15edo: Difference between revisions

JI approximation: adopt new template, make the cold table collapsed, and misc
m Theory: sectioning
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== Theory ==
== Theory ==
{{Harmonics in equal|15}}


15edo can be thought of as three sets of [[5edo]] which do not connect by fifths. The fifth at 720 cents is quite wide yet still usable as a perfect fifth. Some would describe the fifth as more shimmery and pungent than anything closer to a just 3/2. The perfect fifth of 15edo returns to the octave if stacked five times which is radically different than a meantone system. Additionally, 15 being equal to 3 × 5 also implies that 15edo contains five sets of [[3edo]].
15edo can be thought of as three sets of [[5edo]] which do not connect by fifths. The fifth at 720 cents is quite wide yet still usable as a perfect fifth. Some would describe the fifth as more shimmery and pungent than anything closer to a just 3/2. The perfect fifth of 15edo returns to the octave if stacked five times which is radically different than a meantone system. Additionally, 15 being equal to 3 × 5 also implies that 15edo contains five sets of [[3edo]].
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A recommended method to the notation of 15edo by some is a system based on porcupine[8] in which eight nominals form the base diatonic scale. In this sense, the "quill" is the name given to the two step interval (160¢) of 15edo while the "small quill" (80¢) is the chroma of 15edo. This produces a very consistent notation for both porcupine[8] and Blackwood[10] and seems to work much better than attempting to put 15edo into a seven nominal based framework.
A recommended method to the notation of 15edo by some is a system based on porcupine[8] in which eight nominals form the base diatonic scale. In this sense, the "quill" is the name given to the two step interval (160¢) of 15edo while the "small quill" (80¢) is the chroma of 15edo. This produces a very consistent notation for both porcupine[8] and Blackwood[10] and seems to work much better than attempting to put 15edo into a seven nominal based framework.


=== Prime harmonics ===
{{Harmonics in equal|15}}
=== Keyboard layouts ===
<gallery widths=300px>
<gallery widths=300px>
File:15_tone_keyboard.png|Porcupine layout for 15edo
File:15_tone_keyboard.png|Porcupine layout for 15edo