Neutral and interordinal intervals in MOS scales: Difference between revisions
Added "semiaugmented" and "semidiminished" as alternate terms for semiperfect intervals. Tags: Mobile edit Mobile web edit |
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Given a tuning of a primitive (i.e. single-period) [[mos]] pattern aLbs{{angbr|E}} with arbitrary [[equave]] E in a specific tuning (i.e. with a specific [[hardness]] value for L/s), we may define two types of notes "in the cracks of" interval categories defined by aLbs{{angbr|E}}: | Given a tuning of a primitive (i.e. single-period) [[mos]] pattern aLbs{{angbr|E}} with arbitrary [[equave]] E in a specific tuning (i.e. with a specific [[hardness]] value for L/s), we may define two types of notes "in the cracks of" interval categories defined by aLbs{{angbr|E}}: | ||
# Given 1 ≤ ''k'' ≤ a + b − 1, the '''neutral''' ''k''-mosstep or ''k''-step (abbrev. n''k''ms, n''k''s) is the interval exactly halfway between the smaller ''k''-step and the larger ''k''-step of the mos. When the mos is generated by a (perfect) ''k''-step, this may instead be called the '''semiperfect''' ''k''-step (abbrev. sP''k''s), since it is halfway between the perfect and imperfect (either diminished or augmented, depending on whether the generator is bright or dark) ''k''-step. Depending on whether the imperfect generator is augmented or diminished, the corresponding semiperfect generator may be called '''semiaugmented''' | # Given 1 ≤ ''k'' ≤ a + b − 1, the '''neutral''' ''k''-mosstep or ''k''-step (abbrev. n''k''ms, n''k''s) is the interval exactly halfway between the smaller ''k''-step and the larger ''k''-step of the mos. When the mos is generated by a (perfect) ''k''-step, this may instead be called the '''semiperfect''' ''k''-step (abbrev. sP''k''s), since it is halfway between the perfect and imperfect (either diminished or augmented, depending on whether the generator is bright or dark) ''k''-step. Depending on whether the imperfect generator is augmented or diminished, the corresponding semiperfect generator may be called '''semiaugmented''' or '''semidiminished'''. | ||
#: The following ''always'' holds for a given interval class of ''k''-steps between 1-steps and (a + b − 1)-steps, inclusive: | #: The following ''always'' holds for a given interval class of ''k''-steps between 1-steps and (a + b − 1)-steps, inclusive: | ||
#: neutral ''k''-step = smaller ''k''-step + c/2 = larger ''k''-step − c/2, where c = L − s is the [[chroma]] of the mos. | #: neutral ''k''-step = smaller ''k''-step + c/2 = larger ''k''-step − c/2, where c = L − s is the [[chroma]] of the mos. | ||