Equal-step tuning: Difference between revisions
"Equal pitch division" is just a synonym |
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''As there are infinite intervals, there are infinite equal scales.'' Barring technicalities, there are large quantities of perceivably different equal scales. Seeing such a diverse menagerie at their disposal, some composers choose to combine multiple equal tunings [[ET_surveys|sequentially]] or [[Polymicrotonality|simultaneously]]. | ''As there are infinite intervals, there are infinite equal scales.'' Barring technicalities, there are large quantities of perceivably different equal scales. Seeing such a diverse menagerie at their disposal, some composers choose to combine multiple equal tunings [[ET_surveys|sequentially]] or [[Polymicrotonality|simultaneously]]. | ||
== Formula == | |||
To find the step size of ''n''-ed-''p'' in terms of [[cent]]s, divide the cents of ''p'' by ''n''. The size ''s'' of ''k'' steps of ''n''-ed-''p'' (''k''\''n'' <''p''>) is | |||
<math>\displaystyle s = 1200 \log_2 (p) \cdot k/n</math> | |||
To find the step size of ''n''-edo in terms of [[frequency ratio]], take the ''n''-th root of ''p''. For example, the step of 12edo is 2<sup>1/12</sup> (≈ 1.059). So the ratio ''c'' of ''k'' steps of ''n''-ed-''p'' is | |||
<math>\displaystyle c = p^{k/n}</math> | |||
In particular, when ''k'' is 0, ''c'' is simply 1, because any number to the 0th power is 1. And when ''k'' = ''n'', ''c'' is simply ''p'', because any number to the 1st power is itself. | |||
== Simultaneous equal divisions == | == Simultaneous equal divisions == | ||