Meantone: Difference between revisions

Tuning spectrum: simplify some ratios under octave equivalence
Formula to calculate n-comma meantone: improvement and converse derivation
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=== Formula to calculate ''n''-comma meantone ===
=== Formula for ''n''-comma meantone ===
A just [[perfect fifth]] is 701.955001 cents, while a [[syntonic comma]] is 21.506290 cents.
The [[generator]] ''g'' of ''n''-comma meantone, where ''n'' is a fraction (like 1/5, 2/9, etc.), can be found by


The [[generator]] ''g'' of ''n''-comma meantone, where ''n'' is a fraction (like 1/5, 2/9, etc.), can be found using the following formula:
<math>\displaystyle g = g_J - ng_c</math>


''g'' = 701.955001-(''n'')*21.50629
where ''g''<sub>''J''</sub> = 701.955001 cents is the size of the just perfect fifth, and ''g''<sub>c</sub> = 21.506290 cents is the size of the syntonic comma.
 
Conversely, ''n'' can be found by
 
<math>\displaystyle n = (g_J - g)/g_c</math>


== Music ==
== Music ==