Neutral and interordinal intervals in MOS scales: Difference between revisions
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=== Statement === | === Statement === | ||
Suppose a > b and gcd(a, b) = 1. | Suppose a > b and gcd(a, b) = 1. | ||
# Every interordinal | # Every interordinal of basic aLbs<E> is a neutral or semiperfect interval of the parent mos bL(a-b)s<E>. | ||
# Every interordinal interval | # Every interordinal interval of the parent mos bL(a-b)s<E> of basic aLbs<E> is a neutral or semiperfect interval of basic aLbs<E>. | ||
# The number (b - 1) counts the places in 2(2a+b)edE (twice the basic mos tuning for aLbs<E>) where the parent's interordinal is two steps away, instead of one step away, from each of the adjacent ordinal categories. | # Except the neutral/semiperfect 1-step and the neutral/semiperfect (a+b-1)-step, every neutral or semiperfect interval of basic aLbs<E> is an interordinal of bL(a-b)s<E>. The number (b - 1) counts the places in 2(2a+b)edE (twice the basic mos tuning for aLbs<E>) where the parent's interordinal is two steps away, instead of one step away, from each of the adjacent ordinal categories. | ||
=== Preliminaries for the proof === | === Preliminaries for the proof === | ||