User:Dummy index/Just odd intonation: Difference between revisions
Dummy index (talk | contribs) Created page with "Widening or narrowing P8 first. ==JO meantone== ===(3/2,5/4)=== 4*P5 = M3 + 2*P8 {| class="wikitable" ! Cents ! Interval ! Ratio |- | 0.0 | P1 | 1/1 |- | 193.157 | M2 | 9/8/(..." |
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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 "1/4-comma 3eantone"=== | ||
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 78: | Line 86: | ||
| 15/8/(81/80)^(3/4) | | 15/8/(81/80)^(3/4) | ||
|- | |- | ||
| | | 1205.377 | ||
| P8 | | P8 | ||
| 2*(81/80)^(1/4) | | 2*(81/80)^(1/4) | ||
| Line 84: | Line 92: | ||
=== | ===eigenmonzos: 3/1, 5/4 "1/6-comma 3eantone"=== | ||
4*P12 = M3 + 6*P8 | 4*P12 = M3 + 6*P8 | ||
= | Octave stretch: +3.6 cents (1/6 of syntonic comma) | ||
{| class="wikitable" | |||
! 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== | ==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) | |||