User:Dummy index/Just odd intonation: Difference between revisions
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Tempering the P8 first. | |||
==JO meantone== | ==JO meantone== | ||
=== | Subgroup: 2.3.5 | ||
[[Comma list]]: 81/80 | |||
===eigenmonzos: 3/2, 5/4 "greedy"=== | |||
4*P5 = M3 + 2*P8 | 4*P5 = M3 + 2*P8 | ||
Octave stretch: +10.8 cents (1/2 of syntonic comma) | |||
{| class="wikitable" | {| class="wikitable" | ||
! Cents | ! Cents | ||
| Line 43: | Line 49: | ||
=== | ===eigenmonzos: 3/1, 5/1 "too meantone"=== | ||
4*P12 = M17 + | 4*P12 = M17 + 4*P8 | ||
Octave stretch: +5.4 cents (1/4 of syntonic comma) | |||
{| class="wikitable" | {| class="wikitable" | ||
! Cents | ! Cents | ||
| Line 84: | Line 92: | ||
=== | ===eigenmonzos: 3/1, 5/4 "just M3"=== | ||
4*P12 = M3 + 6*P8 | 4*P12 = M3 + 6*P8 | ||
Octave stretch: +3.6 cents (1/6 of syntonic comma) | |||
{| class="wikitable" | {| class="wikitable" | ||
! Cents | ! Cents | ||
| Line 124: | Line 134: | ||
|} | |} | ||
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/3eantone continuum]]. | |||
==JO schismatic== | ==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) | |||
Revision as of 15:33, 15 October 2021
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 "too meantone"
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 "just M3"
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/3eantone continuum.
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)