Tetrahanson: Difference between revisions
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CompactStar (talk | contribs) Created page with "The '''tetrakleismic''' temperament is a nonoctave kleismic temperament, tempering out the kleisma in the 4.3.5 subgroup and repeating at the double octave 4/1..." |
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! Cents (CTE) | ! Cents (CTE) | ||
! Approximate ratios | ! Approximate ratios | ||
|- | |||
| -7 | |||
| 1019.413 | |||
| [[9/5]] | |||
|- | |||
| -6 | |||
| 1902.354 | |||
| [[3/1]] | |||
|- | |- | ||
| -5 | | -5 | ||
| Line 49: | Line 57: | ||
| 2014.705 | | 2014.705 | ||
| [[16/5]] | | [[16/5]] | ||
|- | |||
| 6 | |||
| 497.646 | |||
| [[4/3]] | |||
|- | |||
| 7 | |||
| 1380.587 | |||
| 20/9 | |||
|} | |} | ||
Revision as of 21:22, 20 July 2023
The tetrakleismic temperament is a nonoctave kleismic temperament, tempering out the kleisma in the 4.3.5 subgroup and repeating at the double octave 4/1. It is generated by 5/3 and, like in normal hanson temperament, 6 of them make a 4/3. Tetrakleismic does not contain any 5-limit major or minor triads, but it does have different voicings of them (3:4:5 and 12:15:20), which, to a 12edo-accustomed listener, can make it sound like the root is the real root and the perfect fifth above it at the same time.
Interval chain
| Generators | Cents (CTE) | Approximate ratios |
|---|---|---|
| -7 | 1019.413 | 9/5 |
| -6 | 1902.354 | 3/1 |
| -5 | 385.295 | 5/4 |
| -4 | 1268.236 | 25/12 |
| -3 | 2151.177 | 125/36 |
| -2 | 634.118 | 36/25 |
| -1 | 1517.059 | 12/5 |
| 0 | 0.000 | 1/1 |
| 1 | 882.941 | 5/3 |
| 2 | 1765.882 | 25/9 |
| 3 | 248.823 | 144/125 |
| 4 | 1131.764 | 48/25 |
| 5 | 2014.705 | 16/5 |
| 6 | 497.646 | 4/3 |
| 7 | 1380.587 | 20/9 |