25ed7: Difference between revisions
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'''[[Ed7|Division of the 7th harmonic]] into 25 equal parts''' (25ed7) is related to [[9edo | {{Infobox ET}} | ||
'''[[Ed7|Division of the 7th harmonic]] into 25 equal parts''' (25ed7) is related to [[9edo]], but with the 7/1 rather than the 2/1 being just. The octave is about 12.7773 cents stretched and the step size is about 134.7530 cents. | |||
{| class="wikitable" | == Intervals == | ||
{| class="wikitable mw-collapsible" | |||
|+ Intervals of 25ed7 | |||
|- | |- | ||
! | degree | ! | degree | ||
| Line 15: | Line 18: | ||
| | 1 | | | 1 | ||
| | 134.7530 | | | 134.7530 | ||
| | [[27/25]] | | | ([[27/25]]), [[13/12]] | ||
| | | | | | ||
|- | |- | ||
| Line 40: | Line 43: | ||
| | 6 | | | 6 | ||
| | 808.5182 | | | 808.5182 | ||
| | | | | (147/92) | ||
| | | | | | ||
|- | |- | ||
| Line 55: | Line 58: | ||
| | 9 | | | 9 | ||
| | 1212.7773 | | | 1212.7773 | ||
| | | | | 161/80 | ||
| | | | | | ||
|- | |- | ||
| Line 90: | Line 93: | ||
| | 16 | | | 16 | ||
| | 2156.0486 | | | 2156.0486 | ||
| | | | | 80/23 | ||
| | | | | | ||
|- | |- | ||
| Line 105: | Line 108: | ||
| | 19 | | | 19 | ||
| | 2560.3077 | | | 2560.3077 | ||
| | | | | (92/21) | ||
| | | | | | ||
|- | |- | ||
| Line 130: | Line 133: | ||
| | 24 | | | 24 | ||
| | 3234.0729 | | | 3234.0729 | ||
| | 175/27 | | | 84/13, (175/27) | ||
| | | | | | ||
|- | |- | ||
| Line 139: | Line 142: | ||
|} | |} | ||
[[ | == Harmonics == | ||
[[ | {{Harmonics in equal|25|7|1|intervals=prime}} | ||
{{Harmonics in equal|25|7|1|intervals=prime|collapsed=1|start=12}} | |||
==25ed7 as a generator== | |||
25ed7 can also be thought of as a [[generator]] of the 23-limit temperament which tempers out 169/168, 176/175, 208/207, 221/220, 247/245, 256/255, and 361/360, which is a [[cluster temperament]] with nine clusters of notes in an octave. This temperament is supported by [[9edo]], [[71edo]] (using 71d val), [[80edo]], and [[89edo]] among others. | |||
{{todo|expand}} | |||