Octatonic Scales

(Note: Midi files of many of the examples are included at this site. To learn how to play these files on your machine, go to Midi Setup.)
An octatonic scale consists of alternating whole and half steps. It is an eight-tone scale; that is, eight tones are required to fill in the octave. According to McHose, the octatonic scale was first used by Rimski-Korsakov. His student, Igor Stravinsky used it extensively, especially in the Rite of Spring.

The octatonic scale has only two modes. As shown in the next two examples, Mode 1 begins with a whole step and Mode 2 begins with a half step. Mode 1 consists of two minor tetrachords, the second starting at the tritone.

Example 1: Octatonic Mode 1

Mode 2 consists of two diminished tetrachords, the second starting at the tritone.

Example 2: Octatonic Mode 2

The tetrachords shown above recur often within each mode. For example, the minor tetrachord appears on steps 2, 4, 6 and 8 of mode 2. The diminished tetrachord appears on steps 2, 4, 6 and 8 of mode 1. Bartok's Mikrokosmo 101, Diminished Fifths, is based on the polyphonic interplay of the two Mode 1 tetrachords at the tritone.

Debussy based the Nuages ostinato on the diminished tetrachord of Mode 2.

Mode 2, also called the "half-step diminished scale," is used in Jazz improvisation in association with diminished seventh chords.

Though not as extreme as the whole tone scale, pattern redundancy in the octatonic scale creates invariant features. For example, a minor third, a tritone, a diminished triad or a diminished seventh chord can be built above every step of the scale.

Patterns built on bottom note of the whole step or the half step recur on alternating steps. Thus, the chord types shown in Example 3 occur on steps 1, 3, 5 and 7 of Mode 1 (or steps 2, 4, 6 and 8 of Mode 2). Note the polychord made of two diminished seventh chords.

Example 3: Chords on Steps 1, 3, 5 and 7 of Mode 1

The chord types shown in Example 4 occur on steps 1, 3, 5 and 7 of Mode 2 (or steps 2, 4, 6 and 8 of Mode 1). There are more chords possibilities here, especially for more complex tertian chords. Chords containing tritones and dominant funtioning chords are common in this group. Note the polychord made of two diminished seventh chords (the last chord). Not all complex chord possibilities were included in this example.

Example 4: Chords on Steps 1, 3, 5 and 7 of Mode 2

There are only two transpositions that produce a true key change (i.e., a new collection of pitches), up a minor second or up a major second. The melodic inversion of these intervals produces the same transposition. All other transpositions produce the original collection of notes.

The recurring or redundant features discussed above tend to limit how long octatonic passages can be used to sustain interest. On the other hand, an octatonic passage adds fresh harmonies and stresses that give relief to more conventional materials. It can be used to good poetic effect.

Because minor thirds and tritones recur so frequently, octatonic passages always carry the tint of the tritone. Moreover, the underlying harmonies of octatonic passages tend toward tritone bearing chords, especially the hues of altered dominant and leading tone chords.

Sample Octatonic Passages

Minor thirds and tritones can be built on any step of any octatonic scale. Major thirds and perfect fourths recur on alternate steps, points outlined by the notes of diminished seventh chords. This pattern recurrence can be used to generate passages based on repeating figures.

Example 5: Repeating Figures

Example 6 features a melody accompanied by an ostinato based on a minor tetrachord. The melody is based on a diminished tetrachord.

Example 6: Ostinato

The passage in example 7 consists of two shallow lines with contrasting contours. The lower line is rhythmically offset by a quarter note producing a polyphonic. The passage appears to have potential as an ostinato and is similar to a passage in Stravinsky's Rite of Spring.

Example 7: Shallow Contrary Contours

The next example contains mirrored lines in thirds followed by a contrasting response. The response is a slightly modified repetition of the first motive. The response outlines the major third, D-F sharp, suggestion a bitonal context.

Example 8: Mirror Lines

The texture below is accompanied melody. The harmony is in a simple alternating pattern. The melody is a flow of minor third figures. The harmonic effect is bitonal.

Example 9: Homophonic Texture

Example 10 features a line accompanied by unfigured (block) chords. The chords are complex tertian harmonies that reach a peak of complexity at the third measure. All the chords have a dominant or leading-tone chord "feel."

Example 10: Complex Chords in Homophonic Texture

Next is an idea accompanied by a descending ostinato. The ostinato is based on the bottom tetrachord of mode 2. The basic idea is a major third collapsing to a major second. This idea is based on the top tetrachord of mode 2. The interaction of the two tetrachords suggests a bitonal context.

Example 11: Interaction of Two Mode 2 Tetrachords

Example 12 is a polyphonic texture featuring mirror imitation. The lower voice is based on the bottom tetrachord of mode 2. The upper voice is based on the top tetrachord of the mode. This suggests a bitonal context at the tritone.

Example 12: Mirror Imitation

(My apologies for the two temporal "hicoughs" in example 12. It plays back the same way in my scoring program, Overture. Any suggestion will be greatly appreciated.)

An E-E flat ostinato is embedded in the following accompaniment. The chords implied by the interaction of melody and accompaniment are ambiguous and analysis is difficult. One could argue that the passage is bitonal, complicated by alternating chord colors. [The chords could be a C7(flat 5, flat9, sharp 9) or a Cmi7 (flat 5, flat 9) -- or both.]

Example 13: Ambiguous Harmonies

Copyright © 1996, Kenneth R. Rumery, all rights reserved.

Revised September 14, 1996

Special thanks to Randy Wood in Computer Technology Services for helping me with the MIDI playback feature.