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, known as step labels, to express relative sizes. Binary scales, including MOS scales, use letters L ("large") and s ("small"); ternary scales add the letter M ("medium") between L and 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: comparison of two diatonic scales (major mode)

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

Step label spectrum

The set outlined below is used in Scale Workshop 3, making it both human readable and machine executable.

Positive-size step indicators

Below is a list of adjectives related to size ordered simultaneously in ascending ASCII order and descending size order.

• Biggest
• Colossal
• Enormous
• Gigantic
• Huge
• Large
• Medium
• Normal
• minute
• narrow
• petite
• small
• tiny
• unnoticeable
• wee
• zilch

The bolded first letter is intended as a shorthand for step patterns like L, M and s in LLsLLLs for Ionian or LMLsLsLMLs for Blackdye Grave Dorian.

The zilch step is reserved for steps of zero size i.e. repeated notes in the scale.

The anonymous x step is used if there are only steps of one size.

The unspecific P step is used if there is a single positive alongside zero steps or negative steps.

Standard letters

For each step variety (count of basic step sizes, interval variety of 1-steps, not to be confused with variety w.r.t. all interval classes) there is a standard set of letters to use. If possible the sets come in alphabetical order and with an equal number of uppercase and lowercase letters (or one more uppercase letter if the variety is odd).

Standard letters per variety

Step variety	Letters	Example	Name
1	x	xxxxx	5edo
1+0	P, z	PPzPPzP	5edo with repeated steps
2	L, s	LsLsLsL	Sothic
3	L, M, s	LMLsLLsLM	Diasem Melodic Minor
4	L, M, n, s	nMLsLMnMLM	Zarlino[10]
5	H, L, M, n, s	sHnHsHMLH	Zil[9]
6	H, L, M, n, s, t	HLMnst	Harmonics 6::12
7	B, H, L, M, n, s, t	HstnLnMstBtnMs	Rhombi[14]
8	B, H, L, M, n, s, t, w	wtsnMLHB	Subharmonics /16::8
9	B, C, H, L, M, n, s, t, w	CMCLwBHsnt	1-3-5-7-11 Dekany
10	B, C, H, L, M, n, p, s, t, w	MnLsLtBCwpHL	Carlos Super Just

If there are more step sizes than available in the mnemonic list the whole Latin alphabet should be used, again dividing evenly w.r.t. upper- and lowercase. Alternatively, for any step variety r the dollar sign $ followed by numbers 1, 2, ..., r may be used, e.g. in order to avoid spelling out offensive words.

Negative-size step indicators

Machine processing requires standard indicators for descending steps in cases where the user enters unsorted data in error or to enhance playability of the layout.

The Greek lowercase letters are used starting with µ due to its association with the metric prefix micro followed by ε due to association with size in mathematics. Note that ε comes before µ in the Greek alphabet so it's intended for the descending step closer to zero. (Also note that this wiki article uses the Latin micro sign µ instead of the actual Greek μ as a reminder that in machine context the correct codepoint should be used to aid in automatic processing even if there is little difference in visual appearance.)

If there is one positive step size among negative steps P should be used to indicate it.

If there are more than two negative step sizes the whole Greek alphabet should be used.

Example:

• The "Ionian" mode with step sizes 2 and -1 in 8edo would be spelled PPµPPPµ.

Unordered step sizes

U, V, W, X, Y, and Z are reserved for step sizes whose sizes relative to the ordered step sizes are unknown or unspecified.

Examples:

• In the word XYXYX, there are two possibilities: (X, Y) = (L, s) and (X, Y) = (s, L).
• The operation of substituting the MOS word ssLssL into the X slots of XXmXXmXX results in ssmLsmsL.