The Eleven Interval Method

Miller devised THE ELEVEN INTERVAL METHOD in order to compose music which does not adhere to a fixed tonality. A manuscript on this composition technique is now available. Below is the basic construct of the method.

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The Eleven Interval Method is based on the 11 unique intervals between the Unison and the Octave. This is expressed in tonal terms as m2, M2, m3, M3, P4, Tritone, P5, m6, M6, m7, M7 (where m = minor and M = Major) or in their serial terms as 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11. Much like the 12-Tone Method, these eleven Intervals are chosen one by one to create a meaningful shape/phrase. This is the initial all-interval sequence.

Neither the Unison nor the Octave is part of this essential source material. The Unison owns a frequency with a 1:1 ratio. In a purely intonated relationship, that of a sine wave, there is zero distance between the two pitches. While the Unison — as it is heard naturally with its slight imperfections of intonation — is magnificent, it is not included as part of the Eleven Interval Sequence. Octaves possess a 2:1 ratio, signifying the repetition of another cycle. They hold a formal position, that of the beginning and end of a wholly significant cycle of Intervals.

Partials (i.e. m2/1 becoming b9/13) are of a different Octave cycle and clearly sound different from each other in relation to their base root. Although they are used in this interval-based music (as with Unisons and Octaves), they are not part of the initial source material on which this Method is based: a repeating sequence of eleven intervals between the root and its octave.

The 11-Interval Sequence contains 12 pitches. It is called a sequence rather than a row since there are often two or three notes that are identical. Sequences are never called scales. Likewise, no key signatures exist. All 11 Intervals are treated equally as all 12 pitches are in 12-Tone Music. In theory, pitch is secondary – this being the basis behind the term Intervallic Hierarchy.

Techniques in transposition and modulation manage the music intervallically. All-Interval Harmony offers a complete disfigurement of any tonal center, yet that which appears as harmonic anarchy does possess a concise order — as peculiar as it may sound to the common ear.

The 12th note of the sequence - the second pitch of the 11th chosen Interval - is the 1st note of the following sequence’s 1st Interval, whether the sequence is being repeated or otherwise. This is a crucial aspect of the Method and governs the direction of the entire composition.