225edo - Revision history

Eliora: /* Theory */

2026-09-19T04:54:25Z

Theory

← Older revision		Revision as of 04:54, 19 September 2026
Line 7:		Line 7:
	In fact, 225edo sets the sequential record for being worst for integer harmonics as a whole, when evaluated using how close are its harmonic errors to <math>1 - \phi</math> = 38.1966%, the golden ratio, the number most difficult to approximate with rationals. While other edos with poor approximation usually end up approximating the square of that harmonic well, 225edo performs worst due to it setting a record of how close its harmonic errors are to 38.1966%.		In fact, 225edo sets the sequential record for being worst for integer harmonics as a whole, when evaluated using how close are its harmonic errors to <math>1 - \phi</math> = 38.1966%, the golden ratio, the number most difficult to approximate with rationals. While other edos with poor approximation usually end up approximating the square of that harmonic well, 225edo performs worst due to it setting a record of how close its harmonic errors are to 38.1966%.

	It has three mappings ~~possible~~ for the 7-limit:		It has three mappings usable for the 7-limit:
	* {{val\| 225 357 522 632 }} ([[patent val]]),		* {{val\| 225 357 522 632 }} ([[patent val]]),
	* {{val\| 225 '''356''' 522 '''631''' }} (225bd),		* {{val\| 225 '''356''' 522 '''631''' }} (225bd),

2026-08-06T18:55:27Z

← Older revision		Revision as of 18:55, 6 August 2026
Line 3:		Line 3:

	== Theory ==		== Theory ==
	225edo is in[[consistent]] to the [[5-odd-limit]] and higher limits, with rather large errors in [[harmonic]]s [[3/1\|3]], [[5/1\|5]], [[7/1\|7]], [[11/1\|11]], and [[13/1\|13]]. It has three mappings possible for the 7-limit:		225edo is in[[consistent]] to the [[5-odd-limit]] and higher limits, with rather large errors in [[harmonic]]s [[3/1\|3]], [[5/1\|5]], [[7/1\|7]], [[11/1\|11]], and [[13/1\|13]].

			In fact, 225edo sets the sequential record for being worst for integer harmonics as a whole, when evaluated using how close are its harmonic errors to <math>1 - \phi</math> = 38.1966%, the golden ratio, the number most difficult to approximate with rationals. While other edos with poor approximation usually end up approximating the square of that harmonic well, 225edo performs worst due to it setting a record of how close its harmonic errors are to 38.1966%.

			It has three mappings possible for the 7-limit:
	* {{val\| 225 357 522 632 }} ([[patent val]]),		* {{val\| 225 357 522 632 }} ([[patent val]]),
	* {{val\| 225 '''356''' 522 '''631''' }} (225bd),		* {{val\| 225 '''356''' 522 '''631''' }} (225bd),

2026-07-09T01:34:28Z

Undo revision 233541 by Overthink (talk) idk actually

2026-07-09T01:31:51Z

Delete (the edo is only vaguely relevant to the scales)

2025-03-24T13:46:03Z

2025-02-20T14:19:55Z

2024-04-02T06:29:07Z

Cleanup; note its high errors in all the lower primes

← Older revision		Revision as of 06:29, 2 April 2024
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	~~'''~~225edo~~'''~~ is the [[~~EDO~~\|~~equal division of the octave~~]] ~~into 225 parts of~~ 5~~.3333~~ [[~~cent~~]]~~s each~~. It ~~is inconsistent to the 5-limit and higher limit, with~~ three mappings possible for the 7-limit:		{{EDO intro}}
	* {{val\| 225 357 522 632 }} (patent val),
			== Theory ==
			225edo is in[[consistent]] to the [[5-odd-limit]] and higher limits, with rather large errors in [[harmonic]]s [[3/1\|3]], [[5/1\|5]], [[7/1\|7]], [[11/1\|11]], and [[13/1\|13]]. It has three mappings possible for the 7-limit:
			* {{val\| 225 357 522 632 }} ([[patent val]]),
	* {{val\| 225 '''356''' 522 '''631''' }} (225bd),		* {{val\| 225 '''356''' 522 '''631''' }} (225bd),
	* {{val\| 225 357 '''523''' 632 }} (225c).		* {{val\| 225 357 '''523''' 632 }} (225c).
Line 11:		Line 14:
	Using the 225c val, it tempers out 131072000/129140163 (rodan comma) and 30958682112/30517578125 (trisedodge comma) in the 5-limit; 2401/2400, 4375/4374, and 2097152/2066715 in the 7-limit.		Using the 225c val, it tempers out 131072000/129140163 (rodan comma) and 30958682112/30517578125 (trisedodge comma) in the 5-limit; 2401/2400, 4375/4374, and 2097152/2066715 in the 7-limit.

	== ~~Harmonics~~ ==		=== Odd harmonics ===
	{{Harmonics in equal\|225}}		{{Harmonics in equal\|225}}

Line 19:		Line 22:
	* [[Bossier14]]		* [[Bossier14]]

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

2023-06-24T03:38:17Z

Added "harmonics in equal" table

← Older revision		Revision as of 03:38, 24 June 2023
Line 10:		Line 10:

	Using the 225c val, it tempers out 131072000/129140163 (rodan comma) and 30958682112/30517578125 (trisedodge comma) in the 5-limit; 2401/2400, 4375/4374, and 2097152/2066715 in the 7-limit.		Using the 225c val, it tempers out 131072000/129140163 (rodan comma) and 30958682112/30517578125 (trisedodge comma) in the 5-limit; 2401/2400, 4375/4374, and 2097152/2066715 in the 7-limit.

			== Harmonics ==
			{{Harmonics in equal\|225}}

	== Scales ==		== Scales ==

2022-10-04T21:24:54Z

Infobox ET added

← Older revision		Revision as of 21:24, 4 October 2022
Line 1:		Line 1:
			{{Infobox ET}}
	'''225edo''' is the [[EDO\|equal division of the octave]] into 225 parts of 5.3333 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 7-limit:		'''225edo''' is the [[EDO\|equal division of the octave]] into 225 parts of 5.3333 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 7-limit:
	* {{val\| 225 357 522 632 }} (patent val),		* {{val\| 225 357 522 632 }} (patent val),

2022-07-03T18:35:31Z

Sort key

← Older revision		Revision as of 18:35, 3 July 2022
Line 15:		Line 15:
	* [[Bossier14]]		* [[Bossier14]]

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