User:Dummy index/Just odd intonation: Difference between revisions

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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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Line 1: Line 1:
Widening or narrowing P8 first.
Tempering the P8 first.


==JO meantone==
==JO meantone==
===(3/2,5/4)===
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:




===(3/1,5/1)===
===eigenmonzos: 3/1, 5/1 "1/4-comma 3eantone"===
4*P12 = M17 + 2*P8
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)
|-
|-
| 1210.753
| 1205.377
| P8
| P8
| 2*(81/80)^(1/4)
| 2*(81/80)^(1/4)
Line 84: Line 92:




===(3/1,5/4)===
===eigenmonzos: 3/1, 5/4 "1/6-comma 3eantone"===
4*P12 = M3 + 6*P8
4*P12 = M3 + 6*P8


==JO 7-limit meantone==
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)

Latest revision as of 15:00, 21 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 "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)

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