Tetrameantone
The tetrameantone temperament is a nonoctave meantone temperament, tempering out the 81/80 in the 4.3.5 subgroup and repeating at the double octave 4/1. It is generated by 4/3 and, like in normal meantone temperament, 4 of them make a 8/5 plus an octave.
Interval chain
| Generators | Cents (POTE) | Approximate ratios |
|---|---|---|
| -7 | 1273.671 | 25/12 |
| -6 | 1777.432 | 45/16 |
| -5 | 2281.193 | 15/4 |
| -4 | 384.955 | 5/4 |
| -3 | 888.716 | 5/3 |
| -2 | 1392.477 | 9/4, 20/9 |
| -1 | 1896.239 | 3/1 |
| 0 | 0.000 | 1/1 |
| 1 | 503.761 | 4/3 |
| 2 | 1007.523 | 16/9, 9/5 |
| 3 | 1511.284 | 12/5 |
| 4 | 2015.045 | 16/5 |
| 5 | 118.807 | 16/15 |
| 6 | 622.568 | 64/45 |
| 7 | 1126.329 | 48/25 |
Tetrameantone on tritave
Tritave-repeating tetrameantone (3.4.5 subgroup) is made by cutting off the 4/3 interval range of the tetratave scale. extension will start at 3.4.5.14 subgroup. If we want strict no-twos subgroup, will be 3.5.13.
| Generators | Cents (15edt) | Approximate ratios 3.4.5.14 | 3.5.13 |
|---|---|---|---|
| -7 | 253.594 | 7/6 | 15/13 |
| -6 | 760.782 | 25/16, 63/40, 14/9 | 125/81 |
| -5 | 1267.970 | 25/12, 21/10 | 27/13 |
| -4 | 1775.158 | 45/16, 14/5 | 25/9 |
| -3 | 380.391 | 5/4 | 81/65 |
| -2 | 887.579 | 27/16, 5/3 | 5/3 |
| -1 | 1394.767 | 9/4, 20/9 | 729/325 |
| 0 | 0.000 | 1/1 | 1/1 |
| 1 | 507.188 | 4/3, 27/20 | 325/243 |
| 2 | 1014.376 | 16/9, 9/5 | 9/5 |
| 3 | 1521.564 | 12/5 | 65/27 |
| 4 | 126.797 | 16/15, 15/14 | 27/25 |
| 5 | 633.985 | 36/25, 10/7 | 13/9 |
| 6 | 1141.173 | 48/25, 40/21, 27/14 | 243/125 |
| 7 | 1648.361 | 18/7 | 13/5 |
b15 & b4p
Subgroup: 3.5.13
Comma list: 531441/528125
Sval mapping: [⟨1 2 1], ⟨0 -2 5]]
Sval mapping generators: ~3, ~325/243
POTE generator: ~325/243 = 508.099
531441/528125
| Interval information |
531441/528125, the dinos comma, is a small 13-limit comma. It can be expressed as (9/5)/(325/243)2, (9/5)/(4/3)2/(325/324)2 and (81/80)/(325/324)2, among other expressions.
Temperaments
Tempering out this comma means equating a stack of two 325/243 (tridecimal marvelous fourth) with 9/5. This comma is tempered out in some 13-limit temperaments, e.g. flattone.
Etymology
The name "dinos" is proposed by Dummy index in 2024. It means: "miNOr Seventh is divided into 2 equal parts". The same argument holds for 3136/3125 = (9/5)/(75/56)2 (hemimean comma) and 589824/588245 = (9/5)/(343/256)^2 (hewuermera comma), but the comma is no-twos and requires only one additional prime base (3.5 for 9/5 and additional .13 for the comma).