17edo: Difference between revisions
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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 | ||
!Cents | !Cents | ||
!Name | !Name (Neutral diatonic / ADIN) | ||
!Diatonic notation with half sharps/flats | !Diatonic notation with half sharps/flats | ||
|- | |- | ||
| Line 21: | Line 22: | ||
|1 | |1 | ||
|70.6 | |70.6 | ||
| | |(Far)minor second | ||
|Bb, At | |Bb, At | ||
|- | |- | ||
| Line 31: | Line 32: | ||
|3 | |3 | ||
|211.8 | |211.8 | ||
| | |(Far)major second | ||
|B | |B | ||
|- | |- | ||
|4 | |4 | ||
|282.4 | |282.4 | ||
| | |(Far)minor third | ||
|C | |C | ||
|- | |- | ||
| Line 46: | Line 47: | ||
|6 | |6 | ||
|423.5 | |423.5 | ||
| | |(Far)major third | ||
|C#, Dd | |C#, Dd | ||
|- | |- | ||
| Line 56: | Line 57: | ||
|8 | |8 | ||
|564.7 | |564.7 | ||
| | |Semiaugmented/neutral fourth | ||
|Eb, Dt | |Eb, Dt | ||
|- | |- | ||
|9 | |9 | ||
|635.3 | |635.3 | ||
| | |Semidiminished/neutral fifth | ||
|D#, Ed | |D#, Ed | ||
|- | |- | ||
| Line 71: | Line 72: | ||
|11 | |11 | ||
|776.5 | |776.5 | ||
| | |(Far)minor sixth | ||
|F | |F | ||
|- | |- | ||
| Line 81: | Line 82: | ||
|13 | |13 | ||
|917.6 | |917.6 | ||
| | |(Far)major sixth | ||
|F#, Gd | |F#, Gd | ||
|- | |- | ||
|14 | |14 | ||
|988.2 | |988.2 | ||
| | |(Far)minor seventh | ||
|G | |G | ||
|- | |- | ||
| Line 96: | Line 97: | ||
|16 | |16 | ||
|1129.4 | |1129.4 | ||
| | |(Far)major seventh | ||
|G#, Ad | |G#, Ad | ||
|- | |- | ||
| Line 104: | Line 105: | ||
|A | |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 == | == Scales == | ||
| Line 116: | Line 118: | ||
* Lissotonic (3223322) | * Lissotonic (3223322) | ||
* Trachytonic (3313322) | * 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
| 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 | |
