Neutral and interordinal intervals in MOS scales: Difference between revisions
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# Given 0 ≤ ''k'' ≤ a + b − 1, and assuming that the larger ''k''-step < the smaller (''k'' + 1)-step, the '''interordinal''' between ''k''-steps and (''k'' + 1)-steps, denoted ''k''×(''k'' + 1)(m)s (read "''k'' cross (''k'' + 1) (mos)step" or "''k'' inter (''k'' + 1) (mos)step"), is the interval exactly halfway between the larger ''k''-step and the smaller (''k'' + 1)-step. | # Given 0 ≤ ''k'' ≤ a + b − 1, and assuming that the larger ''k''-step < the smaller (''k'' + 1)-step, the '''interordinal''' between ''k''-steps and (''k'' + 1)-steps, denoted ''k''×(''k'' + 1)(m)s (read "''k'' cross (''k'' + 1) (mos)step" or "''k'' inter (''k'' + 1) (mos)step"), is the interval exactly halfway between the larger ''k''-step and the smaller (''k'' + 1)-step. | ||
#: If the smaller (''k'' + 1)-step is ''strictly larger'' than the larger ''k''-step in ''basic'' aLbs, ''k''×(''k'' + 1) is called a '''proper interordinal'''. If a > b, then aLbs{{angbr|E}} has a + 1 proper interordinals, including 0×1ms and (a+b−1)×(a+b)ms. | #: If the smaller (''k'' + 1)-step is ''strictly larger'' than the larger ''k''-step in ''basic'' aLbs, ''k''×(''k'' + 1) is called a '''proper interordinal'''. If a > b, then aLbs{{angbr|E}} has a + 1 proper interordinals, including 0×1ms and (a+b−1)×(a+b)ms. | ||
#: We call s/2 (or 0×1ms) '''interizer'''{{idiosyncratic}}. The interizer is of note since the following holds for any proper interordinal interval ''k''-inter-(''k'' + 1)-step: | #: We call s/2 (or 0×1ms) the '''interizer'''{{idiosyncratic}}. The interizer is of note since the following holds for any proper interordinal interval ''k''-inter-(''k'' + 1)-step: | ||
#: ''k''-inter-(''k'' + 1)-step = larger ''k''-step + s/2 = smaller (''k'' + 1)-step − s/2. | #: ''k''-inter-(''k'' + 1)-step = larger ''k''-step + s/2 = smaller (''k'' + 1)-step − s/2. | ||
Neutral ''k''-steps generalize neutral interval categories based on the diatonic MOS, which are: | Neutral ''k''-steps generalize neutral interval categories based on the diatonic MOS, which are: | ||