User:Dummy index/Just odd intonation - Revision history

Dummy index at 15:00, 21 October 2021

2021-10-21T15:00:40Z

← Older revision		Revision as of 15:00, 21 October 2021
Line 49:		Line 49:


	===eigenmonzos: 3/1, 5/1 "~~too meantone~~"===		===eigenmonzos: 3/1, 5/1 "1/4-comma 3eantone"===
	4P12 = M17 + 4P8		4P12 = M17 + 4P8

Line 92:		Line 92:


	===eigenmonzos: 3/1, 5/4 "~~just M3~~"===		===eigenmonzos: 3/1, 5/4 "1/6-comma 3eantone"===
	4P12 = M3 + 6P8		4P12 = M3 + 6P8

Line 136:		Line 136:
	In these, P8 and P5 are evenly tempered, because 3/1 is unchanged. This is also common in the [[EDT]] -EDO correspondences.		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~~]].		See also [[User:Dummy_index/2-dimensional tuning spectrum]].

	==JO schismatic==		==JO schismatic==

Dummy index at 15:33, 15 October 2021

2021-10-15T15:33:11Z

← Older revision		Revision as of 15:33, 15 October 2021
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"===
	4P5 = M3 + 2P8		4P5 = M3 + 2P8

			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 "too meantone"===
	4P12 = M17 + 2P8		4P12 = M17 + 4P8

			Octave stretch: +5.4 cents (1/4 of syntonic comma)
	{\| class="wikitable"		{\| class="wikitable"
	! Cents		! Cents
Line 84:		Line 92:


	===(3/1,5/4)===		===eigenmonzos: 3/1, 5/4 "just M3"===
	4P12 = M3 + 6P8		4P12 = M3 + 6P8

			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.

	~~==JO 7-limit meantone==~~		See also [[User:Dummy_index/3eantone continuum]].

	==JO schismatic==		==JO schismatic==
			Subgroup: 2.3.5

			[[Comma list]]: 32805/32768

			eigenmonzos: 3/2, 5/4

			8P5 + M3 = 5P8

			Octave stretch: +0.4 cents (1/5 of schisma)

Dummy index at 14:57, 13 October 2021

2021-10-13T14:57:02Z

@@ Line 78: / Line 78: @@
 | 15/8/(81/80)^(3/4)
 |-
-| 1210.753
+| 1205.377
 | P8
 | 2*(81/80)^(1/4)
@@ Line 86: / Line 86: @@
 ===(3/1,5/4)===
 *P12 = M3 + 6*P8
 ==JO 7-limit meantone==
 ==JO schismatic==

Dummy index: Created page with "Widening or narrowing P8 first. ==JO meantone== ===(3/2,5/4)=== 4P5 = M3 + 2P8 {| class="wikitable" ! Cents ! Interval ! Ratio |- | 0.0 | P1 | 1/1 |- | 193.157 | M2 | 9/8/(..."

2021-10-13T14:30:33Z

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/(..."

New page

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/(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)
|}

===(3/1,5/1)===
4*P12 = M17 + 2*P8
{| class="wikitable"
! 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)
|-
| 1210.753
| P8
| 2*(81/80)^(1/4)
|}

===(3/1,5/4)===
4*P12 = M3 + 6*P8

==JO 7-limit meantone==

==JO schismatic==

User:Dummy index/Just odd intonation - Revision history

Dummy index at 15:00, 21 October 2021

Dummy index at 15:33, 15 October 2021

Dummy index at 14:57, 13 October 2021

Dummy index: 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/(..."

Dummy index: Created page with "Widening or narrowing P8 first. ==JO meantone== ===(3/2,5/4)=== 4P5 = M3 + 2P8 {| class="wikitable" ! Cents ! Interval ! Ratio |- | 0.0 | P1 | 1/1 |- | 193.157 | M2 | 9/8/(..."