Tetrahanson
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The tetrahanson 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. Tetrahanson 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 |