Neutral and interordinal intervals in MOS scales: Difference between revisions
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# Given 1 ≤ ''k'' ≤ a + b − 2, and assuming that the larger ''k''-step < the smaller (''k'' + 1)-step, the '''interordinal''' between ''k''-steps and (''k'' + 1)-steps, denoted ''k''x(''k'' + 1)(m)s or ''k''X(''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. The following holds for a given interordinal interval ''k''-inter-(''k'' + 1)-step, ''assuming'' that the smaller (''k'' + 1)-step is ''larger'' than the larger ''k''-step in ''basic'' aLbs: | # Given 1 ≤ ''k'' ≤ a + b − 2, and assuming that the larger ''k''-step < the smaller (''k'' + 1)-step, the '''interordinal''' between ''k''-steps and (''k'' + 1)-steps, denoted ''k''x(''k'' + 1)(m)s or ''k''X(''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. The following holds for a given interordinal interval ''k''-inter-(''k'' + 1)-step, ''assuming'' that the smaller (''k'' + 1)-step is ''larger'' than the larger ''k''-step in ''basic'' aLbs: | ||
#: ''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 diatonic | Neutral ''k''-steps generalize neutral interval categories based on the diatonic mos, which are: | ||
* neutral 1-diastep = neutral 2nd (A-Bd) | * neutral 1-diastep = neutral 2nd (A-Bd) | ||
* neutral 2-diastep = neutral 3rd (A-Ct) | * neutral 2-diastep = neutral 3rd (A-Ct) | ||