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)s or ''k''X(''k'' + 1)s (read "''k'' cross (''k'' + 1) step"), is the interval exactly halfway between the larger ''k''-step and the smaller (''k'' + 1)-step. The name comes from the fact that ''k''-steps in the diatonic mos are conventionally called "(''k'' + 1)ths". | # 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)s or ''k''X(''k'' + 1)s (read "''k'' cross (''k'' + 1) step"), is the interval exactly halfway between the larger ''k''-step and the smaller (''k'' + 1)-step. The name comes from the fact that ''k''-steps in the diatonic mos are conventionally called "(''k'' + 1)ths". | ||
Given such a mos, it's easy to | Given such a mos, it's easy to observe the following properties of the simplest equal tunings for the mos, due to the way they divide the small step (s) and the chroma (L − s): | ||
* The basic equal tuning (2a + b)-ed contains neither neutrals nor interordinals. | * The basic equal tuning (2a + b)-ed contains neither neutrals nor interordinals. | ||
* The monohard equal tuning (3a + b)-ed contains neutrals of that mos but not interordinals. | * The monohard equal tuning (3a + b)-ed contains neutrals of that mos but not interordinals. | ||