Mathematics of MOS: Difference between revisions
ArrowHead294 (talk | contribs) |
ArrowHead294 (talk | contribs) |
||
| Line 77: | Line 77: | ||
== MOS in equal tunings == | == MOS in equal tunings == | ||
In an equal tuning, all intervals are integer multiples of a smallest unit. If the equal tuning is N-edo and the period is an octave, the sizes of the large and small steps will be p | In an equal tuning, all intervals are integer multiples of a smallest unit. If the equal tuning is ''N''-edo and the period is an octave, the sizes of the large and small steps will be {{ffac|''p''|''N''}} and {{frac|''q''|''N''}}, with {{nowrap|''p'' > ''q''}}. We then have {{nowrap|''L''({{frac|''p''|''N''}}) + ''s''({{frac|''q''|''N''}}) {{=}} 1}}, which on multiplying through by ''N'' gives us {{nowrap|''Lp'' + ''sq'' {{=}} N}}, which is a linear diophantine equation. Solving this by standard methods, and requiring ''L'' and ''s'' to be positive, gives us the [L, s] pair for the MOS. If some other quantity of equal steps gives the period, we may make the appropriate adjustment. | ||
Lp + sq = N | |||
which is a linear diophantine equation. Solving this by standard methods, and requiring L and s to be positive, gives us the [L, s] pair for the MOS. If some other quantity of equal steps gives the period, we may make the appropriate adjustment. | |||
==Blackwood R constant== | ==Blackwood R constant== | ||