Nonoctave
A nonoctave scale is a scale whose equivalence interval is not the octave (2/1).
Nonoctave scales come in many varieties, but what unites them is an aversion of octaves. A common approach to building a sensible scale without octaves is to divide some nonoctave interval into logarithmically equal parts, as one would divide the octave to arrive at an EDO. Such a scale is sometimes called an EDONOI, short for "equal divisions of a nonoctave interval". One can also build rational scales with nonoctave repeats or no repeat (e.g. Superparticular-Nonoctave-MOS). Nonoctave scales may contain a "near octave" or "tempered octave" which would be an interval near but not exactly 1200¢. In this category, there are stretched octaves and compressed octaves, each having their own character.
Why choose a Nonoctave Scale?
Here are only a few reasons. Add your own!
- The 2/1 octave is distractingly consonant, and gets in the way when exploring xenharmonic resources. If your music is seeking to explore new consonances, then why would you keep the oldest, simplest consonance in the system? It is too easy to fall back on the octave and resolve everything unfamiliar to a plain old characterless octave.
- The 2/1 octave is boring; it doesn't even sound like a distinct interval!
- Octave-repetition is too redundant. In a nonoctave scale, each part of the range offers new intervals. Thus, with only a few tones, a great variety is possible. In an octave-repeating scale, once the octave is reached, there is nothing new to be had.
- Octave stretching and compressing turns boring vanilla octaves into exciting, vibrant, active near-octaves. Near-octaves may provide that function of octave-redundancy, while not introducing the distracting consonance of a 2/1.
- Instruments in different ranges have different pitches available to them. This allows for more interesting polyphony.
- You can play musical scales without repeating at any intervals and it has infinite notes too!
Composers and theorists known for their work in nonoctave scales include X. J. Scott; Wendy Carlos; Gary Morrison; Carlo Serafini; and Heinz Bohlen, John Pierce, and Kees van Prooijen, the latter trio being associated with the Bohlen-Pierce scale.