User:Dummy index/Just odd intonation
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Tempering the P8 first.
JO meantone
Subgroup: 2.3.5
Comma list: 81/80
eigenmonzos: 3/2, 5/4 "greedy"
4*P5 = M3 + 2*P8
Octave stretch: +10.8 cents (1/2 of syntonic comma)
| Cents | Interval | Ratio |
|---|---|---|
| 0.0 | P1 | 1/1 |
| 193.157 | M2 | 9/8/(81/80)^(1/2) |
| 386.314 | M3 | 5/4 |
| 508.798 | P4 | 4/3*(81/80)^(1/2) |
| 701.955 | P5 | 3/2 |
| 895.112 | M6 | 5/3*(81/80)^(1/2) |
| 1088.269 | M7 | 15/8 |
| 1210.753 | P8 | 2*(81/80)^(1/2) |
eigenmonzos: 3/1, 5/1 "1/4-comma 3eantone"
4*P12 = M17 + 4*P8
Octave stretch: +5.4 cents (1/4 of syntonic comma)
| Cents | Interval | Ratio |
|---|---|---|
| 0.0 | P1 | 1/1 |
| 187.780 | M2 | 9/8/(81/80)^(3/4) |
| 375.561 | M3 | 5/4/(81/80)^(1/2) |
| 508.798 | P4 | 4/3*(81/80)^(1/2) |
| 696.578 | P5 | 3/2/(81/80)^(1/4) |
| 884.359 | M6 | 5/3 |
| 1072.139 | M7 | 15/8/(81/80)^(3/4) |
| 1205.377 | P8 | 2*(81/80)^(1/4) |
eigenmonzos: 3/1, 5/4 "1/6-comma 3eantone"
4*P12 = M3 + 6*P8
Octave stretch: +3.6 cents (1/6 of syntonic comma)
| Cents | Interval | Ratio |
|---|---|---|
| 0.0 | P1 | 1/1 |
| 193.157 | M2 | 9/8/(81/80)^(1/2) |
| 386.314 | M3 | 5/4 |
| 505.214 | P4 | 4/3*(81/80)^(1/3) |
| 698.371 | P5 | 3/2/(81/80)^(1/6) |
| 891.527 | M6 | 5/3*(81/80)^(1/3) |
| 1084.684 | M7 | 15/8/(81/80)^(1/6) |
| 1203.584 | P8 | 2*(81/80)^(1/6) |
In these, P8 and P5 are evenly tempered, because 3/1 is unchanged. This is also common in the EDT -EDO correspondences.
See also User:Dummy_index/2-dimensional tuning spectrum.
JO schismatic
Subgroup: 2.3.5
Comma list: 32805/32768
eigenmonzos: 3/2, 5/4
8*P5 + M3 = 5*P8
Octave stretch: +0.4 cents (1/5 of schisma)