MOS substitution

MOS substitution is a procedure for obtaining a ternary (3 step sizes) scale from two MOS patterns. It consists of taking one MOS pattern (called the template MOS), choosing a step size, and overwriting all instances of that step size using the step pattern of another MOS pattern (called the filling MOS). Unlike MV3 scales, a MOS substitution scale may have any combination of step sizes.

Examples

Many familiar ternary scales (in particular, the nicest MV3 scales such as zarlino and diasem) can be constructed as MOS substitutions.

LMsLMLs <- LLsLLLs x LMLML, LssLsLs x MsMs, sMssMss x LsLLs

LLmLLLs <- LLsLLLs x ms

LMsLM <- LLsLL x LMLM

LmLsLmLsL <- LsLsLsLsL x msms

The three standard diaslen scale patterns, denoted 4sL (LsLsLmLsLsm), 4sC (LmLsLsLmLss), and 4sR (LsLmLsLsLms), may be constructed via MOS substitution, giving generator sequences for the three scales:

diaslen scales as MOS substitution scales

chirality	filling MOS	step pattern		generator sequence
		template MOS:	LXLXLXLXLXX	intvl. class of gen.:	2-steps
4sC	mssmss	LmLsLsLmLss		GS(L+m, L+s, L+s)
4sR	smssms	LsLmLsLsLms		GS(L+s, L+m, L+s)
4sL	ssmssm	LsLsLmLsLsm		GS(L+s, L+s, L+m)