User:Moremajorthanmajor/28wtn - Revision history

Sintel: Sintel moved page 28wtn to User:Moremajorthanmajor/28wtn

2025-03-31T17:19:59Z

Sintel moved page 28wtn to User:Moremajorthanmajor/28wtn

← Older revision	Revision as of 17:19, 31 March 2025
(No difference)

Moremajorthanmajor at 02:57, 4 June 2021

2021-06-04T02:57:33Z

← Older revision		Revision as of 02:57, 4 June 2021
Line 1:		Line 1:
	A '''28 tone well tempered nonet''' (28WTN) is related to well temperaments of [[24edo]], but with a nonet rather than the 2/1 being constant. Its patent tunings optimally alternate [[EDF\|division of the just perfect fifth]] into 14 equal parts (14EDF) with sequences of fourteen equal steps of 42.8571 to 57.1429 cents each. This will create fourteen equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth~~. It is also the largest wtn related to well temperaments of a unique edo~~.		A '''28 tone well tempered nonet''' (28WTN) is related to well temperaments of [[24edo]], but with a nonet rather than the 2/1 being constant. Its patent tunings optimally alternate [[EDF\|division of the just perfect fifth]] into 14 equal parts (14EDF) with sequences of fourteen equal steps of 42.8571 to 57.1429 cents each. This will create fourteen equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth.

	==Patent Intervals==		==Patent Intervals==

Moremajorthanmajor: /* Optimal Intervals */

2021-06-03T22:20:34Z

Optimal Intervals

← Older revision		Revision as of 22:20, 3 June 2021
Line 1:		Line 1:
	A '''28 tone well tempered nonet''' (28WTN) is related to well temperaments of ~~[[23edo]] and~~ [[24edo]], but with a nonet rather than the 2/1 being constant. Its patent tunings optimally alternate [[EDF\|division of the just perfect fifth]] into 14 equal parts (14EDF) with sequences of fourteen equal steps of 42.8571 to 57.1429 cents each. This will create fourteen equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth.		A '''28 tone well tempered nonet''' (28WTN) is related to well temperaments of [[24edo]], but with a nonet rather than the 2/1 being constant. Its patent tunings optimally alternate [[EDF\|division of the just perfect fifth]] into 14 equal parts (14EDF) with sequences of fourteen equal steps of 42.8571 to 57.1429 cents each. This will create fourteen equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth. It is also the largest wtn related to well temperaments of a unique edo.

	==~~Optimal~~ Intervals==		==Patent Intervals==
	{\| class="wikitable"		{\| class="wikitable"
	\|+		\|+
	!		\|
	!Target a		!Target
	!~~Target b~~		!Alternating [[edo]] and *ed(9/8)
	\|-		\|-
	!1		\|1
	~~! colspan="2"~~ \|50.1396		\|50.1396
			\|50
	\|-		\|-
	!2		\|2
	~~! colspan="2"~~ \|100.2793		\|100.2793
			\|100
	\|-		\|-
	!3		\|3
	~~! colspan="2"~~ \|150.4189		\|150.4189
			\|150
	\|-		\|-
	!4		\|4
	~~! colspan="2"~~ \|200.5586		\|200.5586
			\|200
	\|-		\|-
	!5		\|5
	~~! colspan="2"~~ \|250.6982		\|250.6982
			\|250
	\|-		\|-
	!6		\|6
	~~! colspan="2"~~ \|300.8379		\|300.8379
			\|300
	\|-		\|-
	!7		\|7
	~~! colspan="2"~~ \|350.9775		\|350.9775
			\|350
	\|-		\|-
	!8		\|8
	~~! colspan="2"~~ \|401.1171		\|401.1171
			\|400
	\|-		\|-
	!9		\|9
	~~! colspan="2"~~ \|451.2568		\|451.2568
			\|450
	\|-		\|-
	!10		\|10
	~~! colspan="2"~~ \|501.3964		\|501.3964
			\|500
	\|-		\|-
	!11		\|11
	~~! colspan="2"~~ \|551.536		\|551.536
			\|550
	\|-		\|-
	!12		\|12
	~~! colspan="2"~~ \|601.6757		\|601.6757
			\|600
	\|-		\|-
	!13		\|13
	~~! colspan="2"~~ \|651.8154		\|651.8154
			\|650
	\|-		\|-
	!14		\|14
	~~! colspan="2"~~ \|701.955		\|701.955
			\|700
	\|-		\|-
	\|15		\|15
	~~\|757.2933~~
	\|751.7595		\|751.7595
			\|750
	\|-		\|-
	\|16		\|16
	~~\|812.6317~~
	\|801.564		\|801.564
			\|800
	\|-		\|-
	\|17		\|17
	~~\|867.97~~
	\|851.3685		\|851.3685
			\|850
	\|-		\|-
	\|18		\|18
	~~\|923.3083~~
	\|901.173		\|901.173
			\|900
	\|-		\|-
	\|19		\|19
	~~\|978.6467~~
	\|950.9775		\|950.9775
			\|950
	\|-		\|-
	\|20		\|20
	~~\|1033.985~~
	\|1000.782		\|1000.782
			\|1000
	\|-		\|-
	\|21		\|21
	~~\|1089.3233~~
	\|1050.6865		\|1050.6865
			\|1050
	\|-		\|-
	\|22		\|22
	~~\|1144.6617~~
	\|1100.391		\|1100.391
			\|1100
	\|-		\|-
	\|23		\|23
	~~\|1200~~
	\|1150.1955		\|1150.1955
			\|1150
	\|-		\|-
	\|24		\|24
	~~\|1255.3383~~
	\|1200		\|1200
			\|1200.000
	\|-		\|-
	\|25		\|25
	~~\|1310.6767~~
	\|1249.8045		\|1249.8045
			\|1250.9775
	\|-		\|-
	\|26		\|26
	~~\|1366.015~~
	\|1299.609		\|1299.609
			\|1301.955
	\|-		\|-
	\|27		\|27
	~~\|1421.3533~~
	\|1349.4135		\|1349.4135
			\|1352.9325
	\|-		\|-
	\|28		\|28
	~~\|1476.6917~~
	\|1399.218		\|1399.218
			\|1403.91
	\|}		\|}

Xenwolf: cat+todo, see comment

2021-06-02T07:04:18Z

cat+todo, see comment

← Older revision		Revision as of 07:04, 2 June 2021
Line 106:		Line 106:
	\|1399.218		\|1399.218
	\|}		\|}

			[[Category:Well tempered nonet]]

			{{todo\|clarify\|unify precision\|comment="Target a" and "Target b" are not self-explanatory, how are the values calculated?\|inline=1}}

Moremajorthanmajor at 00:03, 2 June 2021

2021-06-02T00:03:05Z

← Older revision		Revision as of 00:03, 2 June 2021
Line 1:		Line 1:
	A '''28 tone well tempered nonet''' (28WTN) is related to well temperaments of [[23edo]] and [[24edo]], but with a nonet rather than the 2/1 being constant. Its patent tunings alternate [[EDF\|division of the just perfect fifth]] into 14 equal parts (14EDF) with sequences of fourteen equal steps of 42.8571 to 57.1429 cents each. This will create fourteen equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth.		A '''28 tone well tempered nonet''' (28WTN) is related to well temperaments of [[23edo]] and [[24edo]], but with a nonet rather than the 2/1 being constant. Its patent tunings optimally alternate [[EDF\|division of the just perfect fifth]] into 14 equal parts (14EDF) with sequences of fourteen equal steps of 42.8571 to 57.1429 cents each. This will create fourteen equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth.

	==Optimal Intervals==		==Optimal Intervals==

Moremajorthanmajor: /* Optimal Intervals */

2021-06-01T03:26:56Z

Optimal Intervals

Show changes

Moremajorthanmajor at 18:26, 31 May 2021

2021-05-31T18:26:41Z

← Older revision		Revision as of 18:26, 31 May 2021
Line 1:		Line 1:
	A '''28 tone well tempered nonet''' (28WTN) is related to well temperaments of [[23edo]] and [[24edo]], but with a nonet rather than the 2/1 being constant. ~~It alternates~~ [[EDF\|division of the just perfect fifth]] into 14 equal parts (14EDF) with sequences of fourteen equal steps of 42.8571 to 57.1429 cents each. This will create fourteen equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth.		A '''28 tone well tempered nonet''' (28WTN) is related to well temperaments of [[23edo]] and [[24edo]], but with a nonet rather than the 2/1 being constant. Its patent tunings alternate [[EDF\|division of the just perfect fifth]] into 14 equal parts (14EDF) with sequences of fourteen equal steps of 42.8571 to 57.1429 cents each. This will create fourteen equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth.

	==Optimal Intervals==		==Optimal Intervals==

Moremajorthanmajor: Created page with "A '''28 tone well tempered nonet''' (28WTN) is related to well temperaments of 23edo and 24edo, but with a nonet rather than the 2/1 being constant. It alternates ED..."

2021-05-31T06:03:42Z

Created page with "A '''28 tone well tempered nonet''' (28WTN) is related to well temperaments of 23edo and 24edo, but with a nonet rather than the 2/1 being constant. It alternates ED..."

New page

A '''28 tone well tempered nonet''' (28WTN) is related to well temperaments of [[23edo]] and [[24edo]], but with a nonet rather than the 2/1 being constant. It alternates [[EDF|division of the just perfect fifth]] into 14 equal parts (14EDF) with sequences of fourteen equal steps of 42.8571 to 57.1429 cents each. This will create fourteen equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth.

==Optimal Intervals==
{| class="wikitable"
|+
!
!Minimum a
!Maximum a
!Minimum b
!Maximum b
|-
!1
! colspan="4" |50.1396
|-
!2
! colspan="4" |100.2793
|-
!3
! colspan="4" |150.4189
|-
!4
! colspan="4" |200.5586
|-
!5
! colspan="4" |250.6982
|-
!6
! colspan="4" |300.8379
|-
!7
! colspan="4" |350.9775
|-
!8
! colspan="4" |401.1171
|-
!9
! colspan="4" |451.2568
|-
!10
! colspan="4" |501.3964
|-
!11
! colspan="4" |551.536
|-
!12
! colspan="4" |601.6757
|-
!13
! colspan="4" |651.8154
|-
!14
! colspan="4" |701.955
|-
|15
|755.2883
|759.0979
|749.955
|753.3836
|-
|16
|808.6117
|816.2407
|797.955
|804.8121
|-
|17
|861.955
|873.3836
|845.955
|856.2407
|-
|18
|915.2883
|930.5264
|893.955
|907.6693
|-
|19
|968.6117
|987.6693
|941.955
|959.0979
|-
|20
|1021.955
|1044.8121
|989.955
|1010.5264
|-
|21
|1075.2883
|1101.955
|1037.955
|1061.955
|-
|22
|1128.6117
|1159.0979
|1085.955
|1113.3836
|-
|23
|1181.955
|1216.2407
|1133.995
|1164.8121
|-
|24
|1235.2883
|1273.3836
|1181.955
|1216.2407
|-
|25
|1288.6117
|1330.5264
|1229.995
|1267.6693
|-
|26
|1341.955
|1387.6693
|1277.995
|1319.0979
|-
|27
|1395.2883
|1444.8121
|1325.995
|1370.5264
|-
|28
|1448.6117
|1501.955
|1373.995
|1421.955
|}