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. | ||
# 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 basic aLbs fails. | ||
# 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, but a neutral interval in basic aLbs is not always an interordinal interval in the parent mos. | # 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, but a neutral interval in basic aLbs is not always an interordinal interval in the parent mos. | ||
==== Proof ==== | ==== Proof ==== | ||