15edo: Difference between revisions
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{{Infobox ET | {{Infobox ET | ||
| Prime factorization = 3 × 5 | | Prime factorization = 3 × 5 | ||
| Step size = | | Step size = 80.000¢ | ||
| Fifth = 9\15 = 720¢ (→[[5edo|3\5]]) | | Fifth = 9\15 = 720¢ (→[[5edo|3\5]]) | ||
| Major 2nd = 3\15 (240¢) | | Major 2nd = 3\15 (240¢) | ||
| Semitones = 3:0 (240¢:0¢) | | Semitones = 3:0 (240¢ : 0¢) | ||
| Consistency = 7 | | Consistency = 7 | ||
}} | }} | ||
{{Wikipedia|15 equal temperament}} | {{Wikipedia|15 equal temperament}} | ||
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== Theory == | == Theory == | ||
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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* Porcupine notation bases porcupine[8] LLLLLLLs scale using eight nominals α β χ δ ε φ γ η. Others have proposed ABCDEFGHA but conflicts with european notation have caused many to reject this approach. Thus greek letters can be used in place with a close resemblance to the spelling of ABCDEFGHA. | * Porcupine notation bases porcupine[8] LLLLLLLs scale using eight nominals α β χ δ ε φ γ η. Others have proposed ABCDEFGHA but conflicts with european notation have caused many to reject this approach. Thus greek letters can be used in place with a close resemblance to the spelling of ABCDEFGHA. | ||
=== Interval names for | === Interval names for porcupine[8] === | ||
{| class="wikitable" | {| class="wikitable" | ||
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Some scales commonly used in 15edo, written in a common mode, in steps of 15edo: | Some scales commonly used in 15edo, written in a common mode, in steps of 15edo: | ||
===MOS | === MOS scales === | ||
* Augmented[6]: 414141 | * Augmented[6]: 414141 | ||
* Triforce[6]: 323232 | * Triforce[6]: 323232 | ||
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* Augmented[12]: 211121112111 | * Augmented[12]: 211121112111 | ||
===Other | === Other scales === | ||
* Zarlino/Ptolemy diatonic, "just" major, Ma grama - 3213231 | * Zarlino/Ptolemy diatonic, "just" major, Ma grama - 3213231 | ||
* inverse of Zarlino/Ptolemy diatonic, natural minor - 3123132 | * inverse of Zarlino/Ptolemy diatonic, natural minor - 3123132 | ||