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
Simple examples
Many familiar ternary scales can be constructed as MOS substitutions.
LMsLMLs <- LLsLLLs x LMLML, LssLsLs x MsMs, sMssMss x LsLLs
LLmLLLs <- LLsLLLs x ms
LMsLM <- LLsLL x LMLM
Aberrismic scales
Diasem: LmLsLmLsL <- LsLsLsLsL x msms
Blackdye: sLmLsLmLsL <- sLsLsLsLsL x smsms
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:
| 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) | ||
More general classes of MOS substitutions
- Ternary interleaved-MOS scales such as blackdye (5L2m3s) and whitedye (5L2m7s) are MOS substitution scales. In those, the template MOS is of the form kx ky.
- Non-twisted, non-abacaba MV3 scales are simple examples of MOS substitution scales where the filling MOS is of the form kx ky.
- A ternary scale is always a MOS substitution scale if the L = m and s = 0 monotone-MOS properties are satisfied.
Properties
If the template MOS is single-period, the MOS substitution scale has a generator sequence using only two distinct intervals. The length of this GS is the length of the period of the filling MOS.
Caveats
MOS substitution scales in general still have somewhat messy lattices. If you want an especially nice lattice (with two distinct generators in the GS, and only one generator different in that GS) you should additionally want the number of slot letters in the template MOS's generator to be the generator interval class of the filling MOS, like for diaslen. If you want a short generator sequence, you should use a multiperiod filling MOS, again like for diaslen.
