34edf - Revision history

FloraC: /* Theory */ +subsets and supersets

2025-03-18T16:24:27Z

Theory: +subsets and supersets

← Older revision		Revision as of 16:24, 18 March 2025
Line 10:		Line 10:
	{{Harmonics in equal\|34\|3\|2\|intervals=integer}}		{{Harmonics in equal\|34\|3\|2\|intervals=integer}}
	{{Harmonics in equal\|34\|3\|2\|intervals=integer\|columns=12\|start=12\|collapsed=1\|title=Approximation of harmonics in 34edf (continued)}}		{{Harmonics in equal\|34\|3\|2\|intervals=integer\|columns=12\|start=12\|collapsed=1\|title=Approximation of harmonics in 34edf (continued)}}

			=== Subsets and supersets ===
			Since 34 factors into primes as {{nowrap\| 2 × 17 }}, 34edf contains [[2edf]] and [[17edf]] as subset edfs.

	== Intervals ==		== Intervals ==

FloraC: /* Intervals */ no need to assume octave equivalence here, so only keep the simpler ratios

2025-03-18T16:21:00Z

Intervals: no need to assume octave equivalence here, so only keep the simpler ratios

← Older revision		Revision as of 16:21, 18 March 2025
Line 24:		Line 24:
	\| 1		\| 1
	\| 20.6		\| 20.6
	\| 56/55, 64/63, 81/80, ~~''128~~/~~125''~~		\| ''56/55'', 64/63, 81/80, 91/90, 105/104
	\|-		\|-
	\| 2		\| 2
	\| 41.3		\| 41.3
	\| 36/35, 49/48, 50/49, 55/54		\| 36/35, 40/39, 45/44, 49/48, 50/49, 55/54
	\|-		\|-
	\| 3		\| 3
Line 84:		Line 84:
	\| 16		\| 16
	\| 330.3		\| 330.3
	\| 17/14		\| 17/14, 40/33
	\|-		\|-
	\| 17·		\| 17·
Line 92:		Line 92:
	\| 18		\| 18
	\| 371.6		\| 371.6
	\| 21/17		\| 21/17, 26/21
	\|-		\|-
	\| 19		\| 19
Line 180:		Line 180:
	\| 40		\| 40
	\| 825.8		\| 825.8
	\| 34/21		\| 21/13, 34/21
	\|-		\|-
	\| 41		\| 41
Line 188:		Line 188:
	\| 42		\| 42
	\| 867.1		\| 867.1
	\| 28/17		\| 28/17, 33/20
	\|-		\|-
	\| 43		\| 43
Line 212:		Line 212:
	\| 48		\| 48
	\| 991.0		\| 991.0
	\| 16/9~~, 30/17~~		\| 16/9
	\|-		\|-
	\| 49		\| 49
Line 224:		Line 224:
	\| 51		\| 51
	\| 1052.9		\| 1052.9
	\| 11/6~~, 24/13~~		\| 11/6
	\|-		\|-
	\| 52		\| 52
	\| 1073.6		\| 1073.6
	\| 13/7~~, 28/15~~		\| 13/7
	\|-		\|-
	\| 53		\| 53
	\| 1094.2		\| 1094.2
	\| 15/8, 17/9~~, 32/17~~		\| 15/8, 17/9
	\|-		\|-
	\| 54		\| 54
	\| 1114.9		\| 1114.9
	\| 21/11~~, 40/21, ''48/25''~~		\| 21/11
	\|-		\|-
	\| 55		\| 55
	\| 1135.5		\| 1135.5
	\| 25/13, 27/14~~, 52/27, 64/33~~		\| 25/13, 27/14
	\|-		\|-
	\| 56		\| 56
	\| 1156.2		\| 1156.2
	\| 35/18, 49/25, ~~96/~~49~~, 108~~/55		\| 35/18, 39/20, 49/25
	\|-		\|-
	\| 57		\| 57
	\| 1176.8		\| 1176.8
	\| 55/28, 63/32~~, ''125/64'', 160/81~~		\| 55/28, 63/32
	\|-		\|-
	\| 58		\| 58
Line 256:		Line 256:
	\| 59		\| 59
	\| 1218.1		\| 1218.1
	\| 81/40, ~~112~~/55, ~~128~~/~~63, ''256/125''~~		\| 81/40, 91/45, 105/52
	\|-		\|-
	\| 60		\| 60
	\| 1238.7		\| 1238.7
	\| 49/24~~, 72/35~~, 55/27~~, 100/49~~		\| 45/22, 49/24, 55/27
	\|-		\|-
	\| 61		\| 61
	\| 1259.4		\| 1259.4
	\| 27/13, 33/16~~, 52/25, 56/27~~		\| 27/13, 33/16
	\|-		\|-
	\| 62		\| 62
	\| 1280.0		\| 1280.0
	\| 21/10, 25/12~~, 44/21~~		\| 21/10, 25/12
	\|-		\|-
	\| 63		\| 63
	\| 1300.7		\| 1300.7
	\| 17/8~~, 32/15, 36/17~~		\| 17/8
	\|-		\|-
	\| 64		\| 64
	\| 1321.3		\| 1321.3
	\| 15/7~~, 28/13~~		\| 15/7
	\|-		\|-
	\| 65		\| 65
	\| 1342.0		\| 1342.0
	\| 13/6~~, 24/11~~		\| 13/6
	\|-		\|-
	\| 66		\| 66

FloraC: /* Intervals */ review

2025-03-18T16:00:06Z

Intervals: review

← Older revision		Revision as of 16:00, 18 March 2025
Line 24:		Line 24:
	\| 1		\| 1
	\| 20.6		\| 20.6
	\| 56/55, 64/63, 81/80, 128/125		\| 56/55, 64/63, 81/80, ''128/125''
	\|-		\|-
	\| 2		\| 2
Line 32:		Line 32:
	\| 3		\| 3
	\| 61.9		\| 61.9
	\| ~~25/24,~~ 26/25, 27/26, 28/27, 33/32		\| 26/25, 27/26, 28/27, 33/32
	\|-		\|-
	\| 4		\| 4
	\| 82.6		\| 82.6
	\| 21/20, 22/21		\| 21/20, 22/21, ''25/24''
	\|-		\|-
	\| 5		\| 5
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	\| 6		\| 6
	\| 123.9		\| 123.9
	\| 15/14~~, 14/13~~		\| 14/13, 15/14
	\|-		\|-
	\| 7·		\| 7·
Line 164:		Line 164:
	\| 36		\| 36
	\| 743.2		\| 743.2
	\| 20/13, 26/17~~, 17/11~~		\| 17/11, 20/13, 26/17
	\|-		\|-
	\| 37		\| 37
Line 196:		Line 196:
	\| 44		\| 44
	\| 908.4		\| 908.4
	\| 22/13~~, 17/10~~		\| 17/10, 22/13
	\|-		\|-
	\| 45		\| 45
Line 212:		Line 212:
	\| 48		\| 48
	\| 991.0		\| 991.0
	\| 16/9		\| 16/9, 30/17
	\|-		\|-
	\| 49		\| 49
Line 228:		Line 228:
	\| 52		\| 52
	\| 1073.6		\| 1073.6
	\| 28/15~~, 13/7~~		\| 13/7, 28/15
	\|-		\|-
	\| 53		\| 53
	\| 1094.2		\| 1094.2
	\| 15/8, 32/17~~, 17/9~~		\| 15/8, 17/9, 32/17
	\|-		\|-
	\| 54		\| 54
	\| 1114.9		\| 1114.9
	\| 40/21, 21/11		\| 21/11, 40/21, ''48/25''
	\|-		\|-
	\| 55		\| 55
	\| 1135.5		\| 1135.5
	\| 48/25, 25/13, 52/27~~, 27/14~~, 64/33		\| 25/13, 27/14, 52/27, 64/33
	\|-		\|-
	\| 56		\| 56
	\| 1156.2		\| 1156.2
	\| 35/18, 96/49~~, 49/25~~, 108/55		\| 35/18, 49/25, 96/49, 108/55
	\|-		\|-
	\| 57		\| 57
	\| 1176.8		\| 1176.8
	\| 55/28, 63/32, 160/81~~, 125/64~~		\| 55/28, 63/32, ''125/64'', 160/81
	\|-		\|-
	\| 58		\| 58
Line 256:		Line 256:
	\| 59		\| 59
	\| 1218.1		\| 1218.1
	\| 112/55, 128/63, ~~81/40,~~ 256/125		\| 81/40, 112/55, 128/63, ''256/125''
	\|-		\|-
	\| 60		\| 60
	\| 1238.7		\| 1238.7
	\| 72/35, 49/24, 100/49~~, 55/27~~		\| 49/24, 72/35, 55/27, 100/49
	\|-		\|-
	\| 61		\| 61
	\| 1259.4		\| 1259.4
	\| 25/12, 52/25~~, 27/13~~, 56/27~~, 33/16~~		\| 27/13, 33/16, 52/25, 56/27
	\|-		\|-
	\| 62		\| 62
	\| 1280.0		\| 1280.0
	\| 21/10, 44/21		\| 21/10, 25/12, 44/21
	\|-		\|-
	\| 63		\| 63
	\| 1300.7		\| 1300.7
	\| 32/15~~, 17/8~~, 36/17		\| 17/8, 32/15, 36/17
	\|-		\|-
	\| 64		\| 64
Line 280:		Line 280:
	\| 65		\| 65
	\| 1342.0		\| 1342.0
	\| 24/11~~, 13/5~~		\| 13/6, 24/11
	\|-		\|-
	\| 66		\| 66
	\| 1362.6		\| 1362.6
	\| 11/10		\| 11/5
	\|-		\|-
	\| 67		\| 67

FloraC: Rework

2025-03-18T15:53:16Z

Rework

Show changes

BudjarnLambeth: Same as 35edf

2024-12-18T07:45:43Z

Same as 35edf

← Older revision		Revision as of 07:45, 18 December 2024
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	'''[[EDF\|Division of the just perfect fifth]] into 34 equal parts''' (34EDF) is related to [[58edo~~\|58 edo~~]], but with the 3/2 rather than the 2/1 being just. The octave is about 2.5474 cents ~~compressed~~ and the step size is about 20.6457 cents (corresponding to 58.1234 edo). The patent val has a generally flat tendency for ~~harmonics~~ up to 16, with the exception for 5. Unlike 58edo, it is only consistent up to the [[~~15-odd-limit\|15-~~integer-limit]], with discrepancy for the 16th harmonic (four octaves).		'''[[EDF\|Division of the just perfect fifth]] into 34 equal parts''' (34EDF) is related to [[58edo]], but with the [[3/2]] rather than the [[2/1]] being [[just]]. The [[octave]] is [[Octave shrinking\|compressed]] by about 2.5474 [[cents]] and the step size is about 20.6457 cents (corresponding to 58.1234 edo).

			The [[patent val]] has a generally flat tendency for [[harmonic]]s up to 16, with the exception for 5. Unlike 58edo, it is only consistent up to the 15-[[integer-limit]], with discrepancy for the 16th harmonic (four octaves).

	Lookalikes: [[58edo]], [[92edt]]		Lookalikes: [[58edo]], [[92edt]]

			==Harmonics==
			{{Harmonics in equal\|34\|3\|2\|intervals=prime}}
			{{Harmonics in equal\|34\|3\|2\|intervals=prime\|start=12\|collapsed=1}}

	==Intervals==		==Intervals==
	{\| class="wikitable"		{\| class="wikitable mw-collapsible"
			\|+ Intervals of 34edf
	\|-		\|-
	! \|Degree		! \|Degree
Line 11:		Line 19:
	\|-		\|-
	\| colspan="2" style="text-align:center;" \|0		\| colspan="2" style="text-align:center;" \|0
	\| style="text-align:~~center~~;" \|1/1		\| style="text-align:left;" \|1/1
	\|-		\|-
	\|1		\|1
Line 285:		Line 293:
	\|9/4		\|9/4
	\|}		\|}

			{{todo\|expand}}
	[[Category:Edf]]		[[Category:Edf]]
	[[Category:Edonoi]]		[[Category:Edonoi]]

Plumtree: Infobox ET added

2022-10-05T18:42:29Z

Infobox ET added

← Older revision		Revision as of 18:42, 5 October 2022
Line 1:		Line 1:
			{{Infobox ET}}
	'''[[EDF\|Division of the just perfect fifth]] into 34 equal parts''' (34EDF) is related to [[58edo\|58 edo]], but with the 3/2 rather than the 2/1 being just. The octave is about 2.5474 cents compressed and the step size is about 20.6457 cents (corresponding to 58.1234 edo). The patent val has a generally flat tendency for harmonics up to 16, with the exception for 5. Unlike 58edo, it is only consistent up to the [[15-odd-limit\|15-integer-limit]], with discrepancy for the 16th harmonic (four octaves).		'''[[EDF\|Division of the just perfect fifth]] into 34 equal parts''' (34EDF) is related to [[58edo\|58 edo]], but with the 3/2 rather than the 2/1 being just. The octave is about 2.5474 cents compressed and the step size is about 20.6457 cents (corresponding to 58.1234 edo). The patent val has a generally flat tendency for harmonics up to 16, with the exception for 5. Unlike 58edo, it is only consistent up to the [[15-odd-limit\|15-integer-limit]], with discrepancy for the 16th harmonic (four octaves).

Moremajorthanmajor at 06:20, 19 June 2021

2021-06-19T06:20:08Z

Show changes

Moremajorthanmajor at 22:40, 19 August 2019

2019-08-19T22:40:42Z

← Older revision		Revision as of 22:40, 19 August 2019
Line 9:		Line 9:
	! \|Approx. ratios		! \|Approx. ratios
	\|-		\|-
	\| ~~style~~="~~text-align:center;~~" \|0		\| colspan="2" style="text-align:center;" \|0
	\| style="text-align:center;" \|0
	\| style="text-align:center;" \|1/1		\| style="text-align:center;" \|1/1
	\|-		\|-

Moremajorthanmajor at 16:23, 9 March 2019

2019-03-09T16:23:37Z

← Older revision		Revision as of 16:23, 9 March 2019
Line 283:		Line 283:
	\|68		\|68
	\|1403.91		\|1403.91
	\|9/8		\|9/4
	\|}		\|}
	[[Category:Edf]]		[[Category:Edf]]
	[[Category:Edonoi]]		[[Category:Edonoi]]

Moremajorthanmajor at 15:58, 9 March 2019

2019-03-09T15:58:41Z

@@ Line 244: / Line 244: @@
 | style="text-align:center;" |1197.45265
 | style="text-align:center;" |2/1
 |}
 [[Category:Edf]]
 [[Category:Edonoi]]