Cotoneum: Difference between revisions
add a higher-limit one |
Cut table to 41 generators. The mappings of every interval do not need to be listed. |
||
| Line 1: | Line 1: | ||
{{Infobox regtemp | {{Infobox regtemp | ||
| Title = Cotoneum | | Title = Cotoneum | ||
| Line 14: | Line 13: | ||
| Odd limit 2 = 21 | Mistuning 2 = 2.48 | Complexity 2 = 176 | | Odd limit 2 = 21 | Mistuning 2 = 2.48 | Complexity 2 = 176 | ||
}} | }} | ||
'''Cotoneum''' is a [[rank]]-2 [[regular temperament|temperament]] for the 7- through 19-limit. It is a member of the [[hemimage temperaments]], [[quince clan]], and [[garischismic clan]]. The generator of cotoneum is a perfect fifth sharp by about 0. | '''Cotoneum''' is a [[rank]]-2 [[regular temperament|temperament]] for the 7- through 19-limit. It is a member of the [[hemimage temperaments]], [[quince clan]], and [[garischismic clan]]. The generator of cotoneum is a perfect fifth sharp by about 0.4–0.5 cents, and it maps [[8/7]] to the double-augmented unison (+14 fifths), [[tempering out]] the [[garischisma]]. However, unlike in [[garibaldi]], the schisma is not tempered out, meaning 5/4 is not found at the diminished fourth. Instead, 5/4 is found at the sextuple-diminished octave (–49 fifths). It is a weak extension of the [[2.5.7 subgroup|2.5.7-subgroup]] temperament [[mercy]], with its secor-sized generator mapped to the augmented unison. | ||
It can seen as a detemperament of [[41edo|41 equal temperament]], with the [[countercomp comma|41-comma]] shrunk down to about 5 cents, representing important intervals such as the [[schisma]], [[5120/5103]], [[325/324]], [[352/351]], [[385/384]], [[513/512]], etc. | It can seen as a detemperament of [[41edo|41 equal temperament]], with the [[countercomp comma|41-comma]] shrunk down to about 5 cents, representing many important intervals such as the [[schisma]], [[5120/5103]], [[243/242]], [[273/272]], [[325/324]], [[352/351]], [[385/384]], [[513/512]], [[896/891]], etc. | ||
[[217edo]] is an excellent tuning for cotoneum, with a fifth generator of 127\217, and [[mos scale]]s of 12, 17, 29, 41, 53, 94, 135, or 176 notes are available. | [[217edo]] is an excellent tuning for cotoneum, with a fifth generator of 127\217, and [[mos scale]]s of 12, 17, 29, 41, 53, 94, 135, or 176 notes are available. | ||
| Line 25: | Line 24: | ||
== Interval chain == | == Interval chain == | ||
Odd harmonics and subharmonics 1–21 are in '''bold'''. | |||
{| class="wikitable center-1 right-2" | {| class="wikitable center-1 right-2" | ||
! | ! Fifths | ||
! Cents <br>value* | ! Cents <br>value* | ||
! Approximate Ratios | ! Approximate Ratios | ||
| Line 32: | Line 33: | ||
| 0 | | 0 | ||
| 0.000 | | 0.000 | ||
| 1/1 | | '''1/1''' | ||
|- | |- | ||
| 1 | | 1 | ||
| 702.308 | | 702.308 | ||
| 3/2 | | '''3/2''' | ||
|- | |- | ||
| 2 | | 2 | ||
| 204.615 | | 204.615 | ||
| 9/8 | | '''9/8''' | ||
|- | |- | ||
| 3 | | 3 | ||
| Line 84: | Line 85: | ||
| 13 | | 13 | ||
| 730.001 | | 730.001 | ||
| 32/21 | | '''32/21''' | ||
|- | |- | ||
| 14 | | 14 | ||
| 232.308 | | 232.308 | ||
| 8/7 | | '''8/7''' | ||
|- | |- | ||
| 15 | | 15 | ||
| Line 124: | Line 125: | ||
| 23 | | 23 | ||
| 553.078 | | 553.078 | ||
| 11/8 | | '''11/8''' | ||
|- | |- | ||
| 24 | | 24 | ||
| Line 148: | Line 149: | ||
| 29 | | 29 | ||
| 1166.925 | | 1166.925 | ||
| 51/26, 96/49, <br>108/55, 112/57 | | 51/26, 96/49,<br>108/55, 112/57 | ||
|- | |- | ||
| 30 | | 30 | ||
| Line 196: | Line 197: | ||
| 41 | | 41 | ||
| 1194.618 | | 1194.618 | ||
| | | 351/176, 891/448 | ||
|} | |} | ||
<nowiki>*</nowiki> in 19-limit POTE tuning | <nowiki>*</nowiki> in 19-limit POTE tuning | ||