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On Modes
by Dr. Jody Nagel
 
It seems that the essence of the character of a specific seven-note "white-key" diatonic mode can be demonstrated completely by simply juxtaposing (1) the perfect fifth found between scale degrees 1 and 5 and (2) the tritone contained within that mode. The foreground or background presence of a tonality-producing perfect fifth provides the ear with the sensation of pitch-centeredness,1 while, in predominantly diatonic music, the specific tritone provides the "flavor" or "color" of the modality. Put simply, the perfect fifth between scale degrees 1 and 5 provides tonality, and the placement of the tritone provides a specific modality. It is convenient to label the various possible tritone relationships with respect to a given "tonic-dominant" perfect fifth based on the name of the mode that ordinarily contains that tritone. Thus, relative to a C-G perfect fifth, the pitch classes B and F constitute the "Ionian Tritone." Again relative to a C-G perfect fifth, the pitch classes Eb and A constitute the "Dorian Tritone." The named tritones are each shown in Example 1. It should be remembered that the "Locrian Tritone" completely displaces the structurally important and tonality-producing perfect fifth, and the Locrian mode is really, therefore, an "atonal" mode.2
 


 

1 In this article, the word "tonality" is used synonomously with "pitch-centeredness" and does not in any way refer to any musical style or time period.
2 In order to use the Locrian Mode idiosyncratically, a composer must assert the tonic pitch often and quite strongly, as there is no perfect fifth relationship above scale degree 1 to be had. "Tonality" by single-pitch assertion is basically a different phenomena than tonality based on the pitches of a perfect fifth relationship.

  Example 1


  To demonstrate "the essence of the character of a specific seven-note white-key diatonic mode," consider the modal melodies of Example 2. Within the first measure of each example, using only the pitches of the tritone, as well as scale degrees 1 and 5, a complete sense of the affect of the mode is created. The second measure then contains a variation of the first measure where all the pitches of the mode are "used up." The "other" pitches of the mode, of course, are useful as connective tissue and for creating a richer set of relationships, but they are not essential for achieving a particular modal coloration.

Example 2

The white-key modes, then, can be seen as the set of single-tritone "colorations" possible within a perfect-fifth-centered tonality. There is, however, another set of seven-note diatonic3 modes. Hungarian writer Lajos Bardos4 refers to the Heptatonia Secunda modes (i.e., the second set of seven-tone modes, as opposed to the more usual "first" set of white-key modes.) If the white-key modes are thought of as having been derived by taking the seven possible rotations of the interval pattern (in semitones) 2-2-1-2-2-2-1, then the Heptatonia Secunda modes can be thought of as being derived by taking the seven possible rotations of the interval pattern (in semitones) 2-1-2-2-2-2-1. Put differently, the white-key modes are made of rotations of a [two whole step + three whole step] pattern, while the Heptatonia Secunda modes are made of rotations of a [one whole step + four whole step] pattern. Most of these modes are not usually given names, though the most common of these is the "ascending melodic minor" scale (for example: C, D, Eb, F, G, A, B, C).5 Also common is the major scale with "borrowed" b6 and b7 (for example: C, D, E, F, G, Ab, Bb, C). The major scale with altered #4 and b7 is another of these modes and was used sometimes by Béla Bartók; a good example can be found in the tenor solo and stretto string parts in his Cantata Profana (mm.72-87), which is based on the scale: D, E, F #, G#, A, B, C, D. One additional mode, which the author employed often in his opera Fifty-Third Street, is the natural minor scale with altered b2 and #6; as an example, the "Drinking Song" of Scene 4 is based entirely on the scale: B, C, D, E, F#, G#, A, B. The other three rotations possible within the Heptatonia Secunda system include two modes containing a diminished fifth above the tonic pitch (for example: C, D, Eb, F, Gb, Ab, Bb, C and C, Db, Eb , Fb, Gb, Ab, Bb, C), and one mode which contains an augmented fifth above the tonic pitch (for example, C, D, E, F#, G#, A , B, C). These three modes are analogous to the "Locrian Problem" of the white-key modes; since they lack a perfect fifth above the tonic pitch, they tend to have a strangely "atonal" quality.
 


 

3 Here, the word "diatonic," as applied to seven-tone modes, refers to scales containing successive intervals of only whole-steps or half-steps, and, furthermore, to those scales not containing two or more consecutive half-steps. As an interesting aside, it should be noted that the eight-tone "octatonic" scale is also "diatonic" based on this definition. More thoughts on "Diatonicism."
4 Bardos, Lajos. Selected Writings on Music. Budapest: Editio Musica, 1984, 88ff. English translation by Alexander Farkas and Kata Ittzés, 1984.
5 These next few paragraphs are drawn largely from the Appendix of the author's dissertation, Fifty-Third Street. (1992.)

It should now be pointed out that each of the Heptatonia Secunda modes contains two tritones (a whole step apart), whereas each of the white-key modes contains only one tritone. Assuming that the two tritones, along with the perfect fifth separating scale degrees 1 and 5, are the basis for the modal character of each of these modes, just as was the case for the white-key modes with their single tritone, it becomes possible to create names for these modes by hybridizing the names of the two white-key modes which contain the same tritones as the given Heptatonia Secunda mode. For example, the ascending melodic minor scale C, D, Eb, F, G, A, B, C contains the Dorian tritone Eb-A, and the Ionian tritone F-B. This scale would therefore receive the name "Dorionian." By systematically choosing the lower tritone first, and the tritone a whole step higher second, the set of names found in Example 3 is constructed. These names are highly appropriate considering that they reveal the tritone content of the mode, and therefore the "color" of the mode.
 

Example 3

There is a small curiosity that appears when the Heptatonia Secunda modes are derived from the white-key modes in each of two different ways. In Example 4, this difference can be seen clearly. In "Derivation Method 1," the pitch class "E" in each of the white-key modes is first flatted,6 and secondly the scale is transposed down to begin on pitch class "C." In "Derivation Method 2," the white-key modes are first transposed down to begin on pitch class "C," and secondly the appropriate pitch class is flatted. The first method transforms the Phrygian mode into a mode containing a Lydian tritone and an Aeolian tritone, and is what we have called the "Lydaeolian" mode. The second method, however, transforms the Phrygian mode into a mode containing an Ionian tritone and a Phrygian tritone, and, thus, could be called the "Ioniphrygian" mode. The second method of derivation would seem to be desirable since it should allow pitch-class structures built on "C" (i.e., the transposed white-key modes) to be transformed into other pitch-class structures also built on C (i.e., the transposed Heptatonia Secunda modes). In the case of transforming the transposed Phrygian mode into a Heptatonia Secunda mode, however, it is the tonic pitch itself which must be displaced down a semitone, and the point of reference of the whole system (i.e., "C") is thus lost from the scale. Therefore the second method of derivation, at least as far as creating modal names is concerned, will be rejected in favor of the first method.
 


 

6 If the white-key modes are viewed from a set-theory point-of-view, then pitch class "E" is the pitch class "5" drawn from the septachord
[0, 1, 3, 5, 6, 8, 10] =
[B, C, D, E, F, G, A].
It is this fourth element (p.c. 5) of the prime form of the set constituting the white-key modes which is lowered by one semitone and which then transforms the white-key modes into the Heptatonia Secunda modes (with a prime form of [0, 1, 3, 4, 6, 8, 10].)
Click to see Example 4


 
Now it is time to consider further these 14 diatonic modes, starting once again with the white-key modes, and keeping in mind the importance of scale degrees 1 and 5, and the pitches making up the tritone(s) within the mode. Of the Locrian mode, the tritone content completely overlaps scale degrees 1 and 5. This "degenerative" mode contains only two essential7 pitches (C-Locrian: C, Gb). Of both the Phrygian and the Lydian modes, the tritone content shares one pitch in common with scale degrees 1 and 5. So in C-Phrygian, the pitch G is part of the tritone G-Db, as well as being scale degree 5. In C-Lydian, the pitch C is part of the tritone C-F#, as well as being scale degree 1. Phrygian and Lydian are both modes containing three essential pitches (C-Phrygian: C, Db G; and C-Lydian: C, F#, G). Finally, Ionian, Aeolian, Dorian and Mixolydian are yet even richer pitch systems because each contains four essential pitches; the pitches of the tritone do not overlap the pitches of scale degrees 1 and 5. (The essential pitches of C-Ionian are C, F, G, B. The essential pitches of C-Aeolian are C, D, G, Ab. The essential pitches of C-Dorian are C, Eb, G, A. The essential pitches of C-Mixolydian are C, E, G, Bb.)
 


 
 

7 essential, that is, to the unique affect of the given mode. These "essential" pitches, as stated earlier, include scale degrees 1 and 5, and the pitches of the tritone(s).

Of the Heptatonia Secunda modes, only Dorionian (ascending melodic minor) and Aeomixolydian (major with "borrowed" b6 and b7) contain two pairs of tritone pitches that do not overlap with scale degrees 1 and 5. In C-Dorionian, scale degrees 1 and 5 are C-G, and the two tritones are Eb-A, and F-B. In C-Aeomixolydian, scale degrees 1 and 5 are C-G, and the two tritones are D-Ab, and E-Bb.
 
Another observation about modes is that scale degree 3 seems exclusively to provide the mode with a sense of being either "more major" or "more minor" in character. This, of course, is because the tonic triad of the mode would actually be either major or minor. So Dorian, Phrygian, Dorionian, and Phrygidorian, along with Aeolian, are the "minor" modes; while Lydian, Mixolydian, Aeomixolydian, and Mixolydilydian, along with Ionian, are the "major" modes. Locrian, Locraeolian, and Mixolocrian cannot, of course, contain a true major or minor tonic triad since they contain a diminished fifth above the tonic pitch, but nevertheless, their scale degree 3, being a minor 3rd above the tonic pitch, gives these modes a distinctly "more minor" character than major. Lydaeolian, containing an augmented fifth above the tonic pitch, also cannot contain a true major or minor tonic triad, but nevertheless, its scale degree 3, being a major 3rd above the tonic pitch, gives this mode a distinctly "more major" character than minor.
 

Now, add in scale degree 3 to the general equation. Of all 14 diatonic seven-note modes, only the Ionian mode and the Aeolian mode (major and minor scales) contain tritone pitches which lie completely outside the tonic triad. In other words, in only these two modes do the tritone pitches not overlap either scale degrees 1, 3, or 5. The modes are pitch collections from which music is made, and two important subsets of the collection are the tonic triad pitches and the tritone pitches. Though history is more interested in discussing the development of musica ficta and leading tones, when considering the eventual domination over the other modes by the major and minor scales, it seems reasonable to suppose that, while composers were searching for satisfying ways to bring closure and a sense of resolution to a polyphonic composition, they would gradually begin to choose consistently those tonic sonorities that had every last vestige of the tritone coloration removed from them. A Dorian or Phrygian tonic triad, for example, contains one pitch that also partakes of the tritone coloration, and that coloration is not entirely absent at the moment the final tonic triad sounds.8
 
 
 

8 In the Mixolydian and Dorian modes, the third could be omitted from the final tonic sonority; this creates a more "hollow" sounding tonic, but, to this writer, one which has more of a sense of closure than when the tritone-participating scale degree 3 is present. The choice of omitting the third from the final tonic triad in the cases of the Lydian and Phrygian modes does not result in a perceptible difference in the degree of closure since the third does not participate as a tritone member within these modes.

Why is it desirable to remove the tritone coloration from the final tonic triad? The major or minor tonic triad represents the ultimate asymmetrical pitch structure: the 12 semitones of the octave are divided asymmetrically into 7+5 semitones (perfect 5th + perfect 4th), and the larger of these intervals (the perfect 5th) is divided asymmetrically into 3+4 or 4+3 (major 3rd and minor 3rd.) These intervals maximally separate the individual pitches, thereby preserving their clarity, while simultaneously the asymetricallity assures that the ear can always "know" which of the tones is which, and this is the very essence of the meaning of tonality. By contrast, the tritone represents the ultimate in symmetry, subdividing the octave into 6+6 semitones.9 This interval represents the exact negation of tonality; in itself, it destroys any possible sensation of pitch-centeredness. It only has tonal "meaning" if it exists in juxtaposition with a tonic triad, and the maximum juxtaposition possible occurs only when the pitches of the tritone do not overlap the pitches of the tonic triad. Given the early tradition of avoiding the "Diabolus in musica," it should not be surprising that this avoidance continued in a more abstract manner at a later time. This may never have been a conscious thought on the part of any composer. However, anyone with sensitive hearing would subconsciously detect the lurking presence of the tritone strangely prolonged into the final tonic triad of all diatonic modes other than major and minor scales. Those individuals that are theologically minded surely must excite themselves with the number-symbolism associated with "6" (tritone / Devil / instability) and "7" (perfect fifth / God / stability).
 
 
 

9 Consider, by way of analogy, a perfectly square house that has a flat roof and four walls each containing a door in the center and two windows placed on either side of the door. (The house has no front porch or back porch!) This structure, in and of itself, has no logical "front" and is perfectly symmetrical. If, however, one were to place this structure in the context of a neighborhood whereby one of the walls of the house suddenly "faced the street," then, by that context, one could say that the "front" of the house was the side which faced the street. Likewise, the symmetrical interval of a tritone can be used "tonally" quite well when placed in structural juxtaposition with an asymmetrical tonic triad.


 
Some will point out that the Natural Minor scale is not really used in the music of the Common Practice Era. The more commonly used Harmonic Minor scale, however, employs an augmented second and is therefore a chromatically-altered scale and is not truly diatonic by our definition. (See Footnote 3.) Consider, though, that the Harmonic Minor scale utilizes both the Ionian tritone and the Aeolian tritone. It has a unique intensity because both of the pairs of tritone pitches are eventually removed from the tonal fabric when closure is obtained through the final tonic triad. In times past, the search for effective musical closure led to the use of modes which contained tritones not overlapping the tones of the tonic triad. Now, in our time, it is not necessarily desirable to create such a complete sense of resolution at the end of a piece of music. Perhaps it is more enticing to leave a bit of instability resonating within the final chord of a composition, even a chord consisting simply of a major or minor triad. For contemporary composers who prefer writing music that remains tonal (i.e., pitch-centered), it seems that there is still much to be obtained from experimenting with the different modes. Perhaps 12-tone serial music, with its non-temporal pitch fabric always containing all possible intervals (regardless of the actual temporal succession of intervals), has a tendency, as when mixing all of the colors of paint, to become "brown" after awhile. (The color brown is perfectly nice. . . sometimes!) The white-key modes, each with their "pure color" single tritone, and the somewhat more complex Heptatonia Secunda modes, with their "secondary colors" obtained by the "mixing" of two tritones (not to mention their perhaps even more exotic augmented 5th / diminished 4th pigmentation), remain an important source (along with many other pitch sets) for compositional inspiration. Perhaps the "Diabolus in musica" still has much more to say.
 
 
Dr. Jody Nagel
May 11 & July 22, 1996
Copyright © 1996 by Jody Jay Nagel
 
 
 

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Copyright © 1996 by Jody Nagel. All rights reserved. Call 1-765-759-1013 or Email for additional information.