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 ==
Tetracot is considered as a [[cluster temperament]] with seven clusters of notes in an octave. The chroma interval between adjacent notes in each cluster represents [[40/39]], [[45/44]], [[55/54]], [[65/64]], [[66/65]], [[81/80]], and [[121/120]] all at once. In the following table, odd harmonics and subharmonics 1–15 are in '''bold'''.  
=== 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"
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| 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 ==
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|  
|  
|-
|-
|
|  
|243/200
| 243/200
|168.574
| 168.574
|1/2-comma
| 1/2-comma
|-
|-
| 1\7
| 1\7
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| 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
|-
|-
|  
|  
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|  
|  
|-
|-
|
|  
|81/80
| 81/80
|174.501
| 174.501
|2/7-comma
| 2/7-comma
|-
|-
|  
|  
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| 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
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| 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
|-
|-
|  
|  
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| 5/3
| 5/3
| 176.872
| 176.872
|1/5-comma
| 1/5-comma
|-
|-
|  
|  
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| 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
|-
|-
|  
|  
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|  
|  
| 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
|-
|-
|  
|