User:Aura/Aura's introduction to 159edo - Revision history

Aura at 17:54, 29 November 2025

2025-11-29T17:54:51Z

← Older revision		Revision as of 17:54, 29 November 2025
Line 1,921:		Line 1,921:

	{\| class="mw-collapsible mw-collapsed wikitable center-1"		{\| class="mw-collapsible mw-collapsed wikitable center-1"
	\|+ style="font-size: 105%; white-space: nowrap;" \| Table of basic ~~LYdian~~ triads		\|+ style="font-size: 105%; white-space: nowrap;" \| Table of basic Lydian triads
	\|-		\|-
	! Name		! Name

2025-11-29T17:54:33Z

← Older revision		Revision as of 17:54, 29 November 2025
Line 1,921:		Line 1,921:

	{\| class="mw-collapsible mw-collapsed wikitable center-1"		{\| class="mw-collapsible mw-collapsed wikitable center-1"
	\|+ style="font-size: 105%; white-space: nowrap;" \| Table of basic ~~Ionian~~ triads		\|+ style="font-size: 105%; white-space: nowrap;" \| Table of basic LYdian triads
	\|-		\|-
	! Name		! Name

2025-11-29T17:54:06Z

@@ Line 1,890: / Line 1,890: @@
 | G#↓
 | 78
-| Antitonic (Sycophant)
+| Sycophant
 | [[45/32]]
 |-
@@ Line 1,920: / Line 1,920: @@
 As a consequence of this particular scale structure, you have the following basic chords...
+{| class="mw-collapsible mw-collapsed wikitable center-1"

2025-11-29T17:36:50Z

Fixed the name of a table

← Older revision		Revision as of 17:36, 29 November 2025
Line 1,861:		Line 1,861:

	{\| class="mw-collapsible mw-collapsed wikitable center-1"		{\| class="mw-collapsible mw-collapsed wikitable center-1"
	\|+ style="font-size: 105%; white-space: nowrap;" \| Table of ~~Ionian~~ notes and intervals		\|+ style="font-size: 105%; white-space: nowrap;" \| Table of Lydian notes and intervals
	\|-		\|-
	! Interval Name		! Interval Name

2025-11-29T17:36:23Z

Will eventually add more.

← Older revision		Revision as of 17:36, 29 November 2025
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	\| This tetrad is likely to decompose into a voicing variation on the corresponding triad if the same scale degree is used as a chord root multiple times in a row		\| This tetrad is likely to decompose into a voicing variation on the corresponding triad if the same scale degree is used as a chord root multiple times in a row
	\|}		\|}

			With the above scale steps and chords, this variation of Phrygian in 159edo actually presents unexpected possibilities compared to its more traditional counterpart.

			==== Lydian ====

			This mode is optimized for 5-limit using a variation on the right-handed Zarlino diatonic scale.

			{\| class="mw-collapsible mw-collapsed wikitable center-1"
			\|+ style="font-size: 105%; white-space: nowrap;" \| Table of Ionian notes and intervals
			\|-
			! Interval Name
			! Notation (from D)
			! Steps from Tonic
			! Function
			! Corresponding JI
			\|-
			\| Perfect Unison
			\| D
			\| 0
			\| Tonic
			\| [[1/1]]
			\|-
			\| Pythagorean Major Second
			\| E
			\| 27
			\| Supertonic (Bidominant)
			\| [[9/8]]
			\|-
			\| Ptolemaic Major Third
			\| F#↓
			\| 51
			\| Mesodistomediant
			\| [[5/4]]
			\|-
			\| Perfect Fourth
			\| G#↓
			\| 78
			\| Antitonic (Sycophant)
			\| [[45/32]]
			\|-
			\| Perfect Fifth
			\| A
			\| 93
			\| Dominant
			\| [[3/2]]
			\|-
			\| Pythagorean Major Sixth
			\| B
			\| 120
			\| Proximocontramediant (Tridominant)
			\| [[27/16]]
			\|-
			\| Ptolemaic Major Seventh
			\| C#↓
			\| 144
			\| Distosubcollocant
			\| [[15/8]]
			\|-
			\| Perfect Octave
			\| D
			\| 159
			\| Tonic
			\| [[2/1]]
			\|}

			As a consequence of this particular scale structure, you have the following basic chords...

2025-10-30T23:17:08Z

← Older revision		Revision as of 23:17, 30 October 2025
Line 1,845:		Line 1,845:
	\| 1/(36:45:54:64)		\| 1/(36:45:54:64)
	\| This dissonant tetrad is an option for imperfect half cadences in the 5-limit		\| This dissonant tetrad is an option for imperfect half cadences in the 5-limit
			\|-
			\| Ptolemaic Major Seventh
			\| D, F#↓, A, C#↓
			\| 0, 51, 93, 144
			\| b↑VI
			\| 8:10:12:15
			\| This tetrad is likely to decompose into a voicing variation on the corresponding triad if the same scale degree is used as a chord root multiple times in a row
	\|}		\|}

2025-10-30T23:12:55Z

← Older revision		Revision as of 23:12, 30 October 2025
Line 1,658:		Line 1,658:
	\| I		\| I
	\| 90:108:135:160		\| 90:108:135:160
	\| ~~This dissonant tetrad is perhaps best considered a cross between a suspension and a triad owing to the dissonance of the wolf fifth~~		\|
	\|-		\|-
	\| Pythagorean Major Seventh		\| Pythagorean Major Seventh
Line 1,816:		Line 1,816:
	\| I		\| I
	\| 90:108:135:160		\| 90:108:135:160
	\| ~~This dissonant tetrad is perhaps best considered a cross between a suspension and a triad owing to the dissonance of the wolf fifth~~		\|
	\|-		\|-
	\| Ptolemaic Major Seventh		\| Ptolemaic Major Seventh
Line 1,830:		Line 1,830:
	\| b↑III		\| b↑III
	\| 1/(45:54:64:80)		\| 1/(45:54:64:80)
	\| This dissonant dominant tetrad has a different function than its more traditional counterpart		\| This dissonant dominant tetrad has a slightly different function than its more traditional counterpart
			\|-
			\| Ptolemaic Minor Seventh
			\| D, F↑, A, C↑
			\| 0, 42, 93, 135
			\| IV, bVII
			\| 10:12:15:18
			\|
			\|-
			\| Ptolemaic Parallel Half-Diminished
			\| D, F, Ab↑, C
			\| 0, 39, 81, 132
			\| V
			\| 1/(36:45:54:64)
			\| This dissonant tetrad is an option for imperfect half cadences in the 5-limit
	\|}		\|}

2025-05-16T15:47:52Z

Fixed notation error in chart

← Older revision		Revision as of 15:47, 16 May 2025
Line 1,015:		Line 1,015:
	\| SM6, kUM6		\| SM6, kUM6
	\| Greater Supermajor Second, Narrow Inframinor Seventh		\| Greater Supermajor Second, Narrow Inframinor Seventh
	\| Cb<, Bt<↓, B↑/		\| Cd<, Bt<↓, B↑/
	\| 0		\| 0
	\| 7		\| 7

2025-05-16T14:10:20Z

← Older revision		Revision as of 14:10, 16 May 2025
Line 623:		Line 623:
	\| kkA4, RuA4, kd5		\| kkA4, RuA4, kd5
	\| Diptolemaic Augmented Fourth, Retroptolemaic Diminished Fifth		\| Diptolemaic Augmented Fourth, Retroptolemaic Diminished Fifth
	\| G#↓↓, Ab↓		\| Gt>/, G#↓↓, Ab↓
	\| -3		\| -3
	\| 4		\| 4
Line 695:		Line 695:
	\| KKd5, rUDd5, KA4		\| KKd5, rUDd5, KA4
	\| Diptolemaic Diminished Fifth, Retroptolemaic Augmented Fourth		\| Diptolemaic Diminished Fifth, Retroptolemaic Augmented Fourth
	\| Ab↑↑, G#↑		\| Ad<\, Ab↑↑, G#↑
	\| -3		\| -3
	\| 4		\| 4
Line 719:		Line 719:
	\| Rm5, rUA4		\| Rm5, rUA4
	\| Wide Paraminor Fifth, Retrodiptolemaic Augmented Fourth		\| Wide Paraminor Fifth, Retrodiptolemaic Augmented Fourth
	\| Ad<\, G#↑, Ab↑↑		\| Ad>/, G#↑, Ab↑↑
	\| -1		\| -1
	\| 6		\| 6

2025-05-15T19:41:47Z