148edo - Revision history

FilterNashi: /* Harmonics */

2025-10-25T14:56:25Z

Harmonics

← Older revision		Revision as of 14:56, 25 October 2025
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	The 5-limit [[patent val]] still makes sense, and it tempers out [[2048/2025]], making it a [[diaschismic]] system. In the 7-limit, the [[patent val]] tempers out [[686/675]] and [[1029/1024]], but the alternative mapping {{val\| 148 235 344 '''416''' }} (148d) with a sharp rather than a flat 7 tempers out [[3136/3125]] instead, and provides a better tuning than the patent val tuning of [[80edo]] for 7-, 13-, 17- and 19-limit [[bidia]], the 68 & 80 temperament. In the 11-limit, the patent val tempers out [[385/384]] and [[441/440]], and the alternative mapping with the sharp 7 tempers out [[176/175]], [[896/891]] and [[1375/1372]] instead. In the 13-limit, the patent val tempers out [[325/324]] and [[364/363]], and the alternative val 325/324 again, as well as [[640/637]] and [[847/845]]. It provides the [[optimal patent val]] for [[echidnic]], the 46 & 102 temperament, in the 11-limit, and the 148f val is an excellent tuning for echidnic in the 13- and 17-limit.		The 5-limit [[patent val]] still makes sense, and it tempers out [[2048/2025]], making it a [[diaschismic]] system. In the 7-limit, the [[patent val]] tempers out [[686/675]] and [[1029/1024]], but the alternative mapping {{val\| 148 235 344 '''416''' }} (148d) with a sharp rather than a flat 7 tempers out [[3136/3125]] instead, and provides a better tuning than the patent val tuning of [[80edo]] for 7-, 13-, 17- and 19-limit [[bidia]], the 68 & 80 temperament. In the 11-limit, the patent val tempers out [[385/384]] and [[441/440]], and the alternative mapping with the sharp 7 tempers out [[176/175]], [[896/891]] and [[1375/1372]] instead. In the 13-limit, the patent val tempers out [[325/324]] and [[364/363]], and the alternative val 325/324 again, as well as [[640/637]] and [[847/845]]. It provides the [[optimal patent val]] for [[echidnic]], the 46 & 102 temperament, in the 11-limit, and the 148f val is an excellent tuning for echidnic in the 13- and 17-limit.

	=== ~~Prime harmonics~~ ===		=== Harmonics ===
	{{Harmonics in equal\|148\|columns=9}}		{{Harmonics in equal\|148\|columns=9}}
	{{Harmonics in equal\|148\|columns=9\|start=10\|title=Approximation of odd harmonics in 148edo (continued)}}		{{Harmonics in equal\|148\|columns=9\|start=10\|title=Approximation of odd harmonics in 148edo (continued)}}

FilterNashi: /* Prime harmonics /continued chart for showing 37th harmonic accuracy 148=437

2025-10-25T13:14:00Z

Prime harmonics: continued chart for showing 37th harmonic accuracy 148=4*37

← Older revision		Revision as of 13:14, 25 October 2025
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	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|148}}		{{Harmonics in equal\|148\|columns=9}}
			{{Harmonics in equal\|148\|columns=9\|start=10\|title=Approximation of odd harmonics in 148edo (continued)}}

	=== Subsets and supersets ===		=== Subsets and supersets ===

ArrowHead294 at 17:05, 18 February 2025

2025-02-18T17:05:22Z

← Older revision		Revision as of 17:05, 18 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro}}		{{ED intro}}

	148edo's closest fifth is on the very sharp side, 3.45 cents sharp of just. With better approximations of [[9/1\|9]], [[11/1\|11]], [[15/1\|15]], [[17/1\|17]], and [[21/1\|21]], it commends itself as a 2.9.15.21.11.17 [[subgroup]] system.		148edo's closest fifth is on the very sharp side, 3.45 cents sharp of just. With better approximations of [[9/1\|9]], [[11/1\|11]], [[15/1\|15]], [[17/1\|17]], and [[21/1\|21]], it commends itself as a 2.9.15.21.11.17 [[subgroup]] system.

FloraC: Use val numbers that sum to this edo. Note thte limits where it excels in and +categories

2024-05-18T14:54:45Z

Use val numbers that sum to this edo. Note thte limits where it excels in and +categories

← Older revision		Revision as of 14:54, 18 May 2024
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	148edo's closest fifth is on the very sharp side, 3.45 cents sharp of just. With better approximations of [[9/1\|9]], [[11/1\|11]], [[15/1\|15]], [[17/1\|17]], and [[21/1\|21]], it commends itself as a 2.9.15.21.11.17 [[subgroup]] system.		148edo's closest fifth is on the very sharp side, 3.45 cents sharp of just. With better approximations of [[9/1\|9]], [[11/1\|11]], [[15/1\|15]], [[17/1\|17]], and [[21/1\|21]], it commends itself as a 2.9.15.21.11.17 [[subgroup]] system.

	The 5-limit [[patent val]] still makes sense, and it tempers out [[2048/2025]], making it a [[diaschismic]] system. In the 7-limit, the [[patent val]] tempers out [[686/675]] and [[1029/1024]], but the alternative mapping {{val\| 148 235 344 416 }} with a sharp rather than a flat 7 tempers out [[3136/3125]] instead, and provides a better tuning than the patent val tuning of [[80edo]] for 7- and 13- limit [[bidia]], the 12 & 68 temperament. In the 11-limit, the patent val tempers out [[385/384]] and [[441/440]], and the alternative mapping with the sharp 7 tempers out [[176/175]], [[896/891]] and [[1375/1372]] instead. In the 13-limit, the patent val tempers out [[325/324]] and [[364/363]], and the alternative val 325/324 again, as well as [[640/637]] and [[847/845]]. It provides the [[optimal patent val]] for ~~11-limit~~ [[echidnic]], the 10 & 46 temperament.		The 5-limit [[patent val]] still makes sense, and it tempers out [[2048/2025]], making it a [[diaschismic]] system. In the 7-limit, the [[patent val]] tempers out [[686/675]] and [[1029/1024]], but the alternative mapping {{val\| 148 235 344 '''416''' }} (148d) with a sharp rather than a flat 7 tempers out [[3136/3125]] instead, and provides a better tuning than the patent val tuning of [[80edo]] for 7-, 13-, 17- and 19-limit [[bidia]], the 68 & 80 temperament. In the 11-limit, the patent val tempers out [[385/384]] and [[441/440]], and the alternative mapping with the sharp 7 tempers out [[176/175]], [[896/891]] and [[1375/1372]] instead. In the 13-limit, the patent val tempers out [[325/324]] and [[364/363]], and the alternative val 325/324 again, as well as [[640/637]] and [[847/845]]. It provides the [[optimal patent val]] for [[echidnic]], the 46 & 102 temperament, in the 11-limit, and the 148f val is an excellent tuning for echidnic in the 13- and 17-limit.

	=== Prime harmonics ===		=== Prime harmonics ===
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 148 = 4 × 37, 148edo has subset edos {{EDOs\| 2, 4, 37, and 74 }}.		Since 148 = 4 × 37, 148edo has subset edos {{EDOs\| 2, 4, 37, and 74 }}.

			[[Category:Echidnic]]
			[[Category:Bidia]]

FloraC: Re-analyse it as a 2.9.15.21 subgroup system

2024-05-18T14:43:51Z

Re-analyse it as a 2.9.15.21 subgroup system

← Older revision		Revision as of 14:43, 18 May 2024
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	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro}} 148edo ~~has a~~ fifth on the sharp side, 3.45 cents sharp. The ~~equal temperament~~ tempers out [[2048/2025]] ~~in the 5-limit~~, making it a [[diaschismic]] system. In the 7-limit, the [[patent val]] tempers out [[686/675]] and [[1029/1024]], but the alternative mapping {{val\| 148 235 344 416 }} with a sharp rather than a flat 7 tempers out [[3136/3125]] instead, and provides a better tuning than the patent val tuning of [[80edo]] for 7- and 13- limit [[bidia]], the 12 & 68 temperament. In the 11-limit, the patent val tempers out [[385/384]] and [[441/440]], and the alternative mapping with the sharp 7 tempers out [[176/175]], [[896/891]] and [[1375/1372]] instead. In the 13-limit, the patent val tempers out [[325/324]] and [[364/363]], and the alternative val 325/324 again, as well as [[640/637]] and [[847/845]]. It provides the [[optimal patent val]] for 11-limit [[echidnic]], the 10 & 46 temperament.		{{EDO intro}}

			148edo's closest fifth is on the very sharp side, 3.45 cents sharp of just. With better approximations of [[9/1\|9]], [[11/1\|11]], [[15/1\|15]], [[17/1\|17]], and [[21/1\|21]], it commends itself as a 2.9.15.21.11.17 [[subgroup]] system.

			The 5-limit [[patent val]] still makes sense, and it tempers out [[2048/2025]], making it a [[diaschismic]] system. In the 7-limit, the [[patent val]] tempers out [[686/675]] and [[1029/1024]], but the alternative mapping {{val\| 148 235 344 416 }} with a sharp rather than a flat 7 tempers out [[3136/3125]] instead, and provides a better tuning than the patent val tuning of [[80edo]] for 7- and 13- limit [[bidia]], the 12 & 68 temperament. In the 11-limit, the patent val tempers out [[385/384]] and [[441/440]], and the alternative mapping with the sharp 7 tempers out [[176/175]], [[896/891]] and [[1375/1372]] instead. In the 13-limit, the patent val tempers out [[325/324]] and [[364/363]], and the alternative val 325/324 again, as well as [[640/637]] and [[847/845]]. It provides the [[optimal patent val]] for 11-limit [[echidnic]], the 10 & 46 temperament.

	=== Prime harmonics ===		=== Prime harmonics ===

FloraC: Adopt template: EDO intro (including getting rid of its approximation of the kleisma since it lacks significance anyway); redundant categories; misc. cleanup

2024-05-18T14:38:37Z

Adopt template: EDO intro (including getting rid of its approximation of the kleisma since it lacks significance anyway); redundant categories; misc. cleanup

← Older revision		Revision as of 14:38, 18 May 2024
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	{{Infobox ET}}		{{Infobox ET}}
	~~'''~~148edo''' is the [[equal division of the octave]] into 148 equal parts of 8.108 cents each, near a [[kleisma\|kleisma]]. It provides the [[Optimal_patent_val\|optimal patent val]] for 11-limit [[Diaschismic_family\|echidnic temperament]], the 10&46 temperament. It has a fifth on the sharp side, 3.45 cents sharp. It tempers out 2048/2025 in the 5-limit, making it a diaschismic system. In the 7-limit, the [[~~Patent_val\|~~patent val]] tempers out 686/675 and 1029/1024, but an alternative mapping ~~<~~148 235 344 416\| with a sharp rather than a flat 7 tempers out 3136/3125 instead, and provides a better tuning than the patent val tuning of [[~~80edo\|~~80edo]] for 7- and 13- limit [[~~Diaschismic_family\|~~bidia ~~temperament~~]], the 12&68 temperament. In the 11-limit, the patent val tempers out 385/384 and 441/440, and the alternative mapping with the sharp 7 tempers out 176/175, 896/891 and 1375/1372 instead. In the 13-limit, the patent val tempers out 325/324 and 364/363, and the alternative val 325/324 again, as well as 640/637 and 847/845.		{{EDO intro}} 148edo has a fifth on the sharp side, 3.45 cents sharp. The equal temperament tempers out [[2048/2025]] in the 5-limit, making it a [[diaschismic]] system. In the 7-limit, the [[patent val]] tempers out [[686/675]] and [[1029/1024]], but the alternative mapping {{val\| 148 235 344 416 }} with a sharp rather than a flat 7 tempers out [[3136/3125]] instead, and provides a better tuning than the patent val tuning of [[80edo]] for 7- and 13- limit [[bidia]], the 12 & 68 temperament. In the 11-limit, the patent val tempers out [[385/384]] and [[441/440]], and the alternative mapping with the sharp 7 tempers out [[176/175]], [[896/891]] and [[1375/1372]] instead. In the 13-limit, the patent val tempers out [[325/324]] and [[364/363]], and the alternative val 325/324 again, as well as [[640/637]] and [[847/845]]. It provides the [[optimal patent val]] for 11-limit [[echidnic]], the 10 & 46 temperament.

	~~148 = 4 * 37~~, ~~with divisors 2, 4, 37, 74~~.

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|148}}		{{Harmonics in equal\|148}}

	~~[[Category:Equal divisions of the octave~~\|~~###]] <!-- 3-digit number -->~~		=== Subsets and supersets ===
			Since 148 = 4 × 37, 148edo has subset edos {{EDOs\| 2, 4, 37, and 74 }}.

Aura at 21:15, 18 December 2022

2022-12-18T21:15:56Z

← Older revision		Revision as of 21:15, 18 December 2022
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	148 = 4 * 37, with divisors 2, 4, 37, 74.		148 = 4 * 37, with divisors 2, 4, 37, 74.

			=== Prime harmonics ===
			{{Harmonics in equal\|148}}

	[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->		[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->

Aura at 19:07, 4 October 2022

2022-10-04T19:07:51Z

← Older revision		Revision as of 19:07, 4 October 2022
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			{{Infobox ET}}
	'''148edo''' is the [[equal division of the octave]] into 148 equal parts of 8.108 cents each, near a [[kleisma\|kleisma]]. It provides the [[Optimal_patent_val\|optimal patent val]] for 11-limit [[Diaschismic_family\|echidnic temperament]], the 10&46 temperament. It has a fifth on the sharp side, 3.45 cents sharp. It tempers out 2048/2025 in the 5-limit, making it a diaschismic system. In the 7-limit, the [[Patent_val\|patent val]] tempers out 686/675 and 1029/1024, but an alternative mapping <148 235 344 416\| with a sharp rather than a flat 7 tempers out 3136/3125 instead, and provides a better tuning than the patent val tuning of [[80edo\|80edo]] for 7- and 13- limit [[Diaschismic_family\|bidia temperament]], the 12&68 temperament. In the 11-limit, the patent val tempers out 385/384 and 441/440, and the alternative mapping with the sharp 7 tempers out 176/175, 896/891 and 1375/1372 instead. In the 13-limit, the patent val tempers out 325/324 and 364/363, and the alternative val 325/324 again, as well as 640/637 and 847/845.		'''148edo''' is the [[equal division of the octave]] into 148 equal parts of 8.108 cents each, near a [[kleisma\|kleisma]]. It provides the [[Optimal_patent_val\|optimal patent val]] for 11-limit [[Diaschismic_family\|echidnic temperament]], the 10&46 temperament. It has a fifth on the sharp side, 3.45 cents sharp. It tempers out 2048/2025 in the 5-limit, making it a diaschismic system. In the 7-limit, the [[Patent_val\|patent val]] tempers out 686/675 and 1029/1024, but an alternative mapping <148 235 344 416\| with a sharp rather than a flat 7 tempers out 3136/3125 instead, and provides a better tuning than the patent val tuning of [[80edo\|80edo]] for 7- and 13- limit [[Diaschismic_family\|bidia temperament]], the 12&68 temperament. In the 11-limit, the patent val tempers out 385/384 and 441/440, and the alternative mapping with the sharp 7 tempers out 176/175, 896/891 and 1375/1372 instead. In the 13-limit, the patent val tempers out 325/324 and 364/363, and the alternative val 325/324 again, as well as 640/637 and 847/845.

Fredg999 category edits: Categories

2022-07-02T21:07:45Z

Aura: rewrote opening sentence

2021-01-19T05:40:20Z

rewrote opening sentence

← Older revision		Revision as of 05:40, 19 January 2021
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	~~The~~ ''~~148~~ equal division~~'' divides~~ the octave into 148 equal parts of 8.108 cents each, near a [[kleisma\|kleisma]]. It provides the [[Optimal_patent_val\|optimal patent val]] for 11-limit [[Diaschismic_family\|echidnic temperament]], the 10&46 temperament. It has a fifth on the sharp side, 3.45 cents sharp. It tempers out 2048/2025 in the 5-limit, making it a diaschismic system. In the 7-limit, the [[Patent_val\|patent val]] tempers out 686/675 and 1029/1024, but an alternative mapping <148 235 344 416\| with a sharp rather than a flat 7 tempers out 3136/3125 instead, and provides a better tuning than the patent val tuning of [[80edo\|80edo]] for 7- and 13- limit [[Diaschismic_family\|bidia temperament]], the 12&68 temperament. In the 11-limit, the patent val tempers out 385/384 and 441/440, and the alternative mapping with the sharp 7 tempers out 176/175, 896/891 and 1375/1372 instead. In the 13-limit, the patent val tempers out 325/324 and 364/363, and the alternative val 325/324 again, as well as 640/637 and 847/845.		'''148edo''' is the [[equal division of the octave]] into 148 equal parts of 8.108 cents each, near a [[kleisma\|kleisma]]. It provides the [[Optimal_patent_val\|optimal patent val]] for 11-limit [[Diaschismic_family\|echidnic temperament]], the 10&46 temperament. It has a fifth on the sharp side, 3.45 cents sharp. It tempers out 2048/2025 in the 5-limit, making it a diaschismic system. In the 7-limit, the [[Patent_val\|patent val]] tempers out 686/675 and 1029/1024, but an alternative mapping <148 235 344 416\| with a sharp rather than a flat 7 tempers out 3136/3125 instead, and provides a better tuning than the patent val tuning of [[80edo\|80edo]] for 7- and 13- limit [[Diaschismic_family\|bidia temperament]], the 12&68 temperament. In the 11-limit, the patent val tempers out 385/384 and 441/440, and the alternative mapping with the sharp 7 tempers out 176/175, 896/891 and 1375/1372 instead. In the 13-limit, the patent val tempers out 325/324 and 364/363, and the alternative val 325/324 again, as well as 640/637 and 847/845.

	148 = 4 * 37, with divisors 2, 4, 37, 74.		148 = 4 * 37, with divisors 2, 4, 37, 74.

← Older revision		Revision as of 21:07, 2 July 2022
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	148 = 4 * 37, with divisors 2, 4, 37, 74.		148 = 4 * 37, with divisors 2, 4, 37, 74.

			[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->