10ed7/3 - Revision history

FloraC: Table of harmonics

2026-05-14T18:12:37Z

Table of harmonics

← Older revision		Revision as of 18:12, 14 May 2026
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	== Theory ==		== Theory ==
	10ed7/3 is essentially a tritave stretch of [[13edt]], the equalized [[~~Bohlen-Pierce~~]] scale, and as a result tempers out [[245/243]] and [[3125/3087]] in the [[3.5.7 subgroup]], as well as [[529/525]] and [[1127/1125]] when prime 23 is introduced. It fails to represent any other primes of note within 20 cents. Making this stretch makes [[5/1]] and [[23/1]] closer to just compared to 13edt, while both [[3/1]] and [[7/1]] are about 5 [[cents]] sharp of just.		10ed7/3 is essentially a tritave stretch of [[13edt]], the equalized [[Bohlen–Pierce]] scale, and as a result tempers out [[245/243]] and [[3125/3087]] in the [[3.5.7 subgroup]], as well as [[529/525]] and [[1127/1125]] when prime 23 is introduced. It fails to represent any other primes of note within 20 cents. Making this stretch makes [[5/1]] and [[23/1]] closer to just compared to 13edt, while both [[3/1]] and [[7/1]] are about 5 [[cents]] sharp of just.

	=== Harmonics ===		=== Harmonics ===
	{{Harmonics in equal		{{Harmonics in equal\|10\|7\|3\|columns=11}}
	\| ~~steps =~~ 10		{{Harmonics in equal\|10\|7\|3\|columns=12\|start=12\|collapsed=1\|title=Approximation of harmonics in 10ed7/3 (continued)}}
	\| ~~num =~~ 7
	\| ~~denom~~ = 3
	}}
	{{Harmonics in equal
	\| ~~steps =~~ 10
	\| ~~num =~~ 7
	\| ~~denom~~ = 3
	\| start = 12
	\| collapsed = 1
	}}

	== Intervals ==		== Intervals ==
	{{Interval table}}		{{Interval table}}

Lériendil: don't need all those exo-commas

2025-08-07T12:51:47Z

don't need all those exo-commas

← Older revision		Revision as of 12:51, 7 August 2025
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	{{ED intro}}		{{ED intro}}

	== Theory==		== Theory ==
	~~This tuning tempers out [[16~~/~~15]] in the~~ [[~~5-limit]]; [[28/27~~]], ~~[[50/49]], and [[36/35]] in~~ the [[7-~~limit]]; [[22/21]], [[56/55~~]]~~, 77/75~~, and [[55/54]] ~~in the [[11-limit]]; [[26/25]], [[52/49]], 65/63, [[66/65\|66/65,]] [[78/77]],~~ and [[40/39]] in the [[~~13-limit]]; [[34/33]], 51/49, [[52/51~~]], ~~75/68, 77/68, and 51/50 in the [[17-limit]];~~ [[20/19]]~~, [[64/57]], [[76/75]], [[77/76]],~~ and [[39/38]] ~~in the [[19-limit]]; [[24/~~23~~]],~~ [[70/~~69\|70/69,~~]] and ~~[[46/45]] in the~~ [[23~~-limit]]; [[30/29]], 58/57, and [[32/29]] in the [[29-limit]]; 33/31, [[63~~/62]], ~~65/62, and 34/31 in the~~ [[~~31-limit]]; 38~~/~~37, 39/37, 75/74, 77/74, and 40/37 in the [[37-limit]]; [[42/41~~]] and ~~44/41 in the~~ [[~~41-limit]]; 43/42, 43~~/~~41, and 44/43 in the [[43-limit~~]]~~; [[47/46]], [[48/47]], and 47/45 in the [[47-limit]]; 54/53, 56/53, and 55/53 in the [[53-limit]]; 59/58, 60/59, [[64/59]], and 59/57 in the [~~[~~59-limit]]; 62/61,~~ [[65/61]], 66/61, and 63/61 in the [[61-limit]]; 69/67, 72/67, and 70/67 in the [[67-limit]]; [[71/67]], 71/69, 72/71, and [[71/70]] in the [[71-limit]]; 73/68, 75/73, 76/73, 77/73, 78/73; and 74/73 in the [[73-limit]]; and 81/79 in the [[79-limit]].		10ed7/3 is essentially a tritave stretch of [[13edt]], the equalized [[Bohlen-Pierce]] scale, and as a result tempers out [[245/243]] and [[3125/3087]] in the [[3.5.7 subgroup]], as well as [[529/525]] and [[1127/1125]] when prime 23 is introduced. It fails to represent any other primes of note within 20 cents. Making this stretch makes [[5/1]] and [[23/1]] closer to just compared to 13edt, while both [[3/1]] and [[7/1]] are about 5 [[cents]] sharp of just.

	==~~Intervals==~~		=== Harmonics ===
	~~{{Interval table}}~~

	==~~Harmonics~~==
	{{Harmonics in equal		{{Harmonics in equal
	\| steps = 10		\| steps = 10
	\| num = 7		\| num = 7
	\| denom = 3		\| denom = 3
	~~\| intervals = prime~~
	}}		}}
	{{Harmonics in equal		{{Harmonics in equal
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	\| start = 12		\| start = 12
	\| collapsed = 1		\| collapsed = 1
	~~\| intervals = prime~~
	}}		}}

			== Intervals ==
			{{Interval table}}

MisterShafXen at 17:42, 17 January 2025

2025-01-17T17:42:46Z

← Older revision		Revision as of 17:42, 17 January 2025
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	~~{{Stub}}~~
	{{Infobox ET}}		{{Infobox ET}}
	{{ED intro}}		{{ED intro}}

	== Intervals ==		== Theory==
			This tuning tempers out [[16/15]] in the [[5-limit]]; [[28/27]], [[50/49]], and [[36/35]] in the [[7-limit]]; [[22/21]], [[56/55]], 77/75, and [[55/54]] in the [[11-limit]]; [[26/25]], [[52/49]], 65/63, [[66/65\|66/65,]] [[78/77]], and [[40/39]] in the [[13-limit]]; [[34/33]], 51/49, [[52/51]], 75/68, 77/68, and 51/50 in the [[17-limit]]; [[20/19]], [[64/57]], [[76/75]], [[77/76]], and [[39/38]] in the [[19-limit]]; [[24/23]], [[70/69\|70/69,]] and [[46/45]] in the [[23-limit]]; [[30/29]], 58/57, and [[32/29]] in the [[29-limit]]; 33/31, [[63/62]], 65/62, and 34/31 in the [[31-limit]]; 38/37, 39/37, 75/74, 77/74, and 40/37 in the [[37-limit]]; [[42/41]] and 44/41 in the [[41-limit]]; 43/42, 43/41, and 44/43 in the [[43-limit]]; [[47/46]], [[48/47]], and 47/45 in the [[47-limit]]; 54/53, 56/53, and 55/53 in the [[53-limit]]; 59/58, 60/59, [[64/59]], and 59/57 in the [[59-limit]]; 62/61, [[65/61]], 66/61, and 63/61 in the [[61-limit]]; 69/67, 72/67, and 70/67 in the [[67-limit]]; [[71/67]], 71/69, 72/71, and [[71/70]] in the [[71-limit]]; 73/68, 75/73, 76/73, 77/73, 78/73; and 74/73 in the [[73-limit]]; and 81/79 in the [[79-limit]].

			==Intervals==
	{{Interval table}}		{{Interval table}}

	== Harmonics ==		==Harmonics==
	{{Harmonics in equal		{{Harmonics in equal
	\| steps = 10		\| steps = 10

MisterShafXen: /* Harmonics */

2025-01-17T16:16:07Z

Harmonics

← Older revision		Revision as of 16:16, 17 January 2025
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	\| num = 7		\| num = 7
	\| denom = 3		\| denom = 3
			\| intervals = prime
	}}		}}
	{{Harmonics in equal		{{Harmonics in equal
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	\| start = 12		\| start = 12
	\| collapsed = 1		\| collapsed = 1
			\| intervals = prime
	}}		}}

BudjarnLambeth: Intro intervals harmonics

2024-10-05T03:22:09Z

Intro intervals harmonics

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 {{Stub}}
 {{Infobox ET}}
-{{Harmonics in equal|10|7|3|prec=2|columns=15}}
+== Intervals ==

Lériendil at 04:04, 6 August 2024

2024-08-06T04:04:34Z

← Older revision		Revision as of 04:04, 6 August 2024
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	{{Infobox ET}}		{{Infobox ET}}

			{{Harmonics in equal\|10\|7\|3\|prec=2\|columns=15}}

Francium: Marked page as stub

2023-10-04T08:52:18Z

Marked page as stub

← Older revision		Revision as of 08:52, 4 October 2023
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			{{Stub}}
	{{Infobox ET}}		{{Infobox ET}}

Moremajorthanmajor: Created page with "{{Infobox ET}}"

2023-05-04T02:02:23Z

Created page with "{{Infobox ET}}"

New page