17edo: Difference between revisions

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== Tuning theory ==
== 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 ===
=== 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 ==
Some scales:
* MOS diatonic (5L2s, 3331331)
* Mosh/"malacotonic" (3L4s, 2323232)
* Lissotonic (3223322)
* Trachytonic (3313322)
{{Navbox EDO}}


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

Latest revision as of 02:49, 7 April 2026

This page or section is a work in progress. It may lack sufficient justification, content, or organization, and is subject to future overhaul.

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 (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

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)

Notation

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

Scales

Some scales:

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


View • Talk • EditEqual temperaments
EDOs
Macrotonal 5 • 7 • 8 • 9 • 10 • 11
12-23 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23
24-35 24 • 25 • 26 • 27 • 29 • 31 • 32 • 34 • 35
36-47 36 • 37 • 39 • 40 • 41 • 43 • 44 • 45 • 46 • 47
48-59 48 • 50 • 51 • 53 • 54 • 56 • 57 • 58
60-71 60 • 63 • 64 • 65 • 67 • 68 • 70
72-83 72 • 77 • 80 • 81
84-95 84 • 87 • 89 • 90 • 93 • 94
Large EDOs 99 • 104 • 106 • 111 • 118 • 130 • 140 • 152 • 159 • 171 • 217 • 224 • 239 • 270 • 306 • 311 • 612 • 665
Nonoctave equal temperaments
Tritave 4 • 9 • 13 • 17 • 26 • 39
Fifth 8 • 9 • 11 • 20
Other
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