Neutral and interordinal intervals in MOS scales: Difference between revisions
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=== Statement of the theorem === | === Statement of the theorem === | ||
Suppose a > b and gcd(a, b) = 1. | Suppose a > b and gcd(a, b) = 1. | ||
# Every interordinal in basic aLbs (an interval that is exactly halfway between the larger k-step and the smaller (k+1)-step) is a neutral or semiperfect interval in the parent mos bL(a-b)s | # Every interordinal in basic aLbs (an interval that is exactly halfway between the larger k-step and the smaller (k+1)-step) is a neutral or semiperfect interval in the parent mos bL(a-b)s. Every interordinal interval in bL(a-b)s is a neutral or semiperfect interval in aLbs (albeit the converse need not hold). | ||
# (b - 1) counts the places in 2(2a+b)edo (twice the basic mos tuning for aLbs) where assigning interordinals to the parent mos of basic aLbs fails. | # (b - 1) counts the places in 2(2a+b)edo (twice the basic mos tuning for aLbs) where assigning interordinals to the parent mos of basic aLbs fails. | ||
==== Proof ==== | ==== Proof ==== | ||