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{{interwiki
{{interwiki
| de = 17edo
| de = 17-EDO
| en = 17edo
| en = 17edo
| es = 17 EDO
| es = 17 EDO
| ja = 17平均律
| ja = 17平均律
}}
}}
__FORCETOC__
{{Infobox ET}}
{{ED intro}}
{{Wikipedia|17 equal temperament}}


'''17 tone equal temperament''', or '''17-EDO''', divides the octave in 17 equal steps, each 70.588 [[cent]]s in size. It is the seventh [[prime numbers|prime]] [[EDO]], following [[13edo]] and coming before [[19edo]].
== Theory ==
17edo is the next smallest edo to have a [[5L 2s|diatonic]] [[3/2|perfect fifth]] after [[12edo]], and is quite popular for that reason. The perfect fifth is around 4 cents sharp of just, and around 6 cents sharp of 12edo's, lending itself to a diatonic scale with more constrasting large and small steps, so it can be seen as a tuning that emphasizes the [[hard]]ness of [[Pythagorean tuning]] rather than mellowing it out as in [[meantone]]. It completely misses [[harmonic]] [[5/1|5]], with [[5/4]] and [[6/5]] both being about halfway between its steps,  but it approximates harmonics [[7/1|7]], [[11/1|11]], [[13/1|13]], and [[23/1|23]] acceptably, with a sharp tuning for all of them. It can thus be treated as a temperament of the 2.3.25.7.11.13.23 [[subgroup]] or any of its subsets, where it is quite accurate for its size.  


==Theory==
A notable [[comma]] it [[tempering out|tempers out]] is [[64/63]], which equates the harmonic seventh [[7/4]] with the pythagorean minor seventh [[16/9]], while its patent val does not temper out [[81/80]]. This makes 17edo by default a [[superpyth]]agorean system rather than a [[meantone]] one, being very close to 1/7-comma superpyth. Other commas it tempers out can be found in the [[#Commas]] section, each of which has its own effect on the structure of 17edo. If one wants to approximate JI with prime 5, then 17edo would not be the best option, and it would be better to use other systems like [[19edo]], [[22edo]], [[27edo]], or [[31edo]] instead. That said, the 17c [[val]] (written using [[wart notation]]) does temper out 81/80 (while improving consistency as shown below in [[#Approximation to JI]]), while still tempering out 64/63, thus placing it on the meantone spectrum with the [[dominant (temperament)|dominant]] [[extension]].
An introduction to 17-EDO theory, through the eyes of the [[SeventeenTonePianoProject]]: [[SeventeenTheory]].


Another introduction into 17-EDO theory: [http://anaphoria.com/Secor17puzzle.pdf The 17-tone Puzzle] by George Secor.
=== As a means of extending harmony ===
The diatonic [[major triad]], which is 0–6–10 steps, is quite [[dissonant]] compared to [[4:5:6]], as the major third is over 37 cents sharp from the traditional [[5/4]], and is instead closer to [[9/7]] or [[14/11]]. Instead, a different construction based on the [[2.3.7 subgroup]] follows naturally from its [[support]] of [[superpyth]], and may be preferred. Such chords include the tetrads [[6:7:8:9]] and its utonal inverse, realized in 17edo as 0–4–7–10 and 0–3–6–10, respectively, in addition to the sus2-4 chord, realized as 0–3–7–10. Possible chromatic alterations include but are not limited to an approximation of 12:13:16:18, 0–2–7–10, and an approximation of 8:9:11:12, 0–3–8–10. It is important to note that the chromatic semitone in 17edo is 2 steps, rather than 1 step as in [[12edo]] or [[19edo]]. Similarly, the fourth-spanning triad [[6:7:8]] and its inverse can be used, with their wide voicing realized in 17edo as 0–14–27 and 0–13–27, respectively. Extensions of these chords include 0–12–14–27, representing 8:13:14:24, and 0–13–15–27, representing 7:12:13:21.


[[17edo Solfege]]. [[17edo tetrachords]]. [http://microtonalismo.com/proyecto-xvii Proyect 17-Perú] {{forbidden}}
Since the intervals of the 2.3.7-subgroup cluster around [[5edo]], a [[Pentatonic Functional Just System|pentatonic system of interval classification]] may be preferred over the [[heptatonic]] one, with [[7/6]] becoming a major interval and [[8/7]]~[[9/8]] becoming a minor one.


17-EDO can plausibly be treated as a 2.3.25.7.11.13.23 subgroup temperament, for which it is quite accurate (though the 7-limit ratios are generally not as well-represented as those of the other integers). Because the 3, 7, 11, and 13 are all sharp, it adapts well to octave shrinking; [[27edt]] (a variant of 17edo in which the octaves are flattened by ~2.5 cents) is a good alternative. Another one is [[44ed6]].
Of course, scales generated by the perfect fifth are not the only scales 17edo contains. Another type of scale is [[neutral third scales]], which are generated by half a fifth (5\17), and take the mos patterns [[4L 3s]] (mosh) and [[7L 3s]] (dicoid). Other notable scales include that of [[bleu]] and [[glacier]] (generated by 2\17), and [[skwares]] (generated by 6\17). Non-mos scales also exist; a more complete list can be found in the [[#Scales]] section.


As a no-fives system, it is best used with timbres in which harmonic multiples of 5 are attenuated or absent. Also, the standard major chord (4:5:6) cannot be used since it includes the fifth harmonic.
Because the 5th harmonic is not well approximated, using timbres with attenuated 5th harmonics (and its multiples) may reduce audible beating.


Instead, the tonic chords of 17-EDO could be considered to be the tetrad 6:7:8:9 and its utonal inversion, the former of which is a subminor chord with added fourth, and the latter a supermajor chord with added second (resembling the [https://en.wikipedia.org/wiki/Mu_chord mu chord] of Steely Dan fame). These are realized in 17-EDO as 0-4-7-10 and 0-3-6-10, respectively. Both of these have distinct moods, and are stable and consonant, if somewhat more sophisticated than their classic 5-limit counterparts. To this group we could also add the 0-3-7-10 (which is a sus4 with added second, or sus2 with added fourth). These three chords comprise the three ways to divide the 17-EDO perfect fifth into two whole tones and one subminor third. Chromatic alterations of them also exist, for example, the 0-3-7-10 chord may be altered to 0-2-7-10 (which approximates 12:13:16:18) or 0-3-8-10 (which approximates 8:9:11:12). The 0-3-8-10 chord is impressive-sounding, resembling a sus4 but with even more tension; it resolves quite nicely to 0-3-6-10.
=== Odd harmonics ===
{{Harmonics in equal|17|intervals=odd|columns=11}}
{{Harmonics in equal|17|intervals=odd|columns=12|start=12|collapsed=true|title=Approximation of odd harmonics in 17edo (continued)}}


=Intervals=
=== Subsets and supersets ===
17edo is the seventh [[prime edo]], following [[13edo]] and coming before [[19edo]]. It does not contain any nontrivial subset edos, though it contains [[17ed4]] and [[17ed8]]. 17ed8, built by taking every third step of 17edo, is a system where all odd harmonics up to the 21st are mapped exactly as in 17edo, except for the 11th. Beyond that, the 27th, 31st, 35th, and 39th harmonics are likewise mapped identically.


{| class="wikitable"
[[34edo]], which doubles 17edo, provides a great correction to harmonics 5 and 17; while [[68edo]], which quadruples it, provides additionally the primes 7, 19, and 31.
|-
 
! rowspan="2" | Degree
== Intervals ==
! colspan="2" | Cents
{{See also| 17edo solfege }}
! rowspan="2" | Names of Intervals
 
! colspan="3" rowspan="2" | [[Ups and Downs Notation|ups and downs notation]]
{| class="wikitable center-all right-2 left-3"
! rowspan="2" | Approximate Ratios*
! rowspan="2" | Temperament(s)generated
|-
|-
!Pure octave
! #
!25/24et
! Cents
! Approximate ratios<ref group="note">{{sg|limit=2.3.25.7.11.13.85.23&nbsp;subgroup}}</ref>
! colspan="2" | [[Circle-of-fifths notation]]<ref group="note">Half-sharps and half-flats (denoted "t" and "d", respectively) can be used to alter the note by a single step, since sharps and flats each span two edosteps. Using half-sharps and half-flats may be preferable for compatibility with the ups-and-downs notation in 34edo, in which an up or down respectively constitute a quarter-sharp or quarter-flat. </ref>
! colspan="3" | [[Ups and downs notation]]<br>([[Enharmonic unisons in ups and downs notation|EUs]]: vvA1 and ^d2)
! colspan="3" | [[SKULO interval names|SKULO notation]] {{nowrap|(U {{=}} 1)}}
|-
|-
| colspan="3" | 0
| 0
| | Unison
| 0.0
| style="text-align:center;" | unison
| [[1/1]]
| style="text-align:center;" | P1
| Unison
| style="text-align:center;" | C
| D
| style="text-align:center;" | 1/1
| unison
| |
| P1
| D
| unison
| P1
| D
|-
|-
| | 1
| 1
| | 70.59
| 70.6
|70.67
| [[24/23]], [[25/24]], [[26/25]], [[27/26]], [[28/27]]
| | Super Unison/Minor Second
| Minor 2nd<br>(Semiaugmented 1sn)
| style="text-align:center;" | minor 2nd
| Eb<br>(Dt)
| style="text-align:center;" | m2
| up unison, <br>minor 2nd
| style="text-align:center;" | Db
| ^1, m2
| style="text-align:center;" | [[25/24]], [[26/25]], [[33/32]]
| Eb
| |  
| uber unison, <br>minor 2nd
| U1, m2
| UD, Eb
|-
|-
| | 2
| 2
| | 141.18
| 141.2
|141.345
| [[12/11]], [[13/12]], [[14/13]], [[25/23]]
| | Augmented Unison/Neutral Second
| Augmented 1sn<br>(Neutral 2nd)
| style="text-align:center;" | mid 2nd
| D#<br>(Ed)
| style="text-align:center;" | ~2
| augmented 1sn, <br>mid 2nd
| style="text-align:center;" | vD
| A1, ~2
| style="text-align:center;" | [[13/12]], [[12/11]], [[14/13]]
| vE
| | [[Bleu]]
| neutral 2nd
| N2
| UEb, uE
|-
|-
| | 3
| 3
| | 211.765
| 211.8
|212.02
| [[8/7]], [[9/8]], [[17/15]], [[25/22]], [[26/23]]
| | Major Second/Sub Third
| Major 2nd
| style="text-align:center;" | major 2nd
| E
| style="text-align:center;" | M2
| major 2nd
| style="text-align:center;" | D
| M2
| style="text-align:center;" | [[9/8]], [[25/22]], [[8/7]], [[28/25]]
| E
| | [[Machine]]
| major 2nd
| M2
| E
|-
|-
| | 4
| 4
| | 282.35
| 282.4
|282.69
| [[7/6]], [[13/11]], [[20/17]]
| | Minor Third/Super Second
| Minor 3rd
| style="text-align:center;" | minor 3rd
| F
| style="text-align:center;" | m3
| minor 3rd
| style="text-align:center;" | Eb
| m3
| style="text-align:center;" | [[13/11]], [[7/6]]
| F
| | [[Huxley]]
| minor 3rd
| m3
| F
|-
|-
| | 5
| 5
| | 352.94
| 352.9
|353.36
| [[11/9]], [[27/22]], [[16/13]], [[39/32]]
| | Augmented Second/Neutral Third/
| Diminished 4th<br>(Neutral 3rd)
Diminished Fourth
| Gb<br>(Ft)
| style="text-align:center;" | mid 3rd
| mid 3rd
| style="text-align:center;" | ~3
| ~3
| style="text-align:center;" | vE
| ^F
| style="text-align:center;" | [[11/9]], [[16/13]]
| neutral 3rd
| | [[Maqamic]]/[[Hemif]]
| N3
| UF, uF#
|-
|-
| | 6
| 6
| | 423.53
| 423.5
|424.035
| [[9/7]], [[14/11]], [[23/18]], [[32/25]], [[51/40]]
| | Major Third/Sub Fourth
| Major 3rd<br>(Semidiminished 4th)
| style="text-align:center;" | major 3rd
| F#<br>(Gd)
| style="text-align:center;" | M3
| major 3rd
| style="text-align:center;" | E
| M3
| style="text-align:center;" | [[32/25]], [[33/26]], [[9/7]], [[14/11]]
| F#
| | [[Skwares]]
| major 3rd
| M3
| F#
|-
|-
| | 7
| 7
| | 494.12
| 494.1
|494.71
| [[4/3]], [[21/16]], [[85/64]]
| | Perfect Fourth
| Perfect 4th
| style="text-align:center;" | perfect 4th
| G
| style="text-align:center;" | P4
| perfect 4th
| style="text-align:center;" | F
| P4
| style="text-align:center;" | [[4/3]]
| G
| | [[Supra]]
| perfect 4th
| P4
| G
|-
|-
| | 8
| 8
| | 564.71
| 564.7
|565.38
| [[11/8]], [[18/13]], [[25/18]], [[32/23]]
| |Super Fourth/Diminshed Fifth
| Diminished 5th<br>(Semiaugmented 4th)
| style="text-align:center;" | up 4th,
| Ab<br>(Gt)
diminished 5th
| mid 4th, <br>diminished 5th
| style="text-align:center;" | ^4, d5
| ~4, d5
| style="text-align:center;" | ^F, Gb
| ^G, Ab
| style="text-align:center;" | [[11/8]], [[18/13]]
| uber 4th/<br>neutral 4th
| | [[Progress]]
| U4/N4
| UG
|-
|-
| | 9
| 9
| | 635.29
| 635.3
|636.05
| [[13/9]], [[16/11]], [[23/16]], [[36/25]]
| | Augmented Fourth/Sub Fifth
| Augmented 4th<br>(Semidiminished 5th)
| style="text-align:center;" | augmented 4th,
| G#<br>(Ad)
down 5th
| augmented 4th, <br>mid 5th
| style="text-align:center;" | A4, v5
| A4, ~5
| style="text-align:center;" | F#, vG
| G#, vA
| style="text-align:center;" | [[16/11]], [[13/9]], [[23/16]]
| unter 5th/<br>neutral 5th
| | Progress
| u5/N5
| uA
|-
|-
| | 10
| 10
| | 705.88
| 705.9
|706.72
| [[3/2]], [[32/21]], [[128/85]]
| | Perfect Fifth
| Perfect 5th
| style="text-align:center;" | perfect 5th
| A
| style="text-align:center;" | P5
| perfect 5th
| style="text-align:center;" | G
| P5
| style="text-align:center;" | [[3/2]]
| A
| | Supra
| perfect 5th
| P5
| A
|-
|-
| | 11
| 11
| | 776.47
| 776.5
|777.4
| [[11/7]], [[14/9]], [[25/16]], [[36/23]], [[80/51]]
| | Super Fifth/Minor Sixth
| Minor 6th<br>(Semiaugmented 5th)
| style="text-align:center;" | minor 6th
| Bb<br>(At)
| style="text-align:center;" | m6
| minor 6th
| style="text-align:center;" | Ab
| m6
| style="text-align:center;" | [[25/16]], [[14/9]], [[11/7]]
| Bb
| | Skwares
| minor 6th
| m6
| Bb
|-
|-
| | 12
| 12
| | 847.06
| 847.1
|848.07
| [[13/8]], [[18/11]], [[44/27]], [[64/39]]
| | Augmented Fifth/Neutral Sixth/
| Augmented 5th<br>(Neutral 6th)
Diminished Seventh
| A#<br>(Bd)
| style="text-align:center;" | mid 6th
| mid 6th
| style="text-align:center;" | ~6
| ~6
| style="text-align:center;" | vA
| vB
| style="text-align:center;" | [[13/8]], [[18/11]]
| neutral 6th
| | Maqamic/hemif
| N6
| UBb, uB
|-
|-
| | 13
| 13
| | 917.65
| 917.6
|918.74
| [[12/7]], [[17/10]], [[22/13]]
| | Major Sixth/Sub Seventh
| Major 6th
| style="text-align:center;" | major 6th
| B
| style="text-align:center;" | M6
| major 6th
| style="text-align:center;" | A
| M6
| style="text-align:center;" | [[17/10]], [[22/13]],[[12/7]]
| B
| | Huxley
| major 6th
| M6
| B
|-
|-
| | 14
| 14
| | 988.235
| 988.2
|989.41
| [[7/4]], [[16/9]], [[23/13]], [[30/17]], [[44/25]]
| | Minor Seventh/Super Sixth
| Minor 7th
| style="text-align:center;" | minor 7th
| C
| style="text-align:center;" | m7
| minor 7th
| style="text-align:center;" | Bb
| m7
| style="text-align:center;" | [[16/9]], [[7/4]], [[25/14]]
| C
| | Machine
| minor 7th
| m7
| C
|-
|-
| | 15
| 15
| | 1058.82
| 1058.8
|1060.09
| [[11/6]], [[13/7]], [[24/13]], [[46/25]]
| | Augmented Sixth/Neutral Seventh/
| Diminished 8ve<br>(Neutral 7th)
Diminished Octave
| Db<br>(Ct)
| style="text-align:center;" | mid 7th
| mid 7th
| style="text-align:center;" | ~7
| ~7
| style="text-align:center;" | vB
| ^C
| style="text-align:center;" | [[11/6]], [[24/13]], [[13/7]]
| neutral 7th
| | Bleu
| N7
| UC, uC#
|-
|-
| | 16
| 16
| | 1129.41
| 1129.4
|1130.76
| [[23/12]], [[25/13]], [[27/14]], [[48/25]], [[52/27]]
| | Major Seventh/Sub Octave
| Major 7th<br>(Semidiminished 8ve)
| style="text-align:center;" | major 7th
| C#<br>(Dd)
| style="text-align:center;" | M7
| major 7th,<br>down 8ve
| style="text-align:center;" | B
| M7, v8
| style="text-align:center;" | [[25/13]], [[48/25]], [[64/33]]
| C#
| |  
| major 7th,<br>unter octave
| M7, u8
| C#, uD
|-
|-
| | 17
| 17
| | 1200
| 1200.0
|1201.43
| [[2/1]]
| | Perfect Octave
| Octave
| style="text-align:center;" | octave
| D
| style="text-align:center;" | P8
| octave
| style="text-align:center;" | C
| P8
| style="text-align:center;" | [[2/1]]
| D
| |
| octave
| P8
| D
|}
|}
<nowiki>*</nowiki>Ratios based on treating 17edo as a 2.3.7.11.13.25 subgroup
<references group="note" />


=== Interval quality and chord names in color notation ===
Combining ups and downs notation with [[color notation]], qualities can be loosely associated with colors:
Combining ups and downs notation with [[color notation]], qualities can be loosely associated with colors:


{| class="wikitable"
{| class="wikitable center-all"
|-
|-
! | quality
! Quality
! | color
! Color
! | monzo format
! Monzo format
! | examples
! Examples
|-
|-
| style="text-align:center;" | minor
| rowspan="2" | minor
| style="text-align:center;" | zo
| zo
| style="text-align:center;" | {a, b, 0, 1}
| (a, b, 0, 1)
| style="text-align:center;" | 7/6, 7/4
| 7/6, 7/4
|-
|-
| style="text-align:center;" | "
| fourthward wa
| style="text-align:center;" | fourthward wa
| (a, b), b < -1
| style="text-align:center;" | {a, b}, b &lt; -1
| 32/27, 16/9
| style="text-align:center;" | 32/27, 16/9
|-
|-
| style="text-align:center;" | mid
| rowspan="2" | mid
| style="text-align:center;" | ilo
| ilo
| style="text-align:center;" | {a, b, 0, 0, 1}
| (a, b, 0, 0, 1)
| style="text-align:center;" | 11/9, 11/6
| 11/9, 11/6
|-
|-
| style="text-align:center;" | "
| lu
| style="text-align:center;" | lu
| (a, b, 0, 0, -1)
| style="text-align:center;" | {a, b, 0, 0, -1}
| 12/11, 18/11
| style="text-align:center;" | 12/11, 18/11
|-
|-
| style="text-align:center;" | major
| rowspan="2" | major
| style="text-align:center;" | fifthward wa
| fifthward wa
| style="text-align:center;" | {a, b}, b &gt; 1
| (a, b), b > 1
| style="text-align:center;" | 9/8, 27/16
| 9/8, 27/16
|-
|-
| style="text-align:center;" | "
| ru
| style="text-align:center;" | ru
| (a, b, 0, -1)
| style="text-align:center;" | {a, b, 0, -1}
| 9/7, 12/7
| style="text-align:center;" | 9/7, 12/7
|}
|}
=Chord Names=


All 17edo chords can be named using ups and downs. Here are the zo, ilo and ru triads:
All 17edo chords can be named using ups and downs. Here are the zo, ilo and ru triads:


{| class="wikitable"
{| class="wikitable center-all"
|-
|-
! | [[Kite's color notation|color of the 3rd]]
! [[Color notation|Color of the 3rd]]
! | JI chord
! JI chord
! | notes as edosteps
! Notes as edosteps
! | notes of C chord
! Notes of C chord
! | written name
! Written name
! | spoken name
! Spoken name
|-
|-
| style="text-align:center;" | zo
| zo
| style="text-align:center;" | 6:7:9
| 6:7:9
| style="text-align:center;" | 0-4-10
| 0-4-10
| style="text-align:center;" | C Eb G
| C Eb G
| style="text-align:center;" | Cm
| Cm
| style="text-align:center;" | C minor
| C minor
|-
|-
| style="text-align:center;" | ilo
| ilo
| style="text-align:center;" | 18:22:27
| 18:22:27
| style="text-align:center;" | 0-5-10
| 0-5-10
| style="text-align:center;" | C vE G
| C vE G
| style="text-align:center;" | C~
| C~
| style="text-align:center;" | C mid
| C mid
|-
|-
| style="text-align:center;" | ru
| ru
| style="text-align:center;" | 14:18:27
| 14:18:21
| style="text-align:center;" | 0-6-10
| 0-6-10
| style="text-align:center;" | C E G
| C E G
| style="text-align:center;" | C
| C
| style="text-align:center;" | C major or C
| C major or C
|}
|}


Line 306: Line 343:
0-4-10-14 = C Eb G Bb = Cm7 = C minor seven
0-4-10-14 = C Eb G Bb = Cm7 = C minor seven


0-5-10-14 = C vE G Bb = C7(~3) = C seven mid-three
0-5-10-14 = C vE G Bb = C~,7 = C mid add seven
 
0-6-10-15 = C E G vB = C,~7 = C add mid-seven


0-5-10-15 = C vE G vB = C~7 = C mid-seven
0-5-10-15 = C vE G vB = C~7 = C mid-seven


0-6-10-15 = C E G vB = C,~7 = C add mid-seven
For a more complete list, see [[Ups and downs notation #Chords and chord progressions]].
 
== Notation ==
=== Ups and downs notation ===
Spoken as up, sharp, upsharp, etc. Note that up can be respelled as downsharp. The gamut runs D, ^D/Eb, D#/vE, E, F etc.
{{Ups and downs sharpness}}
 
=== Quarter tone notation ===
Since a sharp raises by 2 steps, 17edo can be notated using quarter-tone accidentals.
{{Sharpness-sharp2}}
 
=== Sagittal notation ===
This notation uses the same sagittal sequence as edos [[24edo #Sagittal notation|24]], [[31edo #Sagittal notation|31]], and [[38edo #Sagittal notation|38]], and is a subset of the notation for [[34edo #Sagittal notation|34edo]].
 
==== Evo and Revo flavors ====
{{Sagittal chart|}}
 
==== Alternative Evo flavor ====
{{Sagittal chart|Alternative_Evo}}
 
==== Evo-SZ flavor ====
{{Sagittal chart|Evo-SZ}}
 
Because it contains no Sagittal symbols, this Evo-SZ Sagittal notation is identical to the Stein-Zimmerman notation.


For a more complete list, see [[Ups and Downs Notation#Chords and Chord Progressions|Ups and Downs Notation - Chords and Chord Progressions]].
==== Sagittal songbook diagram ====
From the appendix to [[The Sagittal Songbook]] by [[Jacob Barton|Jacob A. Barton]], a diagram of how to notate 17edo in the Revo flavor of Sagittal:


=Selected just intervals by error=
[[File:17edo Sagittal.png|800px]]
The following table shows how [[Just-24|some prominent just intervals]] are represented in 17edo (ordered by absolute error).


===Best direct mapping, even if inconsistent===
=== 3L 4s (mosh) notation ===
The notation of Neutral[7]. The generator is the perfect 3rd. Notes are denoted as {{nowrap|sLsLsLs {{=}} DEFGABCD}}, and raising and lowering by a chroma {{nowrap|(L − s)}}, 1 edostep in this instance, is denoted by ♯ and ♭.


{| class="wikitable"
{| class="wikitable center-all right-2 left-4 left-5 mw-collapsible mw-collapsed"
|-
|-
| | '''Interval, complement'''
! #
| | '''Error (abs., in [[cent]]s)'''
! Cents
! Note
! Name
! Associated ratios
|-
|-
| style="text-align:center;" | [[18/13]], [[13/9]]
| 0
| style="text-align:center;" | 1.324
| 0.0
| D
| Perfect 1sn
| 1/1
|-
|-
| style="text-align:center;" | [[13/12]], [[24/13]]
| 1
| style="text-align:center;" | 2.604
| 70.6
| D#
| Augmented 1sn
| 33/32
|-
|-
| style="text-align:center;" | [[4/3]], [[3/2]]
| 2
| style="text-align:center;" | 3.927
| 141.2
| Eb
| Minor 2nd
| 12/11
|-
|-
| style="text-align:center;" | [[11/9]], [[18/11]]
| 3
| style="text-align:center;" | 5.533
| 211.8
| E
| Major 2nd
| 9/8
|-
|-
| style="text-align:center;" | [[14/11]], [[11/7]]
| 4
| style="text-align:center;" | 6.021
| 282.4
| Fb
| Diminished 3rd
| 32/27
|-
|-
| style="text-align:center;" | [[16/13]], [[13/8]]
| 5
| style="text-align:center;" | 6.531
| 352.9
| F
| Perfect 3rd
| 11/9, 27/22
|-
|-
| style="text-align:center;" | [[13/11]], [[22/13]]
| 6
| style="text-align:center;" | 6.857
| 423.5
| F#
| Augmented 3rd
| 81/64
|-
|-
| style="text-align:center;" | [[9/8]], [[16/9]]
| 7
| style="text-align:center;" | 7.855
| 494.1
| G
| Minor 4th
| 4/3
|-
|-
| style="text-align:center;" | [[12/11]], [[11/6]]
| 8
| style="text-align:center;" | 9.461
| 564.7
| G#
| Major 4th
| 11/8
|-
|-
| style="text-align:center;" | [[9/7]], [[14/9]]
| 9
| style="text-align:center;" | 11.555
| 635.3
| Ab
| Minor 5th
| 16/11
|-
|-
| style="text-align:center;" | [[14/13]], [[13/7]]
| 10
| style="text-align:center;" | 12.878
| 705.9
| A
| Major 5th
| 3/2
|-
|-
| style="text-align:center;" | [[11/8]], [[16/11]]
| 11
| style="text-align:center;" | 13.388
| 776.5
| Bb
| Diminished 6th
| 128/81
|-
|-
| style="text-align:center;" | [[7/6]], [[12/7]]
| 12
| style="text-align:center;" | 15.482
| 847.1
| B
| Perfect 6th
| 18/11, 44/27
|-
|-
| style="text-align:center;" | [[7/5]], [[10/7]]
| 13
| style="text-align:center;" | 17.806
| 917.6
| B#
| Augmented 6th
| 27/16
|-
|-
| style="text-align:center;" | [[8/7]], [[7/4]]
| 14
| style="text-align:center;" | 19.409
| 988.2
| Cb
| Minor 7th
| 16/9
|-
|-
| style="text-align:center;" | [[15/14]], [[28/15]]
| 15
| style="text-align:center;" | 21.734
| 1058.8
| C
| Major 7th
| 11/6
|-
|-
| style="text-align:center;" | [[11/10]], [[20/11]]
| 16
| style="text-align:center;" | 23.828
| 1129.4
| Db
| Diminished 8ve
| 64/33
|-
|-
| style="text-align:center;" | [[15/11]], [[22/15]]
| 17
| style="text-align:center;" | 27.755
| 1200.0
|-
| D
| style="text-align:center;" | [[10/9]], [[9/5]]
| Perfect 8ve
| style="text-align:center;" | 29.361
| 2/1
|}
 
== Approximation to JI ==
=== 15-odd-limit interval mappings ===
{{Q-odd-limit intervals|17}}
{{Q-odd-limit intervals|17.04|apx=val|header=none|tag=none|title=15-odd-limit intervals by 17c val mapping}}
 
=== Selected 13-limit intervals ===
[[File:17ed2-001.svg|alt=alt : Your browser has no SVG support.]]
 
== Tuning by ear ==
17edo is very close to a circle of seventeen [[25/24]] chromatic semitones: (25/24)<sup>17</sup> is only 1.43131 cents sharp of an octave. This means that if you can tune seventeen 25/24's accurately (by say, tuning 5/4 up, 3/2 down and 5/4 up, taking care to minimize the error at each step), you have a shot at approximating 17edo within melodic just noticeable difference.
 
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
! rowspan="2" | [[Subgroup]]
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br>8ve stretch (¢)
! colspan="2" | Tuning error
|-
|-
| style="text-align:center;" | [[16/15]], [[15/8]]
! [[TE error|Absolute]] (¢)
| style="text-align:center;" | 29.445
! [[TE simple badness|Relative]] (%)
|-
|-
| style="text-align:center;" | [[13/10]], [[20/13]]
| 2.3
| style="text-align:center;" | 30.685
| {{Monzo| 27 -17 }}
| {{Mapping| 17 27 }}
| −1.24
| 1.24
| 1.76
|-
|-
| style="text-align:center;" | [[6/5]], [[5/3]]
| 2.3.7
| style="text-align:center;" | 33.288
| 64/63, 17496/16807
| {{Mapping| 17 27 48 }}
| −3.13
| 2.85
| 4.05
|-
|-
| style="text-align:center;" | [[5/4]], [[8/5]]
| 2.3.7.11
| style="text-align:center;" | 33.373
| 64/63, 99/98, 243/242
| {{Mapping| 17 27 48 59 }}
| −3.31
| 2.49
| 3.54
|-
|-
| style="text-align:center;" | [[15/13]], [[26/15]]
| 2.3.7.11.13
| style="text-align:center;" | 34.612
| 64/63, 78/77, 99/98, 144/143
| {{Mapping| 17 27 48 59 63 }}
| −3.00
| 2.31
| 3.28
|}
|}
* 17et is lower in relative error than any previous equal temperaments in the no-5 11- and 13-limit. The next equal temperaments doing better in these subgroups are [[41edo|41]] and [[207edo|207]], respectively.
=== Uniform maps ===
{{Uniform map|edo=17}}


===Patent val mapping===
=== Commas ===
17et [[tempering out|tempers out]] the following [[comma]]s. (Note: This assumes [[patent val]] {{val| 17 27 39 48 59 63 69 72 77}}, cent values ​​rounded to 1/100 of a cent.)


{| class="wikitable"
{| class="commatable wikitable center-all left-3 right-4 left-6"
|-
! [[Harmonic limit|Prime<br>limit]]
! [[Ratio]]<ref group="note">Ratios longer than 10 digits are presented by placeholders with informative hints.</ref>
! [[Monzo]]
! [[Cent]]s
! [[Color name]]
! Name
|-
| 3
| <abbr title="134217728/129140163">(18 digits)</abbr>
| {{Monzo| 27 -17 }}
| 66.76
| Sasawa
| [[Gothic comma]]
|-
|-
| | '''Interval, complement'''
| 5
| | '''Error (abs., in [[cent]]s)'''
| [[25/24]]
| {{Monzo| -3 -1 2 }}
| 70.76
| Yoyo
| Dicot comma
|-
|-
| style="text-align:center;" | [[18/13]], [[13/9]]
| 5
| style="text-align:center;" | 1.324
| [[32805/32768]]
| {{Monzo| -15 8 1 }}
| 1.95
| Layo
| Schisma
|-
|-
| style="text-align:center;" | [[13/12]], [[24/13]]
| 7
| style="text-align:center;" | 2.604
| [[64/63]]
| {{Monzo| 6 -2 0 -1 }}
| 27.26
| Ru
| Septimal comma
|-
|-
| style="text-align:center;" | [[4/3]], [[3/2]]
| 7
| style="text-align:center;" | 3.927
| [[525/512]]
| {{Monzo| -9 1 2 1 }}
| 43.41
| Lazoyoyo
| Avicennma
|-
|-
| style="text-align:center;" | [[11/9]], [[18/11]]
| 7
| style="text-align:center;" | 5.533
| [[245/243]]
| {{Monzo| 0 -5 1 2 }}
| 14.19
| Zozoyo
| Sensamagic comma
|-
|-
| style="text-align:center;" | [[14/11]], [[11/7]]
| 7
| style="text-align:center;" | 6.021
| [[1728/1715]]
| {{Monzo| 6 3 -1 -3 }}
| 13.07
| Triru-agu
| Orwellisma
|-
|-
| style="text-align:center;" | [[16/13]], [[13/8]]
| 7
| style="text-align:center;" | 6.531
| [[17496/16807]]
| {{Monzo| 3 7 0 -5 }}
| 69.56
| Quinru
| Bleu comma
|-
|-
| style="text-align:center;" | [[13/11]], [[22/13]]
| 7
| style="text-align:center;" | 6.857
| [[19683/19208]]
| {{Monzo| -3 9 0 -4 }}
| 42.29
| Laquadru
| Skwares comma
|-
|-
| style="text-align:center;" | [[9/8]], [[16/9]]
| 7
| style="text-align:center;" | 7.855
| <abbr title="420175/419904">(12 digits)</abbr>
| {{Monzo| -6 -8 2 5 }}
| 1.12
| Quinzo-ayoyo
| [[Wizma]]
|-
|-
| style="text-align:center;" | [[12/11]], [[11/6]]
| 11
| style="text-align:center;" | 9.461
| [[45/44]]
| {{Monzo| -2 2 1 0 -1 }}
| 38.91
| Luyo
| Cake comma
|-
|-
| style="text-align:center;" | [[9/7]], [[14/9]]
| 11
| style="text-align:center;" | 11.555
| [[99/98]]
| {{Monzo| -1 2 0 -2 1 }}
| 17.58
| Loruru
| Mothwellsma
|-
|-
| style="text-align:center;" | [[14/13]], [[13/7]]
| 11
| style="text-align:center;" | 12.878
| [[896/891]]
| {{Monzo| 7 -4 0 1 -1 }}
| 9.69
| Saluzo
| Pentacircle comma
|-
|-
| style="text-align:center;" | [[11/8]], [[16/11]]
| 11
| style="text-align:center;" | 13.388
| [[243/242]]
| {{Monzo| -1 5 0 0 -2 }}
| 7.14
| Lulu
| Rastma, neutral thirds comma
|-
|-
| style="text-align:center;" | [[7/6]], [[12/7]]
| 11
| style="text-align:center;" | 15.482
| [[385/384]]
| {{Monzo| -7 -1 1 1 1 }}
| 4.50
| Lozoyo
| Keenanisma
|-
|-
| style="text-align:center;" | [[8/7]], [[7/4]]
| 13
| style="text-align:center;" | 19.409
| [[40/39]]
| {{Monzo| 3 -1 1 0 0 -1 }}
| 43.83
| Thuyo
| Unintendo comma
|-
|-
| style="text-align:center;" | [[16/15]], [[15/8]]
| 13
| style="text-align:center;" | 29.445
| [[65/64]]
| {{Monzo| -6 0 1 0 0 1 }}
| 26.84
| Thoyo
| Wilsorma
|-
|-
| style="text-align:center;" | [[5/4]], [[8/5]]
| 13
| style="text-align:center;" | 33.373
| [[78/77]]
| {{Monzo| 1 1 0 -1 -1 1 }}
| 22.34
| Tholuru
| Negustma
|-
|-
| style="text-align:center;" | [[15/13]], [[26/15]]
| 13
| style="text-align:center;" | 35.976
| [[144/143]]
| {{Monzo| 4 2 0 0 -1 -1 }}
| 12.06
| Thulu
| Grossma
|-
|-
| style="text-align:center;" | [[6/5]], [[5/3]]
| 13
| style="text-align:center;" | 37.300
| [[169/168]]
| {{Monzo| -3 -1 0 -1 0 2 }}
| 10.27
| Thothoru
| Buzurgisma, dhanvantarisma
|-
|-
| style="text-align:center;" | [[13/10]], [[20/13]]
| 13
| style="text-align:center;" | 39.904
| [[352/351]]
| [5 -3 0 0 1 -1⟩
| 4.93
| Thulo
| Major minthma
|-
|-
| style="text-align:center;" | [[10/9]], [[9/5]]
| 13
| style="text-align:center;" | 41.227
| [[364/363]]
| {{Monzo| 2 -1 0 1 -2 1 }}
| 4.76
| Tholuluzo
| Minor minthma
|-
|-
| style="text-align:center;" | [[15/11]], [[22/15]]
| 13
| style="text-align:center;" | 42.833
| [[512/507]]
| {{Monzo| 9 -1 0 0 0 -2 }}
| 16.99
| Thuthu
| Tridecimal neutral thirds comma
|-
|-
| style="text-align:center;" | [[11/10]], [[20/11]]
| 13
| style="text-align:center;" | 46.760
| [[1352/1331]]
| {{Monzo| 3 0 0 0 -3 2 }}
| 27.10
| Bithotrilu
| Lovecraft comma
|-
|-
| style="text-align:center;" | [[15/14]], [[28/15]]
| 13
| style="text-align:center;" | 48.855
| [[2197/2187]]
| {{Monzo| 0 -7 0 0 0 3 }}
| 7.90
| Satritho
| Threedie
|-
|-
| style="text-align:center;" | [[7/5]], [[10/7]]
| 23
| style="text-align:center;" | 52.782
| [[162/161]]
|}
| {{Monzo| 1 4 0 -1 0 0 0 0 -1 }}
 
| 10.72
[[File:17ed2-001.svg|alt=alt : Your browser has no SVG support.]]
| Twethuru
 
| Minor kirnbergerisma
[[:File:17ed2-001.svg|17ed2-001.svg]]
 
=Commas=
17 EDO [[tempering out|tempers out]] the following [[comma]]s. (Note: This assumes [[val]] &lt; 17 27 39 48 59 63 |, cent values ​​rounded to 5 digits.)
 
{| class="wikitable"
|-
|-
! | Comma
| 23
! | Monzo
| [[208/207]]
! | Cents
| {{Monzo| 4 -2 0 0 0 1 0 0 -1 }}
![[Color notation/Temperament Names|Color Name]]
| 8.34
! | Name 1
| Twethutho
! | Name 2
| Vicetone comma
! | Name 3
|-
|-
| style="text-align:center;" | <span style="display: block; text-align: center;"></span>
| 23
| | {{Monzo | 27 -17 }}
| [[253/252]]
| style="text-align:right;" | 66.765
| {{Monzo| -2 -2 0 -1 1 0 0 0 1 }}
| style="text-align:center;" |Sasawa
| 6.86
| | <span style="display: block; text-align: center;">17-Comma</span>
| Twetholoru
| style="text-align:center;" |
| Middle neutravicema
| |
|-
|-
| style="text-align:center;" | 25/24
| 23
| | {{Monzo | -3 -1 2 }}
| [[529/528]]
| style="text-align:right;" | 70.762
| {{Monzo| -4 -1 0 0 -1 0 0 0 2 }}
| style="text-align:center;" |Yoyo
| 3.28
| | Chromatic semitone
| Bitwetho-alu
| style="text-align:center;" | Dicot comma
| Preziosisma
| |
|-
|-
| style="text-align:center;" | 32805/32768
| 23
| | {{Monzo | -15 8 1 }}
| [[736/729]]
| style="text-align:right;" | 1.9537
| {{Monzo| 5 -6 0 0 0 0 0 0 1 }}
| style="text-align:center;" |Layo
| 16.54
| style="text-align:center;" | Schisma
| Satwetho
| style="text-align:center;" |
| 23-limit Tenney/Cage comma (HEJI)
| style="text-align:center;" |  
|}
<references group="note" />
Note that due to the inaccurate prime 5, the rather large commas [[25/24]], [[525/512]], [[45/44]], and [[40/39]] are all tempered out by 17edo's patent val.
 
=== Rank-2 temperaments ===
* [[List of 17edo rank two temperaments by badness]]
* [[List of edo-distinct 17c rank two temperaments]]
* [[List of edo-distinct 17et rank two temperaments]]
* [[List of edo-distinct 17et no-fives rank two temperaments]]
 
{| class="wikitable center-all right-3 left-5"
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
|-
|-
| style="text-align:center;" | 525/512
! Periods<br>per 8ve
| | {{Monzo | -9 1 2 1 }}
! Generator
| style="text-align:right;" | 43.408
! Cents
| style="text-align:center;" |Zoyoyo
! Associated<br>ratio
| style="text-align:center;" | Avicennma
! Temperament
| style="text-align:center;" | Avicennma's Enharmonic Diesis
| style="text-align:center;" |
|-
|-
| style="text-align:center;" | 64/63
| 1
| | {{Monzo | 6 -2 0 -1 }}
| 2\17
| style="text-align:right;" | 27.264
| 141.18
| style="text-align:center;" |Ru
| 13/12
| style="text-align:center;" | Septimal Comma
| [[Bleu]] / [[progression]] (17c) / [[glacier]]
| style="text-align:center;" | Archytas' Comma
| style="text-align:center;" | Leipziger Komma
|-
|-
| style="text-align:center;" | 245/243
| 1
| | {{Monzo | 0 -5 1 2 }}
| 3\17
| style="text-align:right;" | 14.191
| 211.76
| style="text-align:center;" |Zozoyo
| 8/7~9/8
| style="text-align:center;" | Sensamagic
| [[Machine]]
| style="text-align:center;" |
| style="text-align:center;" |
|-
|-
| style="text-align:center;" | 1728/1715
| 1
| | {{Monzo | 6 3 -1 -3 }}
| 3\17
| style="text-align:right;" | 13.074
| 211.76
| style="text-align:center;" |Triru-agu
| 26/23
| style="text-align:center;" | Orwellisma
| [[Shoal|Shoal (trivial tuning)]]
| style="text-align:center;" | Orwell Comma
| style="text-align:center;" |  
|-
|-
| style="text-align:center;" |
| 1
| | {{Monzo | -6 -8 2 5 }}
| 4\17
| style="text-align:right;" | 1.1170
| 282.35
| style="text-align:center;" |Quinzo-ayoyo
| 13/11
| style="text-align:center;" | Wizma
| [[Huxley]] / [[lovecraft]] / [[subklei]] (17c)
| style="text-align:center;" |
| style="text-align:center;" |
|-
|-
| style="text-align:center;" | 99/98
| 1
| | {{Monzo | -1 2 0 -2 1 }}
| 5\17
| style="text-align:right;" | 17.576
| 352.94
| style="text-align:center;" |Loruru
| 11/9
| style="text-align:center;" | Mothwellsma
| [[Suhajira]] / [[neutrominant]] (17c) / [[beatles]] (17c) / [[dichotic]] (17) <br>[[Hemif]] / [[mohamaq]] (17c) / [[salsa]] (17)
| style="text-align:center;" |
| style="text-align:center;" |
|-
|-
| style="text-align:center;" | 896/891
| 1
| | {{Monzo | 7 -4 0 1 -1 }}
| 6\17
| style="text-align:right;" | 9.6880
| 423.53
| style="text-align:center;" |Saluzo
| 9/7
| style="text-align:center;" | Pentacircle
| [[Skwares]] / [[squares]] (17c) / [[sentinel]] (17) / [[sidi]] (17)
| style="text-align:center;" |
| style="text-align:center;" |
|-
|-
| style="text-align:center;" | 243/242
| 1
| | {{Monzo | -1 5 0 0 -2 }}
| 7\17
| style="text-align:right;" | 7.1391
| 494.12
| style="text-align:center;" |Lulu
| 4/3
| style="text-align:center;" | Rastma
| [[Archy]] / [[supra]] / [[quasisuper]] (17c) / [[dominant (temperament)|dominant]] (17c) / [[superpyth]] (17) / [[schism]] (17)<br>[[Fiventeen]]
| style="text-align:center;" |
| style="text-align:center;" |  
|-
|-
| style="text-align:center;" | 385/384
| 1
| | {{Monzo | -7 -1 1 1 1 }}
| 8\17
| style="text-align:right;" | 4.5026
| 564.71
| style="text-align:center;" |Lozoyo
| 7/5
| style="text-align:center;" | Keenanisma
| [[Lee]] / [[liese]] (17c) / [[pycnic]] (17)<br>[[Progress]] (17c)
| style="text-align:center;" |
| style="text-align:center;" |
|}
|}


Note that despite their relatively large size, the 17-comma, the avicennma and the chromatic semitone are all tempered out by the 13-limit patent val, as stated.
== Octave stretch or compression ==
17edo's approximations of harmonics 3, 7, 11, and 13 are all tempered sharp, so 17edo adapts well to slightly [[stretched and compressed tuning|compressing the octave]], if that is acceptable. [[44ed6]], [[27edt]] and [[zpi|56zpi]] are good demonstrations of this, where the octaves are flattened by about 1.5, 2.5 cents and 3 cents respectively.


=Scales=
== Scales ==
* [[Otonal 17]]
* [[Antipental blues]]: 4 3 1 2 4 3
* [https://web.archive.org/web/20140215081520/http://microtonalismo.com/proyecto-xvii Blues Peruvian 17edo]
* [https://web.archive.org/web/20140215081520/http://microtonalismo.com/proyecto-xvii Blues Peruvian]: 4 3 1 1 1 4 3
* [[17edo neutral scale]]
* [[Hydra]]: 3 3 1 1 2 3 2 1 1
* [[Scorp]]
* [[Maqam|Husayni]] Ascending: 2 2 3 3 2 2 3
* [[Screamapillar]]
* [[Otonal 17]]: 3 2 3 2 2 2 3
* [[Hydra]]
* [[Scorp]]: 3 2 3 1 3 2 3
* [[MOS scales of 17edo]] (horograms)
* [[Screamapillar]]: 3 3 2 2 3 3 1
* sLmLs: 2 5 3 5 2


=Temperaments=
=== MOS scales ===
* [[List of 17edo rank two temperaments by badness]]
{{Main| MOS scales of 17edo }}
* [[List of edo-distinct 17c rank two temperaments]]


=Music=
* diatonic ([[leapfrog]]/[[archy]]) [[5L&nbsp;2s]] 3 3 3 1 3 3 1 (10\17, 1\1)
==Scores==
* [[neutrominant]] [[3L&nbsp;4s]] 3 2 3 2 3 2 2 (5\17, 1\1) (''dedicated article: [[17edo neutral scale]]'')
* [http://home.snafu.de/djwolf/PreludeIn17tet.pdf Prelude] (PDF) by [[Daniel Wolf]]
* [[neutrominant]] [[7L&nbsp;3s]] 2 2 2 1 2 2 1 2 2 1 (5\17, 1\1)
* [http://georghajdu.de/compositions/heptadecatonic-drops/ Heptadecatonic Drops] by [http://georghajdu.de/biography/ Georg Hajdu]
* [[squares]] [[3L&nbsp;5s]] 1 1 4 1 4 1 4 (6\17, 1\1)
* [http://georghajdu.de/compositions/klangmoraste/ Klangmoraste] by Georg Hajdu
* [[squares]] [[3L&nbsp;8s]] 1 3 1 1 3 1 1 3 (6\17, 1\1)
* [http://www.microtonalismo.com/proyecto-xvii Charles Loli 17edo] {{forbidden}} music for guitar heptadecatonic (2001) and armony inductive microtonally (1993)
* lovecraft [[4L&nbsp;5s]] 3 1 3 1 3 1 3 1 1 (4\17, 1\1)
* [http://microtonalismo.com/ microtonalismo] Heptadecatonic Peruvian
* [[Multiverse]] by [[JacobBarton|Jacob Barton]]
* [http://christopherbaileymusic.com/walrus/v/#../../kitwo245m45n698th139rwebm845MQPxiF82J7WovYNRLK6klyq456/balladei.pdf Balladei] by [http://christopherbaileymusic.com/quick-bio/ Christopher Bailey]


==Sound files==
=== Well temperaments ===
* [https://themercurytree.bandcamp.com/album/spidermilk Spidermilk] (prog album) by [https://themercurytree.bandcamp.com/ The Mercury Tree]
* [[Secor wt17|George Secor's well temperament]]
* [https://soundcloud.com/overtoneshock/demanding-two-faces-17-edo Demanding Two Faces] (xen-pop) by [https://soundcloud.com/overtoneshock Stephen Weigel]
* [[User:CritDeathX/Sam's 17-note Well Temperament|Nicolai's 17-note well temperament]]
* [https://soundcloud.com/overtoneshock/where-were-you-during-the-apocalypse-17-edo Where were you at the Apocalypse?] (xen-pop) by [https://soundcloud.com/overtoneshock Stephen Weigel]*
* [[User:FloraC/Flora's 17-note well temperament|Flora's 17-note well temperament]]
* [http://chrisvaisvil.com/shanidar-cave-17-edo/ Shanidar Cave] is a piece in 17 edo that features an electric 17 edo guitar and what is essentially an electric tanpura which ends up making this a sort of fusion of middle eastern and Indian music in a sense. by [[Chris Vaisvil]]
* ''[https://soundcloud.com/aaron-krister-johnson/puhlops-and-lauguas-big-adventure Puhlops and Laugua's Big Adventure]'' by [http://www.untwelve.org/board Aaron Krister Johnson]
* ''[https://soundcloud.com/aaron-krister-johnson/adagio-for-margo Adagio for Margo]'' by [http://www.untwelve.org/board Aaron Krister Johnson]
* ''[http://home.comcast.net/~teamouse/Transformation.mp3 Transformation]'' by [http://home.comcast.net/%7Eteamouse/ Herman Miller] {{dead link}}
* ''[https://christopherbailey.bandcamp.com/track/waltz-in-17-tone-equal-tuning-2006 Waltz]'' by Christopher Bailey
* ''Lost & Found Things #2'' [https://soundcloud.com/zipzappoozoo/lost-and-found-things-2 (studio)] [https://soundcloud.com/zipzappoozoo/lost_found_live (live)] by Christopher Bailey
* ''[https://soundcloud.com/zipzappoozoo/balladei-live-christopher-bailey Balladei (live)]'' (in 17, 29 and 12) by [http://music.columbia.edu/%7Echris/ Christopher Bailey] , CD available [http://www.amazon.com/Christopher-Bailey-Shiau-Uen-Jacob-Rhodebeck/dp/B000TDZSAU/ here] .
* ''[http://www.h-pi.com/mp3/17ET.mp3 Two-Part Invention in 17ET]'' {{dead link}} by Aaron Andrew Hunt
* ''[http://micro.soonlabel.com/gene_ward_smith/Others/McGowan/MSND-Ovtr.mp3 Overture to A Midsummer Night's Dream]'' by [http://azuma-asobi.com/ Rick McGowan]
* ''[http://micro.soonlabel.com/gene_ward_smith/Others/McGowan/FairyLullaby-1.mp3 Fairy Lullaby from A Midsummer Night's Dream]'' by [http://azuma-asobi.com/ Rick McGowan]
* ''[http://micro.soonlabel.com/gene_ward_smith/Others/Igs/City%20Of%20The%20Asleep%20-%2017-A%20Calamitous%20Simultaneity.mp3 A Calamitous Simultaneity]'' by Igliashon Jones (17edo and 22edo)
* ''[http://micro.soonlabel.com/gene_ward_smith/Others/Igs/First%20Impressions.mp3 First Impressions]'' by Igliashon Jones
* [http://micro.soonlabel.com/gene_ward_smith/Others/Igs/I%20Insist.mp3 I Insist] by Igliashon Jones
* ''[http://archive.org/download/EtudeNo1For2PianosIn17EqualTemperament/EtudeForTwoPianosIn17edo.mp3 Etude no1 for 2 Pianos in 17 Equal Temperament]'' {{dead link}} and ''[http://archive.org/download/EtudeNo2For2PianosIn17EqualTemperament/EtudeNo2ForTwoPianosIn17edo.mp3 Etude no2 for 2 Pianos in 17 Equal Temperament]'' {{dead link}} by Jon Lyle Smith
* A number of compositions from [http://www.archive.org/details/seventeenTPP_01 seventeen-tone piano project phase I] , [[SeventeenTPPPhaseTwo|seventeen-tone piano project phase II]], [[SeventeenTPPPhaseThree|seventeen-tone piano project phase III]].
<!-- currently redundant:
* [http://www.archive.org/search.php?query=subject%3A%2217-edo%22 17edo] - 17edo-tagged compositions on www.archive.org
-->
* [http://soundclick.com/share?songid=8839072 sing a blue] by Andrew Heathwaite (composed 2008, recorded 2010). This and the other pieces below by Andrew for cümbüş, steel tubes &amp; voice.
* [http://soundclick.com/share?songid=8839073 stringfinger it everybean] by Andrew Heathwaite (composed 2008, recorded 2010).
* [http://soundclick.com/share?songid=8839069 cat feet belly] by Andrew Heathwaite (composed 2008, recorded 2010).
* ''[http://www.youtube.com/watch?v=a9N_T6LNDaE 17 Tone Jam]'' by Marmalade Man
* [http://www.youtube.com/results?search_query=17edo&search=tag youtube videos tagged with 17edo]
* [http://micro.soonlabel.com/gene_ward_smith/Others/Sanchez/No_Love_by_Gregory_Sanchez_1_on_SoundCloud___Hear_the_world_s_sounds.mp3 No Love] by [https://soundcloud.com/gregory-sanchez-2 Gregory Sanchez]
* [http://webzoom.freewebs.com/ralphjarzombek/micro7(17tet).mp3 Micro7] by Ralph Jarzombek
* [https://drive.google.com/drive/folders/0BwsXD8q2VCYUM0tRdDNhVzNhcHM Helas, pitié] by Alex Ness (in 17edo with stretched octaves)
* by [[Chris Vaisvil]]:
** ''On the Shores of the Dead Sea'': [http://chrisvaisvil.com/?p=784 blog] | [http://www.youtube.com/watch?v=D39MVFhb0Ho video]
** ''Only in Disneyland'': [http://chrisvaisvil.com/?p=466 blog] | [http://micro.soonlabel.com/17-ET/daily20110205-17et-disneyland.mp3 MP3] (guitar solo)
** ''17 Reasons I Hate the Blues'': [http://chrisvaisvil.com/?p=460 blog] | [http://micro.soonlabel.com/17-ET/daily20110125b-17-reasons-I-hate-the-blues.mp3 MP3]
** ''Klingon Opera Overture'': [http://chrisvaisvil.com/?p=422 blog] | [http://micro.soonlabel.com/17-ET/daily20110109-albino-17et.mp3 MP3]
** ''Seventeen Selfless Notes'': [http://chrisvaisvil.com/?p=298 blog] | [http://micro.soonlabel.com/17-ET/if20101028selfless.mp3 MP3]
** ''17et Jazz'': [http://chrisvaisvil.com/?p=76 blog] | [http://micro.soonlabel.com/17-ET/60x60-4001-1-ver2.mp3 MP3] (60 x 60 winner)
** ''17 Pink Tuxedos'': [http://chrisvaisvil.com/?p=742 blog] | [http://micro.soonlabel.com/17-ET/daily20110416-17_pink-tuxes.mp3 MP3]
** ''Devil in the Deep Blue Sea'': [http://chrisvaisvil.com/?p=706 blog] | [http://micro.soonlabel.com/17-ET/daily20110401-17-2-devil_in_the_deep_blue_sea.mp3 MP3] (blues collaboration between The Two Regs (vocals / lyrics) and Norm Harris (percussion) and Chris Vaisvil (17 note per octave electric guitar and fretless bass))
** ''Seventeen Years in the Sixties'': [http://chrisvaisvil.com/?p=585 blog] | [http://micro.soonlabel.com/17-ET/daily20110318-seventeen-years-in-the-sixties.mp3 MP3]
** ''CT Scan'': [http://chrisvaisvil.com/?p=699 blog] | [http://www.youtube.com/watch?v=ZEEuytYwtbo MP3]
** ''Fish and a Grenade'': [http://chrisvaisvil.com/?p=470 blog] | [http://micro.soonlabel.com/17-ET/daily20110208-17-a-fish-and-a-grenade.mp3 MP3] (parental advisory: language)
** ''Seventeen Unsteady Hands'': [http://chrisvaisvil.com/?p=550 blog] | [http://www.youtube.com/watch?v=rAKHCqBNhfc video of performance]
** ''The Pond'': [http://chrisvaisvil.com/?p=38 blog] | [http://www.youtube.com/watch?v=25sC3_uheyA video]
** ''Graveyard'': [http://chrisvaisvil.com/?p=305 blog] | [http://micro.soonlabel.com/17-ET/if20101028-graveyard.mp3 MP3]
** ''For Brass and Voice Choirs in 17 edo'': [http://chrisvaisvil.com/?p=1039 blog] | [http://micro.soonlabel.com/17-ET/daily20110713_q49_17_brass_voice_choirs.mp3 MP3]
** ''And I Became One With My Pet Fungi'': [http://chrisvaisvil.com/?p=1439 blog] | [http://micro.soonlabel.com/17-ET/daily20111015-fungi.mp3 MP3]
** ''Counterintuitive'': [http://chrisvaisvil.com/?p=1427 blog] | [http://micro.soonlabel.com/17-ET/20111014-STE-002-counter-intuitive.mp3 MP3] (guitar solo)
** ''Flying Into O'Hare'': [http://chrisvaisvil.com/?p=6909 blog] | [http://micro.soonlabel.com/17-ET/20161125_linn_speactral_17.MP3 MP3]


=Instruments=
{{Todo|expand scales list}}
* '''[http://www.microtonalismo.com/proyecto-xvii Guitar Heptadecatonic from Peruvian - Charles Loli and Antonio Huamani]''' {{forbidden}}
{{External image| http://sphotos.ak.fbcdn.net/hphotos-ak-snc4/hs883.snc4/71639_167001659983806_100000219181856_601995_1526184_n.jpg {{dead link}} }}
 
* '''[http://www.microtonalismo.com/proyecto-xvii Bass Heptadecatonic from Peruvian - Charles Loli and Antonio Huamani]''' {{forbidden}}
{{External image| http://sphotos.ak.fbcdn.net/hphotos-ak-ash2/hs382.ash2/66019_167001006650538_100000219181856_601987_48585_n.jpg {{dead link}} }}


== Instruments ==
=== Fretted String Instruments ===
* [http://chrisvaisvil.com/?p=436 17 note per octave conversion from a "standard" Stratocaster copy] - conversion by Brad Smith
* [http://chrisvaisvil.com/?p=436 17 note per octave conversion from a "standard" Stratocaster copy] - conversion by Brad Smith


[[File:17P1050829r.JPG|alt=17P1050829r.JPG|17P1050829r.JPG]]
[[File:17P1050829r.JPG|alt=17P1050829r.JPG|17P1050829r.JPG]]


[[Category:17edo| ]] <!-- main article -->
* 17edo soprano Harmony ukulele with a 3D printed fretboard - conversion by [[User:Tristanbay|Tristan Bay]]
[[Category:Edo]]
 
[[Category:Listen]]
[[File:17edo soprano ukulele with 3D printed fretboard.jpg|frameless|640x640px]]
[[Category:Prime EDO]]
 
[[Category:Pythagorean]]
=== Keyboards ===
[[Lumatone mapping for 17edo|Lumatone mappings for 17edo]] are available.
 
The Striso Board can be tuned in many ways, but as it has 17 notes per octave and is organised in a circle of fifths based layout, it works particularly well with 17edo, letting you play far wider stretches of notes than a standard keyboard.
 
[[File:Strisoboard_piano2a_s.jpg|frameless]]
 
It is possible to rebuild some standard MIDI keyboards to have 17 note per octave by combining parts from multiple keyboards, as with the finished product shown in the following videos by [[Stephen Weigel]] and [[Chris Vaisvil]]:
 
* [https://www.youtube.com/watch?v=2B14mttkavA ''Take This Stone (17-TET microtonal cover)''] (2025)
* [https://www.youtube.com/watch?v=nboggmtayk0 ''DIY microtonal piano - 17 notes per octave''] (2026)
 
== Music ==
{{Main| 17edo/Music }}
{{Catrel|17edo tracks}}
 
; [https://www.youtube.com/playlist?list=PLWB50RFxjvduT6F1Mwu0CmPa41LBRdXf5 YouTube playlist of 17edo pieces]
; [https://www.youtube.com/results?search_query=17edo&search=tag YouTube videos tagged with 17edo]
 
; Compositions from the [[SeventeenTonePianoProject|Seventeen Tone Piano Project]]
* [https://www.archive.org/details/seventeenTPP_01 seventeen-tone piano project phase I]
* [[SeventeenTPPPhaseTwo|Seventeen-tone piano project phase II]]
* [[SeventeenTPPPhaseThree|Seventeen-tone piano project phase III]]
<!-- currently redundant:
* [http://www.archive.org/search.php?query=subject%3A%2217-edo%22 17edo] - 17edo-tagged compositions on www.archive.org
-->
 
== Introductory Materials ==
* [[SeventeenTheory]], an introduction to 17edo theory, through the eyes of the [[SeventeenTonePianoProject]].
* [http://anaphoria.com/Secor17puzzle.pdf The 17-tone Puzzle] by George Secor, another introduction into 17edo theory.
* [[17edo tetrachords]]
* [http://microtonalismo.com/proyecto-xvii Proyect 17-Perú] {{forbidden}}
 
[[Category:Teentuning]]
[[Category:Teentuning]]
Retrieved from "https://en.xen.wiki/w/17edo"