53 An Expanded Macro Analysis System for Chromatic Harmony Daniel Sommerville Part One: The rationale for the significance of other chord successions in addition to circle progressions. n the sixth edition of Music in Theory and Practice , authors Bruce Ben- ward and Gary White state that, all tonal music from the beginning of the baroque to the middle of the romantic period contains a pre- ponderance of circle progressions. 1 They then outline a system of analy- sismacro analysisin which circle progressions are readily identied. Letter names for chords are used instead of roman numerals, and under-slurs are used to link those chords that form such progressions (i.e. root movement by descending fth or ascending fourth). With such analysis, one can see at a glance a wealth of information concerning har- monic movement. Prolongation and nested progressions are readily seen, as are circle progressions resulting in strong directional motion. The linking symbol of the under-slur is also useful for training the ear to hear circle progressions as one is studying a score. However, as Benward and White allude, the romantic composers began to incorporate other chord relationships, particularly third relation- ships, into their music. The music of this era was characterized by phras- ing that was more continuous and less punctuated by cadences. Specically, this was manifest in deceptive cadences and other types of chord successions such as third relationships, backward circles, com- mon-tone diminished sevenths and root movement by seconds. The circle progression remained the strongest arbiter of harmonic movement, but certain other chord relationships, specically chromatic third relation- ships, exerted a strong harmonic pull as well. Rameaus statement that the progressions of harmony are nothing but a chain of tonic notes and dominants 2 (i.e. circle progressions) may be an adequate way of describing much of the music of the eighteenth and early nineteenth centuries, but it is certainly less true for music after that time. Later, Rameau published his Gnration Harmonique, in which 1. Bruce Benward and Gary White, Music in Theory and Practice, 6th ed. (Madison, WI: Brown and Benchmark, 1997), vol. 2, 67. 2. Jean Philippe Rameau, Treatise on Harmony , translated by Philip Gossett (New York: Dover, 1971), 288. I
Transcript
An Expanded Macro Analysis System for Chromatic HarmonyDaniel Sommerville
Part One: The rationale for the significance of other chord successions in addition to circle progressions.
n the sixth edition of Music in Theory and Practice, authors Bruce Ben-ward and Gary White state that, Òall tonal music from the beginning of the baroque to the middle of the romantic period contains a pre-
ponderance of circle progressions.Ó1 They then outline a system of analy-sisÑÒmacro analysisÓÑin which circle progressions are readily identiÞed. Letter names for chords are used instead of roman numerals, and under-slurs are used to link those chords that form such progressions (i.e. root movement by descending Þfth or ascending fourth). With such analysis, one can see at a glance a wealth of information concerning har-monic movement. Prolongation and Ònested progressionsÓ are readily seen, as are circle progressions resulting in strong directional motion. The linking symbol of the under-slur is also useful for training the ear to hear circle progressions as one is studying a score.
However, as Benward and White allude, the romantic composers began to incorporate other chord relationships, particularly third relation-ships, into their music. The music of this era was characterized by phras-ing that was more continuous and less punctuated by cadences. SpeciÞcally, this was manifest in deceptive cadences and other types of chord successions such as third relationships, Òbackward circles,Ó com-mon-tone diminished sevenths and root movement by seconds. The circle progression remained the strongest arbiter of harmonic movement, but certain other chord relationships, speciÞcally chromatic third relation-ships, exerted a strong harmonic pull as well.
RameauÕs statement that Òthe progressions of harmony are nothing but a chain of tonic notes and dominantsÓ2 (i.e. circle progressions) may be an adequate way of describing much of the music of the eighteenth and early nineteenth centuries, but it is certainly less true for music after that time. Later, Rameau published his G�n�ration Harmonique, in which
1. Bruce Benward and Gary White, Music in Theory and Practice, 6th ed. (Madison, WI: Brown and Benchmark, 1997), vol. 2, 67.
2. Jean Philippe Rameau, Treatise on Harmony, translated by Philip Gossett (New York: Dover, 1971), 288.
I
53
54 ¥ Musical Insights
he modiÞes his views and allows for a third progression in addition to the Þfth. The third progression he labeled ÒchromaticÓ and the Þfth progres-sion, Òdiatonic.Ó3
Over 150 years later, Moritz HauptmannÕs theory of chord succes-sion takes into account the romantic composersÕ predilection for colorful chromatic relationships: ÒThe succession of two triads is. . . only intelligi-ble in so far as both can be referred to a common element which changes meaning during the passage.Ó4 HauptmannÕs main point was to show the commonality and hence, relationship, between the tonic and dominant, and the tonic and subdominant, as each of these pairs share a common tone. But his principal has signiÞcance for such chromatic relationships as GÄ minor to E minor (used by Wagner, for example, as the ÒTarnhelmÓ motive in The Ring; see example 11).
Because of the importance of other types of chord successions in the music of the romantic composers, it is necessary to devise a means for identifying such successions in macro analysis. Toward this end, what fol-lows is a list of proposed symbols to use in addition to the circle-progres-sion under-slur. Care was taken to make the symbols as intuitive as possible in order to make their usage easy and effective.
Part Two: The SymbolsÑa vocabulary of linking sym-bols and other analytical tools.
Certainly the strongest harmonic pull occurs in circle progressions, and these chord relationships are shown in current macro analysis tech-nique by the under-slur. A double under-slur can be used to show the strongest portion of a circle progression: the authentic cadence. A dotted or dashed under-slur indicates the movement from the leading-tone diminished seventh to its tonic. This latter progression is certainly weaker than the root-movement-by-Þfth circle, but since the dominant seventh and the leading-tone diminished seventh share three pitches, their effect is similar.5
3. Matthew Shirlaw, The Theory of Harmony (London: Novello, 1955), 110.4. Moritz Hauptmann, The Nature of Harmony and Metre, translated and edited by
W.E.Heathcote, (New York: Da Capo Press, 1991), 45.5. Romantic composers would often stack the two sonoritiesÑV7 and viiû7Ñtogether,
forming a ÒsuperdominantÓ sonority, the same as the V§9 chord used in jazz. Beethoven uses this sonority often in his symphonies.
Expanded Macro Analysis ¥ 55
Under-slurs
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Example 1. Bach, Two-Part Invention 13 in A Minor, mm. 1Ð6(circle progressions). The area within parentheses indicates pro-longation of the tonic before signiÞcant harmonic motion begins.
6. Upper-case letters will always refer to major (or augmented) chords, lower case to minor. Since ÒCÓ has the same shape in upper and lower case, the major chord will be notated ÒC,Ó and the minor, Òcm.Ó
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56 ¥ Musical Insights
Example 2. Beethoven, Piano Sonata, Op. 13, ÒPathetique,Ó I,mm. 1Ð5 (leading-tone diminished sevenths and their resolu-tions). Note the signiÞcant circle progression in the last measureof the example, leading to the secondary key of E§.
What follows is a list, with examples, of the analytical symbols that are useful for expanding the chord relationships that can be shown by macro analysis.
A. Predominant chord (other than ii) to dominant. In the baroque era, composers often utilized the diminished seventh chord to provide chromatic color. The recitatives of Bach are full of such unstable sonori-ties. In the classic era, composers focused most of their chromatic efforts on the sonority immediately preceding the dominant (called the Òpre-dominantÓ chord in this discussion). In this predominant position, com-posers used a wide variety of borrowed and secondary-function chords. These chords not only include ii and IV, but also Neapolitan sixth, sec-ondary dominant and leading-tone diminished seventh chords, and aug-mented sixth chords. Augmented sixth chords in particular defy roman numeral analysis because of their chromatic linear resolutions. The strong chromatic pull of the augmented sixth interval to the root in octaves of the dominant is proof that chromatic relationships can effect as strong a harmonic pull as a circle progression. Therefore, such relationships need to be shown in analysis. The symbol is an under-slur in parenthesis. The
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Expanded Macro Analysis ¥ 57
under-slur indicates strong, predictable harmonic movement from pre-dominant to dominant and the parenthesis reminds one that it is not a true circle progression, in terms of root movement by descending Þfth.
Regarding the IV to V movement, I use an under-slur with paren-thesis, although there are good reasons for just using the under-slur with-out parentheses and treating the succession as a true circle progression. Rameau referred to the ii# as a subdominant with an added sixth!7 To him, the root movement from the fourth to the Þfth scale degree was even more important than root movement from the second to the Þfth. This is borne out in the music of the eighteenth century, because the iià chord as predominant certainly appeared much more in Þrst inversion (like a sub-dominant with an added sixth) than it did in root position. Therefore, a case can be made that IV and ii# are interchangeable, as they share three common tones.
When Wagner uses the IV chord as a predominant, he often puts it in Þrst inversion, making it resolve like an augmented sixth chord with-out the chromaticism.
Predominant Chord (other than a ii) to Dominant
( ) IV ( ) V +6 ( ) V
C major: F(6) ( ) G
Example 3. Wagner, from Prelude to Lohengrin. Note IV6 to Vmotion in m. 3. Also see example 19, mm. 5 and 14Ð15.
7. Shirlaw, p. 113.
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58 ¥ Musical Insights
Example 4. Mozart, Piano Sonata in F, K. 332, I, mm. 31Ð41. Thetonality (C major) is labeled between the systems in m. 1 (tonalproÞling will be explained in detail later). Also evident in thisexample are nested circle progressions (m. 37 and 38).
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Expanded Macro Analysis ¥ 59
B. Retrogression. A ÒretrogressionÓ (or ÒregressionÓ) is a back-ward circle progression, i.e. root movement by descending fourth or ascending Þfth. Such root movement is used in a coloristic way, but it also has its antecedent in the ÒsoftÓ plagal cadences of the Renaissance era. The symbol for a retrogression is an over-slur (signifying the opposite of an under-slur).
Retrogression
ii vi iii
G: a e b
Example 5. Mozart, Symphony No. 41, II, mm. 51Ð56. A poignantstring of suspensions is made possible by the long, retrogressivechord movement. The tonic (D minor at this point) is all butobliterated by the combination of melodic and harmonicsequence, retrogression, and the use of all minor chords (real imi-tation).
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60 ¥ Musical Insights
Example 6. Wagner, from Prelude to Parsifal. The harmonicvocabulary of the entire work is based on the plagal cadence,namely, the Dresden Amen, which is itself a retrogression. Wagnerchose this familiar Lutheran Amen in keeping with the Christianthemes of this opera.
C. Deceptive cadences. These chord relationships abound in all tonal music but are exploited in the romantic era. Wagner and Mahler often use deceptive cadences to usher in new tonal areas, and it is impor-tant to have a symbol for this relationship. It is the under-slur with a slash through it, signifying the thwarting of the expected circle progression.
Deceptive Cadences
V vi V §VI
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Expanded Macro Analysis ¥ 61
Example 7. Mahler, Symphony No. 5, IV, Adagietto, mm. 44Ð47.The effect of the deceptive cadence is heightened by the use ofthe predominant ii chord (C minor) before the dominant, by theuse of the lowered VI chord (borrowed from the parallel minor ofthe tonic key, B§§§§), and by the suspensions in the violins.
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62 ¥ Musical Insights
Example 8. Wagner, Prelude from Tristan und Isolde, mm. 14Ð17.The effect of this deceptive cadence is heightened by the Lydian4Ð3 suspension, so often employed by Wagner.
D. Third relationships. There are three types of third relationships between chords. First, a diatonic relationship in which there are two com-mon tones between the chords. In the classic era, this can often be inter-preted as mere chord substitution, e.g. between I and iii. In his classic book on analysis, Guidelines for Style Analysis, Jan La Rue refers to the baroque perception of Òbi-focal tonality,Ó8 showing a close relationship between the major key and its relative minor, but otherwise third relation-ships were usually chord substitutions. In the romantic era, however, the color aspect of diatonic third relationships was exploited. The third rela-tionship is shown by a squared-off under-bracket between chords.
Diatonic Third Relationships
C e fÄ D
8. Jan La Rue, Guidelines for Style Analysis, 2nd ed. (Michigan: Harmonie Park Press, Sec-ond Edition, 1992), 52Ð53.
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Example 9. Wagner, from the Prelude to Parsifal. In listening tothis example, note the difference between the color changes ofthe third relationships (mm. 1Ð3), yielding a sense of staticmotion, or at most, local activity, contrasted against the strongdirectional motion of the circle progressions (mm. 3Ð4, 5Ð6). Thuscan one showÑand hearÑdifferent levels of harmonic motionthrough macro analysis.
The second and third types of third relationships are chromatic relationships. The second type consists of chords that share just one com-mon tone, and where one or both of the linear moves is chromatic (by half-step). ÒChrÓ can be written on the under-bracket to differentiate it from a diatonic third relationship.
Chromatic Third Relationships (one common tone)
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64 ¥ Musical Insights
Example 10. Schubert, ÒDie Liebe hat gelogen,Ó mm. 1Ð6. Notethe contrast between the diatonic third relationship of m. 3, andthe chromatic third relationships of mm. 5Ð6.
Example 11. Wagner, Tarnhelm motive from Das Rheingold. Theeerie character of the music at this point is due to the chromaticthird chord relationships.
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Expanded Macro Analysis ¥ 65
The Þnal (third) level is fully chromatic, where there are no shared tones, and at least two of the linear moves are chromatic.
Chromatic Third Relationships (no common tones)
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Example 12. Dvorak, ÒHear my Prayer,Ó from Biblical Songs, Op.99. Part of the harmonic richness of the Þrst two measures derivesfrom the descending sequence of backward circle progressions(retrogressions), but its real poignancy comes from the fullychromatic relationship between the CÄ major and E minor chordswhich connects the two segments of the sequence.
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66 ¥ Musical Insights
Example 13. Brahms, ÒO Tod, wie bitter bist Du,Ó from Vier Ern-ste Ges�nge, mm. 1Ð6. As with the example from WagnerÕs Parsi-fal (example 9), this example begins with chords based on thirdrelationships, resulting in rich and colorful harmony but nostrong harmonic motion, and ends with strong directionalmotion through circle progression. Note the added interest pro-vided by the chromatic third relationship to the FÄ major chord inm. 2, and the deceptive cadence (in the dominant key) of m. 3.
E. Root movement by second. Often this type of harmonic motion is ornamental, serving to prolong a chord as a neighboring or passing chord, but occasionally it will serve to cloud the tonality or ÒmigrateÓ the tonality to a different key. A diagonal line in the pertinent direction between the chord names indicates this type of movement.
Root Movement by Second
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Expanded Macro Analysis ¥ 67
Example 14. Wagner, from Act III, Scene 2 of Tannh�user. TheÞrst set of chords that moves by seconds actually serves to modu-late, brießy, to a new tonal area (mm. 7Ð9). The second set is moreornamental in nature (mm. 13Ð15). Whenever Wagner uses paral-lel chords in root position, he always moves the bass and sopranoin contrary motion.
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68 ¥ Musical Insights
F. Substitute chords. The main substitutions are between the dom-inant and the leading-tone seventh chord, and between the supertonic triad (or seventh chord) and the subdominant (or their diminished/minor counterparts). I and iii or I and vi could be considered substitutes, as mentioned earlier, or may be considered third relationships, depend-ing on the context and the analystÕs interpretation. Substitute chord rela-tionships would be shown by an ÒequalsÓ sign (=) between the chords, signifying no real harmonic movement, but a slight change in color none-theless.
Substitute ChordsD: cġ7 = A7
=Fm: gû = b§m
Example 15. Wagner, excerpt from Prelude to Lohengrin.Although WagnerÕs music includes passages so contrapuntal asto defy harmonic analysis, nevertheless there are usually pointsof clear harmonic motion even in such passages, as can be seen inthis example (the circle progression from GÄ7 to CÄ minor).
G. Same root, or same root feeling. In the music of the nineteenth
century, there are chord relationships where two successive chords have the same root, but where other chord tones are moved chromatically. Two incidences of this are the common-tone diminished seventh going to its tonic, and a modal shift (C major to C minor, for example). The symbol is a horizontal line between the two chords, signifying no root movement.
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Expanded Macro Analysis ¥ 69
Same Root, or Same Root Feeling
CTû7 I I i
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Example 16. Schubert, Moment Musical No. 6, Op. 94, mm. 29Ð36.Note the common-tone diminished seventh in m. 34. The lettersunder the horizontal lines indicate pedal tones.
For an example of change of mode of a chord, see m. 8 of example 18.
H. Cadential @@@@ chords. The cadential @ is a sonority that occurs through voice-leading means, as the 6 and 4 above the root of the domi-nant resolve to 5 and 3. It is the tonic sonority posing as both a predomi-nant chord and part of the dominant chord with suspensions or appoggiaturas. Because of its hybrid, yet important function, it needs to be shown in analysis in a unique way. A way of notating it that makes such cadences immediately noticeable is with a piano bracket underneath both the cadential @ and the V(7). The chord before the cadential @ (the real predominant) is then connected by under-slur (or dotted line, or under-slur with parentheses) to the middle of the piano bracket, like this:
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70 ¥ Musical Insights
Cadential @ Chords
ii6 I@ V7 I
Ger.+6 i@ V7 I
F: bû7 F@ C7 F
See example 17 at mm. 9Ð10 and 15Ð17. Note the partial cadence at m. 10, to the cadential @, but moving via mode change on to a different tonality.
I. Other symbols for analysis.In addition to the symbols described above, there are a few other analytical symbols that provide useful infor-mation. Whenever possible, it is preferable to keep the analysis on the musical score and not have to resort to separate graphs, tables or charts. For instance, writing the tonal proÞle on the musical score itself saves one from having to constantly go back and forth between a graph, table or chart and the musical score. To this end, I employ LaRueÕs Òrule of threeÓ9 in assigning relative importance to tonalities. The tonal center (key) is written between the staves, with the macro analysis below the staves. Sig-niÞcant tonal centers are circled and brief, insigniÞcant tonicizations are in parenthesis. A middle level is neither circled nor in parenthesis. Such a system can be seen in example 17.
Tonal Centers
1. SigniÞcant tonicÑcircled A§
2. Middle-levelÑnot circled A§
3. Brief, insigniÞcantÑin parenthesis ( A§ )
9. Ibid., p. 5
( )
Expanded Macro Analysis ¥ 71
Example 17. Wagner, from Act III, Scene 2 of Tannh�user, open-ing. The two main tonalities of this section are G minor and B§§§§major. Along the way, there are brief tonicizations of C minorand D minor. Pivot chords are circled.
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72 ¥ Musical Insights
Such a system helps the analyst immediately see how a chord pro-gression is functioning within a key, which has been the strength of roman numeral analysis. At the same time, with highly chromatic music, one is not encumbered by secondary functions, which is what can happen with roman numeral analysis. One can immediately see where a key begins to be established, and making such decisions develops the ear as well as the eye. In example 18, the C minor chord of m. 8 has a dual pur-pose: Þrst, it connects to the previous C major chord as two chords with the same root, but a change in color; second, it becomes the subdominant of a new tonic, G Minor, as it progresses to the dominant, D major, and on to G minor. The analyst can hear the C minor chord, then, as a pivot chord, and the new tonality begins to be established on that chord (as it includes the lowered sixth scale degree), being conÞrmed by the inclusion of the leading tone in the next chord. By putting the beginning of the G minor on the C minor chord, the analyst is taking into account a sophisti-cated level of hearing, that of retrospective listening, where earlier sound-ing chords are re-informed to take on new meaning.
Finally, the notation of inversions and non-harmonic tones must be addressed. Although one of the beauties of the macro analysis system is that the analyst need not be encumbered by the labeling of inversions of chords, still there are places where the analyst may wish to label inver-sions for a variety of reasons. Noting the beauty of a chromatic bass line, labeling passages of fauxbourdon (successive £ß chords), or identifying particularly interesting chord relationships are three instances where inversion notation are useful. I advocate a hybrid system that combines voice leading and inversions in the notation. It should be stressed, how-ever, that such notations are necessary only when the voice leading or inversion of the chord plays a vital role in the music at that point. It does not need to be used constantly.
Inversions are put in parenthesis: (¤ ) or (#) for Þrst inversion, (@) or ($) for second inversion, and (%) for third inversion. Diminished and half diminished sevenths need not be labeled for inversions. A dominant sev-enth is always listed with a Ò7,Ó and the inversion in parenthesis. This way, it is immediately apparent that it is a dominant seventh chordÑno need to decipher the inversion notation. An alternative to using the tradi-tional Þgured-bass symbols for inversions is to write the bass note in pedal-tone notation:
InversionsE§G where G is the bass note.
Expanded Macro Analysis ¥ 73
The identiÞcation of the inversion makes it possible to see at a glance what position the chord is in without having to constantly refer to the bass line.
Voice-leading, especially with nonharmonic tones and their resolu-tions, are not put in parenthesis, but are listed as they relate to the chord in root position, regardless of the chordÕs actual inversion. This is not the same as Þgured bass notation, but as a hybrid it combines aspects of Þg-ured bass notation and chord inversion notation without having to deal with the complexities of both in their purest form. A 4Ð3 suspension is always labeled such, regardless of the chord position.
For example, to show a ÒD dominant seventhÓ with an A in the bass (second inversion), and a melodic movement above of a suspended 4 going to 3, here is the notation:
Nonharmonic Tones
D7 chord and type
( $ ) position of chord
4Ð3 signiÞcant non-harmonic melodic movement
Alternative
D7 4Ð3
A
Part Three: Interpreting the data gained by expanded linking symbols.
In music of the late romantic composers, Wagner for example, it would not be uncommon to see linking symbols between every chord of a section. This is in keeping with WagnerÕs concept of Òendless melody,Ó and the continuity of the harmony further supports that concept. After the analyst has Þgured out the chords and how they relate, he or she can move on to reÞning and interpreting the data that is collected.
The reÞning process is that of identifying broad harmonic gestures and differentiating between such gestures and mere prolongation or nested harmonies. In the next example, linking symbols inside and above broader linking symbols indicate nested harmonies. It is also easy to see the prolongation of B§ in mm. 1Ð2 and 5Ð6 and the broad third rela-tionship between E§ and C, mm. 7Ð8.
74 ¥ Musical Insights
Example 18. Wagner, from Act V of Rienzi. Measures 1Ð2 and 5Ð6can be heard as a prolongation of the B§ chord. It can be arguedthat the chord on the third quarter of m. 3 is really a B§ chord withan accented passing tone in the soprano. However, the deliberatebass line motion from E§ to D, then to B§ adds credence to hearingthis chord as a separate sonority, D minor.
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Expanded Macro Analysis ¥ 75
In further interpreting the data, the analyst can determine relative strength and weakness of harmonic motion in the piece. La Rue speaks of three levels of musical activityÑstrong directional motion, local activity, and stasis or stability.10 A piece of music attains a sense of movement and shape through the varying rates of activity in each of the basic parameters of music: sound (including texture and timbre), harmony, melody, rhythm and growth.11 An example of how these three levels are reßected in harmony is as follows: the circle progression and cadence signify strong directional motion; local activity may be signiÞed by the presence of sequence, or of fauxbourdon, or colorful chord relationships by thirds, etc.; stasis or stability in harmony is usually represented by prolongation of the tonic.
The Þnal two examples are lengthier ones, showing the whole sys-tem in action. The Þrst one, example 19, is interesting because it has strings of retrogressions, chromatic third relationships, modal shifts and root movement by seconds, in addition to circle progressions. The analy-sis makes it possible to hear and see the strong harmonic movement when the music Òshifts gearsÓ into circle progressions.
Example 19. Wagner, Introduction to Act II, The Flying Dutch-man.
10. Ibid., pp. 12Ð14.11. Ibid., Chapter 1.
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76 ¥ Musical Insights
Example 19, continued.
Example 20 is amazing for some false, illusionary chord relation-ships: in m. 1, the chromatic third relationship between the Þrst two chords, A§ and C§ (respelled as B), is replicated by the motion between the third and fourth chords, B moving to B§(¤ ). This replication occurs because of the bass line move of a minor third and because of the half-step linear descent between FÄ and F. In reality, the relationship is root movement by half step. In each measure, a new pitch is tonicized via its leading-tone diminished seventh, and strong circle progressions do not exist here. The pitches tonicized form an augmented triadÑA§, E and C. It is also inter-esting to note that just a few measures after this, the harmony moves into broad, long circle progressions with very strong directional harmonic motion. The harmonic contrast adds to the drama of this portion of the opera.
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Expanded Macro Analysis ¥ 77
Example 20. Wagner, Magic-Fire Scene from Die Walk�re.
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78 ¥ Musical Insights
Conclusion
The addition of other linking symbols to the basic circle under-slur enables the analyst to Þnd out much more about the harmonic style of the romantic composers in particular. It was in the area of harmony that these composers made some of their greatest creative contributions. Eventu-ally, the symbols themselves will aid one in his or her aural perception of the music, as relationships between chords are immediately perceived. With a Þnished macro analysis that includes these expanded linking sym-bols, the analyst is able to effectively scan a piece when searching for spe-ciÞc chord relationships.
Furthermore, the integration of these symbols into a proÞle of har-monic ebb and ßow is an exercise that reaps great rewards for the musi-cian. Such a system can clarify rates of harmonic motion within a piece, and can help the performer determine how harmony contributes to the overall sense of movement and shape. In this way, the performer can be ushered even deeper into the drama of the music as it unfolds, because he or she is able to see the big picture. Such macro analysis gives the per-former the understanding to be able to make interpretive decisions that will allow others to perceive the harmonic shape of a piece, and to get caught up in the drama of it themselves.
Bibliography
Benward, Bruce and Gary White. Music in Theory and Practice. Sixth Edi-tion, Volume I. Madison, Wisconsin: Brown and Benchmark, 1997.
Hauptmann, Moritz. The Nature of Harmony and Metre. Translated from the German and edited by W.E. Heathcote. New York: Da Capo Press, 1991.
La Rue, Jan. Guidelines for Style Analysis. Second Edition. Michigan: Har-monie Park Press, 1992.
Jean Philippe Rameau. Treatise on Harmony. Translated from French by Philip Gossett. New York: Dover, 1971.
Shirlaw, Matthew. The Theory of Harmony. London: Novello, 1955.
