2.3.35 and 2.3.49 - Revision history

Hkm: whoops that isn’t a template

2026-03-20T00:05:13Z

whoops that isn’t a template

← Older revision		Revision as of 00:05, 20 March 2026
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	{{problematic~~}} {{delete~~}}		{{problematic}}

	'''2.3.35''' and '''2.3.49''' are two subsets of the 2.3.5.7 (septimal) group that involve many ratios further from 12edo than 2.3.7. The 35th harmonic (57) perfectly combines the deviations of the 5th and 7th harmonics to be about as far from 12edo as possible, whereas the 49th harmonic (77) overshoots slightly.		'''2.3.35''' and '''2.3.49''' are two subsets of the 2.3.5.7 (septimal) group that involve many ratios further from 12edo than 2.3.7. The 35th harmonic (57) perfectly combines the deviations of the 5th and 7th harmonics to be about as far from 12edo as possible, whereas the 49th harmonic (77) overshoots slightly.

2026-03-20T00:04:52Z

← Older revision		Revision as of 00:04, 20 March 2026
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	{{problematic}}		{{problematic}} {{delete}}

	'''2.3.35''' and '''2.3.49''' are two subsets of the 2.3.5.7 (septimal) group that involve many ratios further from 12edo than 2.3.7. The 35th harmonic (57) perfectly combines the deviations of the 5th and 7th harmonics to be about as far from 12edo as possible, whereas the 49th harmonic (77) overshoots slightly.		'''2.3.35''' and '''2.3.49''' are two subsets of the 2.3.5.7 (septimal) group that involve many ratios further from 12edo than 2.3.7. The 35th harmonic (57) perfectly combines the deviations of the 5th and 7th harmonics to be about as far from 12edo as possible, whereas the 49th harmonic (77) overshoots slightly.

2026-03-14T05:06:30Z

2.3.5.49

2025-12-13T17:49:01Z

← Older revision		Revision as of 17:49, 13 December 2025
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			{{problematic}}

	'''2.3.35''' and '''2.3.49''' are two subsets of the 2.3.5.7 (septimal) group that involve many ratios further from 12edo than 2.3.7. The 35th harmonic (57) perfectly combines the deviations of the 5th and 7th harmonics to be about as far from 12edo as possible, whereas the 49th harmonic (77) overshoots slightly.		'''2.3.35''' and '''2.3.49''' are two subsets of the 2.3.5.7 (septimal) group that involve many ratios further from 12edo than 2.3.7. The 35th harmonic (57) perfectly combines the deviations of the 5th and 7th harmonics to be about as far from 12edo as possible, whereas the 49th harmonic (77) overshoots slightly.

2025-12-04T17:06:15Z

← Older revision		Revision as of 17:06, 4 December 2025
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	81/70 septimal semifourth		81/70 septimal semifourth

	~~The~~ best ~~scales to use~~ 2.3.5.7 with significant emphasis on 35 is a [[Dimension\|rank-3 scale]] consisting of either [[List of regular temperaments\|Meantone or Archy]] diatonic with a 35/32 offset. One small edo to do something like this is 25, which uses the notes of 5edo to approximate Archy.		Some of the best 2.3.5.7 scales with significant emphasis on 35 are a [[Dimension\|rank-3 scale]] consisting of either [[List of regular temperaments\|Meantone or Archy]] diatonic with a 35/32 offset. One small edo to do something like this is 25, which uses the notes of 5edo to approximate Archy. Stacking two offsets to get 10L5s is particularly useful.

	===2.3.5.49===		===2.3.5.49===

2025-12-04T17:03:22Z

← Older revision		Revision as of 17:03, 4 December 2025
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	81/70 septimal semifourth		81/70 septimal semifourth

			The best scales to use 2.3.5.7 with significant emphasis on 35 is a [[Dimension\|rank-3 scale]] consisting of either [[List of regular temperaments\|Meantone or Archy]] diatonic with a 35/32 offset. One small edo to do something like this is 25, which uses the notes of 5edo to approximate Archy.

	===2.3.5.49===		===2.3.5.49===

2025-10-26T13:59:45Z

← Older revision		Revision as of 13:59, 26 October 2025
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	2/1		2/1

	~~RTT information:~~ Tempering out 245/243 equates the two smallest steps, leaving 5L2m8s. Tempering out 1029/1024 equates 256/147 to 7/4. Tempering out both commas leads to Rodan temperament (2.3.5.7 41 & 46), an extension of Slendric which also notably tempers out 5120/5103.		<adv>Tempering out 245/243 equates the two smallest steps, leaving 5L2m8s. Tempering out 1029/1024 equates 256/147 to 7/4. Tempering out both commas leads to Rodan temperament (2.3.5.7 41 & 46), an extension of Slendric which also notably tempers out 5120/5103.</adv>

	{\| class="wikitable"		{\| class="wikitable"

2025-10-26T13:18:19Z

← Older revision		Revision as of 13:18, 26 October 2025
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	2.3.35 intervals are the difference between a 5-over and 7-under interval, or vice versa.		2.3.35 intervals are the difference between a 5-over and 7-under interval, or vice versa.

	36/35 septimal quarter tone		36/35 septimal quarter tone (flat of 28/27 by 245/243)

	35/32 septimal neutral second		35/32 septimal neutral second
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	2/1		2/1

	Tempering out 245/243 equates the two smallest steps, leaving 5L2m8s. Tempering out 1029/1024 equates 256/147 to 7/4.		RTT information: Tempering out 245/243 equates the two smallest steps, leaving 5L2m8s. Tempering out 1029/1024 equates 256/147 to 7/4. Tempering out both commas leads to Rodan temperament (2.3.5.7 41 & 46), an extension of Slendric which also notably tempers out 5120/5103.

	{\| class="wikitable"		{\| class="wikitable"

2025-10-26T13:08:48Z

← Older revision		Revision as of 13:08, 26 October 2025
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	Tempering out 245/243 equates the two smallest steps, leaving 5L2m8s. Tempering out 1029/1024 equates 256/147 to 7/4.		Tempering out 245/243 equates the two smallest steps, leaving 5L2m8s. Tempering out 1029/1024 equates 256/147 to 7/4.

			{\| class="wikitable"
			\|+ Over-49 Chain
			\|-
			! 3^ !! /49 !! 245/243 !! 1029/1024
			\|-
			\| -1 \|\| 256/147 \|\| 1280/729 \|\| 7/4
			\|-
			\| 0 \|\| 64/49 \|\| 320/243 \|\| 21/16
			\|-
			\| 1 \|\| 96/49 \|\| 160/81 \|\| 63/32
			\|-
			\| 2 \|\| 72/49 \|\| 40/27 \|\| 189/128
			\|-
			\| 3 \|\| 54/49 \|\| 10/9 \|\| 567/512
			\|-
			\| 4 \|\| 81/49 \|\| 5/3 \|\| 1701/1024
			\|-
			\| 5 \|\| 243/196 \|\| 5/4 \|\| 5103/4096
			\|}

2025-10-26T12:58:53Z

← Older revision		Revision as of 12:58, 26 October 2025
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	49/40 neutral third		49/40 neutral third

			2.3.5.49 tripentatonic 5L2m5s3a (blackdye A Aeolian with added chain of 5/49 offset)

			81/80

			54/49

			9/8

			6/5

			64/49

			4/3

			27/20

			72/49

			3/2

			8/5

			256/147

			16/9

			9/5

			96/49

			2/1

			Tempering out 245/243 equates the two smallest steps, leaving 5L2m8s. Tempering out 1029/1024 equates 256/147 to 7/4.