17edo - Revision history

Vector at 02:49, 7 April 2026

2026-04-07T02:49:43Z

← Older revision		Revision as of 02:49, 7 April 2026
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	=== 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 ==

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	!Edostep		!Edostep
	!Cents		!Cents
	!Name		!Name (Neutral diatonic / ADIN)
	!Diatonic notation with half sharps/flats		!Diatonic notation with half sharps/flats
	\|-		\|-
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	\|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
	\|-		\|-

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Intervals

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

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Prime harmonic approximations

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	\|A		\|A
	\|}		\|}

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

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

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Tuning theory

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 == Tuning theory ==
 === Prime approximations ===
 {{Harmonics in ED|17|23}}

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			{{problematic}}

	'''17edo''', or 17 equal divisions of the octave, is the equal tuning featuring steps of (1200/17) ~= 70.6 cents, 17 of which stack to the octave 2/1.		'''17edo''', or 17 equal divisions of the octave, is the equal tuning featuring steps of (1200/17) ~= 70.6 cents, 17 of which stack to the octave 2/1.

2026-01-26T01:21:57Z

← Older revision		Revision as of 01:21, 26 January 2026
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	'''17edo''', or 17 equal divisions of the octave, is the equal tuning featuring steps of (1200/17) ~= 70.6 cents, 17 of which stack to the octave 2/1.		'''17edo''', or 17 equal divisions of the octave, is the equal tuning featuring steps of (1200/17) ~= 70.6 cents, 17 of which stack to the octave 2/1.

	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.		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.

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