User:Holger Stoltenberg/sandbox: Difference between revisions

Line 58:

Example 1: A just major third relates the first element ''(m=1)'' of a Mode 4 ''(n=4)'' overtone scale to the tonic ''(m=0)'' of Mode 4 and we get

::::<math>

Line 77:

[[#example01|Example 1]]) has an intonation interval of -14 ¢, which represents the ''distance to the nearest vertical 12edo line''. (Note that we generally evaluate intonation beginning at the 12edo pitch. This results in a minus sign for the intonation of the upper note of a just a third.)

To calculate the intonation

==== Calculate intonation ====

To calculate the signed intonation interval

*compute the ''remainder'' of the interval’s ''value in cents'' by a modulo division (386 ¢ ''mod''100), the intermediate result is 86 ¢

*compute the ''remainder'' of the original interval’s ''value in cents'' by a modulo division <math>(386</math> ¢ <math>mod(100))</math>, the intermediate result is 86 ¢

*Test: If the intermediate result is greater than 50 ¢ then subtract 100 ¢

*The test is true and the final result is 86 ¢ -100 ¢ = -14 ¢

To determine the 12edo interval the intonation is applied to, get the original interval ''rcents '' and do some integer arithmetic:

==== Determine the nearest 12edo interval ====

To determine the nearest 12edo interval the intonation is applied to, get the original interval ''rcents '' and do some integer arithmetic:

::::<math>

r_{12edo}=integer\left (\frac{r_{cents}+50c}{100.0} \right )\cdot 100</math>

@@ Line 58: / Line 58: @@
 <span id="example01"></span>
 <u>Example 1</u>: A just major third relates the first element ''(m=1)'' of a Mode 4 ''(n=4)'' overtone scale to the tonic ''(m=0)'' of Mode 4 and we get
 ::::<math>
@@ Line 77: / Line 77: @@
 [[#example01|Example 1]]) has an intonation interval of -14 ¢, which represents the ''distance to the nearest vertical 12edo line''. (Note that we generally evaluate intonation beginning at the 12edo pitch. This results in a minus sign for the intonation of the upper note of a just a third.)
-To calculate the intonation
+==== Calculate intonation ====
+To calculate the signed intonation interval
-*compute the ''remainder'' of the interval’s ''value in cents'' by a modulo division (386 ¢ ''mod''100), the <br>intermediate result is 86 ¢
+*compute the ''remainder'' of the original interval’s ''value in cents'' by a modulo division <small><math>(386</math> ¢ <math>mod(100))</math></small>, the <br>intermediate result is 86 ¢
 *Test: If the intermediate result is greater than 50 ¢ then subtract 100 ¢
 *The test is true and the final result is 86 ¢ -100 ¢ = -14 ¢
-To determine the 12edo interval the intonation is applied to, get the original interval ''r<sub>cents </sub>'' and do some integer arithmetic:
+==== Determine the nearest 12edo interval ====
+To determine the nearest 12edo interval the intonation is applied to, get the original interval ''r<sub>cents </sub>'' and do some integer arithmetic:
 ::::<math>
 r_{12edo}=integer\left (\frac{r_{cents}+50c}{100.0}  \right )\cdot 100</math> <br>