Ringer scale - Revision history

Lériendil: this ringer is technically in the 8d val

2026-02-05T02:36:19Z

this ringer is technically in the 8d val

← Older revision		Revision as of 02:36, 5 February 2026
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	9:10:12:14:16:17:18		9:10:12:14:16:17:18

	'''Ringer 8:''' 7:8:'''17/2''':9:10:11:12:13:14		'''Ringer 8d:''' 7:8:'''17/2''':9:10:11:12:13:14

	9:10:11:12:13:14:16:17:18		9:10:11:12:13:14:16:17:18

BudjarnLambeth: Navbox

2025-12-28T00:40:21Z

Navbox

← Older revision		Revision as of 00:40, 28 December 2025
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	* [[Neji]]		* [[Neji]]

			{{navbox scale gallery}}
	[[Category:Just intonation scales]]		[[Category:Just intonation scales]]
	[[Category:Pages with proofs]]		[[Category:Pages with proofs]]

Tristanbay: /* List of ringer scales */Added ringer 16 scales and corrected formatting for ringer 15 and 12 entries

2025-11-28T20:29:21Z

List of ringer scales: Added ringer 16 scales and corrected formatting for ringer 15 and 12 entries

← Older revision		Revision as of 20:29, 28 November 2025
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	'''Ringer 12:''' 11:12:'''[25/2''':13(f) OR 13:'''27/2]''':14:15:16:17:18:19:20:21:22		'''Ringer 12:''' 11:12:'''[25/2''':13(f) OR 13:'''27/2]''':14:15:16:17:18:19:20:21:22

	14:15:16:17:18:19:20:21:22:24:[25:26 OR 26:27]:28		14:15:16:17:18:19:20:21:22:24:[25:26(f) OR 26:27]:28

	'''Ringer 13g:''' 9:10:'''21/2''':11:'''23/2''':12:13:14:'''29/2''':15:16:'''33/2''':17:18		'''Ringer 13g:''' 9:10:'''21/2''':11:'''23/2''':12:13:14:'''29/2''':15:16:'''33/2''':17:18
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	'''Ringer 15:''' 13:14:'''29/2''':15:16:'''[33/2''':17(g) OR 17:'''35/2]''':18:19:20:21:22:23:24:25:26		'''Ringer 15:''' 13:14:'''29/2''':15:16:'''[33/2''':17(g) OR 17:'''35/2]''':18:19:20:21:22:23:24:25:26

	18:19:20:21:22:23:24:25:26:28:29:30:32:[33:34 OR 34:35]:36		18:19:20:21:22:23:24:25:26:28:29:30:32:[33:34(g) OR 34:35]:36

			'''Ringer 16:'''
			13:'''55/4''':14:15:'''31/2''':16:17:18:'''[37/2''':19 OR 19:'''39/2(h)]''':20:21:22:23:24:25:26

			28:30:31:32:34:36:[37:38 OR 38:39(h)]:40:42:44:46:48:50:52:55:56

	'''Ringer 17cffg:''' 13:14:'''29/2''':15:16:'''33/2''':17:18:19:'''[77/4''' OR '''79/4]''':20:21:22:23:24:'''49/2''':25:26		'''Ringer 17cffg:''' 13:14:'''29/2''':15:16:'''33/2''':17:18:19:'''[77/4''' OR '''79/4]''':20:21:22:23:24:'''49/2''':25:26

BudjarnLambeth at 18:20, 5 November 2024

2024-11-05T18:20:24Z

← Older revision		Revision as of 18:20, 5 November 2024
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	75:76:77:78:79:80:81:82:83:84:85:86:87:88:89:90:91:92:93:94:96:'''97''':98:'''99''':100:102:'''103''':104:106:'''107''':108:'''109''':110:112:'''113''':114:116:'''[117''':118(q=59) OR 118:'''119]''':120:'''[121:122(rr=61)''' OR 122:'''123]''':124:126:128:'''129''':130:132:134:136:'''137''':138:140:142:144:146:148:'''149''':150		75:76:77:78:79:80:81:82:83:84:85:86:87:88:89:90:91:92:93:94:96:'''97''':98:'''99''':100:102:'''103''':104:106:'''107''':108:'''109''':110:112:'''113''':114:116:'''[117''':118(q=59) OR 118:'''119]''':120:'''[121:122(rr=61)''' OR 122:'''123]''':124:126:128:'''129''':130:132:134:136:'''137''':138:140:142:144:146:148:'''149''':150

	=== See also ===		== See also ==
	* [[Neji]]		* [[Neji]]

	[[Category:Just intonation scales]]		[[Category:Just intonation scales]]
	[[Category:Pages with proofs]]		[[Category:Pages with proofs]]

BudjarnLambeth: Add see also

2024-11-05T18:20:13Z

Add see also

← Older revision		Revision as of 18:20, 5 November 2024
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	75:76:77:78:79:80:81:82:83:84:85:86:87:88:89:90:91:92:93:94:96:'''97''':98:'''99''':100:102:'''103''':104:106:'''107''':108:'''109''':110:112:'''113''':114:116:'''[117''':118(q=59) OR 118:'''119]''':120:'''[121:122(rr=61)''' OR 122:'''123]''':124:126:128:'''129''':130:132:134:136:'''137''':138:140:142:144:146:148:'''149''':150		75:76:77:78:79:80:81:82:83:84:85:86:87:88:89:90:91:92:93:94:96:'''97''':98:'''99''':100:102:'''103''':104:106:'''107''':108:'''109''':110:112:'''113''':114:116:'''[117''':118(q=59) OR 118:'''119]''':120:'''[121:122(rr=61)''' OR 122:'''123]''':124:126:128:'''129''':130:132:134:136:'''137''':138:140:142:144:146:148:'''149''':150

			=== See also ===
			* [[Neji]]

	[[Category:Just intonation scales]]		[[Category:Just intonation scales]]
	[[Category:Pages with proofs]]		[[Category:Pages with proofs]]

Godtone: /* Ringer scales */

2024-09-14T02:03:30Z

Ringer scales

← Older revision		Revision as of 02:03, 14 September 2024
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	This section will detail known ringers for edos smaller than 100. Because [[wart]]s are limited when it comes to large primes, any primes past 43 are explicitly listed in the form [p, q, r, ...] rather than abbreviated (rather cryptically) as letters. A quick summary of all the warts up to 43 is:		This section will detail known ringers for edos smaller than 100. Because [[wart]]s are limited when it comes to large primes, any primes past 43 are explicitly listed in the form [p, q, r, ...] rather than abbreviated (rather cryptically) as letters. A quick summary of all the warts up to 43 is:

	b means 3 gets a next-best mapping, c means 5 gets a next-best mapping, d means 7 gets a next-best mapping and so on: e means 11, f means 13, g means 17, h means 19, i means 23, j means 29, k means 31, l means 37, m means 41, n means 43. (2 = a is not used as it must always be patent.)		b means 3 gets a next-best mapping, c means 5 gets a next-best mapping, d means 7 gets a next-best mapping and so on: e means 11, f means 13, g means 17, h means 19, i means 23, j means 29, k means 31, l means 37, m means 41, n means 43 and finally o means 47. (2 = a is not used as it must always be patent.)

	There should be at least two forms listed. One will be in the form used for the example of Ringer 15. One will be in the minimum mode of the harmonic series that contains all harmonics. Both can be pasted directly into scale workshop using the enumerate chord feature or into other programs, but the latter form is useful in case a program does not support the other notation.		There should be at least two forms listed. One will be in the form used for the example of Ringer 15. One will be in the minimum mode of the harmonic series that contains all harmonics. Both can be pasted directly into scale workshop using the enumerate chord feature or into other programs, but the latter form is useful in case a program does not support the other notation.

Lériendil: /* Perfect ringer scales */

2024-08-03T16:52:24Z

Perfect ringer scales

← Older revision		Revision as of 16:52, 3 August 2024
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	A perfect ringer ''n'' scale is one that by some val can map the first ''n'' odd harmonics to distinct numbers of steps up to [[octave equivalence]]. These are the only perfect ringer scales:		A perfect ringer ''n'' scale is one that by some val can map the first ''n'' odd harmonics to distinct numbers of steps up to [[octave equivalence]]. These are the only perfect ringer scales:

	'''Ringer 1:''' 1:2		'''Ringer 1:''' 1:2 (val: {{val\| 1 }})

	'''Ringer 2:''' 2:3:4		'''Ringer 2:''' 2:3:4 (val: {{val\| 2 3 }})

	'''Ringer 3:''' 3:4:5:6		'''Ringer 3:''' 3:4:5:6 (val: {{val\| 3 5 7 }})

	'''Ringer 4:''' 4:5:6:7:8		'''Ringer 4:''' 4:5:6:7:8 (val: {{val\| 4 6 9 11 }})

	'''Ringer 5:''' 5:6:7:8:9:10		'''Ringer 5:''' 5:6:7:8:9:10 (val: {{val\| 5 8 12 14 }})

	'''Ringer 7:''' 7:8:9:10:11:12:13:14		'''Ringer 7:''' 7:8:9:10:11:12:13:14 (val: {{val\| 7 11 16 20 24 26 }})

	Notice how all of these do not skip any harmonics while representing the harmonic series ''completely'' up to some [[odd-limit]].		Notice how all of these do not skip any harmonics while representing the harmonic series ''completely'' up to some [[odd-limit]].

Lériendil at 01:44, 10 July 2024

2024-07-10T01:44:29Z

← Older revision		Revision as of 01:44, 10 July 2024
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	== Perfect ringer scales ==		== Perfect ringer scales ==
	A perfect ringer ''n'' scale is one that by some val can map the first ''n'' odd harmonics to distinct numbers of steps up to [[octave equivalence]]. ~~It is conjectured that these~~ are the only perfect ringer scales:		A perfect ringer ''n'' scale is one that by some val can map the first ''n'' odd harmonics to distinct numbers of steps up to [[octave equivalence]]. These are the only perfect ringer scales:

	'''Ringer 1:''' 1:2		'''Ringer 1:''' 1:2
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	Notice how all of these do not skip any harmonics while representing the harmonic series ''completely'' up to some [[odd-limit]].		Notice how all of these do not skip any harmonics while representing the harmonic series ''completely'' up to some [[odd-limit]].

			Such a scale will either contain a pair of intervals (n+2):n and [(3/2)n+3]:[(3/2)n] if ''n'' is even so long as (3/2)n+3 ≤ 2n and therefore n ≥ 6, or (n+3):(n+1) and [(3/2)(n+1)+3]:[(3/2)(n+1)] if ''n'' is odd so long as (3/2)(n+1)+3 = (3/2)(n+3) ≤ 2n and therefore n ≥ 9. Between these two conditions, it is apparent that ''n'' = 1, 2, 3, 4, 5, and 7 create the only constant structures representing the entire harmonic series from ''n'' to ''2n''.

	Also note that there is a "Perfect Pseudoringer 9" if we allow a pair of harmonics to be swapped/out of order in order to preserve the constant structure property. It is not known how many "Perfect Pseudoringers" there are.		Also note that there is a "Perfect Pseudoringer 9" if we allow a pair of harmonics to be swapped/out of order in order to preserve the constant structure property. It is not known how many "Perfect Pseudoringers" there are.

Godtone: /* List of ringer scales */

2024-07-10T00:45:55Z

List of ringer scales

← Older revision		Revision as of 00:45, 10 July 2024
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	10:11:12:13:14:15:16:18:19:20		10:11:12:13:14:15:16:18:19:20

	'''Ringer 10:''' 10:'''21/2''':11:12:13:14:15:16:17:18~~:20~~		'''Ringer 10:''' 9:10:'''21/2''':11:12:13:14:15:16:17:18

	11:12:13:14:15:16:17:18:20:21:22		11:12:13:14:15:16:17:18:20:21:22

Inthar at 22:32, 9 February 2024

2024-02-09T22:32:01Z

← Older revision		Revision as of 22:32, 9 February 2024
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	[[Category:Just intonation scales]]		[[Category:Just intonation scales]]
	[[Category:~~Articles~~ with proofs]]		[[Category:Pages with proofs]]