256edo - Revision history

Francium: changed EDO intro to ED intro

2025-02-20T17:11:25Z

changed EDO intro to ED intro

← Older revision		Revision as of 17:11, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|256~~}}		{{ED intro}}

	256edo is [[enfactoring\|enfactored]] in the [[5-limit]] with the same tuning as [[128edo]], and the error of [[harmonic]] [[7/1\|7]] leads to in[[consistency]], which is likely one of the reasons this edo attracts little interest. To start with, consider the sharp-tending 256c [[val]] {{val\| 256 406 '''595''' 719 886 }}, which [[tempering out\|tempers out]] [[2401/2400]], [[3388/3375]], [[5120/5103]], so that it [[support]]s 7-limit [[hemififths]] and [[11-limit]] [[semihemi]]. The [[patent val]] {{val\| 256 406 '''594''' 719 886 }} tempers out [[540/539]], 2200/2187, [[4000/3969]], 12005/11979, among others. It is best tuned in the 2.3.7.11 [[subgroup]], in which it is consistent to the [[11-odd-limit]] minus intervals involving [[5/1\|5]].		256edo is [[enfactoring\|enfactored]] in the [[5-limit]] with the same tuning as [[128edo]], and the error of [[harmonic]] [[7/1\|7]] leads to in[[consistency]], which is likely one of the reasons this edo attracts little interest. To start with, consider the sharp-tending 256c [[val]] {{val\| 256 406 '''595''' 719 886 }}, which [[tempering out\|tempers out]] [[2401/2400]], [[3388/3375]], [[5120/5103]], so that it [[support]]s 7-limit [[hemififths]] and [[11-limit]] [[semihemi]]. The [[patent val]] {{val\| 256 406 '''594''' 719 886 }} tempers out [[540/539]], 2200/2187, [[4000/3969]], 12005/11979, among others. It is best tuned in the 2.3.7.11 [[subgroup]], in which it is consistent to the [[11-odd-limit]] minus intervals involving [[5/1\|5]].

FloraC: Review (note that enfactoring is resolved by including any single harmonic that is mapped to an odd step); +subsets and supersets

2024-03-14T08:49:37Z

Review (note that enfactoring is resolved by including any single harmonic that is mapped to an odd step); +subsets and supersets

← Older revision		Revision as of 08:49, 14 March 2024
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	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|256}}		{{EDO intro\|256}}
	~~== Theory ==~~
	~~{{harmonics in equal\|256}}~~
	256edo is [[contorted]] in the 5-limit, and the error of harmonic 7 leads to inconsistency, which is likely one of the reasons this EDO attracts little interest. 256edo is good at the 2.23.43.47 subgroup. If the error below 40% is considered "good", 256edo can be used to play no-fives 17 limit.

	256edo ~~can also be played using non~~-~~contorted harmonics, no matter how bad~~ the ~~approximation. Under such rule~~, ~~256edo supports~~ the 2.7~~.13.19 subgroup. In~~ the 2.~~7.13.19 subgroup in~~ the ~~patent~~ val, ~~256edo~~ tempers out ~~32851~~/~~32768~~, ~~and~~ [[support]]s the ~~corresponding 20 & 73 & 256 rank~~ 3 ~~temperament~~.		256edo is [[enfactoring\|enfactored]] in the [[5-limit]] with the same tuning as [[128edo]], and the error of [[harmonic]] [[7/1\|7]] leads to in[[consistency]], which is likely one of the reasons this edo attracts little interest. To start with, consider the sharp-tending 256c [[val]] {{val\| 256 406 '''595''' 719 886 }}, which [[tempering out\|tempers out]] [[2401/2400]], [[3388/3375]], [[5120/5103]], so that it [[support]]s 7-limit [[hemififths]] and [[11-limit]] [[semihemi]]. The [[patent val]] {{val\| 256 406 '''594''' 719 886 }} tempers out [[540/539]], 2200/2187, [[4000/3969]], 12005/11979, among others. It is best tuned in the 2.3.7.11 [[subgroup]], in which it is consistent to the [[11-odd-limit]] minus intervals involving [[5/1\|5]].

	~~[[Category:Equal divisions of~~ the ~~octave~~\|~~###]] <!-- 3-digit number -->~~		In the higher limits, it approximates harmonics 23, 43, and 47 quite accurately.

			=== Odd harmonics ===
			{{Harmonics in equal\|256}}

			=== Subsets and supersets ===
			Since 256 factors into {{factorization\|256}}, 256edo has subset edos {{EDOs\| 2, 4, 8, 16, 32, 64, and 128 }}.

Eliora: /* Theory */

2022-12-25T22:37:57Z

Theory

← Older revision		Revision as of 22:37, 25 December 2022
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	{{EDO intro\|256}}		{{EDO intro\|256}}
	== Theory ==		== Theory ==
	{{harmonics in equal}}		{{harmonics in equal\|256}}
	256edo is [[contorted]] in the 5-limit, and the error of harmonic 7 leads to inconsistency, which is likely one of the reasons this EDO attracts little interest. 256edo is good at the 2.23.43.47 subgroup. If the error below 40% is considered "good", 256edo can be used to play no-fives 17 limit.		256edo is [[contorted]] in the 5-limit, and the error of harmonic 7 leads to inconsistency, which is likely one of the reasons this EDO attracts little interest. 256edo is good at the 2.23.43.47 subgroup. If the error below 40% is considered "good", 256edo can be used to play no-fives 17 limit.

Eliora: oops

2022-12-25T22:37:41Z

oops

← Older revision		Revision as of 22:37, 25 December 2022
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	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro}}		{{EDO intro\|256}}
	== Theory ==		== Theory ==
	{{harmonics in equal}}		{{harmonics in equal}}

Eliora at 22:37, 25 December 2022

2022-12-25T22:37:31Z

← Older revision		Revision as of 22:37, 25 December 2022
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	{{Infobox ET}}		{{Infobox ET}}
	The 256 equal division divides the [[octave]] into 256 equal parts of exactly 4.6875 [[cent]]s each. It is [[contorted]] in the 5-limit, and the error of harmonic 7 leads to inconsistency, which is likely one of the reasons this EDO ~~attracts little interest.~~		{{EDO intro}}

	== Theory ==		== Theory ==
	{{~~Primes~~ in ~~edo\|256\|columns=15~~}}		{{harmonics in equal}}
	256edo is good at the 2.23.43.47 subgroup. If the error below 40% is considered "good", 256edo can be used to play no-fives 17 limit.		256edo is [[contorted]] in the 5-limit, and the error of harmonic 7 leads to inconsistency, which is likely one of the reasons this EDO attracts little interest. 256edo is good at the 2.23.43.47 subgroup. If the error below 40% is considered "good", 256edo can be used to play no-fives 17 limit.

	256edo can also be played using non-contorted harmonics, no matter how bad the approximation. Under such rule, 256edo supports the 2.7.13.19 subgroup. In the 2.7.13.19 subgroup in the patent val, 256edo tempers out 32851/32768, and [[support]]s the corresponding 20 & 73 & 256 rank 3 temperament.		256edo can also be played using non-contorted harmonics, no matter how bad the approximation. Under such rule, 256edo supports the 2.7.13.19 subgroup. In the 2.7.13.19 subgroup in the patent val, 256edo tempers out 32851/32768, and [[support]]s the corresponding 20 & 73 & 256 rank 3 temperament.

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

Plumtree: Infobox ET added

2022-10-04T21:28:24Z

Infobox ET added

← Older revision		Revision as of 21:28, 4 October 2022
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			{{Infobox ET}}
	The 256 equal division divides the [[octave]] into 256 equal parts of exactly 4.6875 [[cent]]s each. It is [[contorted]] in the 5-limit, and the error of harmonic 7 leads to inconsistency, which is likely one of the reasons this EDO attracts little interest.		The 256 equal division divides the [[octave]] into 256 equal parts of exactly 4.6875 [[cent]]s each. It is [[contorted]] in the 5-limit, and the error of harmonic 7 leads to inconsistency, which is likely one of the reasons this EDO attracts little interest.

Fredg999 category edits: Sort key

2022-07-03T19:05:19Z

Sort key

← Older revision		Revision as of 19:05, 3 July 2022
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	256edo can also be played using non-contorted harmonics, no matter how bad the approximation. Under such rule, 256edo supports the 2.7.13.19 subgroup. In the 2.7.13.19 subgroup in the patent val, 256edo tempers out 32851/32768, and [[support]]s the corresponding 20 & 73 & 256 rank 3 temperament.		256edo can also be played using non-contorted harmonics, no matter how bad the approximation. Under such rule, 256edo supports the 2.7.13.19 subgroup. In the 2.7.13.19 subgroup in the patent val, 256edo tempers out 32851/32768, and [[support]]s the corresponding 20 & 73 & 256 rank 3 temperament.
	[[Category:Equal divisions of the octave]]
			[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->

Eliora: /* Theory */

2022-01-30T23:27:02Z

Theory

← Older revision		Revision as of 23:27, 30 January 2022
Line 3:		Line 3:
	== Theory ==		== Theory ==
	{{Primes in edo\|256\|columns=15}}		{{Primes in edo\|256\|columns=15}}
	256edo is good at the 2.23.43.47 subgroup. If the error below 40% is considered "good", 256edo can be used to play no-fives 17 limit. If the "prime number obsession" approach found in math circles is applied - then 256edo can be played using the coprime harmonics, no matter how bad the approximation. Under such rule, 256edo supports the 2.7.13.19 subgroup.		256edo is good at the 2.23.43.47 subgroup. If the error below 40% is considered "good", 256edo can be used to play no-fives 17 limit.

	In the 2.7.13.19 subgroup in the patent val, 256edo tempers out 32851/32768, and [[support]]s the corresponding 20 & 73 & 256 rank 3 temperament.		256edo can also be played using non-contorted harmonics, no matter how bad the approximation. Under such rule, 256edo supports the 2.7.13.19 subgroup. In the 2.7.13.19 subgroup in the patent val, 256edo tempers out 32851/32768, and [[support]]s the corresponding 20 & 73 & 256 rank 3 temperament.
	[[Category:Equal divisions of the octave]]		[[Category:Equal divisions of the octave]]

Cmloegcmluin at 17:51, 25 January 2022

2022-01-25T17:51:50Z

← Older revision		Revision as of 17:51, 25 January 2022
Line 5:		Line 5:
	256edo is good at the 2.23.43.47 subgroup. If the error below 40% is considered "good", 256edo can be used to play no-fives 17 limit. If the "prime number obsession" approach found in math circles is applied - then 256edo can be played using the coprime harmonics, no matter how bad the approximation. Under such rule, 256edo supports the 2.7.13.19 subgroup.		256edo is good at the 2.23.43.47 subgroup. If the error below 40% is considered "good", 256edo can be used to play no-fives 17 limit. If the "prime number obsession" approach found in math circles is applied - then 256edo can be played using the coprime harmonics, no matter how bad the approximation. Under such rule, 256edo supports the 2.7.13.19 subgroup.

	In the 2.7.13.19 subgroup in the patent val, 256edo tempers out 32851/32768, and ~~supports~~ the corresponding 20 & 73 & 256 rank 3 temperament.		In the 2.7.13.19 subgroup in the patent val, 256edo tempers out 32851/32768, and [[support]]s the corresponding 20 & 73 & 256 rank 3 temperament.
	[[Category:Equal divisions of the octave]]		[[Category:Equal divisions of the octave]]

Eliora at 17:17, 5 January 2022

2022-01-05T17:17:24Z

← Older revision		Revision as of 17:17, 5 January 2022
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	The 256 equal division divides the [[octave]] into 256 equal parts of exactly 4.6875 [[cent]]s each. It is [[contorted]] in the 5-limit, and the error of harmonic 7 leads to inconsistency, which is likely one of the reasons this EDO attracts little interest.		The 256 equal division divides the [[octave]] into 256 equal parts of exactly 4.6875 [[cent]]s each. It is [[contorted]] in the 5-limit, and the error of harmonic 7 leads to inconsistency, which is likely one of the reasons this EDO attracts little interest.

			== Theory ==
			{{Primes in edo\|256\|columns=15}}
			256edo is good at the 2.23.43.47 subgroup. If the error below 40% is considered "good", 256edo can be used to play no-fives 17 limit. If the "prime number obsession" approach found in math circles is applied - then 256edo can be played using the coprime harmonics, no matter how bad the approximation. Under such rule, 256edo supports the 2.7.13.19 subgroup.

			In the 2.7.13.19 subgroup in the patent val, 256edo tempers out 32851/32768, and supports the corresponding 20 & 73 & 256 rank 3 temperament.
	[[Category:Equal divisions of the octave]]		[[Category:Equal divisions of the octave]]