87edo: Difference between revisions
Improve intro and links, apply distinction of et and edo |
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{{Infobox ET | {{Infobox ET | ||
| Prime factorization = 3 × 29 | | Prime factorization = 3 × 29 | ||
| Step size = 13. | | Step size = 13.793¢ | ||
| Fifth = 51\87 | | Fifth = 51\87 (703.448¢) (→ [[29edo|17\29]]) | ||
| Major 2nd = 15\87 | | Major 2nd = 15\87 (207¢) | ||
| | | Semitones = 9:6 (124¢ : 83¢) | ||
| | | Consistency = 15 | ||
}} | }} | ||
The '''87 equal divisions of the octave''' ('''87edo'''), or the '''87(-tone) equal temperament''' ('''87tet''', '''87et''') when viewed from a [[regular temperament]] perspective, is the tuning system derived by dividing the [[octave]] into 87 [[equal]]ly-sized steps, where each step is 13. | The '''87 equal divisions of the octave''' ('''87edo'''), or the '''87(-tone) equal temperament''' ('''87tet''', '''87et''') when viewed from a [[regular temperament]] perspective, is the tuning system derived by dividing the [[octave]] into 87 [[equal]]ly-sized steps, where each step is about 13.8 [[cent]]s. | ||
== Theory == | == Theory == | ||
87edo is solid as both a [[13-limit]] (or [[15-odd-limit]]) and as a [[5-limit]] system, and of course does well enough in any limit in between. It represents the [[13-odd-limit]] [[tonality diamond]] both uniquely and [[consistent]]ly (see [[87edo/13-limit detempering]]), and is the smallest edo to do so. It is a [[zeta peak integer edo]]. | 87edo is solid as both a [[13-limit]] (or [[15-odd-limit]]) and as a [[5-limit]] system, and of course does well enough in any limit in between. It represents the [[13-odd-limit]] [[tonality diamond]] both uniquely and [[consistent]]ly (see [[87edo/13-limit detempering]]), and is the smallest edo to do so. It is a [[zeta peak integer edo]]. | ||