17edo - Revision history

Inthar: /* Scales */

2026-10-11T19:44:25Z

Scales

← Older revision		Revision as of 19:44, 11 October 2026
Line 142:		Line 142:
	* [[Diatonic#MOS diatonic\|MOS diatonic]] (5L2s, 3331331)		* [[Diatonic#MOS diatonic\|MOS diatonic]] (5L2s, 3331331)
	* [[Mosh]] (3L4s, 2323232)		* [[Mosh]] (3L4s, 2323232)
	* Lissotonic<sup>1</sup> (3223322)		* Lissotonic<sup>1</sup> (3223322): modes of the ascending mode of Maqam Rast
	* Trachytonic<sup>1</sup> (3313322)		* Trachytonic<sup>1</sup> or screamapillar<sup>2</sup> (3313322)

	<sup>1</sup> CellularAutomaton's names		<sup>1</sup> CellularAutomaton's names

			<sup>2</sup> Xen Wiki's name

	{{Navbox EDO}}		{{Navbox EDO}}

	{{cat\|Edos}}		{{cat\|Edos}}

Inthar: /* Scales */

2026-10-08T11:34:43Z

Scales

← Older revision		Revision as of 11:34, 8 October 2026
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	* Trachytonic<sup>1</sup> (3313322)		* Trachytonic<sup>1</sup> (3313322)

	<sup>1</sup> CellularAutomaton's ~~name~~		<sup>1</sup> CellularAutomaton's names

	{{Navbox EDO}}		{{Navbox EDO}}

	{{cat\|Edos}}		{{cat\|Edos}}

Inthar: /* Scales */

2026-10-08T11:24:11Z

Scales

← Older revision		Revision as of 11:24, 8 October 2026
Line 142:		Line 142:
	* [[Diatonic#MOS diatonic\|MOS diatonic]] (5L2s, 3331331)		* [[Diatonic#MOS diatonic\|MOS diatonic]] (5L2s, 3331331)
	* [[Mosh]] (3L4s, 2323232)		* [[Mosh]] (3L4s, 2323232)
	* Lissotonic (3223322)		* Lissotonic<sup>1</sup> (3223322)
	* Trachytonic (3313322)		* Trachytonic<sup>1</sup> (3313322)

			<sup>1</sup> CellularAutomaton's name

	{{Navbox EDO}}		{{Navbox EDO}}

	{{cat\|Edos}}		{{cat\|Edos}}

Unque at 00:32, 8 October 2026

2026-10-08T00:32:55Z

← Older revision		Revision as of 00:32, 8 October 2026
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	=== Intervals ===		=== Intervals ===
	17edo can be notated with [[diatonic notation]] with #/b = 2\17. Since the sharp can be split in two, half-sharps and half-flats for 1\17 alterations can be used too.		17edo can be notated with [[diatonic notation]] with #/b = 2\17. Since the sharp can be split in two, half-sharps and half-flats for 1\17 alterations can be used too. These can be written in Unicode-supported text as t/d, or with ^/v; occasionally ‡ is used for a semisharp.
	{\| class="wikitable"		{\| class="wikitable"
	!Edostep		!Edostep
Line 27:		Line 27:
	\|70.6		\|70.6
	\|(Far)minor second		\|(Far)minor second
	\|Bb, At		\|B♭, At
	\|25/24		\|25/24
	\|-		\|-
Line 33:		Line 33:
	\|141.2		\|141.2
	\|Neutral second		\|Neutral second
	\|A#, Bd		\|A♯, C♭ Bd
	\|13/12		\|13/12
	\|-		\|-
Line 39:		Line 39:
	\|211.8		\|211.8
	\|(Far)major second		\|(Far)major second
	\|B		\|B, Cd
	\|9/8		\|9/8
	\|-		\|-
Line 45:		Line 45:
	\|282.4		\|282.4
	\|(Far)minor third		\|(Far)minor third
	\|C		\|C, Bt
	\|33/28, 32/27		\|33/28, 32/27
	\|-		\|-
Line 51:		Line 51:
	\|352.9		\|352.9
	\|Neutral third		\|Neutral third
	\|Db, Ct		\|B♯, D♭, Ct
	\|16/13		\|16/13
	\|-		\|-
Line 57:		Line 57:
	\|423.5		\|423.5
	\|(Far)major third		\|(Far)major third
	\|C#, Dd		\|C♯, Dd
	\|14/11		\|14/11
	\|-		\|-
Line 69:		Line 69:
	\|564.7		\|564.7
	\|Semiaugmented/neutral fourth		\|Semiaugmented/neutral fourth
	\|Eb, Dt		\|E♭, Dt
	\|25/18, 18/13		\|25/18, 18/13
	\|-		\|-
Line 75:		Line 75:
	\|635.3		\|635.3
	\|Semidiminished/neutral fifth		\|Semidiminished/neutral fifth
	\|D#, Ed		\|D♯, F♭, Ed
	\|36/25, 13/9		\|36/25, 13/9
	\|-		\|-
Line 81:		Line 81:
	\|705.9		\|705.9
	\|Perfect fifth		\|Perfect fifth
	\|E		\|E, Fd
	\|3/2		\|3/2
	\|-		\|-
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	\|776.5		\|776.5
	\|(Far)minor sixth		\|(Far)minor sixth
	\|F		\|F, Et
	\|11/7		\|11/7
	\|-		\|-
Line 93:		Line 93:
	\|847.1		\|847.1
	\|Neutral sixth		\|Neutral sixth
	\|Gb, Ft		\|E♯, G♭, F
	\|13/8		\|13/8
	\|-		\|-
Line 99:		Line 99:
	\|917.6		\|917.6
	\|(Far)major sixth		\|(Far)major sixth
	\|F#, Gd		\|F♯, Gd
	\|56/33, 27/16		\|56/33, 27/16
	\|-		\|-
Line 111:		Line 111:
	\|1058.9		\|1058.9
	\|Neutral seventh		\|Neutral seventh
	\|Ab, Gt		\|A♭, Gt
	\|24/13		\|24/13
	\|-		\|-
Line 117:		Line 117:
	\|1129.4		\|1129.4
	\|(Far)major seventh		\|(Far)major seventh
	\|G#, Ad		\|G♯, Ad
	\|48/25		\|48/25
	\|-		\|-
Line 140:		Line 140:
	== Scales ==		== Scales ==
	Some scales:		Some scales:
	* MOS diatonic (5L2s, 3331331)		* [[Diatonic#MOS diatonic\|MOS diatonic]] (5L2s, 3331331)
	* Mosh~~/"malacotonic"~~ (3L4s, 2323232)		* [[Mosh]] (3L4s, 2323232)
	* Lissotonic (3223322)		* Lissotonic (3223322)
	* Trachytonic (3313322)		* Trachytonic (3313322)

Inthar at 11:54, 8 June 2026

2026-06-08T11:54:31Z

← Older revision		Revision as of 11:54, 8 June 2026
Line 4:		Line 4:

	17edo is the smallest edo that has a sharper-than-just diatonic fifth (705.8c, compared to just 3/2 = 702.0c), not counting the degenerate case 5edo. 17edo has discordant diatonic major thirds and provides no good approximation of 5/4, which to some extent forces one to use nonfunctional and modal harmony instead of standard functional harmony. It is also notable for having neutral intervals.		17edo is the smallest edo that has a sharper-than-just diatonic fifth (705.8c, compared to just 3/2 = 702.0c), not counting the degenerate case 5edo. 17edo has discordant diatonic major thirds and provides no good approximation of 5/4, which to some extent forces one to use nonfunctional and modal harmony instead of standard functional harmony. It is also notable for having neutral intervals.

			Since 17edo's perfect eleventh is highly divisible (24 steps), you can do 2\17 x 12, 3\17 x 8, 4\17 x 6, 6\17 x 4, 8\17 x 3, or 12\17 x 2 movements to pump this "comma".

	== Tuning theory ==		== Tuning theory ==

Vector at 00:03, 20 April 2026

2026-04-20T00:03:46Z

← Older revision		Revision as of 00:03, 20 April 2026
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	!Cents		!Cents
	!Name (Neutral diatonic / ADIN)		!Name (Neutral diatonic / ADIN)
	!~~Diatonic notation with half sharps~~/~~flats~~		!Notation
			!JI interpretation (2.3.25.(11/7).13, 68edo subset)
	\|-		\|-
	\|0		\|0
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	\|Unison		\|Unison
	\|A		\|A
			\|1/1
	\|-		\|-
	\|1		\|1
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	\|(Far)minor second		\|(Far)minor second
	\|Bb, At		\|Bb, At
			\|25/24
	\|-		\|-
	\|2		\|2
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	\|Neutral second		\|Neutral second
	\|A#, Bd		\|A#, Bd
			\|13/12
	\|-		\|-
	\|3		\|3
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	\|(Far)major second		\|(Far)major second
	\|B		\|B
			\|9/8
	\|-		\|-
	\|4		\|4
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	\|(Far)minor third		\|(Far)minor third
	\|C		\|C
			\|33/28, 32/27
	\|-		\|-
	\|5		\|5
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	\|Neutral third		\|Neutral third
	\|Db, Ct		\|Db, Ct
			\|16/13
	\|-		\|-
	\|6		\|6
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	\|(Far)major third		\|(Far)major third
	\|C#, Dd		\|C#, Dd
			\|14/11
	\|-		\|-
	\|7		\|7
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	\|Perfect fourth		\|Perfect fourth
	\|D		\|D
			\|4/3
	\|-		\|-
	\|8		\|8
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	\|Semiaugmented/neutral fourth		\|Semiaugmented/neutral fourth
	\|Eb, Dt		\|Eb, Dt
			\|25/18, 18/13
	\|-		\|-
	\|9		\|9
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	\|Semidiminished/neutral fifth		\|Semidiminished/neutral fifth
	\|D#, Ed		\|D#, Ed
			\|36/25, 13/9
	\|-		\|-
	\|10		\|10
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	\|Perfect fifth		\|Perfect fifth
	\|E		\|E
			\|3/2
	\|-		\|-
	\|11		\|11
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	\|(Far)minor sixth		\|(Far)minor sixth
	\|F		\|F
			\|11/7
	\|-		\|-
	\|12		\|12
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	\|Neutral sixth		\|Neutral sixth
	\|Gb, Ft		\|Gb, Ft
			\|13/8
	\|-		\|-
	\|13		\|13
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	\|(Far)major sixth		\|(Far)major sixth
	\|F#, Gd		\|F#, Gd
			\|56/33, 27/16
	\|-		\|-
	\|14		\|14
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	\|(Far)minor seventh		\|(Far)minor seventh
	\|G		\|G
			\|16/9
	\|-		\|-
	\|15		\|15
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	\|Neutral seventh		\|Neutral seventh
	\|Ab, Gt		\|Ab, Gt
			\|24/13
	\|-		\|-
	\|16		\|16
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	\|(Far)major seventh		\|(Far)major seventh
	\|G#, Ad		\|G#, Ad
			\|48/25
	\|-		\|-
	\|17		\|17
Line 104:		Line 122:
	\|Octave		\|Octave
	\|A		\|A
			\|2/1
	\|}		\|}
			The major third is a farmajor third, interpreted as 14/11 either with 17edo's patent val or as a subset of 68edo; 17edo is at the upper edge of [[gentle tuning]]. While 17edo has reasonable approximations of 7 and 11, they are not shared with 68edo, although their ratio 14/11 is.

			The edostep is a near-just 25/24, sometimes seen as the optimal size for a leading tone.

	=== Prime approximations ===		=== Prime approximations ===
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	=== Notation ===		=== Notation ===
	Because a sharp is 2 steps in 17edo, it may be notated with neutral [[diatonic notation]] (semisharps and semiflats).		Because a sharp is 2 steps in 17edo, it may be notated with neutral [[diatonic notation]] (semisharps and semiflats).

			=== Tuning properties ===

	== Scales ==		== Scales ==

Vector at 02:49, 7 April 2026

2026-04-07T02:49:43Z

← Older revision		Revision as of 02:49, 7 April 2026
Line 108:		Line 108:
	=== Prime approximations ===		=== Prime approximations ===
	{{Harmonics in ED\|17\|23}}		{{Harmonics in ED\|17\|23}}

			=== Notation ===
			Because a sharp is 2 steps in 17edo, it may be notated with neutral [[diatonic notation]] (semisharps and semiflats).

	== Scales ==		== Scales ==

Vector at 01:15, 14 February 2026

2026-02-14T01:15:34Z

← Older revision		Revision as of 01:15, 14 February 2026
Line 115:		Line 115:
	* Lissotonic (3223322)		* Lissotonic (3223322)
	* Trachytonic (3313322)		* Trachytonic (3313322)

			{{Navbox EDO}}

	{{cat\|Edos}}		{{cat\|Edos}}

Vector at 01:14, 14 February 2026

2026-02-14T01:14:56Z

← Older revision		Revision as of 01:14, 14 February 2026
Line 22:		Line 22:
	\|1		\|1
	\|70.6		\|70.6
	\|~~Minor~~ second		\|(Far)minor second
	\|Bb, At		\|Bb, At
	\|-		\|-
Line 32:		Line 32:
	\|3		\|3
	\|211.8		\|211.8
	\|~~Major~~ second		\|(Far)major second
	\|B		\|B
	\|-		\|-
	\|4		\|4
	\|282.4		\|282.4
	\|~~Minor~~ third		\|(Far)minor third
	\|C		\|C
	\|-		\|-
Line 47:		Line 47:
	\|6		\|6
	\|423.5		\|423.5
	\|~~Major~~ third		\|(Far)major third
	\|C#, Dd		\|C#, Dd
	\|-		\|-
Line 72:		Line 72:
	\|11		\|11
	\|776.5		\|776.5
	\|~~Minor~~ sixth		\|(Far)minor sixth
	\|F		\|F
	\|-		\|-
Line 82:		Line 82:
	\|13		\|13
	\|917.6		\|917.6
	\|~~Major~~ sixth		\|(Far)major sixth
	\|F#, Gd		\|F#, Gd
	\|-		\|-
	\|14		\|14
	\|988.2		\|988.2
	\|~~Minor~~ seventh		\|(Far)minor seventh
	\|G		\|G
	\|-		\|-
Line 97:		Line 97:
	\|16		\|16
	\|1129.4		\|1129.4
	\|~~Major~~ seventh		\|(Far)major seventh
	\|G#, Ad		\|G#, Ad
	\|-		\|-

Vector at 01:10, 14 February 2026

2026-02-14T01:10:12Z

← Older revision		Revision as of 01:10, 14 February 2026
Line 12:		Line 12:
	!Edostep		!Edostep
	!Cents		!Cents
	!Name		!Name (Neutral diatonic / ADIN)
	!Diatonic notation with half sharps/flats		!Diatonic notation with half sharps/flats
	\|-		\|-
Line 57:		Line 57:
	\|8		\|8
	\|564.7		\|564.7
	\|~~Small tritone~~		\|Semiaugmented/neutral fourth
	\|Eb, Dt		\|Eb, Dt
	\|-		\|-
	\|9		\|9
	\|635.3		\|635.3
	\|~~Large tritone~~		\|Semidiminished/neutral fifth
	\|D#, Ed		\|D#, Ed
	\|-		\|-