Step pattern
The step pattern of a scale is the sequence of the interval sizes of its steps, usually in ascending order of pitch.
An abstract step pattern contains letters such as L ("large"), M ("medium") and s ("small") to express relative sizes (L > M > s). A concrete step pattern contains interval sizes instead, which can be frequency ratios, numbers of steps in an equal tuning, etc.
For an octave-repeating scale, the step pattern usually spans an octave; more generally, for a periodic scale, the step pattern usually spans a period or an equave. Different rotations of the same step pattern can be used to express different modes.
A scale pattern may be condensed into a scale signature or step signature, displaying only the number of steps of any given size, no matter where they occur in the scale. For example, the scale signature for the diatonic scale, LLsLLLs, is 5L 2s. In some cases, the scale signature can be used to uniquely identify a scale: for example, given a binary scale signature (aL bs), there is only one possible MOS scale with that signature.
Example
| Tuning | Abstract step pattern | Step ratio | Concrete step pattern | List of degrees |
|---|---|---|---|---|
| 3-limit JI | LLsLLLs | L:s ≈ 2.26 | 9/8 9/8 256/243 9/8 9/8 9/8 256/243 | 9/8 81/64 4/3 3/2 27/16 243/128 2/1 |
| 31edo | LLsLLLs | L:s = 5:3 ≈ 1.67 | 5 5 3 5 5 5 3 | 5 10 13 18 23 28 31 |