Neutral and interordinal intervals in MOS scales: Difference between revisions
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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<E> is a neutral or semiperfect interval in the parent mos bL(a-b)s<E>. | # Every interordinal in basic aLbs<E> is a neutral or semiperfect interval in the parent mos bL(a-b)s<E>. | ||
# Every interordinal interval in the parent mos bL(a-b)s<E> of basic aLbs<E> is a neutral or semiperfect interval in 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. | # Every interordinal interval in the parent mos bL(a-b)s<E> of basic aLbs<E> is a neutral or semiperfect interval in 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. | |||
=== Preliminaries for the proof === | === Preliminaries for the proof === | ||