User:Holger Stoltenberg/sandbox: Difference between revisions
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A just major third relates the first (m=1) interval of a Mode 4 overtone scale to the tonic of Mode 4 (n=4, m=0) and we get | A just major third relates the first (m=1) interval of a Mode 4 overtone scale to the tonic of Mode 4 (n=4, m=0) and we get | ||
::::<math> | ::::<math> | ||
r=\frac{4+1}{4}=\frac{5}{4}</math> | r=\frac{4+1}{4}=\frac{5}{4}</math> | ||
::::<math> | ::::<math> | ||
r_{cents}= ln(r)\cdot\frac{1200}{ln(2)} \approx 386 </math> ¢ | r_{cents}= ln(r)\cdot\frac{1200}{ln(2)} \approx 386 </math> ¢ | ||
==Intonation== | ==Intonation== | ||
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* The test is true and the final result is -14 ¢ | * The test is true and the final result is -14 ¢ | ||
To determine the 12edo interval the intonation is applied to, get the original interval ''r<sub>cents </sub>'' and do some more integer arithmetic: | To determine the 12edo interval the intonation is applied to, get the original interval ''r<sub>cents </sub>'' and do some more integer arithmetic: | ||
::::<math> | |||
r_{12edo}=integer\left (\frac{r_{cents}+50c}{100.0} \right )\cdot 100</math> | |||
::::<math> | |||
r_{12edo}=integer\left (\frac{386c+50c}{100.0} \right )\cdot 100=400</math> ¢ | |||