User:Holger Stoltenberg/sandbox: Difference between revisions
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In the context of this model, we use 12edo pitches as the reference scale for measuring intonation. To describe intonation precisely (and without reference to concert pitch or absolute frequency), we define | In the context of this model, we use 12edo pitches as the reference scale for measuring intonation. To describe intonation precisely (and without reference to concert pitch or absolute frequency), we define | ||
:: ''Intonation is the signed interval between...'' | :: ''Intonation is the signed interval between...'' | ||
::* ''a pitch, generated by a key with a given key descriptor (such as A3, B3, C4, C#4, ...), <br>that rings exactly in tune with 12-tone equal temperament (12edo) and'' | ::* ''a pitch, generated by a key with a given key descriptor (such as A3, B3, C4, C#4, ...), <br>that rings exactly in tune with 12-tone equal temperament (12edo) and'' | ||
::* ''a deviating pitch referenced by the same key descriptor'' | ::* ''a deviating pitch referenced by the same key descriptor'' | ||
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To calculate the intonation | To calculate the intonation | ||
* compute the ''remainder'' of the interval’s value in cents by a modulo division (386 ¢ | * compute the ''remainder'' of the interval’s value in cents by a modulo division (386 ¢ ''mod''100) – <br>the intermediate result is 86 ¢ | ||
* Test: If the intermediate result is greater than 50 ¢ then subtract 100 ¢ | |||
* Test: If the | * 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: | |||
* 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 | |||