EDO: Difference between revisions
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To find the step size of ''n''-edo in terms of [[cent]]s, divide 1200 by ''n''. The size ''s'' of ''k'' steps of ''n''-edo (''k''\''n'') is | To find the step size of ''n''-edo in terms of [[cent]]s, divide 1200 by ''n''. The size ''s'' of ''k'' steps of ''n''-edo (''k''\''n'') is | ||
<math>\displaystyle s = 1200 \cdot k/n</math> | <center><math>\displaystyle s = 1200 \cdot k/n</math></center> | ||
To find the step size of ''n''-edo in terms of [[frequency ratio]], take the ''n''-th root of 2. For example, the step of 12edo is 2<sup>1/12</sup> (≈ 1.059). So the ratio ''c'' of the ''k'' steps of ''n''-edo is | To find the step size of ''n''-edo in terms of [[frequency ratio]], take the ''n''-th root of 2. For example, the step of 12edo is 2<sup>1/12</sup> (≈ 1.059). So the ratio ''c'' of the ''k'' steps of ''n''-edo is | ||
<math>\displaystyle c = 2^{k/n}</math> | <center><math>\displaystyle c = 2^{k/n}</math></center> | ||
In particular, when ''k'' is 0, ''c'' is simply 1, because any number to the 0th power is 1. And when {{nowrap|''k'' {{=}} ''n''}}, ''c'' is simply 2, because any number to the 1st power is itself. | In particular, when ''k'' is 0, ''c'' is simply 1, because any number to the 0th power is 1. And when {{nowrap|''k'' {{=}} ''n''}}, ''c'' is simply 2, because any number to the 1st power is itself. | ||