View source for 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.
{| class="wikitable"
!Edostep
!Cents
!Name (Neutral diatonic / ADIN)
!Diatonic notation with half sharps/flats
|-
|0
|0
|Unison
|A
|-
|1
|70.6
|(Far)minor second
|Bb, At
|-
|2
|141.2
|Neutral second
|A#, Bd
|-
|3
|211.8
|(Far)major second
|B
|-
|4
|282.4
|(Far)minor third
|C
|-
|5
|352.9
|Neutral third
|Db, Ct
|-
|6
|423.5
|(Far)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
|(Far)minor sixth
|F
|-
|12
|847.1
|Neutral sixth
|Gb, Ft
|-
|13
|917.6
|(Far)major sixth
|F#, Gd
|-
|14
|988.2
|(Far)minor seventh
|G
|-
|15
|1058.9
|Neutral seventh
|Ab, Gt
|-
|16
|1129.4
|(Far)major seventh
|G#, Ad
|-
|17
|1200
|Octave
|A
|}

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

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

{{cat|Edos}}