DKW theory - Revision history

FloraC: Cleanup on the table

2025-09-11T05:35:44Z

Cleanup on the table

← Older revision		Revision as of 05:35, 11 September 2025
Line 41:		Line 41:
	Note all commas considered here (aside from complexity-1) are those that contain at least one minus sign in their signature expression.		Note all commas considered here (aside from complexity-1) are those that contain at least one minus sign in their signature expression.

	{\| class="wikitable center-~~1 center-2 center-3 center-4~~"		{\| class="wikitable center-all"
	\|-		\|-
	! ~~rowspan="2" \|~~ Comma		! Comma
	! ~~rowspan="2" \|~~ Defined temperament		! Defined<br>temperament
	! ~~rowspan="2" \|~~ Complexity		! Complexity
	! ~~rowspan="2" \|~~ Subgroup monzo (9/8.16/15.25/24)		! Subgroup monzo<br>(9/8.16/15.25/24)
	\|-
	!
	\|-		\|-
	\| [[9/8]]		\| [[9/8]]
	\| [[~~Very_low_accuracy_temperaments~~#Antitonic\|Antitonic]]		\| [[Very low accuracy temperaments #Antitonic\|Antitonic]]
	\| 1		\| 1
	\| {{~~monzo~~\| 1 0 0 }}		\| {{Monzo\| 1 0 0 }}
	\|-		\|-
	\| [[16/15]]		\| [[16/15]]
	\| [[Father]]		\| [[Father]]
	\| 1		\| 1
	\| {{~~monzo~~\| 0 1 0 }}		\| {{Monzo\| 0 1 0 }}
	\|-		\|-
	\| [[25/24]]		\| [[25/24]]
	\| [[Dicot]]		\| [[Dicot]]
	\| 1		\| 1
	\| {{~~monzo~~\| 0 0 1 }}		\| {{Monzo\| 0 0 1 }}
	\|-		\|-
	\| [[27/25]]		\| [[27/25]]
	\| [[Bug]]		\| [[Bug]]
	\| 2		\| 2
	\| {{~~monzo~~\| 1 0 -1 }}		\| {{Monzo\| 1 0 -1 }}
	\|-		\|-
	\| [[135/128]]		\| [[135/128]]
	\| [[Mavila]]		\| [[Mavila]]
	\| 2		\| 2
	\| {{~~monzo~~\| 1 -1 0 }}		\| {{Monzo\| 1 -1 0 }}
	\|-		\|-
	\| [[128/125]]		\| [[128/125]]
	\| [[Augmented]]		\| [[Augmented (temperament)\|Augmented]]
	\| 2		\| 2
	\| {{~~monzo~~\| 0 1 -1 }}		\| {{Monzo\| 0 1 -1 }}
	\|-		\|-
	\| [[648/625]]		\| [[648/625]]
	\| [[~~Dimipent~~]]		\| [[Diminished (temperament)\|Diminished]]
	\| 3		\| 3
	\| {{~~monzo~~\| 1 0 -2 }}		\| {{Monzo\| 1 0 -2 }}
	\|-		\|-
	\| [[2048/2025]]		\| [[2048/2025]]
	\| [[Diaschismic]]		\| [[Diaschismic]]
	\| 3		\| 3
	\| {{~~monzo~~\| -1 2 0 }}		\| {{Monzo\| -1 2 0 }}
	\|-		\|-
	\| [[3125/3072]]		\| [[3125/3072]]
	\| [[Magic]]		\| [[Magic]]
	\| 3		\| 3
	\| {{~~monzo~~\| 0 -1 2 }}		\| {{Monzo\| 0 -1 2 }}
	\|-		\|-
	\| [[81/80]]		\| [[81/80]]
	\| [[Meantone]]		\| [[Meantone]]
	\| 3		\| 3
	\| {{~~monzo~~\| 1 -1 -1 }}		\| {{Monzo\| 1 -1 -1 }}
	\|}		\|}

VectorGraphics at 00:11, 13 June 2025

2025-06-13T00:11:59Z

← Older revision		Revision as of 00:11, 13 June 2025
Line 46:		Line 46:
	! rowspan="2" \| Defined temperament		! rowspan="2" \| Defined temperament
	! rowspan="2" \| Complexity		! rowspan="2" \| Complexity
	! rowspan="2" \| ~~Smonzo~~ (9/8.16/15.25/24)		! rowspan="2" \| Subgroup monzo (9/8.16/15.25/24)
	\|-		\|-
	!		!

Lériendil: Undo revision 153850 by Lériendil (talk)

2024-09-03T13:20:46Z

Undo revision 153850 by Lériendil (talk)

← Older revision		Revision as of 13:20, 3 September 2024
Line 47:		Line 47:
	! rowspan="2" \| Complexity		! rowspan="2" \| Complexity
	! rowspan="2" \| Smonzo (9/8.16/15.25/24)		! rowspan="2" \| Smonzo (9/8.16/15.25/24)
			\|-
			!
			\|-
	\| [[9/8]]		\| [[9/8]]
	\| [[Very_low_accuracy_temperaments#Antitonic\|Antitonic]]		\| [[Very_low_accuracy_temperaments#Antitonic\|Antitonic]]

Lériendil: /* DKW theory in the 5-limit */

2024-09-03T13:20:30Z

DKW theory in the 5-limit

← Older revision		Revision as of 13:20, 3 September 2024
Line 47:		Line 47:
	! rowspan="2" \| Complexity		! rowspan="2" \| Complexity
	! rowspan="2" \| Smonzo (9/8.16/15.25/24)		! rowspan="2" \| Smonzo (9/8.16/15.25/24)
	\|-
	!
	\|-
	\| [[9/8]]		\| [[9/8]]
	\| [[Very_low_accuracy_temperaments#Antitonic\|Antitonic]]		\| [[Very_low_accuracy_temperaments#Antitonic\|Antitonic]]

Lériendil: /* DKW theory in the 5-limit */

2024-09-03T13:20:18Z

DKW theory in the 5-limit

← Older revision		Revision as of 13:20, 3 September 2024
Line 47:		Line 47:
	! rowspan="2" \| Complexity		! rowspan="2" \| Complexity
	! rowspan="2" \| Smonzo (9/8.16/15.25/24)		! rowspan="2" \| Smonzo (9/8.16/15.25/24)
			\|-
			!
	\|-		\|-
	\| [[9/8]]		\| [[9/8]]

Lériendil: /* DKW theory in the 5-limit */

2024-09-03T13:19:40Z

DKW theory in the 5-limit

← Older revision		Revision as of 13:19, 3 September 2024
Line 47:		Line 47:
	! rowspan="2" \| Complexity		! rowspan="2" \| Complexity
	! rowspan="2" \| Smonzo (9/8.16/15.25/24)		! rowspan="2" \| Smonzo (9/8.16/15.25/24)
	!
	\|-		\|-
	\| [[9/8]]		\| [[9/8]]

Lériendil: /* DKW theory in the 5-limit */

2024-09-03T13:19:33Z

DKW theory in the 5-limit

← Older revision		Revision as of 13:19, 3 September 2024
Line 47:		Line 47:
	! rowspan="2" \| Complexity		! rowspan="2" \| Complexity
	! rowspan="2" \| Smonzo (9/8.16/15.25/24)		! rowspan="2" \| Smonzo (9/8.16/15.25/24)
	\|-
	!		!
	\|-		\|-

Lériendil: /* DKW theory in the 5-limit */

2024-08-01T21:51:26Z

DKW theory in the 5-limit

@@ Line 39: / Line 39: @@
 Below are commas with simple expressions in terms of these intervals, with "complexity" measured as the sum of the absolute values of powers of '''A''', '''B''', and '''C'''.
-tbd
+Note all commas considered here (aside from complexity-1) are those that contain at least one minus sign in their signature expression.
 [[Category:Regular temperament tuning]]
 [[Category:Diamond]]
 {{Todo| add examples }}

Lériendil: /* DKW theory in the 5-limit */

2024-08-01T21:35:32Z

DKW theory in the 5-limit

← Older revision		Revision as of 21:35, 1 August 2024
Line 36:		Line 36:

	== DKW theory in the 5-limit ==		== DKW theory in the 5-limit ==
	By far the most important three-prime subgroup is the [[5-limit]], i.e. the 2.3.5 subgroup. It turns out that the 2.3.5 tonality diamond's ordering is type ''N-VI'', and that its signature is '''C''' = [[9/8]] : '''B'' = [[16/15]] : '''A''' = [[25/24]].		By far the most important three-prime subgroup is the [[5-limit]], i.e. the 2.3.5 subgroup. It turns out that the 2.3.5 tonality diamond's ordering is type ''N-VI'', and that its signature is '''C''' = [[9/8]] : '''B''' = [[16/15]] : '''A''' = [[25/24]].

	Below are commas with simple expressions in terms of these intervals, with "complexity" measured as the sum of the absolute values of powers of '''A''', '''B''', and '''C'''.		Below are commas with simple expressions in terms of these intervals, with "complexity" measured as the sum of the absolute values of powers of '''A''', '''B''', and '''C'''.

Lériendil at 21:35, 1 August 2024

2024-08-01T21:35:18Z

← Older revision		Revision as of 21:35, 1 August 2024
Line 36:		Line 36:

	== DKW theory in the 5-limit ==		== DKW theory in the 5-limit ==
	By far the most important three-prime subgroup is the [[5-limit]], i.e. the 2.3.5 subgroup.		By far the most important three-prime subgroup is the [[5-limit]], i.e. the 2.3.5 subgroup. It turns out that the 2.3.5 tonality diamond's ordering is type ''N-VI'', and that its signature is '''C''' = [[9/8]] : '''B'' = [[16/15]] : '''A''' = [[25/24]].

			Below are commas with simple expressions in terms of these intervals, with "complexity" measured as the sum of the absolute values of powers of '''A''', '''B''', and '''C'''.
			tbd
	[[Category:Regular temperament tuning]]		[[Category:Regular temperament tuning]]
	[[Category:Diamond]]		[[Category:Diamond]]
	{{Todo\| add examples }}		{{Todo\| add examples }}