Tetracot: Difference between revisions
m Cleanup on infobox |
+ as a detemp |
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See [[Tetracot family]] for more technical data. | See [[Tetracot family]] for more technical data. | ||
== Interval chain == | == Intervals == | ||
=== Interval chain === | |||
In the following table, odd harmonics and subharmonics 1–15 are in '''bold'''. | |||
{| class="wikitable right-1 right-2" | {| class="wikitable right-1 right-2" | ||
| Line 101: | Line 102: | ||
| 15/13 | | 15/13 | ||
|} | |} | ||
<nowiki />* In 2.3.5.11.13 subgroup CTE tuning | <nowiki/>* In 2.3.5.11.13 subgroup CTE tuning | ||
=== As a detemperament of 7et === | |||
[[File: Tetracot 7et Detempering.png|thumb|Tetracot as a 34-tone 7et detempering]] | |||
Tetracot is considered as a [[cluster temperament]] with 7 clusters of notes in an octave, so it is naturally a [[detemperament]] of the [[7edo|7 equal temperament]]. The diagram on the right shows a 34-tone detempered scale, with a generator range of -16 to +17, which covers all the intervals in the no-7 13-odd-limit. Each category is divided into four or five qualities separated by 7 generator steps, which represent [[40/39]], [[45/44]], [[55/54]], [[65/64]], [[66/65]], [[81/80]], and [[121/120]] all at once. | |||
== Scales == | == Scales == | ||
| Line 122: | Line 128: | ||
| | | | ||
|- | |- | ||
| | | | ||
|243/200 | | 243/200 | ||
|168.574 | | 168.574 | ||
|1/2-comma | | 1/2-comma | ||
|- | |- | ||
| 1\7 | | 1\7 | ||
| Line 132: | Line 138: | ||
| Lower bound of 2.3.5.11 subgroup 11-odd-limit, <br />2.3.5.11.13 subgroup 13- and 15-odd-limit diamond monotone | | Lower bound of 2.3.5.11 subgroup 11-odd-limit, <br />2.3.5.11.13 subgroup 13- and 15-odd-limit diamond monotone | ||
|- | |- | ||
| | | | ||
|27/20 | | 27/20 | ||
|173.184 | | 173.184 | ||
|1/3-comma | | 1/3-comma | ||
|- | |- | ||
| | | | ||
| Line 142: | Line 148: | ||
| | | | ||
|- | |- | ||
| | | | ||
|81/80 | | 81/80 | ||
|174.501 | | 174.501 | ||
|2/7-comma | | 2/7-comma | ||
|- | |- | ||
| | | | ||
| Line 160: | Line 166: | ||
| 11/8 | | 11/8 | ||
| 175.132 | | 175.132 | ||
| 2.3.5.11 subgroup 11-odd-limit minimax | | 2.3.5.11-subgroup 11-odd-limit minimax | ||
|- | |- | ||
| | | | ||
| 3/2 | | 3/2 | ||
| 175.489 | | 175.489 | ||
|1/4-comma | | 1/4-comma | ||
|- | |- | ||
| 6\41 | | 6\41 | ||
| Line 175: | Line 181: | ||
| 13/11 | | 13/11 | ||
| 175.899 | | 175.899 | ||
| 2.3.5.11.13 subgroup 13- and 15-odd-limit minimax | | 2.3.5.11.13-subgroup 13- and 15-odd-limit minimax | ||
|- | |- | ||
| | | | ||
| Line 205: | Line 211: | ||
| 5/3 | | 5/3 | ||
| 176.872 | | 176.872 | ||
|1/5-comma | | 1/5-comma | ||
|- | |- | ||
| | | | ||
| Line 222: | Line 228: | ||
| Upper bound of 2.3.5.11.13 subgroup 13- and 15-odd-limit diamond monotone | | Upper bound of 2.3.5.11.13 subgroup 13- and 15-odd-limit diamond monotone | ||
|- | |- | ||
| | | | ||
|27/25 | | 27/25 | ||
|177.794 | | 177.794 | ||
|1/6-comma | | 1/6-comma | ||
|- | |- | ||
| | | | ||
|243/125 | | 243/125 | ||
|178.452 | | 178.452 | ||
|1/7-comma | | 1/7-comma | ||
|- | |- | ||
| | | | ||
| Line 245: | Line 251: | ||
| | | | ||
| 180.000 | | 180.000 | ||
| Upper bound of 2.3.5.11 subgroup 11-odd-limit diamond monotone | | Upper bound of 2.3.5.11-subgroup 11-odd-limit diamond monotone | ||
|- | |- | ||
| | | | ||