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User:VectorGraphics/Vector's introduction to 15edo/Scales: Difference between revisions

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== Periodicity ==
Let's bring up the harmonic table:
{| class="wikitable"
|'''0c'''
|400c
|800c
|'''0c'''
|400c
|800c
|'''0c'''
|400c
|800c
|'''0c'''
|400c
|800c
|'''0c'''
|-
|480c
|880c
|80c
|480c
|880c
|80c
|480c
|880c
|80c
|480c
|880c
|80c
|480c
|-
|960c
|160c
|560c
|960c
|160c
|560c
|960c
|160c
|560c
|960c
|160c
|560c
|960c
|-
|240c
|640c
|1040c
|240c
|640c
|1040c
|240c
|640c
|1040c
|240c
|640c
|1040c
|240c
|-
|720c
|1120c
|320c
|720c
|1120c
|320c
|720c
|1120c
|320c
|720c
|1120c
|320c
|720c
|-
|'''0c'''
|400c
|800c
|'''0c'''
|400c
|800c
|'''0c'''
|400c
|800c
|'''0c'''
|400c
|800c
|'''0c'''
|-
|480c
|880c
|80c
|480c
|880c
|80c
|480c
|880c
|80c
|480c
|880c
|80c
|480c
|-
|960c
|160c
|560c
|960c
|160c
|560c
|960c
|160c
|560c
|960c
|160c
|560c
|960c
|-
|240c
|640c
|1040c
|240c
|640c
|1040c
|240c
|640c
|1040c
|240c
|640c
|1040c
|240c
|-
|720c
|1120c
|320c
|720c
|1120c
|320c
|720c
|1120c
|320c
|720c
|1120c
|320c
|720c
|-
|'''0c'''
|400c
|800c
|'''0c'''
|400c
|800c
|'''0c'''
|400c
|800c
|'''0c'''
|400c
|800c
|'''0c'''
|-
|480c
|880c
|80c
|480c
|880c
|80c
|480c
|880c
|80c
|480c
|880c
|80c
|480c
|-
|960c
|160c
|560c
|960c
|160c
|560c
|960c
|160c
|560c
|960c
|160c
|560c
|960c
|-
|240c
|640c
|1040c
|240c
|640c
|1040c
|240c
|640c
|1040c
|240c
|640c
|1040c
|240c
|-
|720c
|1120c
|320c
|720c
|1120c
|320c
|720c
|1120c
|320c
|720c
|1120c
|320c
|720c
|-
|'''0c'''
|400c
|800c
|'''0c'''
|400c
|800c
|'''0c'''
|400c
|800c
|'''0c'''
|400c
|800c
|'''0c'''
|-
|480c
|880c
|80c
|480c
|880c
|80c
|480c
|880c
|80c
|480c
|880c
|80c
|480c
|-
|960c
|160c
|560c
|960c
|160c
|560c
|960c
|160c
|560c
|960c
|160c
|560c
|960c
|-
|240c
|640c
|1040c
|240c
|640c
|1040c
|240c
|640c
|1040c
|240c
|640c
|1040c
|240c
|-
|720c
|1120c
|320c
|720c
|1120c
|320c
|720c
|1120c
|320c
|720c
|1120c
|320c
|720c
|-
|'''0c'''
|400c
|800c
|'''0c'''
|400c
|800c
|'''0c'''
|400c
|800c
|'''0c'''
|400c
|800c
|'''0c'''
|}
In 15edo, as I mentioned in the Intervals section, there are four types of semitones: the diatonic, chromatic, ptolemaic, and compound semitones.
{| class="wikitable"
|80c - ptolemaic semitone
|480c
|880c
|80c - compound semitone
|-
|560c
|960c
|160c
|560c
|-
|1040c
|240c
|640c
|1040c
|-
|320c
|720c
|1120c
|320c
|-
|800c
|'''0c'''
|400c
|800c
|-
|80c - diatonic semitone
|480c
|880c
|80c - chromatic semitone
|}
The standard zarlino scale can be defined by having the chromatic and ptolemaic semitones as its "chromas": if we create a tile that repeats at each multiple of these two chromas, the intervals within that tile are precisely those in the zarlino scale. The zarlino scale may be called the chromatic-ptolemaic scale because of that.


WIP
However, we can choose a different pair of semitones as our chromas, and get a different scale. Here's the chromatic-compound scale.
 
█▒▒███▒██▒█▒████ - elena
 
█▒▒███▒█▒██▒████ - kee'ra
 
There are two variants as, since the compound semitone can be created by stacking two augmented fourths, the augmented fourth and diminished fifth fall precisely on the edge.
 
And the ptolemaic-diatonic scale:
 
█▒▒▒█▒▒█▒▒█▒▒█▒█ - myn
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