Neutral and interordinal intervals in MOS scales: Difference between revisions
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== | == The Interordinal Theorem == | ||
Recall that the “impropriety number” (b - 1) of a primitive (i.e. single-period) mos aLbs satisfies: | Recall that the “impropriety number” (b - 1) of a primitive (i.e. single-period) mos aLbs satisfies: | ||
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==== Proof ==== | ==== Proof ==== | ||
=== | === Statemwnt of the theorem === | ||
Suppose a > b and gcd(a, b) = 1. | Suppose a > b and gcd(a, b) = 1. | ||
# The impropriety number (b - 1) of the mos aLbs counts the places in 2(2a+b)edo (twice the basic mos tuning for aLbs) where assigning interordinals to the parent mos of aLbs fails. | # The impropriety number (b - 1) of the mos aLbs counts the places in 2(2a+b)edo (twice the basic mos tuning for aLbs) where assigning interordinals to the parent mos of aLbs fails. | ||