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


<center><math>\displaystyle s = 1200 \cdot k/n</math></center>
$$ s = 1200 \cdot k/n $$


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 ''r'' of the ''k'' steps of ''n''-edo is


<center><math>\displaystyle c = 2^{k/n}</math></center>
$$ r = 2^{k/n} $$


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, ''r'' is simply 1, because any number to the 0th power is 1. And when {{nowrap|''k'' {{=}} ''n''}}, ''r'' is simply 2, because any number to the 1st power is itself.


== Properties ==
== Properties ==
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