17edo - Revision history

Inthar at 11:54, 8 June 2026

2026-06-08T11:54:31Z

← Older revision		Revision as of 11:54, 8 June 2026
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	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
Line 39:		Line 44:
	\|(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
Line 69:		Line 80:
	\|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
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	\|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
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	* 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
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	\|1		\|1
	\|70.6		\|70.6
	\|~~Minor~~ second		\|(Far)minor second
	\|Bb, At		\|Bb, At
	\|-		\|-
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	\|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
	\|-		\|-
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	\|6		\|6
	\|423.5		\|423.5
	\|~~Major~~ third		\|(Far)major third
	\|C#, Dd		\|C#, Dd
	\|-		\|-
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	\|11		\|11
	\|776.5		\|776.5
	\|~~Minor~~ sixth		\|(Far)minor sixth
	\|F		\|F
	\|-		\|-
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	\|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
	\|-		\|-
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	\|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
	\|-		\|-

Inthar: /* Intervals */

2026-01-27T14:22:01Z

Intervals

← Older revision		Revision as of 14:22, 27 January 2026
Line 8:		Line 8:

	=== 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.
	{\| class="wikitable"		{\| class="wikitable"
	!Edostep		!Edostep

Inthar: /* Prime harmonic approximations */

2026-01-27T14:06:15Z

Prime harmonic approximations

← Older revision		Revision as of 14:06, 27 January 2026
Line 104:		Line 104:
	\|A		\|A
	\|}		\|}

	~~=== Prime harmonic approximations ===~~

	=== Prime approximations ===		=== Prime approximations ===

Inthar: /* Tuning theory */

2026-01-27T14:06:00Z

Tuning theory

@@ Line 6: / Line 6: @@
 == Tuning theory ==
 === Prime approximations ===
 {{Harmonics in ED|17|23}}

Inthar at 13:52, 27 January 2026

2026-01-27T13:52:42Z

← Older revision		Revision as of 13:52, 27 January 2026
Line 8:		Line 8:
	=== Prime approximations ===		=== Prime approximations ===
	{{Harmonics in ED\|17\|23}}		{{Harmonics in ED\|17\|23}}

			== Scales ==
			Some scales:
			* MOS diatonic (5L2s, 3331331)
			* Mosh/"malacotonic" (3L4s, 2323232)
			* Lissotonic (3223322)
			* Trachytonic (3313322)

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