15edo: Difference between revisions
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== Theory == | == Theory == | ||
15edo can be thought of as three sets of [[5edo]] which do not connect by [[3/2|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. In regular temperament terms, this means the [[Pythagorean limma]] is tempered out, which is radically different than a meantone system. This has a variety of ramifications for chord progressions based on {{w|Function (music)|functional harmony}}, because if you use the equipentatonic as your "diatonic scale", the same interval can have multiple functions. Additionally, 15 being equal to {{nowrap|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 [[3/2|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. In regular temperament terms, this means the [[Pythagorean limma]] is tempered out, which is radically different than a meantone system. This has a variety of ramifications for chord progressions based on {{w|Function (music)|functional harmony}}, because if you use the equipentatonic as your "diatonic scale", the same interval can have multiple functions. Additionally, 15 being equal to {{nowrap|3 × 5}} also implies that 15edo contains five sets of [[3edo]]. | ||
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15edo is also the second-smallest edo (after [[10edo]]) that maintains [[minimal consistent EDOs|25% or lower relative error]] on all of the first eight harmonics of the [[harmonic series]]. | 15edo is also the second-smallest edo (after [[10edo]]) that maintains [[minimal consistent EDOs|25% or lower relative error]] on all of the first eight harmonics of the [[harmonic series]]. | ||
=== Prime harmonics === | |||
{{Harmonics in equal|15}} | {{Harmonics in equal|15}} | ||
=== Composition theory === | |||
* [[User:Unque/15edo Composition Theory|Unque's approach]] - covers scales, chords, intervals, and functional harmony. | |||
* [[15edo/Vector's compositional guides|Vector's guides]] - covers the construction of scales, the kinds of chords found in 15edo, and a possible notation system. | |||
* [[Metallic harmony]] - harmony involving stacking sevenths instead of thirds; 15edo is one of the systems it is intended for. | |||
==Intervals== | ==Intervals== | ||