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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
}}
}}
{{Infobox ET
{{Infobox ET}}
| Prime factorization = 17 is a prime
{{ED intro}}
| Step size = 70.58824¢
{{Wikipedia|17 equal temperament}}
| Fifth = 10\17 ≈ 706¢
| Major 2nd = 3\17 ≈ 212¢
| Minor 2nd = 1\17 ≈ 71¢
| Augmented 1sn = 2\17 ≈ 141¢
}}
'''17 tone equal temperament''', or '''17edo''', divides the octave in 17 equal steps, each around 70.6 [[cent]]s in size. It is the seventh [[prime numbers|prime]] [[EDO]], following [[13edo]] and coming before [[19edo]].


== Theory ==
== Theory ==
{| class="wikitable center-all"
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.
! colspan="2" | <!-- empty cell -->
 
! prime 2
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]].
! prime 3
 
! prime 5
=== As a means of extending harmony ===
! prime 7
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.
! prime 11
 
! prime 13
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.
! prime 17
 
! prime 19
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.
! prime 23
 
|-
Because the 5th harmonic is not well approximated, using timbres with attenuated 5th harmonics (and its multiples) may reduce audible beating.
! rowspan="2" | Error
! absolute ([[cent|¢]])
| 0.0
| +3.9
| -33.4
| +19.4
| +13.4
| +6.5
| -34.3
| -15.2
| +7.0
|-
! [[Relative error|relative]] (%)
| 0
| +6
| -47
| +27
| +19
| +9
| -49
| -21
| +10
|-
! colspan="2" | [[Nearest edomapping]]
| 17
| 10
| 5
| 14
| 8
| 12
| 1
| 4
| 9
|-
! colspan="2" | [[Fifthspan]]
| 0
| +1
| -8
| -2
| -6
| +8
| -5
| -3
| +6
|}


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]].
=== 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)}}


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.
=== 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.


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.
[[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.


== Intervals ==
== Intervals ==
{{See also| 17edo solfege }}


{| class="wikitable center-all right-2 left-8"
{| class="wikitable center-all right-2 left-3"
|-
|-
! Edosteps
! #
! Cents
! Cents
! colspan="2" | Extended [[circle-of-fifths notation]]
! Approximate ratios<ref group="note">{{sg|limit=2.3.25.7.11.13.85.23&nbsp;subgroup}}</ref>
! colspan="3" | [[Ups and Downs Notation]]
! 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>
! Approximate Ratios*
! 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)}}
|-
|-
| 0
| 0
| 0.00
| 0.0
| [[1/1]]
| Unison
| Unison
| D
| D
Line 97: Line 52:
| P1
| P1
| D
| D
| 1/1
| unison
| P1
| D
|-
|-
| 1
| 1
| 70.59
| 70.6
| Minor 2nd
| [[24/23]], [[25/24]], [[26/25]], [[27/26]], [[28/27]]
| Eb
| Minor 2nd<br>(Semiaugmented 1sn)
| minor 2nd
| Eb<br>(Dt)
| m2
| up unison, <br>minor 2nd
| ^1, m2
| Eb
| Eb
| [[25/24]], [[26/25]], [[33/32]], [[24/23]]
| uber unison, <br>minor 2nd
| U1, m2
| UD, Eb
|-
|-
| 2
| 2
| 141.18
| 141.2
| Neutral 2nd
| [[12/11]], [[13/12]], [[14/13]], [[25/23]]
| Ed
| Augmented 1sn<br>(Neutral 2nd)
| mid 2nd
| D#<br>(Ed)
| ~2
| augmented 1sn, <br>mid 2nd
| A1, ~2
| vE
| vE
| [[13/12]], [[12/11]], [[14/13]], [[25/23]]
| neutral 2nd
| N2
| UEb, uE
|-
|-
| 3
| 3
| 211.76
| 211.8
| [[8/7]], [[9/8]], [[17/15]], [[25/22]], [[26/23]]
| Major 2nd
| Major 2nd
| E
| E
Line 124: Line 88:
| M2
| M2
| E
| E
| [[9/8]], [[8/7]], [[28/25]], [[25/22]], [[26/23]]
| major 2nd
| M2
| E
|-
|-
| 4
| 4
| 282.35
| 282.4
| [[7/6]], [[13/11]], [[20/17]]
| Minor 3rd
| Minor 3rd
| F
| F
Line 133: Line 100:
| m3
| m3
| F
| F
| [[13/11]], [[7/6]]
| minor 3rd
| m3
| F
|-
|-
| 5
| 5
| 352.94
| 352.9
| Neutral 3rd
| [[11/9]], [[27/22]], [[16/13]], [[39/32]]
| F+
| Diminished 4th<br>(Neutral 3rd)
| Gb<br>(Ft)
| mid 3rd
| mid 3rd
| ~3
| ~3
| ^F
| ^F
| [[11/9]], [[16/13]], [[28/23]]
| neutral 3rd
| N3
| UF, uF#
|-
|-
| 6
| 6
| 423.53
| 423.5
| Major 3rd
| [[9/7]], [[14/11]], [[23/18]], [[32/25]], [[51/40]]
| Major 3rd<br>(Semidiminished 4th)
| F#<br>(Gd)
| major 3rd
| M3
| F#
| F#
| major 3rd
| major 3rd
| M3
| M3
| F#
| F#
| [[32/25]], [[9/7]], [[14/11]], [[33/26]], [[23/18]]
|-
|-
| 7
| 7
| 494.12
| 494.1
| [[4/3]], [[21/16]], [[85/64]]
| Perfect 4th
| Perfect 4th
| G
| G
Line 160: Line 136:
| P4
| P4
| G
| G
| [[4/3]]
| perfect 4th
| P4
| G
|-
|-
| 8
| 8
| 564.71
| 564.7
| Diminshed 5th, <br>super 4th
| [[11/8]], [[18/13]], [[25/18]], [[32/23]]
| G+
| Diminished 5th<br>(Semiaugmented 4th)
| Ab<br>(Gt)
| mid 4th, <br>diminished 5th
| mid 4th, <br>diminished 5th
| ~4, d5
| ~4, d5
| ^G, Ab
| ^G, Ab
| [[11/8]], [[18/13]], [[32/23]]
| uber 4th/<br>neutral 4th
| U4/N4
| UG
|-
|-
| 9
| 9
| 635.29
| 635.3
| Augmented 4th, <br>sub 5th
| [[13/9]], [[16/11]], [[23/16]], [[36/25]]
| Ad
| Augmented 4th<br>(Semidiminished 5th)
| G#<br>(Ad)
| augmented 4th, <br>mid 5th
| augmented 4th, <br>mid 5th
| A4, ~5
| A4, ~5
| G#, vA
| G#, vA
| [[16/11]], [[13/9]], [[23/16]]
| unter 5th/<br>neutral 5th
| u5/N5
| uA
|-
|-
| 10
| 10
| 705.88
| 705.9
| [[3/2]], [[32/21]], [[128/85]]
| Perfect 5th
| Perfect 5th
| A
| A
Line 187: Line 172:
| P5
| P5
| A
| A
| [[3/2]]
| perfect 5th
| P5
| A
|-
|-
| 11
| 11
| 776.47
| 776.5
| Minor 6th
| [[11/7]], [[14/9]], [[25/16]], [[36/23]], [[80/51]]
| Minor 6th<br>(Semiaugmented 5th)
| Bb<br>(At)
| minor 6th
| m6
| Bb
| Bb
| minor 6th
| minor 6th
| m6
| m6
| Bb
| Bb
| [[25/16]], [[14/9]], [[11/7]], [[52/33]], [[36/23]]
|-
|-
| 12
| 12
| 847.06
| 847.1
| Neutral 6th
| [[13/8]], [[18/11]], [[44/27]], [[64/39]]
| Bd
| Augmented 5th<br>(Neutral 6th)
| A#<br>(Bd)
| mid 6th
| mid 6th
| ~6
| ~6
| vB
| vB
| [[13/8]], [[18/11]], [[23/14]]
| neutral 6th
| N6
| UBb, uB
|-
|-
| 13
| 13
| 917.65
| 917.6
| [[12/7]], [[17/10]], [[22/13]]
| Major 6th
| Major 6th
| B
| B
Line 214: Line 208:
| M6
| M6
| B
| B
| [[17/10]], [[22/13]],[[12/7]]
| major 6th
| M6
| B
|-
|-
| 14
| 14
| 988.24
| 988.2
| [[7/4]], [[16/9]], [[23/13]], [[30/17]], [[44/25]]
| Minor 7th
| Minor 7th
| C
| C
Line 223: Line 220:
| m7
| m7
| C
| C
| [[16/9]], [[7/4]], [[25/14]], [[44/25]], [[23/13]]
| minor 7th
| m7
| C
|-
|-
| 15
| 15
| 1058.82
| 1058.8
| Neutral 7th
| [[11/6]], [[13/7]], [[24/13]], [[46/25]]
| C+
| Diminished 8ve<br>(Neutral 7th)
| Db<br>(Ct)
| mid 7th
| mid 7th
| ~7
| ~7
| ^C
| ^C
| [[11/6]], [[24/13]], [[13/7]], [[46/25]]
| neutral 7th
| N7
| UC, uC#
|-
|-
| 16
| 16
| 1129.41
| 1129.4
| Major 7th
| [[23/12]], [[25/13]], [[27/14]], [[48/25]], [[52/27]]
| Major 7th<br>(Semidiminished 8ve)
| C#<br>(Dd)
| major 7th,<br>down 8ve
| M7, v8
| C#
| C#
| major 7th
| major 7th,<br>unter octave
| M7
| M7, u8
| C#
| C#, uD
| [[25/13]], [[48/25]], [[64/33]], [[23/12]]
|-
|-
| 17
| 17
| 1200.00
| 1200.0
| [[2/1]]
| Octave
| Octave
| D
| D
Line 250: Line 256:
| P8
| P8
| D
| D
| [[2/1]]
| octave
| P8
| D
|}
|}
<nowiki>*</nowiki> Ratios based on treating 17edo as a 2.3.7.11.13.23.25 subgroup
<references group="note" />
 
In 17edo, ups and downs can respectively be substituted with half-sharps and half-flats,
since sharps and flats each span two edo steps.
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.


=== 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 center-all"
{| class="wikitable center-all"
! quality
! color
! monzo format
! examples
|-
|-
| minor
! Quality
! Color
! Monzo format
! Examples
|-
| rowspan="2" | minor
| zo
| zo
| {a, b, 0, 1}
| (a, b, 0, 1)
| 7/6, 7/4
| 7/6, 7/4
|-
|-
| "
| fourthward wa
| fourthward wa
| {a, b}, b &lt; -1
| (a, b), b < -1
| 32/27, 16/9
| 32/27, 16/9
|-
|-
| mid
| rowspan="2" | mid
| ilo
| ilo
| {a, b, 0, 0, 1}
| (a, b, 0, 0, 1)
| 11/9, 11/6
| 11/9, 11/6
|-
|-
| "
| lu
| lu
| {a, b, 0, 0, -1}
| (a, b, 0, 0, -1)
| 12/11, 18/11
| 12/11, 18/11
|-
|-
| major
| rowspan="2" | major
| fifthward wa
| fifthward wa
| {a, b}, b &gt; 1
| (a, b), b > 1
| 9/8, 27/16
| 9/8, 27/16
|-
|-
| "
| ru
| ru
| {a, b, 0, -1}
| (a, b, 0, -1)
| 9/7, 12/7
| 9/7, 12/7
|}
|}
== Notations ==
From the appendix to [[The Sagittal Songbook]] by [[JacobBarton|Jacob A. Barton]], a diagram of how to notate 17-EDO in the Revo flavor of Sagittal:
[[File:17edo Sagittal.png|800px]]
== 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:
Line 310: Line 304:
{| class="wikitable center-all"
{| 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
|-
|-
| zo
| zo
Line 355: Line 349:
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


For a more complete list, see [[Ups and Downs Notation #Chords and Chord Progressions]].
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}}


== JI approximation ==
Because it contains no Sagittal symbols, this Evo-SZ Sagittal notation is identical to the Stein-Zimmerman notation.
=== 15-odd-limit mappings ===
The following table shows how [[15-odd-limit intervals]] are represented in 17edo (ordered by absolute error). Prime harmonics are in '''bold'''; inconsistent intervals are in ''italic''.  


{| class="wikitable sortable center-1 right-2"
==== Sagittal songbook diagram ====
|+Direct mapping (even if inconsistent)
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:
 
[[File:17edo Sagittal.png|800px]]
 
=== 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 center-all right-2 left-4 left-5 mw-collapsible mw-collapsed"
|-
|-
! class="unsortable" | Interval, complement
! #
! Error (abs, [[Cent|¢]])
! Cents
! Note
! Name
! Associated ratios
|-
|-
| [[18/13]], [[13/9]]
| 0
| 1.324
| 0.0
| D
| Perfect 1sn
| 1/1
|-
|-
| [[13/12]], [[24/13]]
| 1
| 2.604
| 70.6
| D#
| Augmented 1sn
| 33/32
|-
|-
| '''[[4/3]], [[3/2]]'''
| 2
| '''3.927'''
| 141.2
| Eb
| Minor 2nd
| 12/11
|-
|-
| [[11/9]], [[18/11]]
| 3
| 5.533
| 211.8
| E
| Major 2nd
| 9/8
|-
|-
| [[14/11]], [[11/7]]
| 4
| 6.021
| 282.4
| Fb
| Diminished 3rd
| 32/27
|-
|-
| '''[[16/13]], [[13/8]]'''
| 5
| '''6.531'''
| 352.9
| F
| Perfect 3rd
| 11/9, 27/22
|-
|-
| [[13/11]], [[22/13]]
| 6
| 6.857
| 423.5
| F#
| Augmented 3rd
| 81/64
|-
|-
| [[9/8]], [[16/9]]
| 7
| 7.855
| 494.1
| G
| Minor 4th
| 4/3
|-
|-
| [[12/11]], [[11/6]]
| 8
| 9.461
| 564.7
| G#
| Major 4th
| 11/8
|-
|-
| [[9/7]], [[14/9]]
| 9
| 11.555
| 635.3
| Ab
| Minor 5th
| 16/11
|-
|-
| [[14/13]], [[13/7]]
| 10
| 12.878
| 705.9
| A
| Major 5th
| 3/2
|-
|-
| '''[[11/8]], [[16/11]]'''
| 11
| '''13.388'''
| 776.5
| Bb
| Diminished 6th
| 128/81
|-
|-
| [[7/6]], [[12/7]]
| 12
| 15.482
| 847.1
| B
| Perfect 6th
| 18/11, 44/27
|-
|-
| ''[[7/5]], [[10/7]]''
| 13
| ''17.806''
| 917.6
| B#
| Augmented 6th
| 27/16
|-
|-
| '''[[8/7]], [[7/4]]'''
| 14
| '''19.409'''
| 988.2
| Cb
| Minor 7th
| 16/9
|-
|-
| ''[[15/14]], [[28/15]]''
| 15
| ''21.734''
| 1058.8
| C
| Major 7th
| 11/6
|-
|-
| ''[[11/10]], [[20/11]]''
| 16
| ''23.828''
| 1129.4
| Db
| Diminished 8ve
| 64/33
|-
|-
| ''[[15/11]], [[22/15]]''
| 17
| ''27.755''
| 1200.0
|-
| D
| ''[[10/9]], [[9/5]]''
| Perfect 8ve
| ''29.361''
| 2/1
|-
| [[16/15]], [[15/8]]
| 29.445
|-
| ''[[13/10]], [[20/13]]''
| ''30.685''
|-
| ''[[6/5]], [[5/3]]''
| ''33.288''
|-
| '''[[5/4]], [[8/5]]'''
| '''33.373'''
|-
| ''[[15/13]], [[26/15]]''
| ''34.612''
|}
|}


{| class="wikitable center-1 right-2"
== Approximation to JI ==
|+Patent val mapping
=== 15-odd-limit interval mappings ===
|-
{{Q-odd-limit intervals|17}}
! Interval, complement
{{Q-odd-limit intervals|17.04|apx=val|header=none|tag=none|title=15-odd-limit intervals by 17c val mapping}}
! Error (abs, [[Cent|¢]])
|-
| [[18/13]], [[13/9]]
| 1.324
|-
| [[13/12]], [[24/13]]
| 2.604
|-
| '''[[4/3]], [[3/2]]'''
| '''3.927'''
|-
| [[11/9]], [[18/11]]
| 5.533
|-
| [[14/11]], [[11/7]]
| 6.021
|-
| '''[[16/13]], [[13/8]]'''
| '''6.531'''
|-
| [[13/11]], [[22/13]]
| 6.857
|-
| [[9/8]], [[16/9]]
| 7.855
|-
| [[12/11]], [[11/6]]
| 9.461
|-
| [[9/7]], [[14/9]]
| 11.555
|-
| [[14/13]], [[13/7]]
| 12.878
|-
| '''[[11/8]], [[16/11]]'''
| '''13.388'''
|-
| [[7/6]], [[12/7]]
| 15.482
|-
| '''[[8/7]], [[7/4]]'''
| '''19.409'''
|-
| [[16/15]], [[15/8]]
| 29.445
|-
| '''[[5/4]], [[8/5]]'''
| '''33.373'''
|-
| ''[[15/13]], [[26/15]]''
| ''35.976''
|-
| ''[[6/5]], [[5/3]]''
| ''37.300''
|-
| ''[[13/10]], [[20/13]]''
| ''39.904''
|-
| ''[[10/9]], [[9/5]]''
| ''41.227''
|-
| ''[[15/11]], [[22/15]]''
| ''42.833''
|-
| ''[[11/10]], [[20/11]]''
| ''46.760''
|-
| ''[[15/14]], [[28/15]]''
| ''48.855''
|-
| ''[[7/5]], [[10/7]]''
| ''52.782''
|}


=== Selected 13-limit intervals ===
=== Selected 13-limit intervals ===
[[File:17ed2-001.svg|alt=alt : Your browser has no SVG support.]]
[[File:17ed2-001.svg|alt=alt : Your browser has no SVG support.]]


== Tuning 17edo by ear ==
== Tuning by ear ==
17edo is very close to a circle of seventeen [[25/24]] chromatic semitones: (25/24)^17 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.
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 ==
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
{| class="wikitable center-4 center-5 center-6"
! rowspan="2" | Subgroup
! rowspan="2" | [[Subgroup]]
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | [[Mapping]]
Line 537: Line 522:
|-
|-
| 2.3
| 2.3
| {{monzo| 27 -17 }}
| {{Monzo| 27 -17 }}
| [{{val| 17 27 }}]
| {{Mapping| 17 27 }}
| -1.24
| −1.24
| 1.24
| 1.24
| 1.76
| 1.76
Line 545: Line 530:
| 2.3.7
| 2.3.7
| 64/63, 17496/16807
| 64/63, 17496/16807
| [{{val| 17 27 48 }}]
| {{Mapping| 17 27 48 }}
| -3.13
| −3.13
| 2.85
| 2.85
| 4.05
| 4.05
Line 552: Line 537:
| 2.3.7.11
| 2.3.7.11
| 64/63, 99/98, 243/242
| 64/63, 99/98, 243/242
| [{{val| 17 27 48 59 }}]
| {{Mapping| 17 27 48 59 }}
| -3.31
| −3.31
| 2.49
| 2.49
| 3.54
| 3.54
Line 559: Line 544:
| 2.3.7.11.13
| 2.3.7.11.13
| 64/63, 78/77, 99/98, 144/143
| 64/63, 78/77, 99/98, 144/143
| [{{val| 17 27 48 59 63 }}]
| {{Mapping| 17 27 48 59 63 }}
| -3.00
| −3.00
| 2.31
| 2.31
| 3.28
| 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.


17et is lower in relative error than any previous equal temperaments in the no-5 11- and 13-limit. The next ETs better in these subgroups are 41 and 207, respectively.
=== Uniform maps ===
{{Uniform map|edo=17}}


=== Commas ===
=== Commas ===
17 EDO [[tempers out]] the following [[comma]]s. (Note: This assumes [[val]] {{val| 17 27 39 48 59 63 }}, cent values ​​rounded to 5 digits.)
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="commatable wikitable center-all left-3 right-4 left-6"
{| class="commatable wikitable center-all left-3 right-4 left-6"
|-
|-
! [[Harmonic limit|Prime<br>Limit]]
! [[Harmonic limit|Prime<br>limit]]
! [[Ratio]]<ref>Ratios longer than 10 digits are presented by placeholders with informative hints</ref>
! [[Ratio]]<ref group="note">Ratios longer than 10 digits are presented by placeholders with informative hints.</ref>
! [[Monzo]]
! [[Monzo]]
! [[Cent]]s
! [[Cent]]s
! [[Color name]]
! [[Color name]]
! Name(s)
! Name
|-
|-
| 3
| 3
| [[134217728/129140163|(18 digits)]]
| <abbr title="134217728/129140163">(18 digits)</abbr>
| {{Monzo | 27 -17 }}
| {{Monzo| 27 -17 }}
| 66.765
| 66.76
| Sasawa
| Sasawa
| [[17-comma]]
| [[Gothic comma]]
|-
|-
| 5
| 5
| [[25/24]]
| [[25/24]]
| {{Monzo | -3 -1 2 }}
| {{Monzo| -3 -1 2 }}
| 70.762
| 70.76
| Yoyo
| Yoyo
| Chromatic semitone, dicot comma
| Dicot comma
|-
|-
| 5
| 5
| [[32805/32768]]
| [[32805/32768]]
| {{Monzo | -15 8 1 }}
| {{Monzo| -15 8 1 }}
| 1.9537
| 1.95
| Layo
| Layo
| Schisma
| Schisma
|-
|-
| 7
| 7
| [[525/512]]
| [[64/63]]
| {{Monzo | -9 1 2 1 }}
| {{Monzo| 6 -2 0 -1 }}
| 43.408
| 27.26
| Zoyoyo
| Ru
| Avicennma, Avicennma's enharmonic diesis
| Septimal comma
|-
|-
| 7
| 7
| [[64/63]]
| [[525/512]]
| {{Monzo | 6 -2 0 -1 }}
| {{Monzo| -9 1 2 1 }}
| 27.264
| 43.41
| Ru
| Lazoyoyo
| Septimal comma, Archytas' comma, Leipziger Komma
| Avicennma
|-
|-
| 7
| 7
| [[245/243]]
| [[245/243]]
| {{Monzo | 0 -5 1 2 }}
| {{Monzo| 0 -5 1 2 }}
| 14.191
| 14.19
| Zozoyo
| Zozoyo
| Sensamagic
| Sensamagic comma
|-
|-
| 7
| 7
| [[1728/1715]]
| [[1728/1715]]
| {{Monzo | 6 3 -1 -3 }}
| {{Monzo| 6 3 -1 -3 }}
| 13.074
| 13.07
| Triru-agu
| Triru-agu
| Orwellisma, orwell comma
| Orwellisma
|-
| 7
| [[17496/16807]]
| {{Monzo| 3 7 0 -5 }}
| 69.56
| Quinru
| Bleu comma
|-
| 7
| [[19683/19208]]
| {{Monzo| -3 9 0 -4 }}
| 42.29
| Laquadru
| Skwares comma
|-
|-
| 7
| 7
| <abbr title="420175/419904">(12 digits)</abbr>
| <abbr title="420175/419904">(12 digits)</abbr>
| {{Monzo | -6 -8 2 5 }}
| {{Monzo| -6 -8 2 5 }}
| 1.1170
| 1.12
| Quinzo-ayoyo
| Quinzo-ayoyo
| [[Wizma]]
| [[Wizma]]
|-
| 11
| [[45/44]]
| {{Monzo| -2 2 1 0 -1 }}
| 38.91
| Luyo
| Cake comma
|-
|-
| 11
| 11
| [[99/98]]
| [[99/98]]
| {{Monzo | -1 2 0 -2 1 }}
| {{Monzo| -1 2 0 -2 1 }}
| 17.576
| 17.58
| Loruru
| Loruru
| Mothwellsma
| Mothwellsma
Line 644: Line 652:
| 11
| 11
| [[896/891]]
| [[896/891]]
| {{Monzo | 7 -4 0 1 -1 }}
| {{Monzo| 7 -4 0 1 -1 }}
| 9.6880
| 9.69
| Saluzo
| Saluzo
| Pentacircle
| Pentacircle comma
|-
|-
| 11
| 11
| [[243/242]]
| [[243/242]]
| {{monzo| -1 5 0 0 -2 }}
| {{Monzo| -1 5 0 0 -2 }}
| 7.1391
| 7.14
| Lulu
| Lulu
| [[Rastma]]
| Rastma, neutral thirds comma
|-
|-
| 11
| 11
| [[385/384]]
| [[385/384]]
| {{monzo| -7 -1 1 1 1 }}
| {{Monzo| -7 -1 1 1 1 }}
| 4.5026
| 4.50
| Lozoyo
| Lozoyo
| Keenanisma
| Keenanisma
|-
| 13
| [[40/39]]
| {{Monzo| 3 -1 1 0 0 -1 }}
| 43.83
| Thuyo
| Unintendo comma
|-
| 13
| [[65/64]]
| {{Monzo| -6 0 1 0 0 1 }}
| 26.84
| Thoyo
| Wilsorma
|-
| 13
| [[78/77]]
| {{Monzo| 1 1 0 -1 -1 1 }}
| 22.34
| Tholuru
| Negustma
|-
| 13
| [[144/143]]
| {{Monzo| 4 2 0 0 -1 -1 }}
| 12.06
| Thulu
| Grossma
|-
| 13
| [[169/168]]
| {{Monzo| -3 -1 0 -1 0 2 }}
| 10.27
| Thothoru
| Buzurgisma, dhanvantarisma
|-
| 13
| [[352/351]]
| [5 -3 0 0 1 -1⟩
| 4.93
| Thulo
| Major minthma
|-
| 13
| [[364/363]]
| {{Monzo| 2 -1 0 1 -2 1 }}
| 4.76
| Tholuluzo
| Minor minthma
|-
| 13
| [[512/507]]
| {{Monzo| 9 -1 0 0 0 -2 }}
| 16.99
| Thuthu
| Tridecimal neutral thirds comma
|-
|-
| 13
| 13
| [[1352/1331]]
| [[1352/1331]]
| {{monzo| 3 0 0 0 -3 2 }}
| {{Monzo| 3 0 0 0 -3 2 }}
| 27.101
| 27.10
| Bithotrilu
| Bithotrilu
| Lovecraft comma
| Lovecraft comma
|-
|-
| 13
| 13
| [[364/363]]
| [[2197/2187]]
| {{monzo| 2 -1 0 1 -2 1 }}
| {{Monzo| 0 -7 0 0 0 3 }}
| 4.763
| 7.90
| Tholuluzo
| Satritho
| Gentle comma
| Threedie
|-
| 23
| [[162/161]]
| {{Monzo| 1 4 0 -1 0 0 0 0 -1 }}
| 10.72
| Twethuru
| Minor kirnbergerisma
|-
| 23
| [[208/207]]
| {{Monzo| 4 -2 0 0 0 1 0 0 -1 }}
| 8.34
| Twethutho
| Vicetone comma
|-
| 23
| [[253/252]]
| {{Monzo| -2 -2 0 -1 1 0 0 0 1 }}
| 6.86
| Twetholoru
| Middle neutravicema
|-
| 23
| [[529/528]]
| {{Monzo| -4 -1 0 0 -1 0 0 0 2 }}
| 3.28
| Bitwetho-alu
| Preziosisma
|-
| 23
| [[736/729]]
| {{Monzo| 5 -6 0 0 0 0 0 0 1 }}
| 16.54
| Satwetho
| 23-limit Tenney/Cage comma (HEJI)
|}
|}
<references/>
<references group="note" />
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.
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 ===
=== Rank-2 temperaments ===
* [[List of 17edo rank two temperaments by badness]]
* [[List of 17edo rank two temperaments by badness]]
* [[List of edo-distinct 17c rank two temperaments]]
* [[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"
{| class="wikitable center-all right-3 left-5"
|+Table of rank-2 temperaments by generator
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
! Periods<br>per Octave
|-
! Periods<br>per 8ve
! Generator
! Generator
! Cents
! Cents
! Associated<br>Ratio
! Associated<br>ratio
! Temperament
! Temperament
|-
|-
Line 696: Line 798:
| 141.18
| 141.18
| 13/12
| 13/12
| [[Bleu]] / [[progression]] (17c)
| [[Bleu]] / [[progression]] (17c) / [[glacier]]
|-
|-
| 1
| 1
Line 703: Line 805:
| 8/7~9/8
| 8/7~9/8
| [[Machine]]
| [[Machine]]
|-
| 1
| 3\17
| 211.76
| 26/23
| [[Shoal|Shoal (trivial tuning)]]
|-
|-
| 1
| 1
Line 708: Line 816:
| 282.35
| 282.35
| 13/11
| 13/11
| [[Huxley]]{{clarify}}<br>[[Lovecraft]]
| [[Huxley]] / [[lovecraft]] / [[subklei]] (17c)
|-
|-
| 1
| 1
Line 714: Line 822:
| 352.94
| 352.94
| 11/9
| 11/9
| [[Neutral]]<br>[[Suhajira]] / [[maqamic]] (17c) / [[beatles]] (17c) / [[dicotic]] (17) <br>[[Hemif]] / [[mohamaq]] (17c) / [[salsa]] (17)
| [[Suhajira]] / [[neutrominant]] (17c) / [[beatles]] (17c) / [[dichotic]] (17) <br>[[Hemif]] / [[mohamaq]] (17c) / [[salsa]] (17)
|-
|-
| 1
| 1
Line 726: Line 834:
| 494.12
| 494.12
| 4/3
| 4/3
| [[Archy]] / [[supra]] / [[quasisuper]] (17c) / [[dominant]] (17c) / [[superpyth]] (17) / [[schism]] (17)
| [[Archy]] / [[supra]] / [[quasisuper]] (17c) / [[dominant (temperament)|dominant]] (17c) / [[superpyth]] (17) / [[schism]] (17)<br>[[Fiventeen]]
|-
|-
| 1
| 1
Line 734: Line 842:
| [[Lee]] / [[liese]] (17c) / [[pycnic]] (17)<br>[[Progress]] (17c)
| [[Lee]] / [[liese]] (17c) / [[pycnic]] (17)<br>[[Progress]] (17c)
|}
|}
== 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
* [[Screamapillar]]: 3 3 2 2 3 3 1
* sLmLs: 2 5 3 5 2


=== MOS scales ===
=== MOS scales ===
{{main| MOS scales of 17edo }}
{{Main| MOS scales of 17edo }}


* diatonic ([[leapfrog]]/[[archy]]) 5L2s 3331331 (10\17, 1\1)
* diatonic ([[leapfrog]]/[[archy]]) [[5L&nbsp;2s]] 3 3 3 1 3 3 1 (10\17, 1\1)
* [[maqamic]] 3L4s 3232322 (5\17, 1\1)
* [[neutrominant]] [[3L&nbsp;4s]] 3 2 3 2 3 2 2 (5\17, 1\1) (''dedicated article: [[17edo neutral scale]]'')
* [[maqamic]] 7L3s 2221221221 (5\17, 1\1)
* [[neutrominant]] [[7L&nbsp;3s]] 2 2 2 1 2 2 1 2 2 1 (5\17, 1\1)
* [[squares]] 3L5s 1141414 (6\17, 1\1)
* [[squares]] [[3L&nbsp;5s]] 1 1 4 1 4 1 4 (6\17, 1\1)
* [[squares]] 3L8s 13113113 (6\17, 1\1)
* [[squares]] [[3L&nbsp;8s]] 1 3 1 1 3 1 1 3 (6\17, 1\1)
* Pathological [[squares]] 3L11s 11211121112 (6\17, 1\1)  
* lovecraft [[4L&nbsp;5s]] 3 1 3 1 3 1 3 1 1 (4\17, 1\1)
* [[lovecraft]] 4L5s 313131311 (4\17, 1\1)
* Pathological [[1L 13s]] 4 1 1 1 1 1 1 1 1 1 1 1 1 (1\17, 1\1)
* Pathological [[1L 13s|1L 14s]] 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 (1\17, 1\1)
* Pathological [[2L 13s]] 2 1 1 1 1 1 1 1 2 1 1 1 1 1 1 (8\17, 1\1)
* Pathological 1L 15s 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 (1\17, 1\1)


=== Well temperaments ===
=== Well temperaments ===
* [[Secor wt17|George Secor’s well temperament of this tuning]]
* [[Secor wt17|George Secor's well temperament]]
* [[User:CritDeathX/Sam's 17-note Well Temperament|Nicolai's 17-note Well Temperament]]
* [[User:CritDeathX/Sam's 17-note Well Temperament|Nicolai's 17-note well temperament]]
* [[User:FloraC/Flora's 17-note well temperament|Flora's 17-note well temperament]]
* [[User:FloraC/Flora's 17-note well temperament|Flora's 17-note well temperament]]


== Introductory materials ==
{{Todo|expand scales list}}
* [[File:17edo_1MC.mp3|270px]] 17-edo example composition by [[User:Schrodingasdawg|Schrodingasdawg]] ([[File:17edo_1MC_score.pdf|score]])
 
* [[SeventeenTheory]], an introduction to 17-EDO theory, through the eyes of the [[SeventeenTonePianoProject]].
== Instruments ==
* [http://anaphoria.com/Secor17puzzle.pdf The 17-tone Puzzle] by George Secor, another introduction into 17-EDO theory.
=== Fretted String Instruments ===
* [[17edo Solfege]]
* [http://chrisvaisvil.com/?p=436 17 note per octave conversion from a "standard" Stratocaster copy] - conversion by Brad Smith
* [[17edo tetrachords]]
 
* [http://microtonalismo.com/proyecto-xvii Proyect 17-Perú] {{forbidden}}
[[File:17P1050829r.JPG|alt=17P1050829r.JPG|17P1050829r.JPG]]
 
* 17edo soprano Harmony ukulele with a 3D printed fretboard - conversion by [[User:Tristanbay|Tristan Bay]]
 
[[File:17edo soprano ukulele with 3D printed fretboard.jpg|frameless|640x640px]]
 
=== 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 ==
== Music ==
=== Scores ===
{{Main| 17edo/Music }}
* [http://home.snafu.de/djwolf/PreludeIn17tet.pdf Prelude] (PDF) by [[Daniel Wolf]]
{{Catrel|17edo tracks}}
* [http://georghajdu.de/compositions/heptadecatonic-drops/ Heptadecatonic Drops] by [http://georghajdu.de/biography/ Georg Hajdu]
* [http://georghajdu.de/compositions/klangmoraste/ Klangmoraste] by Georg Hajdu
* [http://www.microtonalismo.com/proyecto-xvii Charles Loli 17edo] {{forbidden}} music for guitar heptadecatonic (2001) and armony inductive microtonally (1993)
* [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]
* [[:File:Locrian Suite Sarabande Score.pdf|Sarabande from the Locrian Suite]] by [[User:IlL|Inthar]]


=== Sound files ===
; [https://www.youtube.com/playlist?list=PLWB50RFxjvduT6F1Mwu0CmPa41LBRdXf5 YouTube playlist of 17edo pieces]
* [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]
* [https://youtu.be/vISyCcogrOs "17-tone equal temperament"] by benyamind
 
* [https://youtu.be/aU8RmEeXap8 Arm's Length by Diamond Doll (xen-pop)]
; Compositions from the [[SeventeenTonePianoProject|Seventeen Tone Piano Project]]
* [https://themercurytree.bandcamp.com/album/spidermilk Spidermilk] (prog album) by [https://themercurytree.bandcamp.com/ The Mercury Tree]
* [https://www.archive.org/details/seventeenTPP_01 seventeen-tone piano project phase I]
* [https://soundcloud.com/overtoneshock/demanding-two-faces-17-edo Demanding Two Faces] (xen-pop) by [https://soundcloud.com/overtoneshock Stephen Weigel]
* [[SeventeenTPPPhaseTwo|Seventeen-tone piano project phase II]]
* [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]*
* [[SeventeenTPPPhaseThree|Seventeen-tone piano project phase III]]
* [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]''  {{Dead link}} by Igliashon Jones
* [http://micro.soonlabel.com/gene_ward_smith/Others/Igs/I%20Insist.mp3 I Insist] {{Dead link}} 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]].
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* [http://www.archive.org/search.php?query=subject%3A%2217-edo%22 17edo] - 17edo-tagged compositions on www.archive.org
* [http://www.archive.org/search.php?query=subject%3A%2217-edo%22 17edo] - 17edo-tagged compositions on www.archive.org
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* [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)
* [https://soundcloud.com/user-455564099/march-of-the-mushrooms March of the Mushrooms] by [https://en.xen.wiki/w/User:Jutomi Jutomi]
* 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 ==
== Introductory Materials ==
* '''[http://www.microtonalismo.com/proyecto-xvii Guitar Heptadecatonic from Peruvian - Charles Loli and Antonio Huamani]''' {{forbidden}}
* [[SeventeenTheory]], an introduction to 17edo theory, through the eyes of the [[SeventeenTonePianoProject]].
{{External image| http://sphotos.ak.fbcdn.net/hphotos-ak-snc4/hs883.snc4/71639_167001659983806_100000219181856_601995_1526184_n.jpg {{dead link}} }}
* [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}}


* '''[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}} }}
* [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]]
[[Category:17edo| ]] <!-- main article -->
[[Category:Equal divisions of the octave]]
[[Category:Listen]]
[[Category:Prime EDO]]
[[Category:Pythagorean]]
[[Category:Teentuning]]
[[Category:Teentuning]]
{{todo| cleanup }}
Retrieved from "https://en.xen.wiki/w/17edo"