Jody Nagel
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The Chromatic Modal Scale:
Proper Spelling for Tonal Voice-Leading

 
 
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The Chromatic Modal Scale:
Proper Spelling for Tonal Voice-Leading

by Dr. Jody Nagel
 
The "Chromatic Modal Scale" includes the twelve equal-tempered pitches of an octave spelled as follows:
Example 0
 
Thus, for example, in a C-tonality, the Chromatic Modal Scale would be spelled: C, Db, D, Eb, E, F, F#, G, Ab, A, Bb, B, C.  In an A-Tonality, it would be spelled: A, Bb, B, C, C#, D, D#, E, F, F#, G, G#, A.  Notice that scale degrees 1 & 5 are fixed. There are then two chromatic versions for each of the other scale degrees: 2, 3, 4, 6 & 7.
 
The Chromatic Modal Scale simultaneously includes the "proper spellings" for all traditional seven-tone modes that contain a perfect fifth above the tonic note. For example, the C-Phrygian mode is spelled C, Db, Eb, F, G, Ab, Bb, C, which is a subset of the C-Chromatic Modal Scale. The C-Harmonic and C-Melodic Minor scales, and the C-Ionian, C-Dorian, C-Lydian, C-Mixolydian, and C-Aeolian modes are also subsets of the C-Chromatic Modal Scale. It is true that some modes lack a perfect fifth above the tonic, though these modes are difficult to perceive in "tonal" terms. For our purposes, a passage of music will be considered "tonal" if the ear can detect a significant perfect fifth (a Do-Sol relationship) against which the other tones are heard in relation. By employing the Chromatic Modal Scale, substantially more complex (i.e., chromatic) relationships can still easily be heard with "tonal ears." Indeed, each of the twelve pitches can be heard with a clear, tonal understanding.
 
In chromatic harmonic progressions of the nineteenth century, where one frequently encounters traditional tertian structures that are not "spelled in thirds properly," one usually notices that the composer's "strange" chordal spellings are done purposely with an eye towards linear voice-leading; it is the Chromatic Modal Scale which usually accounts for the composer's spelling choice. However, for our first example, let us look at the complete chromatic scale that W. A. Mozart employs just prior to the recapitulation of the first movement of his excellent A-Minor piano sonata.
Example 1
Notice, in the first bar of Example 1 that Mozart's chromatic scale includes a Bb rather than an A#. Mozart undoubtedly was exposed to the convention that chromatic scales are to be spelled in sharps when ascending, and in flats when descending. The presence of the Bf in the above example shows that Mozart "heard" a tonal scale-degree function for each pitch of the chromatic scale. This is an example of a complete A-Chromatic Modal Scale (starting from scale degree 5 and moving up one octave), which Mozart places just prior to the recapitulation, just prior to the return to the principal theme and the confirmation of A-minor tonality.
 
Let us consider, now, the spelling issues involving "vertical" and "horizontal" concerns when notating harmonic progressions. Traditional diatonic chord relationships are based on the primacy of the seven-note scale. We use seven letter names for our pitches. We use seven Roman Numerals to indicate chords with roots built on those seven scale degrees. Two of those scale degrees (1 & 5) largely account for our sense of tonality; by asymmetrically subdividing an octave into two unequal chunks of seven and five semitones (e.g., C up to G is seven semitones, then G up to C is five semitones), the ear becomes capable of orienting to pitch relations, or, in other words, tonality itself is made possible. On the other hand, scale degree 3 seems uniquely to determine an overall sense of "major-ness" or "minor-ness" to a scale. Thus, the Lydian, Mixolydian and Ionian modes seem to be more "major" in character, while Dorian, Aeolian, and Phrygian seem to be more "minor" in character. Consider that a C-Major scale and a C-Melodic-Minor scale differ only by their third scale degree - a difference great enough to lable one "major" and the other "minor." Finally, this leaves scale degrees 7 & 2 as neighbor-tones to the tonic note, and scale degrees 4 & 6 as neighbor-tones to the dominant note.
 
With the above categorization of the seven scale degrees, it is easy to show that all diatonic triads, which then progress (using closest voice-leading) to a tonic triad, are constituted as a combination of common-tones and neighbor-tones with the tonic triad. A voice is never more than one scale-step away from some pitch within the tonic triad, which is itself spelled "in thirds." Example 2 shows the six primary-tonic diatonic-triad relationships of the key of C-Major; each of these diatonic triads can be "spelled in thirds."
Example 2

Just as Einstein's theory of gravity eventually replaced and subsumed Newton's, Jean Philippe Rameau's1 notion of "spelling chords in thirds" needs to be subsumed by a larger theoretical system. The diatonic harmonic relationships that were known to Rameau are, indeed, easily "spelled in thirds." More chromatic relationships, however, do not work so nicely within Rameau's framework. The Chromatic Modal Scale, on the other hand, accounts for diatonic and chromatic relationships with equal ease and with the same fundamental logic. So let us leave the small 7-pitch-based "solar system" of diatonic relationships and enter the 12-pitch-based galaxy of chromatic relationships (which does also include the diatonic relationships).
1Jean Philippe Rameau (1683-1764). French composer and music theorist who helped spread the use of Roman Numerals to designate triads within a scale.

Once again, let us preserve special places for scale degrees 1 & 5 (which enable tonal hearing) and 3 & b3 (which govern our sense of "major" and "minor"). This leaves b7, 7, b2 & 2 as neighbor-notes to the tonic pitch, and 4, #4, b6 & 6 as neighbor-notes to the dominant pitch. Now we can consider all 12 major and minor triads in relationship to a specified tonic triad. These are all the primary-tonic triad-relationships that are chromatically obtainable. Note that many, but not all, of these triads are able to be "spelled in thirds." However, ALL are spelled as members of the Chromatic Modal Scale, and reveal tonally sensible voice-leading relative to the tonic triad. (The tonic triad is always "spelled in thirds.") Example 3 shows all triadic relationships to (3a) a C-Major tonic triad, and to (3b) a C-Minor tonic triad.
Click to see Example 3.
 
It should be emphasized, at this point, that we are currently dealing with "primary-tonic" relationships, and the Chromatic Modal Scale reveals the correct way to spell chords as they relate to the primary tonic. To clarify, for example, a V/ii chord in the key of C-Major is an A-Major triad that presumably then progresses to a D-Minor triad. The V/ii chord (in this key) is traditionally spelled A, C#, E, "in thirds," and does not seem to support the spelling suggested by a C-Chromatic Modal Scale (since C# is not found within a C-Chromatic Modal Scale). However, C: V/ii is a secondary-tonic relationship (not a primary-tonic relationship) since it is momentarily relating to D-Minor as tonic, rather than C-Major as tonic. The "proper" spelling of this chord requires that we shift to the D-Chromatic Modal Scale (D, Ef, E, F, F#, G, G#, A, Bf, B, C, C#, D) which, of course, produces the traditional spelling, A, C#, E. Any primary-tonic relationship postulated by the Chromatic Modal Scale can be employed as a secondary-tonic relationship for the purposes of tonicization and modulation. However, even more basic is the notion of chord-to-chord relationships within an otherwise "diatonic" progression. Consider the progression in the key of C-Major: C - F - G - C. This is traditionally called: I - IV - V - I. Nevertheless, as each chord progresses to the next chord, the chord of arrival could be viewed as a type of micro-tonicization. So, as C moves to F, it is possible to detect a tiny hint of F: V - I; and as F moves to G, it is possible to detect a tiny hint of G: bVII - I. In this progression, each pair of chords is spelled "properly" if the Chromatic Modal Scale based on the chord of arrival is utilized.
 
Consider a highly chromatic progression: a major-3rd cycle, such as C - E - Ab - C. If C is the overall tonic, then the progression is I - III - bVI - I. Yet each pair of chords is in a secondary bVI - I relationship. As C moves to E (E: bVI - I) the E-Chromatic Modal Scale (E, F, F#, G, G#, A, A#, B, C, C#, D, D#, E) determines that the C triad should be spelled C, E, G. Likewise, as E moves to Ab, the Ab-Chromatic Modal Scale (Ab, Bbb, Bb, Cb, C, Db, D, Eb, Fb, F, Gb, G, Ab) would ideally have us spell the E-Major triad as an Fb-Major triad (Fb, Ab, Cb). Finally, the progression from Ab to C would have us use the C-Chromatic Modal Scale and the Ab triad would be spelled Ab, C, Eb. This example reveals one of the spelling problems inherent in chromatic harmony: we cannot simultaneously spell the 2nd chord of this progression as E, G#, B and Fb, Ab, Cb. In this case, the E, G#, B spelling would be preferred since the overall key is C-Major, and the pitch E is scale-degree 3 in the C-"Major" Chromatic Modal Scale, whereas Fb is not a member of the C-"Major" Chromatic Modal Scale. Perhaps even better, however, would be to spell the E-Major triad as E, Ab, B, since each of these pitches is a member of the C-Chromatic Modal Scale.
 
When a chord is used to pivot from one key area to another, the chord in question is probably best spelled based on the key it is going to, rather than on the key it is coming from. Example 4 is an excerpt from Felix Mendelssohn's Songs Without Words, Venetian Boat Song, Op. 19, No. 6. The chord under the asterisk is a G-half-diminished seventh chord used in a passage that will soon cadence in D-Minor. This d: ivø7 chord is spelled G, Bb, C#, F, which is based on the D-Chromatic Modal Scale (D, Ef, E, F, F#, G, G#, A, Bf, B, C, C#, D)
Example 4
According to Rameau, a G-half-diminished seventh chord "should" be spelled G - Bb - Db - F. If Mendelssohn had spelled this chord "in thirds," then the voice-leading entailed would include Db - D, the D-flat being a lowered scale-degree-1 that needed to be chromatically altered to D-natural upon resolution. This does not make for intuitive tonal voice-leading and it is clear from the composer's choice in spelling that he gave priority to sensible linear tonal voice-leading rather than to "rules" requiring chords to be spelled "in thirds." The problem for Rameau is that a ivø7 chord does not exist within a diatonic minor key, and he had simply never encountered such a chord. Thus, he never had to consider "linear vs. vertical" spelling issues. Mendelssohn spells the ivø7 chord as Fa - Le - Ti - Me, so that when it moves to a i-chord, the voice-leading includes only sensible tonal motions: Fa-Me; Le-Sol; Ti-Do; Me-Me. This is the advantage of spelling chords based on the Chromatic Modal Scale.
 
Another wonderful example of chromatic harmony can be found in the opening theme of the first movement of Edvard Grieg's famous A-Minor Piano Concerto. In Example 5, the chord under the asterisk is a major-minor seventh chord built from the leading-tone of the key, which we will label as a VII7 chord. Grieg does not spell the chord "in thirds;"  however, once again, it is clear that the Chromatic Modal Scale (in A: A, Bb, B, C, C#, D, D#, E, F, F#, G, G#, A) governs the spelling of the chord: G# - C - D# - F#.
Example 5
Half-diminished and major-minor seventh chords can be built on any of the twelve chromatic pitches, but to understand them as tonal entities, involving tonal voice-leading, we must spell them using the Chromatic Modal Scale. Shown in Example 6 are (6a) all possible major-minor seventh chords and (6b) all possible half-diminished seventh chords in a primary relationship with a major tonic triad, and (6c) all possible major-minor seventh chords and (6d) all possible half-diminished seventh chords in a primary relationship with a minor tonic triad.
Click to see Example 6.
 
The famous opening of Richard Wagner's Prelude to Tristan und Isolde, along with a couple passages later within the same piece, gives us a very compelling usage of the Chromatic Modal Scale. The well-known "Tristan Chord" of m.2 consists of an F-half-diminished seventh chord spelled F, G#, B, D#. The implied opening tonality is A-Minor, and the Fø7 chord could therefore be labeled bviø7. The A-Chromatic Modal Scale is A, Bb, B, C, C#, D, D#, E, F, F#, G, G#, A, and, we see, the Fø7 chord is spelled properly within the A-tonality. See Example 7.
Example 7
Near the end of the Prelude, the same four pitch-classes (i.e., the same Fø7 chord) is found arpeggiated in the bass line in the context of C-Minor tonality. Here, it is spelled F, Ab, B, Eb, and could be labeled ivø7. The C-Chromatic Modal Scale is C, Db, D, Eb, E, F, F#, G, Ab, A, Bb, B, C, and, we see again, the Fø7 chord is spelled properly within the C-tonality. See Example 8.
Example 8
During the climax of the Prelude, the Fø7 chord is again used, though here it is as a iiø7 chord within an implied Eb-Minor tonality. The Eb-Chromatic Modal Scale is Eb, Fb, F, Gb, G, Ab, A, Bb, Cb, C, Db, D, Eb, and the Fø7 chord is now properly spelled as F, Ab, Cb, Eb as is fitting to this tonality. At the very height of this climactic section, however, Wagner employs the now-famous case of "tritone substitution," whereby the implied Eb-Minor tonality is suddenly wrenched back to A-Minor tonality. The Fø7 chord is currently sounding as all this energy comes crashing down, and, upon landing, Wagner restores the spelling of the The Fø7 chord to F, G#, B, D#, as it should be spelled in an A-tonality. See Example 9.
Example 9
Now that we have seen the usefulness of the Chromatic Modal Scale for determining chord spellings in chromatic (tonal) progressions, we must now admit to two small variants, one of which regularly takes place in actual practice. So far, we have acknowledged voice-leadings that involve common-tone or neighbor motion to scale degrees 1 and 5. Concerning scale degrees 3 or b3, we have indicated their roles in determining "major-ness" and "minor-ness," respectively. Of course, actual voice-leadings between chords often involve common-tone or neighbor motion to scale degree 3 or b3, as well. If the primary tonic is major, then neighbor-tone stepwise motion to scale-degree 3, according to the Chromatic Modal Scale, might involve scale degree 2, b3, 4, or #4. If the primary tonic is minor, then neighbor-tone stepwise motion to scale-degree b3 might involve scale degree b2, 2, 3, or 4.
 
In actual practice, some composers choose always to use a different scale-degree number for neighbor motion to the third of the major tonic triad. So, for a major primary tonic triad, neighbor motion to scale degree 3 might include scale degrees 2, #2, 4, or #4; our first "exception" is that, for a major primary tonic triad, #2 might replace b3 within the Chromatic Modal Scale. By similar reasoning (though not found as often in actual practice), for a minor primary tonic triad, neighbor motion to scale degree b3 might include scale degrees b2, 2, b4, or 4; our second "exception" is that, for a minor primary tonic triad, b4 might replace 3 within the Chromatic Modal Scale. These variants are shown in Example 10.
Example 10
There seems to be less compelling reasons for deciding whether to spell a semitone lower-neighbor to scale-degree-3 as b3 or #2, and whether to spell a semitone upper-neighbor to scale-degree-b3 as 3 or b4, than there are for determining the spelling of the other parts of the Chromatic Modal Scale. For example, in the key of C-Major, a IV7 chord might be spelled F, A, C, Eb; if followed by a tonic triad, then, in this case, the E-flat moving to the E-natural within the C-Major tonic triad suggests that the composer senses the subtle modality shift between "C-Minor" (in the chord containing the E-flat) and "C-Major" (in the chord containing the E-natural). On the other hand, a composer might spell the IV7 chord as F, A, C, D#; if followed by a tonic triad, then, in this case, the D# moving to the E within the C-Major tonic triad suggests that the composer is aware of the inherent "augmented-sixth-style" voice-leading that is hereby possible when both pitches, F & D#, move in contrary motion by semitone to a doubled E within the C-Major triad. See Example 11.
Example 11
Other harmonic examples that frequently employ #2, rather than b3, when progressing to a major tonic triad include the "Common-tone Diminished 7th chord" (in C-Major, usually spelled D#, F#, A, C) and the "Doubly-Augmented 4th" variant of the German Augmented-Sixth chord (in C-Major, sometimes spelled Ab, C, D#, F#). In Example 12, we see Beethoven employing the same Common-tone Diminished 7th chord at two different points and spelling it first one way (m266: D#, F#, [A,] C) and then the other (m.280: F#, A, C, Eb). The voice-leading in both cases is the same: D# or Eb moves to E-natural; F# moves to G; and a common-tone on C. Presumably the second spelling, in m.280, is to suggest the secondary relationship vii°7 / V, since the tonic triad in m.281 is in second inversion.
Example 12
At the other end of the spectrum, however, stands the bIII chord. In a bIII-I progression (such as in C-Major: Eb - C), the bIII chord is invariably spelled b3, 5, b7, rather than #2, 5, b7. The closest voicings will include, Eb-E-natural, G-G, and Bb-C.
 
In any case, the progressions shown in Example 13a all involve a chord containing #2 or b3 which then moves to a major tonic triad; readers can decide for themselves which one is preferable in each case. Example 13b, then, shows chords containing 3 or b4 which then moves to a minor tonic triad.
Click to see Example 13.
 
In spite of the spelling "inconsistency" concerning semitone neighboring motion to the third of the tonic triad, the Chromatic Modal Scale overall reveals many normative spelling procedures within chromatic harmonic progressions. Whenever Augmented-Sixth chords are encountered in traditional music theory courses, they are invariably treated as anomolus "voice-leading" chords, rather than "normal" spelled-in-thirds kind of chords. By using the Chromatic Modal Scale, first of all, it is clear that something as simple as V-I is still, by any account, an example of "voice-leading" chords. All tonal progressions, diatonic or chromatic, are "voice-leading" progressions, and the Chromatic Modal Scale governs the spelling of all of them. Here are some observations concerning the German Augmented-Sixth chord:
 

  • When a German Augmented-Sixth chord expands outwards to an octave on the fifth of a tonic triad, the chord in question is simply bVI7, but spelled according to the Chromatic Modal Scale.
     
  • When a German Augmented-Sixth chord expands outwards to an octave on the root of a tonic triad, the chord in question is simply bII7, spelled according to the Chromatic Modal Scale.
     
  • When a German Augmented-Sixth chord expands outwards to an octave on the third of a Major tonic triad, the chord in question is IV7, spelled according to the Chromatic Modal Scale (or its "Major" variant).
     
  • When a German Augmented-Sixth chord expands outwards to an octave on the third of a Minor tonic triad, the chord in question is III7, spelled according to the Chromatic Modal Scale (or its "Minor" variant).
     
  • When a German Augmented-Sixth chord expands outwards to an octave on the root of a dominant triad, the chord in question is actually bVI7, but we note that this could be viewed as the secondary relationship [ bII7 - I ] / V.
Another observation about the Chromatic Modal Scale concerns itself with the interval of the augmented 2nd. If we consider each of the three-semitone-sized intervals contained within the standard Chromatic Modal Scale, we discover there are only three augmented 2nds: between b2-3, b3-#4, and b6-7. The other nine three-semitone-sized intervals are all minor 3rds. See Example 14.
 
Example 14, all twelve three-semitone-sized intervals found within the C-Chromatic Modal Scale
 
Eb E F F# G Ab A Bb B C Db D
C Db D Eb E F F# G Ab A Bb B
m2 Aug2 m2 Aug2 m2 m2 m2 m2 Aug2 m2 m2 m2

These three augmented 2nds are precisely those most commonly found in augmented-2nd-containing modes that also include a perfect fifth above the tonic:
 
  • The Harmonic Minor scale contains b6-7, as is demonstrated here in the key of C: C, D, Eb, F, G, Ab, B, C, which is a subset of the C-Chromatic Modal Scale.
     
  • The scale sometimes known as the "Hungarian Minor" contains both b6-7 and b3-#4, as is demonstrated here in the key of C: C, D, Eb, F#, G, Ab, B, C, which is a subset of the C-Chromatic Modal Scale.
     
  • A scale sometimes associated with Jewish culture contains b2-3, as is demonstrated here in the key of C: C, Db, E, F, G, Ab, Bb, C, which is a subset of the C-Chromatic Modal Scale. This scale, of course, is a "mode" of the Harmonic Minor scale; F-Harmonic Minor beginning on its fifth scale degree is also C, Db, E, F, G, Ab, Bb, C.
Whereas (1) all three-semitone-sized intervals in atonal music are merely transpositions of one another and are considered to be, more or less, equal, (2) in tonal music, there are twelve three-semitone-sized intervals each in a different relationship with the tonic pitch. Atonal music would seem to offer twelve primary intervals (including the unison/octave), any transposition of which is identical in sound to any other transposition of the same interval. In tonal music, each of the twelve interval sizes can be placed in any of twelve distances from a tonic pitch, which creates a tapestry of 144 subtly different intervals. From this perspective, tonal music would seem to have a much richer set of resources than atonal music. A complete tonal interval chart, based on the Chromatic Modal Scale, is shown in Example 15.
Click to see Example 15.
 
In spite of numerous instances of chromatic chords not "spelled in thirds," it would be foolhardy not to recognize that some instrumentalists, especially keyboard players, are thoroughly trained according to the conventions of Rameau. Especially in keyboard music, chords are usually "spelled in thirds." However, in the string and wind parts of orchestral music, and also in choral music, the lines will most likely reflect the Chromatic Modal Scale and logical tonal voice-leading.
 
Appendix 1. Suggested labeling system for triads and seventh chords: Roman Numeral plus the appropriate figured bass symbols.
 
Chord Symbol Example
Major triad: Upper-case Roman Numeral bVI
Minor triad: Lower-case Roman Numeral bvi
Diminished triad: Lower-case Roman Numeral with "degree" circle bvi°
Augmented triad: Upper-case Roman Numeral with "plus" sign bVI+
Major-minor 7th: Upper-case Roman Numeral bVI7
Minor-minor 7th: Lower-case Roman Numeral bvi7
Half-Diminished 7th: Lower-case Roman Numeral with "slashed" circle bviø7
Augmented-minor 7th: Upper-case Roman Numeral with "+" bVI+7
Major-major 7th: Upper-case Roman Numeral with small "M" bVIM7
Minor-major 7th: Lower-case Roman Numeral with small "M" bviM7
Diminished-major 7th: Lower-case Roman Numeral with "degree" sign and "M" bvi°M7
Augmented-major 7th: Upper-case Roman Numeral with "+" and "M" bVI+M7
Fully-Diminished 7th: Lower-case Roman Numeral with "degree" circle bvi°7
French-Augmented-6th: Upper-case Roman Numeral with "-5" bVI7-5
Major-major 7th with flat 5th: Upper-case Roman Numeral with "M" and "-5" bVIM7-5

A label should employ the appropriate Roman Numeral as defined by the Chromatic Modal Scale of the current key. The key signature designated by the composer, other than determining whether the tonic triad is major or minor, should not be the basis for determining Roman Numerals. For example, whether the key signature indicates C-Major or C-minor, in both cases an Ab-Major triad would be designated bVI, an A-Minor triad would be designated vi, an A-Major triad would be designated VI, and an Ab-Minor triad would be labeled bvi. The Roman Numerals for major and minor triads of the Chromatic Modal Scale are:
 
I bII II bIII III IV #IV V bVI VI bVII VII  and
i bii ii biii iii iv #iv v bvi vi bvii vii.  

Again, these designations are for primary-tonic relationships, not for secondary-tonic relationships. If an A-Major-Minor seventh chord progresses to a C-Major triad, the proper labels would be VI7 - I. On the other hand, if an A-Major-Minor seventh chord progresses to a D-Minor triad prior to an authentic cadence in C, the labels would be V7/ii - ii - V - I. In the first case, the A7 chord would be spelled A Db, E, F, according to the C-Chromatic Modal Scale. In the second case, it would be spelled A C#, E, G, according to the D-Chromatic Modal Scale. (See Appendix 2 for a complete listing of triads and seventh chords spelled properly for C-tonality.)
 
Here is the proper spelling, in C tonality, for all the "flat-six" chords listed above.
 
Example 16
 
Dr. Jody Nagel
February 11-14, 2007
Copyright © 2007 by Jody Jay Nagel
 
 
 

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