87edo: Difference between revisions

87edo is solid as both a [[13-limit]] (or [[15-odd-limit]]) and as a [[5-limit]] system, and does well enough in any limit in between. It is the smallest edo that is [[distinctly consistent]] in the [[13-odd-limit]] [[tonality diamond]], the smallest edo that is [[purely consistent]]{{idiosyncratic}} in the [[15-odd-limit]] (maintains [[relative interval error]]s of no greater than 25% on all of the first 16 [[harmonic]]s of the [[harmonic series]]). It is also a [[zeta peak integer edo]]. Since {{nowrap|87 {{=}} 3 × 29}}, 87edo shares the same perfect fifth with [[29edo]].  

87edo can be written using [[Kite's ups and downs notation]]. Note that quudsharp (quadruple-down sharp) is equivalent to quip (quintuple-up) and that quupsharp (quadruple-up sharp) is equivalent to quid (quintuple-down):

{{Ups and downs sharpness|87}}

| {{mapping| 87 138 202 }}

| {{mapping| 87 138 202 244 }}

| {{mapping| 87 138 202 244 301 }}

| {{mapping| 87 138 202 244 301 322 }}

| {{mapping| 87 138 202 244 301 322 356 }}

| {{mapping| 87 138 202 244 301 322 356 370 }}

<nowiki/>* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct

=== Mos scales ===

{{main|List of MOS scales in 87edo}}

87edo accurately approximates the mode 8 of [[harmonic series]], and the only interval pair not distinct is 14/13 and 15/14. It can also do mode 12 decently.  

The scale in adjacent steps is 15, 13, 12, 11, 10, 9, 9, 8.  

The scale in adjacent steps is 10, 9, 9, 8, 7, 7, 6, 6, 6, 6, 5.