7-limit - Revision history

Inthar: /* Zil[14] */

2026-06-21T02:58:57Z

Zil[14]

← Older revision		Revision as of 02:58, 21 June 2026
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	Zil (from the temperament Godzilla which the zil series serves as a detempering of) is a series of 7-limit JI scales created from a [[generator sequence]] GS(8/7, 7/6, 8/7, 7/6, 8/7, 7/6, 8/7, 189/160).		Zil (from the temperament Godzilla which the zil series serves as a detempering of) is a series of 7-limit JI scales created from a [[generator sequence]] GS(8/7, 7/6, 8/7, 7/6, 8/7, 7/6, 8/7, 189/160).
	==== Zil[14] ====		==== Zil[14] ====
	The most discussed of the zil scales is zil[14] which is chiral depending on the chirality of the [[interleaving\|interleaved]] 5-limit [[zarlino]] copies. Note that Zil[14]'s lexicographical chirality is the opposite of the lexicographical chirality of the Zarlino versions used.		The most discussed of the zil scales is zil[14] which is chiral depending on the chirality of the [[interleaving\|interleaved]] 5-limit [[zarlino]] copies. Note that Zil[14]'s lexicographical chirality label is the opposite of the lexicographical chirality of the Zarlino versions used.

	LH zil[14] = [[cross-set]] of RH zarlino and 7/4		LH zil[14] = [[cross-set]] of RH zarlino and 7/4

Inthar: /* Zil[14] */

2026-06-19T20:51:25Z

Zil[14]

← Older revision		Revision as of 20:51, 19 June 2026
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	Zil (from the temperament Godzilla which the zil series serves as a detempering of) is a series of 7-limit JI scales created from a [[generator sequence]] GS(8/7, 7/6, 8/7, 7/6, 8/7, 7/6, 8/7, 189/160).		Zil (from the temperament Godzilla which the zil series serves as a detempering of) is a series of 7-limit JI scales created from a [[generator sequence]] GS(8/7, 7/6, 8/7, 7/6, 8/7, 7/6, 8/7, 189/160).
	==== Zil[14] ====		==== Zil[14] ====
	The most discussed of the zil scales is zil[14] which is chiral depending on the chirality of the [[interleaving\|interleaved]] 5-limit [[zarlino]] copies:		The most discussed of the zil scales is zil[14] which is chiral depending on the chirality of the [[interleaving\|interleaved]] 5-limit [[zarlino]] copies. Note that Zil[14]'s lexicographical chirality is the opposite of the lexicographical chirality of the Zarlino versions used.

	LH zil[14] = [[cross-set]] of RH zarlino and 7/4		LH zil[14] = [[cross-set]] of RH zarlino and 7/4

Inthar: /* Zil[14] */ Correct lexicographical chirality for Zil[14]; interleaving RH Zarlino results in LH Zil[14]

2026-06-19T20:49:41Z

Zil[14]: Correct lexicographical chirality for Zil[14]; interleaving RH Zarlino results in LH Zil[14]

← Older revision		Revision as of 20:49, 19 June 2026
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	The most discussed of the zil scales is zil[14] which is chiral depending on the chirality of the [[interleaving\|interleaved]] 5-limit [[zarlino]] copies:		The most discussed of the zil scales is zil[14] which is chiral depending on the chirality of the [[interleaving\|interleaved]] 5-limit [[zarlino]] copies:

	RH zil[14] = [[cross-set]] of RH zarlino and 7/4		LH zil[14] = [[cross-set]] of RH zarlino and 7/4
	<pre>		<pre>
	35/32; 9/8; 315/256; 5/4; 21/16; 45/32; 189/128; 3/2; 105/64; 27/16; 7/4; 15/8; 63/32; 2/1		35/32; 9/8; 315/256; 5/4; 21/16; 45/32; 189/128; 3/2; 105/64; 27/16; 7/4; 15/8; 63/32; 2/1
	</pre>		</pre>

	LH zil[14] = cross-set of LH zarlino and 7/4		RH zil[14] = cross-set of LH zarlino and 7/4
	<pre>		<pre>
	21/20; 9/8; 7/6; 6/5; 21/16; 4/3; 7/5; 3/2; 63/40; 8/5; 7/4; 9/5; 63/32; 2/1		21/20; 9/8; 7/6; 6/5; 21/16; 4/3; 7/5; 3/2; 63/40; 8/5; 7/4; 9/5; 63/32; 2/1

Lériendil: added hemithirds[31]

2026-05-22T22:48:45Z

added hemithirds[31]

← Older revision		Revision as of 22:48, 22 May 2026
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	<pre>		<pre>
	33075/32768; 525/512; 135/128; 2205/2048; 35/32; 9/8; 147/128; 4725/4096; 75/64; 1225/1024; 315/256; 5/4; 1323/1024; 21/16; 675/512; 11025/8192; 175/128; 45/32; 735/512; 189/128; 3/2; 49/32; 1575/1024; 25/16; 6615/4096; 105/64; 27/16; 441/256; 7/4; 225/128; 3675/2048; 945/512; 15/8; 245/128; 63/32; 2/1		33075/32768; 525/512; 135/128; 2205/2048; 35/32; 9/8; 147/128; 4725/4096; 75/64; 1225/1024; 315/256; 5/4; 1323/1024; 21/16; 675/512; 11025/8192; 175/128; 45/32; 735/512; 189/128; 3/2; 49/32; 1575/1024; 25/16; 6615/4096; 105/64; 27/16; 441/256; 7/4; 225/128; 3675/2048; 945/512; 15/8; 245/128; 63/32; 2/1
			</pre>

			=== A Hemithirds[31] detemper ===
			<pre>
			525/512; 21/20; 16/15; 35/32; 28/25; 8/7; 75/64; 25/21; 128/105; 5/4; 32/25; 21/16; 4/3; 175/128; 7/5; 10/7; 256/175; 3/2; 32/21; 25/16; 8/5; 105/64; 42/25; 128/75; 7/4; 25/14; 64/35; 15/8; 40/21; 1024/525; 2/1
	</pre>		</pre>

Vector at 20:49, 22 May 2026

2026-05-22T20:49:52Z

@@ Line 28: / Line 28: @@
 * [[Aberschismic]] ({{e|41}} & {{e|46}} & {{e|53}}): equates the 2.3.5 and 2.3.7 formal commas, 81/80 and 64/63; medium-high accuracy.
 * [[Marvel]] ({{e|19}} & {{e|22}} & {{e|41}}): equates 25/16 and 14/9; medium accuracy.
 == Full 7-limit JI scales ==

Inthar: /* Mode 5 */

2026-04-23T13:35:56Z

Mode 5

← Older revision		Revision as of 13:35, 23 April 2026
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	8:9:10:12:14:16		8:9:10:12:14:16
	</pre>		</pre>
	The simplest full 7-limit JI scale~~. This scale is notably used in the music of the Wagogo people in Tanzania~~.		The simplest full 7-limit JI scale.

	=== /2 Mixolydian ===		=== /2 Mixolydian ===

Vector at 02:15, 16 April 2026

2026-04-16T02:15:13Z

← Older revision		Revision as of 02:15, 16 April 2026
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	The simplest full 7-limit JI scale. This scale is notably used in the music of the Wagogo people in Tanzania.		The simplest full 7-limit JI scale. This scale is notably used in the music of the Wagogo people in Tanzania.

	=== ~~Rooted~~ Mixolydian ===		=== /2 Mixolydian ===
	<pre>		<pre>
	16:18:20:21:24:27:28:32		16:18:20:21:24:27:28:32
	</pre>		</pre>

	=== ~~Rooted~~ Ionian ===		=== /2 Ionian ===
	<pre>		<pre>
	16:18:20:21:24:27:30:32		16:18:20:21:24:27:30:32
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	The most discussed of the zil scales is zil[14] which is chiral depending on the chirality of the [[interleaving\|interleaved]] 5-limit [[zarlino]] copies:		The most discussed of the zil scales is zil[14] which is chiral depending on the chirality of the [[interleaving\|interleaved]] 5-limit [[zarlino]] copies:

	RH zil[14] = ~~RH zarlino~~ [[cross-set~~\|by~~]] 7/4		RH zil[14] = [[cross-set]] of RH zarlino and 7/4
	<pre>		<pre>
	35/32; 9/8; 315/256; 5/4; 21/16; 45/32; 189/128; 3/2; 105/64; 27/16; 7/4; 15/8; 63/32; 2/1		35/32; 9/8; 315/256; 5/4; 21/16; 45/32; 189/128; 3/2; 105/64; 27/16; 7/4; 15/8; 63/32; 2/1
	</pre>		</pre>

	LH zil[14] = ~~LH zarlino [[~~cross-set~~\|by]]~~ 7/4		LH zil[14] = cross-set of LH zarlino and 7/4
	<pre>		<pre>
	21/20; 9/8; 7/6; 6/5; 21/16; 4/3; 7/5; 3/2; 63/40; 8/5; 7/4; 9/5; 63/32; 2/1		21/20; 9/8; 7/6; 6/5; 21/16; 4/3; 7/5; 3/2; 63/40; 8/5; 7/4; 9/5; 63/32; 2/1
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	</pre>		</pre>

	=== 12:14:16:18:21:24 ~~[[cross-set\|by]]~~ 5/4 ===		=== Cross-set of 12:14:16:18:21:24 and 5/4 ===
	A 10-note scale with an analogous structure to zil[14] (note that these are subsets of both zil[14] chiralities):		A 10-note scale with an analogous structure to zil[14] (note that these are subsets of both zil[14] chiralities):

Inthar: /* Zil[14] */

2026-04-16T00:22:10Z

Zil[14]

← Older revision		Revision as of 00:22, 16 April 2026
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	The most discussed of the zil scales is zil[14] which is chiral depending on the chirality of the [[interleaving\|interleaved]] 5-limit [[zarlino]] copies:		The most discussed of the zil scales is zil[14] which is chiral depending on the chirality of the [[interleaving\|interleaved]] 5-limit [[zarlino]] copies:

	RH zil[14] = RH zarlino by 7/4		RH zil[14] = RH zarlino [[cross-set\|by]] 7/4
	<pre>		<pre>
	35/32; 9/8; 315/256; 5/4; 21/16; 45/32; 189/128; 3/2; 105/64; 27/16; 7/4; 15/8; 63/32; 2/1		35/32; 9/8; 315/256; 5/4; 21/16; 45/32; 189/128; 3/2; 105/64; 27/16; 7/4; 15/8; 63/32; 2/1
	</pre>		</pre>

	LH zil[14] = LH zarlino by 7/4		LH zil[14] = LH zarlino [[cross-set\|by]] 7/4
	<pre>		<pre>
	21/20; 9/8; 7/6; 6/5; 21/16; 4/3; 7/5; 3/2; 63/40; 8/5; 7/4; 9/5; 63/32; 2/1		21/20; 9/8; 7/6; 6/5; 21/16; 4/3; 7/5; 3/2; 63/40; 8/5; 7/4; 9/5; 63/32; 2/1

Inthar: /* 12:14:16:18:21:24 by 5/4 */

2026-04-16T00:21:36Z

12:14:16:18:21:24 by 5/4

← Older revision		Revision as of 00:21, 16 April 2026
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	</pre>		</pre>

	=== 12:14:16:18:21:24 by 5/4 ===		=== 12:14:16:18:21:24 [[cross-set\|by]] 5/4 ===
	A 10-note scale with an analogous structure to zil[14] (note that these are subsets of both zil[14] chiralities):		A 10-note scale with an analogous structure to zil[14] (note that these are subsets of both zil[14] chiralities):

Inthar: /* An Aberschismic 34edo detemper */

2026-04-15T14:38:31Z

An Aberschismic 34edo detemper

← Older revision		Revision as of 14:38, 15 April 2026
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	<pre>		<pre>
	81/80; 21/20; 16/15; 35/32; 10/9; 9/8; 7/6; 189/160; 6/5; 315/256; 5/4; 35/27; 21/16; 4/3; 27/20; 7/5; 45/32; 35/24; 189/128; 3/2; 14/9; 63/40; 8/5; 105/64; 5/3; 27/16; 7/4; 16/9; 9/5; 28/15; 15/8; 35/18; 63/32; 2/1		81/80; 21/20; 16/15; 35/32; 10/9; 9/8; 7/6; 189/160; 6/5; 315/256; 5/4; 35/27; 21/16; 4/3; 27/20; 7/5; 45/32; 35/24; 189/128; 3/2; 14/9; 63/40; 8/5; 105/64; 5/3; 27/16; 7/4; 16/9; 9/5; 28/15; 15/8; 35/18; 63/32; 2/1
			</pre>

			Use 81/64 instead of 35/27 to get a Pyth[7] subset:
			<pre>
			81/80; 21/20; 16/15; 35/32; 10/9; 9/8; 7/6; 189/160; 6/5; 315/256; 5/4; 81/64; 21/16; 4/3; 27/20; 7/5; 45/32; 35/24; 189/128; 3/2; 14/9; 63/40; 8/5; 105/64; 5/3; 27/16; 7/4; 16/9; 9/5; 28/15; 15/8; 35/18; 63/32; 2/1
	</pre>		</pre>