Kostka categorizes scale formations according to the number of notes in the scale. For our purposes, you should keep track of the following (for each scale):
- The possibility of triads and seventh chords in the scale.
- What modes, if any, are possible with a given scale.
- How many transpositions of the scale are possible.
For the final category, if the scale cannot be transposed to all twelve pitches to produce a unique set of notes, then the scale is what Olivier Messiaen termed a Mode of Limited Transposition. This will usually apply to scales that are symmetrical in construction.
Keep in mind that I’m not delving into all the details of each scale, but merely a summary to help you categorize them. Also, it is most common that composers will employ a number of scales within a single piece, changing between them as if changing tonality.
Pentatonic (5-Note) Scale
Any five-note scale is technically pentatonic, but the pentatonic scale refers to the five-note arrangement (starting on C): C – D – E – G – A. You can think of the scale as scale degrees ^1 – ^2 – ^3 – ^5 – ^6 of a major scale. This arrangement doesn’t have any half-steps.
- Only one major triad, one minor triad, and one minor seventh chord is possible from the scale.
- Five modes are possible. Rotating to start on each note will provide a unique order of intervals.
- All twelve transpositions are possible.
Whole-Tone Scale (6 Notes)
The whole-tone scale is constructed entirely of major seconds, and is symmetrical in construction.
- Only augmented triads, and V7 chords with a raised or lowered fifth, are possible.
- There is only one mode. Rotating the order of pitches produces the same order of intervals.
- The whole-tone scale has only two transpositions: WT-0 (which contains a C) and WT-1 (Db).
Octatonic Scale (8 Notes)
The octatonic scale alternates whole steps and half steps. The particular choice of spelling is variable, since it will always include one repeated pitch letter. Since a whole step (interval 2) and a half step (interval 1) add up to a minor third (interval 3), the scale is symmetrical. The scale is sometimes called the diminished scale, in part because it can be constructed from the combination of two fully-diminished seventh chords.
- The octatonic scale is rich in triads and seventh chords.
- Only two modes are available. One starting with a whole step, and one starting with a half step. The whole-step mode produces two minor tetrachords, a tritone apart, and is commonly associated with folk-music inspired compositions. The half-step mode appears more in neo-classical compositions, as major and minor triads are possible on the tonic note (and every minor third related interval), along with dominant and minor seventh chords.
- Since the scale is symmetrical at the interval of minor thirds, there are only three transpositions possible.
Diatonic Modes (7 Notes)
Technically, modes are not new scale formations, but their use in 20th/21st-century music is very popular. We generally leave out Locrian (diminished fifth above tonic), Ionian (major), and Aeolian (natural minor) from our discussions.
- Many triads and seventh chords are possible.
- Modes are transposable to all pitches.
It helps to understand the modes as major-related and minor-related, and how they differ from a major scale or natural minor scale. For each mode, only one alteration from major or natural minor is needed.
- Major-related: Lydian (#^4), and Mixolydian (b^7)
- Minor-related: Dorian (#^6) and Phrygian (b^2)
Other Scales
The book talks about chromatic scales, but pieces that use the chromatic scale tend to be serial or otherwise atonal. The Webern example in the exercises isn’t a great choice – it is a classic serial atonal work. Microtonal scales are possible, with several systems of notating intervals smaller than a half step. You can also have arbitrarily constructed scales.
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