.” [60]
“Guido knew he could never reveal his pagan source.” [61]
36. “Church psalm books printed in the later 1500’s began to include the starting letters of the solfege
syllables near the notes written on the staff.” [62, 63]
37. “Around 1800, after the development of chordal harmonic theory and practice, an English music
teacher named Sarah Anne Glover revived and adapted Guido’s solfege method. [...] In order for
each syllable to have a unique starting letter, she changed the seventh scale-step from ‘Si’ to ‘Ti.’”
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[63]
38. “John Curwen, an English minister and a student of Miss Glover, became an enthusiastic promoter
of her ideas. [...] Curwen’s most important and lasting contribution was a system of hand signals
that are derived from the mental impression of each step of the scale.” [64]
39. “The Islamic world uses the same solfege as the West, which it received during cultural trades at
some point after Guido’s time. Ancient Greece used syllables to sing the notes of the tetrachord,
what we would sing as la-sol-fa-mi, using syllables such as ta and te. Hindu traditional music uses
the syllables sa-re-ga-ma-pa-dha-ni; their pitch is adjusted to the pattern of notes for a particular
raag. Byzantine music uses syllables derived from the greek alphabet: pa (alpha), vu (beta), ga
(gamma), di (delta), ke (epsilon), zo (zeta), ni (eta). Related methods exist in Japanese tradition as
well.” [66]
40. “So with the keyboard in view and under hand, people started to develop a more fixed conception of
the musical notes. Instead of thinking of notes purely in relational terms, as men had done
throughout history, they began to conceive of absolute, unchanging pitches fixed in one place.” [66]
41. “In the fixed system of the Romance languages, “Do” always refers to “C” regardless of the scale or
key in which the note occurs [...] . In the movable system, “Do” always means the sound of the tonic
note of the key [...] .” [67]
42. “There is a further respect in which fixed solfege is in fact superior for advanced musical training:
the handling, in real-time, of notes that do not belong to the major scale.” [68]
43. “The scale is the measuring framework of pitch, which makes note relationships intelligible. It is
the brain’s fundamental integrating core, the central nexus for its processing of music. It is the basic
form of musical context.” [69]
44. “A simple way to encapsulate the diatonic scale in our modern context is: the pattern of white notes
on the keyboard.” [69]
45. “The symmetrical divisions of the octave are the leading examples of this type of artificial
construct.” [70]
This includes the chromatic scale, the whole-tone scale, and the octatonic scale.
46. “A diatonic scale is one built out of diatonic tetrachords—four-note stepwise units filling the span of
the perfect fourth (3:4), con- taining two whole steps and one half-step, the most basic form of
tetrachord making the ratio 15:16:18:20.” [70]
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Chapter 4: Rhythm
Answers
1. “The first and simplest form of locomotion seems to have been the flagellum, a hair protruding
from a single-cell organism which it flapped around to propel itself.” [71]
2. Answers vary. See page 72.
3. “The faculty of reason brings a new dimension to all aspects of life including one’s bodily
movements. For man, there is not only the fact of physical motion, there is the question of his
self-conception. A certain way of moving means something to a man.” [72]
4. “Rhythm is an experiential time measurement enabling the integration of complex human action,
both physical and mental.” [73]
5. “Man is capable of integrating his action in a fashion much more complex and wide-ranging than
for the lower animals. [...] It is the power of his mind. ” [74]
6. “A central means by which the mind integrates action is measurement, whether implicit or
explicit.” [75]
7. “Measurement requires a uniform unit that serves as the basis for interrelating quantities.” [75]
8. “A beat is a regularly recurring pulse measuring human action. [...] A beat or pulse is a physical,
kinesthetic unit, one which we feel in moving.” [75]
9. “Rhythm is an experiential measurement of time, not a scientific one. The purpose of rhythm is not
to explicitly, numerically identify a quantity of time, although we use explicit numerical
measurement to help us understand and deal with rhythm.” [75]
10. “A basic principle of regularity is mandatory for rhythm; but absolutely unwavering, scientifically
and mechanically precise regularity is not needed, and is in many cases contrary to nature.” [75]
11. “Measurement of rhythm is hierarchical—there are levels of time division.” [76]
12. “Meter is a regularly recurring pattern of strong and weak beats. A measure (or bar) is one instance
of a metrical pattern.” [76]
13. “There are two basic types of meter: duple and triple. In duple meter, the strong and weak beats
alternate; every second beat is stressed. A march is a duple meter. [...] The cleanly marked and
sharply articulated left-right-left, military feel of a march exemplifies this.” [76]
14. “In triple meter, each strong beat is followed by two weak ones; every third beat is stressed. A
waltz is a triple meter. [...] Triple meter arouses more curved, arc-tracing motions of the body.” [76]
15. “The meter is the background measuring framework; the rhythm of the music operates within that
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context and by conformity to it as the underlying structure.” [77]
16. “There are two basic divisions: duple which subdivides the beat into two equal parts and triple
which subdivides it into three.” [77]
17. Answers vary. See page 79.
18. “Poetry is a helpful way of considering the mental aspect because talking about the language of a
poem is easier than talking about the abstract rhythmic patterns of music.” [80]
19. “The quadruple meter invests the poem with decisiveness and resolution, creating a feeling of the
lady’s determination not to dispel her veil of obscurity; the flowing triple subdivision softens that,
making the feeling not sharp and decisive but somewhat rounded, gentle, more feminine. Thus the
rhythm of the poem helps create the aura of both the lady’s determination and her demureness.”
[81]
20. “The metronome came very late in history. Dietrich Nikolaus Winkel invented it in 1812 [...] . The
name of the instrument is of Greek origin: metron = measure, nomos = regulating.” [81]
21. “A common problem in music is ‘stuttering’ or permitting oneself a lot of stops and starts instead of
a continuous regular flow, which is necessary in practicing as much as performing. The
metronome can help a student stay on track.” [82]
22. “However, the metronome also led to a more mechanistic way of thinking, as though men were to
be judged by the standards of machines instead of the other way around.” [82]
23. “One of the effects was a re-interpretation of tempo markings. [...] Instead this broad conceptual
approach was restricted down to a focus on one measurement of one parameter—an impoverished
and unmusical approach to music.” [82]
24. “The pleasure of rhythm is nature’s reward for successfully coordinated action.” [83]
25. “Rhythmic events can be measured explicitly and numerically, but the essence of rhythm is the
experience of action coordinated in beats.” [83]
26. “The beat is the unit of measurement. Meter is a recurring pattern of strong and weak beats.” [83]
27. “Metrical organization is hierarchical in that there are small subdivisions and larger spans
organized in levels of measurement like marks of length on a ruler.” [83]
28. “Rhythm is a phenomenon present in the entire animal kingdom, but it has a special emotional
power for man, who is capable of integrating actions much more complex and wide-ranging than
those of the lower animals.” [83]
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Chapter 5: Polyphony
Answers
1. “The glory of Western Music, its distinctive achievement and the source of its great power, is the
control of lines sounding together, blended in harmony.” [85]
2. “It is Gregorian chant which formed the starting point for the development of polyphony.” [85]
3. “Plato upheld a superior dimension of perfect Ideas such as the Form of the Good, and looked down
on the earthly world around us as an imperfect reflection of the higher Reality.” [85]
4. “Plato’s philosophy became the foundation of the Christian religion.” [86]
5. “A crucial figure in the transition between Plato and full Medieval Christianity was Augustine.” [86]
6. “The music that resulted is known as Gregorian chant.” [87]
7. “Gregory, who lived 540 to 604 AD, was a major figure who organized the Catholic Church and
consolidated its leadership role in the chaos following the collapse of the Roman Empire. [...]
Rather, the attribution of the chants to Gregory should be understood as a propaganda story that
the Church used to make people accept its chants as the one and only music, coming directly from
God.” [87]
8. “The music is a single line sung by men’s voices merging anonymously in unison.” [88]
9. “The sound is spiritually pure, austere, giving a suggestion of mourning, vast mystery and of
melancholy longing for the divine.” [88] See Page 88 for more descriptions.
10. “[Charlemagne] was a leader and unifier who used his mind and who valued learning.” [89]
11. “His reign meant, among other things, that the music used in the church had to be written down,
copied, disseminated and taught throughout Europe.” [89]
12. “Musical life all-around was much smaller, less developed, and more constrained than it had been in
the vibrant culture of Greece, or even in the Roman Empire whose warrior culture had despised
music as effeminate and frivolous.” [89]
13. “Around the year 900, one hundred years after Charlemagne’s unification of Europe, a ‘Handbook
on Music’ (Musica enchiriadis) by an unknown author gave an account of musical practices,
complete with examples written in an early form of music notation.” [90]
14. “The first stage of this progression was simply to have two groups sing the same line at the same
time, but starting on different notes.” [90]
15. “First they confronted the issue that if they wanted to sing in parallel fourths, there was a problem
because one of the fourths in the diatonic scale is augmented (from F up to B). [...] To avoid that
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sound, a rule was made that one voice should stay on the same note at certain times, and only move
when the ‘diabolus in musica’ was safely avoided.” [90/91]
16. “It deserves to be stressed that the first idea for how to make a new line vary from the main line, the
first rule of composition, was propelled by the need to avoid the harshness, the ugliness and the
jarring nature of dissonance that did not integrate into the flow of the music.” [91]
17. “In the post-Charlemagne period, three things began to develop hand-in-hand: polyphony,
notation, and rules.” [91]
18. Polyphonic music requires notation as the means of coordinating the lines and similarly demands the
formulation of principles of order by which one can coordinate the lines in such a way as to achieve a flowing,
beautifully integrated sonority through time. [91]
19. “Notation in turn facilitates composition and performance.” [91] See page 91 for more details.
20. “The rules for coordinating the lines in turn enable the composition of an ever-more complex
fabric. The increased understanding men develop by identifying abstract rules stimulates a demand
for greater precision and detail in the notation.” [92]
21. “It was Greek principles—the antithesis of Christian self-abnegation and self-doubt—which led to
the new progress. [...] Aristotle’s focus on this world, and the value he placed on worldly happiness,
are what were finding expression in the post-Charlemagne rebirth of the mind.” [92]
22. “In the 1500s, the High Renaissance, polyphony reached a culmination, exemplified especially in
the music of Giovanni Pierluigi da Palestrina. [...] Palestrina’s music is remarkable for its sweet
harmony, its beauty and smoothness of progression.” [93]
23. “In these musics one hears the change from the sadness and dark serenity of a passive mind to the
fulfillment of a stimulated, challenged, active one. The change in music was an exact reflection of
the underlying change in metaphysics from a Platonic, otherworldly, impersonal asceticism to an
Aristotelian, this-worldly acceptance of the value of pleasure, enjoyment and intensely personal
expression governed by laws of harmonious synthesis.” [94]
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Chapter 6: Tonality
Answers
1. The crucial principle is man's volition.
“During the Renaissance, the conception of man as a self-determined being, guided by the power of
his own psyche, his life-course steered by his own judgment and virtue, found expression in all the
arts.” [95]
2. “The motion of polyphonic music was highly directional.” [96]
3. “The lines can play off of one another, build up the level of activity and finally come together at a
phrase ending.” [96]
4. “The moment of closure of a phrase or composition was called the cadence after the Latin 'cadere'
meaning 'to fall.'” [96]
5. “One of the means of creating a feeling of goal-direction in polyphonic music is the introduction
and resolution of dissonances between the voices.” [97]
6. Gioseffo Zarlino formulated the principle of tonality.
“Tonality was a revolutionary and comprehensive new system of unity in music, a system that
most intensely expressed the feeling of goal-direction.” [97]
7. “Zarlino began with the law that consonance comes first [...] .” [97]
8. “Zarlino also followed the implications, applying the pattern to longer time spans, and creating a
fundamental new principle: just as dissonant notes are ornamentations of consonances, so are all the
notes of a composition part of an elaborate ornamentation over time of the central sonority of the
composition.” [98]
9. “He originates the definition of tonality—the principle that a composition is oriented around a
single tone (and the scale built on it, and the triad built on it), and that all of the music moves in
relation to that center.” [98]
10. “'Tonality' is one of several important musical terms deriving from the Greek 'tonos' meaning 'to
stretch' [...] . Thus the tonic note is 'stretched' over time in the mind as the reference note even
when it is not literally sounding.” [98]
11. “Zarlino answered that question: it is the triad. [...] The central triad of a scale consists of scale-steps
1-3-5.” [99]
12. “[...] 1. sonorities with less than a triadic combination are not as full or rich, 2. any other notes
which are added (aside from doublings of the existing notes) introduce dissonances and are
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therefore not elementary, and 3. other sonorities can be reduced back to the triad, as inversions or
elaborations.” [99]
13. “Thus Zarlino has injected into Western thought the idea of unity of mode, of the consistency of
the central sonority, and central mood, of the composition.” [99]
14. “Thus musical integrity does not involve only simultaneous relationships, but relationships
between retained past sensations and presently sounding tones.” [100]
15. “Zarlino started with the local rule of counterpoint that a dissonance must resolve by step to a
consonance.” [100]
16. “They also began to harness the most powerful dissonance of all: the tritone (ratio 5:7). The tritone
occurs in the complete scale between steps 4 and 7. [...] But used in its natural role in the scale, it has
a special kind of effect that no other interval has: it is the interval that defines the key.” [100]
17. “The first factor determining the quality of a scale-note is the interval between that note and the
tonic.” [101]
18. “The second factor determining the quality of a scale-note is the set of intervals between that note
and the other, non-tonic notes in the scale.” [101]
19. “The tonic note is the most stable and settled note of the scale; it has the strongest possible sound
and offers the greatest satisfaction as a note of arrival and resolution.” [102]
20. “The supertonic is an unstable tone with the buzzing energy of a tendency tone pulling downward
toward 1; yet as a whole-step rather than a half-step above the tonic it is a mellower, gentler
tendency tone.” [102]
21. “The mediant is a stable, warm tone which does give repose but not the complete closure that a
melody reaches on the tonic.” [102]
22. “The subdominant has a strong sound to it because of the perfect interval between it and the tonic,
but it is a tendency tone because of the biting quality of the fourth and because of the dissonant
tritone between 4 and 7.” [102]
23. “The dominant is the most stable and settled note after the tonic, and is the secondary central note
of the scale.” [102]
24. “The submediant is a warm, expressive tone which tends to move by step to 5 for repose or, in a
more energized rising motion, up by scale through 7 to 1.” [102]
25. “The leading tone forms the most piercingly dissonant interval with the tonic, and it therefore
pulls as strongly as possible upward to 1. [...] When the seventh step of the scale is lowered it is not
called the leading tone because it no longer has the same pull upward; instead it is called the
subtonic.” [102]
26. “Other tones replace notes of the scale and thus shift the context, reorienting the mind to a new
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scale. This is called modulation. [...] The term ‘modulation’ comes from modulari, meaning
‘regulate, measure off properly.’ Originally it meant alteration of pitch by measured degrees, but it
came to name something more complicated: change from one scale to another by altering the
pitches.” [105]
27. A chromatic tone can be either a temporary ornamentation, or an accidental replacing a note of a scale and thus
reorienting the scale to a new tonic (ornamentation or modulation). See page 105.
28. “A key means a major or minor scale oriented around a particular main note.” [106]
29. “In music of the mature Western system of tonality, when an established tone [...] is replaced by a
new inflection [...] that changes the scale and therefore reorients the music to a new tonic note.”
[106]
30. “The addition of a flat was originally referred to using words related to ‘soft’ indicating the way in
which the flat usually gets rid of a tritone and therefore eliminates that interval’s harshness.” [106]
31. “The sharp enters later than the first flat, and originally came to be for the purpose of creating a
leading tone.” [106]
32. “When a note is altered without changing which pitch is the main scale tone, we generally do not
consider that a ‘modulation’ but merely a ‘modal borrowing’ or some form of ornamentation: a
change from C major to C minor is not a modulation exactly, but a change of mode.” [106]
33. “The basic pattern of tonal music is: first, establish the sound of the main harmony and the main
key, then depart from it, and then return to it. [...] It can be implemented on a very small scale or a
very large one; it can be the pattern of a few chords in a short sequence, or the scheme of
modulation spanning an entire symphony.” [108]
34. “Relative major and minor share a key signature but have a different tonic note.” [109]
35. “On the other hand, when a major and minor key differ in key signature but have the same tonic
note (as with A major and A minor), they are called parallel keys.” [109]
36. “The drive toward the cadence, using rhythm as well as the melodic shape to create a sense of
momentum to the resolution.” [110]
37. “The introduction and resolution of dissonances, including the powerful, key-defining dissonance
of the tritone.” [110]
38. “The use of the notes of the scale, including the tendency tones such as the leading tone, according
to their contextual function ultimately leading toward the tonic.” [110]
39. “The use of modal borrowing and changes of key—to close keys or distant ones, reached smoothly or
abruptly, with the concomitant reinterpretation of common tones—to create expressive effects
including especially the feeling of departure, journey, and return to the main key.” [110]
40. “As we will see shortly, the use of chords according to the function of the chord in the scale also
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contributed to the sense of direction.” [110]
41. “This knowledge underlies a long future development of musical art.” [110]
Examples on page 110 include Palestrina, Vivaldi, the Mannheim school, Haydn Mozart, Beethoven, Brahms,
Dvořák, and Tchaikovsky.
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Chapter 7: Counterpoint
Answers
1. The science or art of coordinating voices is called “counterpoint”, from “punctus contra punctum” or “point
against point.” See page 113.
2. “The first rules of counterpoint came about to prevent dissonances from causing disruption or
jarring ugliness—and to instead create note combinations of smooth, expressive beauty.” [113]
3. “This tradition was continued by such important thinkers as Guido d’Arezzo, who also dealt (in
Micrologus of 1026 AD) with how to combine lines so that they flow together beautifully.” [113]
“These included Zarlino and, earlier, Flemish composer and music theorist Johannes Tinctoris.”
[113]
4. Fux, born in 1660, was the court composer in the Hapsburg dynasty and music master at the principal church
of the Empire, St. Stephen's. See page 114.
5. The Gradus ad Parnassum, or “Steps to Parnassus,” is Fux's book for teaching musical composition by a
newly systematic, step-by-step method. See page 114.
6. “When Fux’s Gradus was published in 1725, it represented the condensation of the entire Western
musical achievement over millennia, as summarized by its leading and most knowledgeable
practitioner, coming from the central cultural capital of the Western World.” [114]
7. Practitioners of Fux's theories include Haydn, Mozart, Beethoven, Chopin, Rossini, Cherubini, Berlioz,
Meyerbeer, Auber, Paganini, Moscheles, Hummel, Liszt, Schubert, Brahms, and Strauss.
8. The four types of relative motion are as follows: voices moving in the same direction by the same interval is
parallel motion; voices moving in the same direction by a different interval is similar motion; voices moving in
opposite directions is contrary motion; one voice holding while the other voice moves is oblique motion. See
Figure 7.1 on page 118.
9. “The first species of counterpoint study consists of writing a new counter-line against a fixed voice,
with the counter-line being the most basic. We use only the simplest relationships.” [118]
10. “We are aiming here to create two different lines that fit well together.” [118]
“Since we are looking for unity in variety, not just unity, avoid parallel fifths and octaves.” [119]
11. “To combine these points and state them in positive terms: approach octaves and fifths by contrary
motion.” [119]
12. “In order to keep sufficient variety and independence of the lines, no more than three consecutive
instances of the same parallel interval should be used.” [119]
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13. “In order to keep track of the intervals, write the number of the interval between the staves.” [119]
14. “So the simultaneous intervals available for first species counterpoint are: P1 (& P8) P5 3rds 6ths.”
[119]
15. Answers vary. See pages 118 to 120.
16. “The Iterative Method consists, in essence, of repeatedly creating versions of your product, each of
which has all the essentials required for completeness.” [120]
17. “The process of creating versions enables you to refine and expand your product, but while having a
complete thing at each stage.” [120]
“Part of the reason the Iterative Method takes the stress and pressure out of the process is by helping
you accept that it is okay for the first version of the product to be bare-bones, very rough, even
crude as long as it is complete in the sense of having all the main parts the finished product has to
have.” [121]
18. “In the second stage of species counterpoint, we compose against the fixed voice a new line of half
notes.” [122]
19. “However, we now have the opportunity of introducing dissonances (2, 4, 7 & d or A) on the second
half of the measure.” [122]
20. “Stepwise approach into, and stepwise departure from the dissonant tone makes it integrate into the
overall harmonious structure.” [123]
21. “A passing tone fills in the space between two notes a third apart. It is the middle note of a
three-note scale motion. [...] A neighboring tone is the middle note of this pattern: an initial
consonant tone moves up (or down) a step and then returns to the original note.” [123]
22. “As much as possible use leaps in the middle of the measure but avoid leaps over the barline.” [123]
23. Answers vary. See pages 122 to 123.
24. “One is the authoritarian view, which follows the pattern of religion and demands that you follow
certain dictates because an authority figure says so.” [123]
25. “Another school, the common one today, is the rebel’s view; it regards rules as an arbitrary
restriction on your freedom, as a subjective construct with no basis in reality and which gets in the
way of self-expression.” [123]
26. “It begins with the perspective that in studying counterpoint one has the goal of making
something, of creating a beautiful little musical composition, but in this case one that is deliberately
delimited and controlled in its possibilities so that you can master musical techniques on each level
of complexity.” [123]
27. “Rational creativity means a process which holds the purpose in mind and uses logical thinking and
analysis to achieve it.” [124]
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28. “Irrational creativity means a process which rejects logical thinking and analysis, and which instead
adopts whim—unexplained emotional impulse—as the absolute.” [124]
29. “Sensationalism means a human mind seeking not an intelligent comprehension of an integrated
whole, but a reaction to a local, isolated particle of stimulus.” [125]
30. “Third species counterpoint divides time values further. The counter-line is built of quarter notes,
for a time ratio with the cantus firmus of 4:1.” [126]
31. “The last note of the counter-line is, as always, a whole note on the tonic.” [127]
32. “The counter-line should begin with a quarter rest in order to offset it from the cantus.” [127]
33. “As in second species, the first tone of each measure must be consonant with the cantus. The
remaining tones may be dissonant, as passing or neighboring tones.” [127]
34. “Since this species has so many more notes, more changes of direction within the line are
appropriate and necessary.” [127]
35. “This species also introduces two idiomatic figures which you see illustrated above: the
double-neighbor figure (bars 2 and 7), and the ‘nota cambiata’ (bar 3).” [127]
36. Answers vary. See pages 126 to 127.
37. “Fourth species counterpoint deals with syncopation.” [127]
38. “The term ‘syncopation’ derives from the Latin syncopationem meaning ‘shortening’ or
‘contraction.’ Even earlier, the term derives from the Greek synkoptein ‘to cut up.’ [...] But a
syncopated note begins on a weak beat and continues into a strong one.” [127]
39. “This is like using whole notes (as in first species), only shifted over one half measure.” [128]
40. “A suspension means just what the word suggests: a holding over. We use the term mainly for the
situation in which a note holds on longer than is usual in the meter, thus causing a dissonance.”
[128]
41. “The simplest and most complete pattern for the suspension has three elements: preparation,
dissonance, and resolution.” [128]
42. “It is absolutely essential that the note resolve by step.” [128]
43. “The term ‘resolution’ comes from the Latin resolutionem meaning ‘process of reducing things into
simpler forms,’ and originally in the sense of ‘solving’ (as of mathematical problems).” [128]
44. “A chain of suspensions is a repeated series of the same type, such as 4-3, 4-3, 4-3 or 7-6, 7-6, 7-6
(see the last few bars of figure 7.5). These can work well and give a sense of musically rolling ahead,
but for the sake of variety don’t use more than three in a row.” [129]
45. “[Breaking the species] means using half notes without ties instead of with. The half notes are
governed by the rules of second species.” [129]
46. Answers vary. See pages 127 to 129.
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47. The five types of ornaments are anticipation, escape tone, chordal skip, lower neighbor eighths, and upper
neighbor eighths. See page 129.
48. Answers vary. See pages 129 to 130.
49. “Fifth species counterpoint is the combination and culmination of all previous species. [...] Each
note value is governed by the rules of the species to which it belongs.” [130]
50. “Begin with a rest to set the counter-line off from the cantus. A half-rest prepares for half-note
motion; a quarter-rest prepares for quarter-note motion.” [131]
51. “Don’t use a single note value for too long (two or 2.5 bars) because it makes the subsequent change
jarring.” [131]
52. “As always, be wary of melodic leaps over the barline as they tend to make the downbeat very heavy.
Music flows well when it moves through the barline, smoothing it over instead of making a break.”
[131]
53. “The following events can break the continuity: notes of too long a duration such as whole notes or
dotted half notes; changes from half to quarter notes on the downbeat which gives the feeling of a
start of a new section; using quarter-note motion into a half note on a weak beat, which usually
feels like a sudden, awkward lurch.” [131]
54. Answers vary. See pages 130 to 131.
55. “The upper line, the violin melody, is essentially a ‘fifth species’ line.” [132]
56. “This level teaches us to use fuller sonorities, and to create a beautifully rich sound.” [133]
57. “In three parts, we contend not only with the relation of each new line to the fixed voice, but also
with the relation between the two new lines.” [133]
Specifically, this includes the interval between the two new voices must be consonant, and the interval between
both lines and the bass.
58. “There are two possible full sonorities, sonorities in which each voice has a unique note. Other
sonorities are possible with octave (or unison) doubling.” [133]
The two full sonorities are 5-3 and 6-3 combinations.
59. “The outer voices are more prominent. This doesn’t mean the middle voice is mere filler; it should
have quality and character as well.” [134]
60. Answers vary. See pages 133 to 134.
For questions 61 to 69, see the summary on page 135.
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Chapter 8: Harmony
Answers
1. “'Accord' in turn, had come from the Latin ‘ad-cordis,’ meaning, ‘to be of one heart.’ That is indeed
where the musical chord came from: it is a means of bringing multiple melodic lines into expressive
harmony with one another.” [137]
2. “The triad, the basic form of chord, consists of a root note with a third and a fifth above it. For
example, scale steps 1-3-5, or the notes C-E-G or D-F-A.” [137]
3. “'Voice-leading' means simply the way to lead the voices so that they form the chords you want.”
[138]
4. “Counterpoint is the science of polyphony, and was geared toward coordinating the motions of
many voices which moved independently, which contrasted with one another and created an
interplay. The science of harmony and voice-leading, in contrast, used chords and their
connections as the means of simplifying and boiling down the wide variety of possible contrapuntal
motions.” [138]
5. “Harmonic progression is a matter of using chords according to their role in the musical scale.”
[139]
6. “The primary fact about a chord is the scale degree of its fundamental note, its root.” [140]
7. “The Roman numeral identifies the scale degree of the root of the chord.” [140]
8. “The bass line is the controlling element of the harmony.” [140]
9. “While melody is characterized primarily by stepwise motion, the bass line is characterized
primarily by leaps.” [140]
10. “Its distinctive function is to leap to the roots of chords, which means most of all to leap by perfect
intervals (4,5,8).” [140]
11. The simplest, most elementary harmonic progression is I-V-I, Tonic-Dominant-Tonic. See page 140.
12. “In order to fully flesh out the scale—in order to provide the ear with the full musical context—one
further chord is needed. This is the role of the dominant preparation chord.” [141]
13. “First, Weber designates a chord by giving the note name of the root, plus a figure.” [141]
14. “Second, he devises a method of designating chord in relation to key.” [141]
15. “He specified the quality of the chord in the symbol: a major chord was given a capital Roman
numeral, a minor chord a lowercase one; other qualities were shown with further symbols.” [141]
16. “The two forms of authentic cadence, progressing from V to I, create strong closure.” [142]
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17. “The imperfect authentic, in which the melody does not land on the tonic, gives a more suspended
or floating feeling—a sense that this is only one closure, not the ultimate and final one.” [142]
18. “The perfect authentic cadence, in which the melody lands on the tonic, is indeed the absolute and
total closure and conclusion; it gives the strongest possible feeling of completeness and finality.” [142]
19. “The half cadence, which arrives on the V chord, creates a landing which is still open; it is settled in
some way but not completely and therefore gives a unique combination of rest and anticipation of
what will come next.” [142]
20. “The plagal cadence gives a gentle sense of worship, of repose, of yielding, of broad majesty and
solemnity.” [142]
21. “The deceptive cadence, moving largely like the perfect authentic cadence, creates an expectation of
closure which is then suddenly swept away and rendered incomplete by the stepwise movement of
the bass.” [142]
22. “The term for the Baroque period arrangement is ‘basso continuo’ or ‘continuous bass’ because it
provided not the tune or counter-melodies, but the bass line and the steady rhythmic continuity.” [143]
23. “The word derives from ‘same voice’ in the sense that the voices generally move together in the
form of chord changes, but the essential meaning of the term is the pattern of a single prominent
melody supported and enhanced by a subordinate accompaniment.” [144]
24. “In homophonic style, the principle structure is the relation between the outer voices—the melody
and bass.” [144]
25. “In music, the Camerata demanded clarity of words, the expression in music of the affection of the
poetry being set, and a single prominent melody. These ideas led to experiments in vocal-theatrical
music, and created a new genre: opera.” [145]
26. “This meant the music had to be suited to the ability of the untrained public, so the melodies had to
be simple, and florid polyphony was not appropriate.” [146]
27. “The chord enabled composers to deal with simultaneous note combinations more efficiently,
placing less of a tax on working memory by boiling down the vast array of possible flows of voices
into a small number of possible chord-connections.” [147]
28. “The keyboardist could play the accompaniment at sight without the need of having all the notes
written out—since he knew the pat- terns of chord connection.” [148]
29. “The new style was homophony—a single prominent melody accompanied by subordinate voices
which merely filled out the harmony in a simple way without detracting attention from the tune.”
[148]
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Chapter 9: Primacy of Line vs. Primacy of Chord
Answers
1. “That music required and called upon understanding of melodic shape, the scale, the organization
of musical elements in time, the arts of counterpoint and chordal harmony. It required knowing,
calling upon, and maximizing the principle of tonality—of unity, direction, and motion to
resolution.” [149]
2. “The original Greek concept ‘harmoniai,’ the root of our term ‘harmony,’ meant the synthesis of
notes over time into a melodic line with continuity and coherence.” [150]
3. “A number of historical developments precipitated a change in the meaning of the term, such that
today it is associated primarily with simultaneous combinations of notes.” [150]
4. “The chord enabled the creation of a new style of music, homophonic style, which became essential
to a powerful new genre: opera.” [150] See page 150 for more reasons.
5. “This selection already reflected a neglect of the fact of time—of the temporal nature of musical
perception, cognition and experience.” [150]
6. “It is not that one of these is inherently superior; however this is part of a shift from a dominantly
‘horizontal’ (linear) conception to a dominantly ‘vertical’ (chordal) one.” [150]
7. “The overtone series contains elements in the upper partials which don’t comport with our musical
system.” [151]
8. “As the name suggests, the school advocated reason—this philosophy was a part of the historical Age
of Reason—but essential to the ideology is a certain conception or definition of reason. Reason,
according to this school, was not a primarily extrospective faculty, looking out at the world, but
primarily an introspective one, operating abstractly in a sphere of its own.” [152]
9. “Rameau’s Treatise on Harmony begins not with any survey of human music, but ‘On the
Relationship between Harmonic Ratios and Proportions’—those of the overtone series. This
conception of a stack of notes sounding at once in harmonic ratio is the central fact which ‘may be
used to make music perfect.’” [153]
10. “In Rameau’s thought, the conception of a fundamental tone, with harmonic tones sounding above
it, became the central model and starting point.” [153]
11. “Lines are treated as derived from and determined by the chord progression.” [153]
12. “Rameau’s solitary positive contribution to musical thought is the idea of looking at chords in terms
of the root and to consider the chord in relation to the key (which, we may point out, is an issue of
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temporal context).” [154]
13. “Rameau, on the other hand, has the temerity to insist that students begin learning music by
writing in four parts [...] .” [154]
14. “Rameau’s thought, that product of the ‘Age of Reason,’ became successful by catering to those who
do not wish to think.” [156]
15. “Most students who go through chord-centered curricula don’t understand why things are done
that way (unsurprising since the method makes no sense), and simply feel bored.” [156]
16. “Unfortunately, Western thought has essentially lost the concept of ‘harmoniai.’ It has been
transformed into its opposite: instead of naming the synthesis of tones in the flow over time, it came
to mean chords and the science of chords.” [158]
17. “All the objectivity of modern science, all the prestige of ages-old mathematical knowledge, all the
poetic majesty of Greek philosophy, even a misguided notion of speedy practicality—all of these have
their weight thrown onto the wrong concept.” [158]
18. “Man has been around for well more than 40,000 years, but the chord is only around 500 years
old—it has existed for only about 1% of human history.” [158]
19. “It was the product of a complex development of practical knowledge, and a new level of conceptual
product, and a means of summarizing prior observa- tions about intervals and lines.” [158]
20. “When we listen to music, we attend to, follow and remember the melody; in more polyphonic or
symphonic music, we let the ear follow one line such as the oboe, then pick up and follow the
violins, and so on, always attending to lines and how they relate to one another.” [159]
21. “A single melody by itself is music; a single chord by itself is not.” [159]
22. “At a certain point, he becomes familiar enough with the composite sound and its inner relations,
and can recognize it instantly—but that is a skill acquired by means of linear, temporal cognition.”
[160]
23. See page 162.
24. “A proper understanding of music must acknowledge that an ‘equal partnership’ between melody
and harmony is equivalent to imagining a building whose first and fiftieth floors are in the same
place. It is a contradiction.” [161]
25. “Born in 1868 in Poland and raised in the twilight of 19th-century Romanticism, Schenker
developed a revolutionary new theory of music which strongly reasserted the importance of linear
connections, and which provided profound new insights into the nature of human musical
cognition.” [161]
26. “Schenker writes that he ‘must certainly endorse’ a statement that ‘the study of music must begin
with melody.’” [161]
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27. “Schenker regarded the scale as the fundamental basis and integrating framework of music, and
scale degree as ‘the generator of [musical] content.’” [161]
28. “Particularly with the advent of philosophical Subjectivism, people of a certain type took this as the
excuse to declare ‘anything goes’—that the old system of musical order had been exploded,
disproved, overturned, invalidated.” [163]
29. “He solved the problem of instrumental technique by showing that the complexities of
instrumental music were elaborations of the simpler underlying patterns of species counterpoint.”
[163]
30. “He showed how the new innovations did not explode or overturn the prior laws of order, but
rather used those laws, counted on them, depended on them as the basis of intelligibility.” [163]
31. “Schenker viewed the various notes and chords in a piece as having radically different levels of
importance—some were mere ornaments on the surface, others were part of the musical flow in a
deeper way, and some represented key structural pillars of the piece.” [163]
32. “Schenker first conceptualized music as having levels of structure; he formed the conception of
three levels: the foreground, middleground, and background (or immediate, intermediate and
remote).” [164]
33. “Thus Schenker discovered and systematically developed a theory of music based on the principle
that we understand the complex by means of the simple.” [166]
34. “Through Schenker’s vast experience over his productive life he came to the conclusion that all
integrated tonal music is ultimately an elaboration of a super-fundamental, ultra-simple
underlying pattern or archetype he called the Urzatz.” [166]
35. “The fundamental melodic line, called the Urlinie, marches by scale from a stable note of the tonic
triad down to the tonic.” [166]
36. “The most common Urlinie is the melodic progression through scale degrees 3-2-1. More rarely,
5-4-3-2-1 or even a progression down a full octave.” [166]
37. “The one significant shortcoming in Schenker’s theory of music is its neglect of emotion.” [167]
38. “In marked contrast to Rameau’s wish to be known for his theory more than his compositions,
Schenker was eminently practical in mindset.” [168]
39. “Schenker’s theory is a tremendous advance upon and completion of that idea: his perspective
regards a central tonic and its harmony as the persistent background conso- nance retained by the
brain, to which all other elements relate as blending or clashing, with the result that the ultimate
completion is the resolution of all discords back to the original core.” [168]
40. “Linear synthesis is the fundamental of music.” [168]
41. “A musical line or melody becomes coherent by means of its shape moving from beginning to
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climax to cadence.” [168]
42. “Melody moves not by gradual fluctuation of pitch, like the rise and fall of the wind, but by definite
motion from one discrete point of pitch to another. Essential to melody is the fact of the distance
from one note to another, the pitch interval.” [168]
43. The three categories are perfect consonances, imperfect consonances, and dissonances. [168/169]
44. “A dissonance, by itself, is the musical equivalent of a contradiction; the brain cannot resolve the
note-relationship.” [169]
45. “One of its fundamental tenets is: consonance is primary; consonance provides the framework or
structure within which dissonances can be made intelligible.” [168]
46. “‘Polyphony’ is the name for the confluence of many independent, contrasting voices.” [169]
47. “‘Homophony’ is the name for a single prominent melody with harmonic accompaniment.” [169]
48. “Chord progressions are merely a means of coordinating or holding together, as a package, a bunch
of bits of linear motion.” [169]
49. “The correct and profound conception of ‘harmony’ has to do not with chords as such, but with the
overall phenomenon of the relation of tones to the scale that forms their context.” [170]
50. “The scale is the basic and controlling form of musical context.” [170]
51. “Rhythm means action coordinated in time, using the uniform unit that is the beat or pulse as the
measuring unit.” [170]
52. “Meter, a regularly recurring pattern of strong and weak beats, provides a hierarchical structure to
time measurement, like the marks on a ruler provide a hierarchical structure to length
measurement.” [170]
53. “The diatonic scale is able to provide the mind with an orienting framework because it is not
symmetrical; the array of note relationships around each scale tone is unique and distinctive, giving
each tone an unmistakable position and role within the scale, and enabling the mind to orient itself
in the musical context.” [171]
54. “Modulation to closely related keys, those which require the alteration of only one note, are smooth
and subtle. Modulation to distant keys, those which require the alteration of many notes of the
scale, are more bold, disruptive, and dramatic.” [171]
55. “Tonality, an innovation of the Renaissance and the foundation of several centuries of magnificent
music, is the principle of creating and using the gravitational pull of the tonic note to evoke a
feeling of journey in music, a sense of goal-direction.” [171]
56. “Thus we see how melody, its intervals, the scale, rhythm, polyphony, counterpoint, harmony,
and tonality all express the same basic principle: the integration, the synthesis over time, of many
distinct elements into one unified whole, grasped and used by man’s mind.” [172]
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57. “The music has the integrity of building everything out of the theme, with no extraneous
elements.” [173]
58. “All this is integrated in a tremendous symphonic sweep that is the embodiment of man, the whole
being—man the inseparable unity of rational intelligence and passionate moral integrity.” [173]
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