Neutral and interordinal intervals in MOS scales: Difference between revisions

Inthar (talk | contribs)
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Inthar (talk | contribs)
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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 the parent mos bL(a-b)s of basic aLbs is a neutral or semiperfect interval in basic aLbs. The converse does not hold unless b = 1; (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.
# Every interordinal interval in the parent mos bL(a-b)s of basic aLbs is a neutral or semiperfect interval in basic aLbs. The number (b - 1) counts the places in 2(2a+b)edo (twice the basic mos tuning for aLbs) where the parent's interordinal is two steps away from the ordinal categories.


=== Preliminaries ===
=== Preliminaries ===