Octacot (temperament): Difference between revisions
From Xenharmonic Reference
Created page with "'''Octacot''', 2.3.5.7[27 & 41], is a 7-limit rank-2 temperament that splits 3/2 into 8 equal parts, each representing 21/20. == Interval chain == In the following table, odd harmonics and subharmonics 1–21 are in '''bold'''. {| class="wikitable right-1 right-2" |- ! # ! Cents* ! Approximate ratios |- | 0 | 0.0 | '''1/1''' |- | 1 | 87.7 | 21/20 |- | 2 | 175.5 | 10/9 |- | 3 | 263.2 | 7/6 |- | 4 | 351.0 | 49/40 |- | 5 | 438.7 | 9/7 |- | 6 | 526.5 | 27/20 |- | 7 | 614.2 |..." |
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'''Octacot''', 2.3.5.7[27 & 41], is a 7-limit rank-2 temperament that splits 3/2 into 8 equal parts, each representing 21/20. | '''Octacot''', 2.3.5.7{[[27edo|27]] & [[41edo|41]]}, is a 7-limit rank-2 temperament that splits 3/2 into 8 equal parts, each representing 21/20. It is the most important weak extension of [[Tetracot (temperament)|Tetracot]]. | ||
== Interval chain == | == Interval chain == | ||
In the following table, odd harmonics and subharmonics 1–21 are in '''bold'''. | In the following table, odd harmonics and subharmonics 1–21 are in '''bold'''. | ||
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<nowiki/>* in exact-3/2 tuning | <nowiki/>* in exact-3/2 tuning | ||
{{Navbox | {{Navbox EDO}} | ||
{{Navbox regtemp}} | {{Navbox regtemp}} | ||
{{Cat|Temperaments}} | |||
Latest revision as of 03:01, 2 April 2026
Octacot, 2.3.5.7{27 & 41}, is a 7-limit rank-2 temperament that splits 3/2 into 8 equal parts, each representing 21/20. It is the most important weak extension of Tetracot.
Interval chain
In the following table, odd harmonics and subharmonics 1–21 are in bold.
| # | Cents* | Approximate ratios |
|---|---|---|
| 0 | 0.0 | 1/1 |
| 1 | 87.7 | 21/20 |
| 2 | 175.5 | 10/9 |
| 3 | 263.2 | 7/6 |
| 4 | 351.0 | 49/40 |
| 5 | 438.7 | 9/7 |
| 6 | 526.5 | 27/20 |
| 7 | 614.2 | 10/7 |
| 8 | 702.0 | 3/2 |
| 9 | 789.7 | 63/40 |
| 10 | 877.4 | 5/3 |
| 11 | 965.2 | 7/4 |
| 12 | 1052.9 | |
| 13 | 1140.7 | 27/14 |
| 14 | 28.4 | 81/80 |
| 15 | 116.2 | 15/14 |
| 16 | 203.9 | 9/8 |
| 17 | 291.7 | |
| 18 | 379.4 | 5/4 |
| 19 | 467.1 | 21/16 |
| 20 | 554.9 |
* in exact-3/2 tuning
