124ed8 - Revision history

Overthink: cleanup

2026-01-27T04:09:46Z

cleanup

← Older revision		Revision as of 04:09, 27 January 2026
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	{{Infobox ET}} 124 equal divisions of the 8th harmonic (abbreviated 124ed8), is the tuning system that divides the 8th harmonic into 124 equal parts of about 29.03226 ¢ each. Each step represents a frequency ratio of <math>8^{~~\frac~~{~~1}{124~~}}~~</math>, or the 124th root of 8.~~		{{Infobox ET}}
			{{ED intro}}

	== ~~Context~~ ==		== Theory ==

	124ed8 is an alternative version of [[143ed11]], ~~the best~~ 5.7~~.8.9~~.11.13.17.23 equal step tuning ~~in the world~~. 124ed8 is for people who absolutely need a locked pure [[8/1]] when using some software or hardware. As a trade-off, 124ed8 has a slightly sharp tendency above the optimal ~~5.7.8.9.11.13.17.23~~ tuning. Comparared to [[143ed11]], 124ed8 stretches the 11th harmonic by about 0.295 ¢ and the mapping of the 8th harmonic (now pure) by about 0.256 ¢.		124ed8 is an alternative version of [[143ed11]], which is a strong 8.9.5.7.11.13.17.23 subgroup equal step tuning. 124ed8 is for people who absolutely need a locked pure [[8/1]] when using some software or hardware. As a trade-off, 124ed8 has a slightly sharp tendency above the optimal tuning for the subgroup. Comparared to [[143ed11]], 124ed8 stretches the 11th harmonic by about 0.295 ¢ and the mapping of the 8th harmonic (now pure) by about 0.256 ¢.

			{{Harmonics in equal\|124\|8\|columns=11}}
			{{Harmonics in equal\|124\|8\|columns=11\|start=12}}

	== Intervals and approximation to JI ==		== Intervals and approximation to JI ==
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	! 124ed8<br>degree		! 124ed8<br>degree
	! Cents		! Cents
	! Ratios in the<br>5.7~~.8.9~~.11.13.17.23<br>subgroup		! Ratios in the<br>8.9.5.7.11.13.17.23<br>subgroup
	! Error (abs, [[Cent\|¢]])		! Error (abs, [[Cent\|¢]])
	! Error (rel, [[Relative cent\|%]])		! Error (rel, [[Relative cent\|%]])

BudjarnLambeth: Uncategorised page

2025-12-28T00:16:29Z

Uncategorised page

← Older revision		Revision as of 00:16, 28 December 2025
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	124 equal divisions of the 8th harmonic (abbreviated 124ed8), is the tuning system that divides the 8th harmonic into 124 equal parts of about 29.03226 ¢ each. Each step represents a frequency ratio of <math>8^{\frac{1}{124}}</math>, or the 124th root of 8.		{{Infobox ET}} 124 equal divisions of the 8th harmonic (abbreviated 124ed8), is the tuning system that divides the 8th harmonic into 124 equal parts of about 29.03226 ¢ each. Each step represents a frequency ratio of <math>8^{\frac{1}{124}}</math>, or the 124th root of 8.

	== Context ==		== Context ==

Contribution at 02:37, 28 October 2025

2025-10-28T02:37:09Z

← Older revision		Revision as of 02:37, 28 October 2025
Line 3:		Line 3:
	== Context ==		== Context ==

	124ed8 is an alternative version of [[143ed11]], the best 5.7.8.9.11.13.17.23 equal step tuning in the world. 124ed8 is for people who absolutely need a locked pure [[8/1]] when using some software or hardware. As a trade-off, 124ed8 has a slightly sharp tendency above the optimal ~~[[143ed11]]~~ 5.7.8.9.11.13.17.23 tuning. Comparared to [[143ed11]], 124ed8 stretches the 11th harmonic by about 0.295 ¢ and the mapping of the 8th harmonic (now pure) by about 0.256 ¢.		124ed8 is an alternative version of [[143ed11]], the best 5.7.8.9.11.13.17.23 equal step tuning in the world. 124ed8 is for people who absolutely need a locked pure [[8/1]] when using some software or hardware. As a trade-off, 124ed8 has a slightly sharp tendency above the optimal 5.7.8.9.11.13.17.23 tuning. Comparared to [[143ed11]], 124ed8 stretches the 11th harmonic by about 0.295 ¢ and the mapping of the 8th harmonic (now pure) by about 0.256 ¢.

	== Intervals and approximation to JI ==		== Intervals and approximation to JI ==

Contribution at 01:31, 28 October 2025

2025-10-28T01:31:04Z

← Older revision		Revision as of 01:31, 28 October 2025
Line 3:		Line 3:
	== Context ==		== Context ==

	124ed8 is an alternative version of [[143ed11]], the best 5.7.8.9.11.13.17.23 equal step tuning in the world, for ~~those~~ who absolutely need a locked pure [[8/1]] when using some software or hardware. 124ed8 ~~now have~~ a slightly sharp tendency above the optimal 5.7.8.9.11.13.17.23 tuning. Comparared to [[143ed11]], 124ed8 stretches the 11th harmonic by about 0.295 ¢ and the mapping of the 8th harmonic (now pure) by about 0.256 ¢.		124ed8 is an alternative version of [[143ed11]], the best 5.7.8.9.11.13.17.23 equal step tuning in the world. 124ed8 is for people who absolutely need a locked pure [[8/1]] when using some software or hardware. As a trade-off, 124ed8 has a slightly sharp tendency above the optimal [[143ed11]] 5.7.8.9.11.13.17.23 tuning. Comparared to [[143ed11]], 124ed8 stretches the 11th harmonic by about 0.295 ¢ and the mapping of the 8th harmonic (now pure) by about 0.256 ¢.

	== Intervals and approximation to JI ==		== Intervals and approximation to JI ==

BudjarnLambeth: /* Context */ professional tone

2025-10-28T01:23:32Z

Context: professional tone

← Older revision		Revision as of 01:23, 28 October 2025
Line 3:		Line 3:
	== Context ==		== Context ==

	124ed8 is an alternative version of [[143ed11]], the ~~bestest~~ 5.7.8.9.11.13.17.23 equal step tuning in the world, for those who absolutely need a locked pure [[8/1]] when using some software or hardware. 124ed8 now have a slightly sharp tendency above the optimal 5.7.8.9.11.13.17.23 tuning. Comparared to [[143ed11]], 124ed8 stretches the 11th harmonic by about 0.295 ¢ and the mapping of the 8th harmonic (now pure) by about 0.256 ¢.		124ed8 is an alternative version of [[143ed11]], the best 5.7.8.9.11.13.17.23 equal step tuning in the world, for those who absolutely need a locked pure [[8/1]] when using some software or hardware. 124ed8 now have a slightly sharp tendency above the optimal 5.7.8.9.11.13.17.23 tuning. Comparared to [[143ed11]], 124ed8 stretches the 11th harmonic by about 0.295 ¢ and the mapping of the 8th harmonic (now pure) by about 0.256 ¢.

	== Intervals and approximation to JI ==		== Intervals and approximation to JI ==

Contribution: Created page with "124 equal divisions of the 8th harmonic (abbreviated 124ed8), is the tuning system that divides the 8th harmonic into 124 equal parts of about 29.03226 ¢ each. Each step represents a frequency ratio of $8^{\frac{1}{124}}$ , or the 124th root of 8. == Context == 124ed8 is an alternative version of 143ed11, the bestest 5.7.8.9.11.13.17.23 equal step tuning in the world, for those who absolutely need a locked pure 8/1 when using some software or hardw..."

2025-10-27T17:33:36Z

Created page with "124 equal divisions of the 8th harmonic (abbreviated 124ed8), is the tuning system that divides the 8th harmonic into 124 equal parts of about 29.03226 ¢ each. Each step represents a frequency ratio of <math>8^{\frac{1}{124}}</math>, or the 124th root of 8. == Context == 124ed8 is an alternative version of 143ed11, the bestest 5.7.8.9.11.13.17.23 equal step tuning in the world, for those who absolutely need a locked pure 8/1 when using some software or hardw..."

New page

124 equal divisions of the 8th harmonic (abbreviated 124ed8), is the tuning system that divides the 8th harmonic into 124 equal parts of about 29.03226 ¢ each. Each step represents a frequency ratio of <math>8^{\frac{1}{124}}</math>, or the 124th root of 8.

== Context ==

124ed8 is an alternative version of [[143ed11]], the bestest 5.7.8.9.11.13.17.23 equal step tuning in the world, for those who absolutely need a locked pure [[8/1]] when using some software or hardware. 124ed8 now have a slightly sharp tendency above the optimal 5.7.8.9.11.13.17.23 tuning. Comparared to [[143ed11]], 124ed8 stretches the 11th harmonic by about 0.295 ¢ and the mapping of the 8th harmonic (now pure) by about 0.256 ¢.

== Intervals and approximation to JI ==

{| class="wikitable sortable center-all right-2 left-3"
|-
! 124ed8<br>degree
! Cents
! Ratios in the<br>5.7.8.9.11.13.17.23<br>subgroup
! Error (abs, [[Cent|¢]])
! Error (rel, [[Relative cent|%]])
|-
| 5
| 145.2
| [[25/23]]
| 0.808
| 2.8
|-
| 7
| 203.2
| [[9/8]]
| -0.684
| -2.4
|-
| 8
| 232.3
| [[8/7]]
| 1.084
| 3.7
|-
| 10
| 290.3
| [[13/11]]
| 1.113
| 3.8
|-
| 12
| 348.4
| [[11/9]]
| 0.979
| 3.4
|-
| 15
| 435.5
| [[9/7]]
| 0.4
| 1.4
|-
| 16
| 464.5
| [[17/13]]
| 0.088
| 0.3
|-
| 18
| 522.6
| [[23/17]]
| -0.738
| -2.5
|-
| 19
| 551.6
| [[11/8]]
| 0.295
| 1.0
|-
| 20
| 580.6
| [[7/5]]
| -1.867
| -6.4
|-
| 22
| 638.7
| [[13/9]]
| 2.092
| 7.2
|-
| 23
| 667.7
| [[25/17]]
| 0.07
| 0.2
|-
| 26
| 754.8
| [[17/11]]
| 1.201
| 4.1
|-
| 27
| 783.9
| [[11/7]]
| 1.379
| 4.7
|-
| 28
| 812.9
| [[8/5]]
| -0.783
| -2.7
|-
| 29
| 841.9
| [[13/8]]
| 1.408
| 4.8
|-
| 34
| 987.1
| [[23/13]]
| -0.65
| -2.2
|-
| 35
| 1016.1
| [[9/5]]
| -1.467
| -5.1
|-
| 37
| 1074.2
| [[13/7]]
| 2.492
| 8.6
|-
| 38
| 1103.2
| [[17/9]]
| 2.18
| 7.5
|-
| 39
| 1132.3
| [[25/13]]
| 0.158
| 0.5
|-
| 44
| 1277.4
| [[23/11]]
| 0.463
| 1.6
|-
| 45
| 1306.5
| [[17/8]]
| 1.496
| 5.2
|-
| 47
| 1364.5
| [[11/5]]
| -0.488
| -1.7
|-
| 49
| 1422.6
| [[25/11]]
| 1.271
| 4.4
|-
| 53
| 1538.7
| [[17/7]]
| 2.58
| 8.9
|-
| 56
| 1625.8
| [[23/9]]
| 1.442
| 5.0
|-
| 57
| 1654.8
| [[13/5]]
| 0.625
| 2.2
|-
| 61
| 1771.0
| [[25/9]]
| 2.25
| 7.8
|-
| 63
| 1829.0
| [[23/8]]
| 0.758
| 2.6
|-
| 68
| 1974.2
| [[25/8]]
| 1.566
| 5.4
|-
| 71
| 2061.3
| [[23/7]]
| 1.842
| 6.3
|-
| 73
| 2119.4
| [[17/5]]
| 0.713
| 2.5
|-
| 76
| 2206.5
| [[25/7]]
| 2.65
| 9.1
|-
| 91
| 2641.9
| [[23/5]]
| -0.025
| -0.1
|-
| 96
| 2787.1
| [[5/1]]
| 0.783
| 2.7
|-
| 116
| 3367.7
| [[7/1]]
| -1.084
| -3.7
|-
| 124
| 3600.0
| [[8/1]]
| 0.0
| 0.0
|-
| 131
| 3803.2
| [[9/1]]
| -0.684
| -2.4
|-
| 143
| 4151.6
| [[11/1]]
| 0.295
| 1.0
|-
| 153
| 4441.9
| [[13/1]]
| 1.408
| 4.8
|-
| 169
| 4906.5
| [[17/1]]
| 1.496
| 5.2
|-
| 187
| 5429.0
| [[23/1]]
| 0.758
| 2.6
|-
| 192
| 5574.2
| [[25/1]]
| 1.566
| 5.4
|}