256ed5 - Revision history

Fredg999 category edits: Removing from Category:Ed5 using Cat-a-lot

2025-08-01T18:39:04Z

2024-12-22T04:13:53Z

2024-10-06T01:35:27Z

Harmonics

← Older revision		Revision as of 01:35, 6 October 2024
Line 5:		Line 5:

	== Theory ==		== Theory ==
	~~{{Harmonics in equal\|256\|5}}~~
	In 256ed5, the just perfect fifth of [[3/2]], corresponds to approximately 64.5 steps, thus occurring almost halfway between the [[quarter-comma meantone]] fifth and it's next step.		In 256ed5, the just perfect fifth of [[3/2]], corresponds to approximately 64.5 steps, thus occurring almost halfway between the [[quarter-comma meantone]] fifth and it's next step.

	Uniquely, 6/5 is nearly perfect.		Uniquely, [[6/5]] is nearly perfect.

			== Harmonics ==
			{{Harmonics in equal
			\| steps = 256
			\| num = 5
			\| denom = 1
			}}
			{{Harmonics in equal
			\| steps = 256
			\| num = 5
			\| denom = 1
			\| start = 12
			\| collapsed = 1
			}}

	== Table of intervals ==		== Table of intervals ==

2022-10-05T20:40:31Z

Infobox ET added

← Older revision		Revision as of 20:40, 5 October 2022
Line 1:		Line 1:
			{{Infobox ET}}
	'''256 equal divisions of the 5th harmonic''' is an equal-step tuning where each step represents a frequency ratio of 256th root of 5, which amounts to 3.90625 millipentaves or about 10.884 cents. It is equivalent to 110.2532 EDO.		'''256 equal divisions of the 5th harmonic''' is an equal-step tuning where each step represents a frequency ratio of 256th root of 5, which amounts to 3.90625 millipentaves or about 10.884 cents. It is equivalent to 110.2532 EDO.

2022-03-13T09:13:27Z

← Older revision		Revision as of 09:13, 13 March 2022
Line 1:		Line 1:
	'''256 equal divisions of the 5th harmonic''' is an equal-step tuning where each step represents a frequency ratio of 256th root of 5, which amounts to 3.90625 millipentaves or about 10.884 cents. It is equivalent to 110.2532 EDO.		'''256 equal divisions of the 5th harmonic''' is an equal-step tuning where each step represents a frequency ratio of 256th root of 5, which amounts to 3.90625 millipentaves or about 10.884 cents. It is equivalent to 110.2532 EDO.

	256ed5 combines [[dual-fifth ~~temperaments~~]] with [[quarter-comma meantone]].		256ed5 combines [[Dual-fifth system\|dual-fifth systems]] with [[quarter-comma meantone]].

	== Theory ==		== Theory ==

2022-03-13T09:11:13Z

@@ Line 1: / Line 1: @@
-'''256 equal divisions of the 5th harmonic''' is an equal-step tuning of 10.884 cents per each step. It is equivalent to 110.2532 EDO.
+'''256 equal divisions of the 5th harmonic''' is an equal-step tuning where each step represents a frequency ratio of 256th root of 5, which amounts to 3.90625 millipentaves or about 10.884 cents. It is equivalent to 110.2532 EDO.
 ed5 combines [[dual-fifth temperaments]] with [[quarter-comma meantone]].
@@ Line 8: / Line 8: @@
 Uniquely, 6/5 is nearly perfect.
 == See also ==

2022-01-17T23:09:39Z

Theory

@@ Line 4: / Line 4: @@
 == Theory ==
-{| class="wikitable center-all"
+{{Harmonics in equal|256|5}}
 In 256ed5, the just perfect fifth of [[3/2]], corresponds to approximately 64.5 steps, thus occurring almost halfway between the [[quarter-comma meantone]] fifth and it's next step.
 == See also ==

2021-11-28T15:12:19Z

add see-also section

← Older revision		Revision as of 15:12, 28 November 2021
Line 42:		Line 42:
	\|}		\|}
	In 256ed5, the just perfect fifth of [[3/2]], corresponds to approximately 64.5 steps, thus occurring almost halfway between the [[quarter-comma meantone]] fifth and it's next step.		In 256ed5, the just perfect fifth of [[3/2]], corresponds to approximately 64.5 steps, thus occurring almost halfway between the [[quarter-comma meantone]] fifth and it's next step.

			== See also ==
			* [[Ed5]]
			* [[110edo]]

	[[Category:Ed5]]		[[Category:Ed5]]

2021-11-28T15:07:58Z

(optional) format refinements

← Older revision		Revision as of 15:07, 28 November 2021
Line 4:		Line 4:

	== Theory ==		== Theory ==
	{\| class="wikitable"		{\| class="wikitable center-all"
			\|-
	\|+Approximation of prime harmonics in 256 e.d. 5		\|+Approximation of prime harmonics in 256 e.d. 5
	~~\|'''P'''~~
	\|2
	\|3
	\|5
	\|7
	~~\|11~~
	~~\|13~~
	~~\|17~~
	~~\|19~~
	~~\|23~~
	\|-		\|-
	\|~~'''~~Error (rc)~~'''~~		! style="text-align:right" \| Prime
	\|25		! 2
			! 3
			! 5
			! 7
			! 11
			! 13
			! 17
			! 19
			! 23
			\|-
			! style="text-align:right" \| Error (rc)
			\| +25
	\| -26		\| -26
	\|0		\| 0
	\| -48		\| -48
	\|41		\| +41
	\| -1		\| -1
	\| -34		\| -34
	\|35		\| +35
	\| -26		\| -26
	\|-		\|-
	\|~~'''~~Steps (reduced)~~'''~~		! style="text-align:right" \| Steps (reduced)
	\|110 (110)		\| 110 (110)
	\|175 (175)		\| 175 (175)
	\|256 (0)		\| 256 (0)
	\|310 (54)		\| 310 (54)
	\|381 (125)		\| 381 (125)
	\|408 (152)		\| 408 (152)
	\|451 (195)		\| 451 (195)
	\|468 (212)		\| 468 (212)
	\|499 (243)		\| 499 (243)
	\|}		\|}
	In 256ed5, the just perfect fifth of [[3/2]], corresponds to approximately 64.5 steps, thus occurring almost halfway between the [[quarter-comma meantone]] fifth and it's next step.		In 256ed5, the just perfect fifth of [[3/2]], corresponds to approximately 64.5 steps, thus occurring almost halfway between the [[quarter-comma meantone]] fifth and it's next step.

			[[Category:Ed5]]

2021-11-28T14:58:53Z

Theory: correct reduction to: 256 mod 256 = 0

← Older revision		Revision as of 14:58, 28 November 2021
Line 31:		Line 31:
	\|110 (110)		\|110 (110)
	\|175 (175)		\|175 (175)
	\|256 (~~256~~)		\|256 (0)
	\|310 (54)		\|310 (54)
	\|381 (125)		\|381 (125)
Line 39:		Line 39:
	\|499 (243)		\|499 (243)
	\|}		\|}
	In 256ed5, the just perfect fifth of [[3/2]], corresponds to approximately 64.5 steps, thus ~~occuring~~ almost halfway between the [[quarter-comma meantone]] fifth and it's next step.		In 256ed5, the just perfect fifth of [[3/2]], corresponds to approximately 64.5 steps, thus occurring almost halfway between the [[quarter-comma meantone]] fifth and it's next step.