Tetracot: Difference between revisions
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== Intervals == | == 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 ~ 121/120 all tempered together. | 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 ~ 121/120 all tempered together. In the following table, prime harmonics are in '''bold'''. | ||
{| class="wikitable right-1" | {| class="wikitable right-1 right-2" | ||
|- | |- | ||
! # | ! # | ||
| Line 24: | Line 24: | ||
| 0 | | 0 | ||
| 0.00 | | 0.00 | ||
| 1/1 | | '''1/1''' | ||
|- | |- | ||
| 1 | | 1 | ||
| Line 32: | Line 32: | ||
| 2 | | 2 | ||
| 352.39 | | 352.39 | ||
| 11/9, 16/13 | | 11/9, '''16/13''' | ||
|- | |- | ||
| 3 | | 3 | ||
| Line 40: | Line 40: | ||
| 4 | | 4 | ||
| 704.79 | | 704.79 | ||
| 3/2 | | '''3/2''' | ||
|- | |- | ||
| 5 | | 5 | ||
| Line 60: | Line 60: | ||
| 9 | | 9 | ||
| 385.77 | | 385.77 | ||
| 5/4 | | '''5/4''' | ||
|- | |- | ||
| 10 | | 10 | ||
| 561.96 | | 561.96 | ||
| 11/8, 18/13 | | '''11/8''', 18/13 | ||
|- | |- | ||
| 11 | | 11 | ||
| Line 89: | Line 89: | ||
=== Monkey === | === Monkey === | ||
{| class="wikitable right-1" | {| class="wikitable right-1 right-2" | ||
|- | |- | ||
! # | ! # | ||
! Cents< | ! Cents<nowiki>*</nowiki> | ||
! Approximate Ratios | ! Approximate Ratios | ||
|- | |- | ||
| Line 105: | Line 105: | ||
| 2 | | 2 | ||
| 351.24 | | 351.24 | ||
| 11/9, 16/13 | | 11/9, '''16/13''' | ||
|- | |- | ||
| 3 | | 3 | ||
| Line 113: | Line 113: | ||
| 4 | | 4 | ||
| 702.49 | | 702.49 | ||
| 3/2 | | '''3/2''' | ||
|- | |- | ||
| 5 | | 5 | ||
| Line 125: | Line 125: | ||
| 7 | | 7 | ||
| 29.36 | | 29.36 | ||
| | | 55/54, 45/44, 40/39 | ||
|- | |- | ||
| 8 | | 8 | ||
| Line 133: | Line 133: | ||
| 9 | | 9 | ||
| 380.60 | | 380.60 | ||
| 5/4 | | '''5/4''' | ||
|- | |- | ||
| 10 | | 10 | ||
| 556.22 | | 556.22 | ||
| 11/8, 18/13 | | '''11/8''', 18/13 | ||
|- | |- | ||
| 11 | | 11 | ||
| Line 153: | Line 153: | ||
| 14 | | 14 | ||
| 58.71 | | 58.71 | ||
| | | 33/32, 27/26, 25/24 | ||
|- | |- | ||
| 15 | | 15 | ||
| 234.34 | | 234.34 | ||
| 8/7, 15/13 | | '''8/7''', 15/13 | ||
|- | |- | ||
| 16 | | 16 | ||
| Line 165: | Line 165: | ||
| 17 | | 17 | ||
| 585.58 | | 585.58 | ||
| | | 45/32 | ||
|- | |- | ||
| 18 | | 18 | ||
| Line 205: | Line 205: | ||
| 27 | | 27 | ||
| 1141.80 | | 1141.80 | ||
| | | 27/14 | ||
|- | |- | ||
| 28 | | 28 | ||
| Line 214: | Line 214: | ||
=== Bunya === | === Bunya === | ||
{| class="wikitable right-1" | {| class="wikitable right-1 right-2" | ||
|- | |- | ||
! # | ! # | ||
! Cents< | ! Cents<nowiki>*</nowiki> | ||
! Approximate Ratios | ! Approximate Ratios | ||
|- | |- | ||
| Line 230: | Line 230: | ||
| 2 | | 2 | ||
| 351.77 | | 351.77 | ||
| 11/9, 16/13 | | 11/9, '''16/13''' | ||
|- | |- | ||
| 3 | | 3 | ||
| Line 238: | Line 238: | ||
| 4 | | 4 | ||
| 703.54 | | 703.54 | ||
| 3/2 | | '''3/2''' | ||
|- | |- | ||
| 5 | | 5 | ||
| Line 262: | Line 262: | ||
| 10 | | 10 | ||
| 558.86 | | 558.86 | ||
| 11/8, 18/13 | | '''11/8''', 18/13 | ||
|- | |- | ||
| 11 | | 11 | ||
| Line 326: | Line 326: | ||
| 26 | | 26 | ||
| 973.03 | | 973.03 | ||
| 7/4 | | '''7/4''' | ||
|- | |- | ||
| 27 | | 27 | ||
| Line 339: | Line 339: | ||
=== Modus === | === Modus === | ||
{| class="wikitable right-1" | {| class="wikitable right-1 right-2" | ||
|- | |- | ||
! # | ! # | ||
! Cents< | ! Cents<nowiki>*</nowiki> | ||
! Approximate Ratios | ! Approximate Ratios | ||
|- | |- | ||
| Line 355: | Line 355: | ||
| 2 | | 2 | ||
| 353.91 | | 353.91 | ||
| 11/9, 16/13 | | 11/9, '''16/13''' | ||
|- | |- | ||
| 3 | | 3 | ||
| Line 363: | Line 363: | ||
| 4 | | 4 | ||
| 707.81 | | 707.81 | ||
| 3/2 | | '''3/2''' | ||
|- | |- | ||
| 5 | | 5 | ||
| Line 379: | Line 379: | ||
| 8 | | 8 | ||
| 215.63 | | 215.63 | ||
| 9/8, 8/7 | | 9/8, '''8/7''' | ||
|- | |- | ||
| 9 | | 9 | ||
| 392.58 | | 392.58 | ||
| 5/4 | | '''5/4''' | ||
|- | |- | ||
| 10 | | 10 | ||
| 569.53 | | 569.53 | ||
| 11/8, 18/13 | | '''11/8''', 18/13 | ||
|- | |- | ||
| 11 | | 11 | ||
| Line 436: | Line 436: | ||
=== Wollemia === | === Wollemia === | ||
{| class="wikitable right-1" | {| class="wikitable right-1 right-2" | ||
|- | |- | ||
! # | ! # | ||
! Cents< | ! Cents<nowiki>*</nowiki> | ||
! Approximate Ratios | ! Approximate Ratios | ||
|- | |- | ||
| Line 452: | Line 452: | ||
| 2 | | 2 | ||
| 354.46 | | 354.46 | ||
| 11/9, 16/13 | | 11/9, '''16/13''' | ||
|- | |- | ||
| 3 | | 3 | ||
| Line 460: | Line 460: | ||
| 4 | | 4 | ||
| 708.92 | | 708.92 | ||
| 3/2 | | '''3/2''' | ||
|- | |- | ||
| 5 | | 5 | ||
| Line 472: | Line 472: | ||
| 7 | | 7 | ||
| 40.62 | | 40.62 | ||
| | | 55/54, 45/44, 40/39 | ||
|- | |- | ||
| 8 | | 8 | ||
| Line 480: | Line 480: | ||
| 9 | | 9 | ||
| 395.08 | | 395.08 | ||
| 5/4, 14/11 | | '''5/4''', 14/11 | ||
|- | |- | ||
| 10 | | 10 | ||
| 572.31 | | 572.31 | ||
| 11/8, 18/13, 7/5 | | '''11/8''', 18/13, 7/5 | ||
|- | |- | ||
| 11 | | 11 | ||
| Line 500: | Line 500: | ||
| 14 | | 14 | ||
| 81.24 | | 81.24 | ||
| | | 27/26, 25/24 | ||
|- | |- | ||
| 15 | | 15 | ||
| Line 520: | Line 520: | ||
| 19 | | 19 | ||
| 967.39 | | 967.39 | ||
| 7/4 | | '''7/4''' | ||
|- | |- | ||
| 20 | | 20 | ||
| Line 748: | Line 748: | ||
{| class="wikitable center-all" | {| class="wikitable center-all" | ||
|- | |- | ||
! [[Eigenmonzo| | ! [[Eigenmonzo|Eigenmonzo<br>(Unchanged-interval)]] | ||
! Generator<br>(¢) | ! Generator<br>(¢) | ||
! Comments | ! Comments | ||
| Line 950: | Line 950: | ||
== Scales == | == Scales == | ||
* [[Tetracot7]] | * [[Tetracot7]] – [[6L 1s]] scale | ||
* [[Tetracot13]] | * [[Tetracot13]] – improper [[7L 6s]] | ||
* [[Tetracot20]] | * [[Tetracot20]] – improper [[7L 13s]] | ||
[[Category:Temperaments]] | [[Category:Temperaments]] | ||