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 proper interordinal of basic aLbs{{angbr|E}} is a neutral or semiperfect interval of the parent mos bL(a | # Every proper interordinal of basic aLbs{{angbr|E}} is a neutral or semiperfect interval of the parent mos bL(a − b)s{{angbr|E}}. | ||
# Every interordinal interval of the parent mos bL(a | # Every interordinal interval of the parent mos bL(a − b)s{{angbr|E}} of basic aLbs{{angbr|E}} is a neutral or semiperfect interval of basic aLbs{{angbr|E}}. | ||
# Except the neutral/semiperfect 1-step and the neutral/semiperfect (a+b | # Except the neutral/semiperfect 1-step and the neutral/semiperfect (a + b − 1)-step, every neutral or semiperfect interval of basic aLbs{{angbr|E}} is a proper interordinal of bL(a − b)s{{angbr|E}}. The number (b − 1) counts the places in 2(2a + b)edE (twice the basic mos tuning for aLbs{{angbr|E}}) where the parent's interordinal is improper, being two steps away, instead of one step away, from each of the adjacent ordinal categories. | ||
=== Preliminaries for the proof === | === Preliminaries for the proof === | ||