17edo

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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 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

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.

Edostep	Cents	Name (Neutral diatonic / ADIN)	Diatonic notation with half sharps/flats
0	0	Unison	A
1	70.6	Minor second	Bb, At
2	141.2	Neutral second	A#, Bd
3	211.8	Major second	B
4	282.4	Minor third	C
5	352.9	Neutral third	Db, Ct
6	423.5	Major third	C#, Dd
7	494.1	Perfect fourth	D
8	564.7	Semiaugmented/neutral fourth	Eb, Dt
9	635.3	Semidiminished/neutral fifth	D#, Ed
10	705.9	Perfect fifth	E
11	776.5	Minor sixth	F
12	847.1	Neutral sixth	Gb, Ft
13	917.6	Major sixth	F#, Gd
14	988.2	Minor seventh	G
15	1058.9	Neutral seventh	Ab, Gt
16	1129.4	Major seventh	G#, Ad
17	1200	Octave	A

Prime approximations

Approximation of prime harmonics in 17edo

Harmonic		2	3	5	7	11	13	17	19	23
Error	Absolute (¢)	0.0	+3.9	-33.4	+19.4	+13.4	+6.5	-34.4	-15.2	+7.0
	Relative (%)	0.0	+5.6	-47.3	+27.5	+19.0	+9.3	-48.7	-21.5	+9.9
Steps (reduced)		17 (0)	27 (10)	39 (5)	48 (14)	59 (8)	63 (12)	69 (1)	72 (4)	77 (9)

Scales

Some scales:

• MOS diatonic (5L2s, 3331331)
• Mosh/"malacotonic" (3L4s, 2323232)
• Lissotonic (3223322)
• Trachytonic (3313322)