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{{interwiki
{{interwiki
| de = 17edo
| de = 17-EDO
| en = 17edo
| en = 17edo
| es = 17 EDO
| es = 17 EDO
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}}
}}
{{Infobox ET}}
{{Infobox ET}}
{{ED intro}}
{{Wikipedia|17 equal temperament}}
{{Wikipedia|17 equal temperament}}
'''17 equal divisions of the octave''' ('''17edo'''), or '''17(-tone) equal temperament''' ('''17tet''', '''17et''') when viewed from a [[regular temperament]] perspective, is the tuning system derived from dividing the octave in 17 [[equal]] steps, each around 70.6 [[cent]]s in size.


== Theory ==
== Theory ==
17edo 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]].
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.  


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 triad is quite dissonant as the major third is closer to 9/7 than the traditional 5/4.  
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]].


Instead, the tonic chords of 17edo could be considered to be the tetrad 6:7:8:9 and its utonal inversion (representing 14:16:18:21 as [[64/63]] is tempered out), the former of which is a subminor chord with added fourth, and the latter a supermajor chord with added second (resembling the [[wikipedia: Mu chord|mu chord]] of Steely Dan fame). These are realized in 17edo 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 17edo 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.  
=== 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.


Another construction of septimal chords involves 4:7:12 and its inversion 7:12:21. These triads span a twelfth, realized in 17edo as 0-14-27 and 0-13-27, respectively. To this we may add 0-12-14-27, representing 8:13:14:24, or 0-13-15-27, representing 7:12:13:21.  
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.
 
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.
 
Because the 5th harmonic is not well approximated, using timbres with attenuated 5th harmonics (and its multiples) may reduce audible beating.


=== Odd harmonics ===
=== Odd harmonics ===
{{Harmonics in equal|17|intervals=odd}}
{{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)}}
 
=== 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.


=== Miscellaneous properties ===
[[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.
17edo is the seventh [[prime edo]], following [[13edo]] and coming before [[19edo]].  


== Intervals ==
== Intervals ==
{{See also|17edo solfege}}
{{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>
! colspan="2" | [[3L 4s]] notation
! colspan="3" | [[Ups and downs notation]]<br>([[Enharmonic unisons in ups and downs notation|EUs]]: vvA1 and ^d2)
! Approximate Ratios†
! colspan="3" | [[SKULO interval names|SKULO notation]] {{nowrap|(U {{=}} 1)}}
|-
|-
| 0
| 0
| 0.00
| 0.0
| [[1/1]]
| Unison
| Unison
| D
| D
Line 43: Line 53:
| D
| D
| unison
| unison
| P1
| D
| D
| 1/1
|-
|-
| 1
| 1
| 70.59
| 70.6
| [[24/23]], [[25/24]], [[26/25]], [[27/26]], [[28/27]]
| Minor 2nd<br>(Semiaugmented 1sn)
| Minor 2nd<br>(Semiaugmented 1sn)
| Eb<br>(D+)
| Eb<br>(Dt)
| up unison,
| up unison, <br>minor 2nd
minor 2nd
| ^1, m2
| ^1, m2
| Eb
| Eb
| augmented 1sn
| uber unison, <br>minor 2nd
| D#
| U1, m2
| [[22/21]], [[25/24]], [[26/25]], [[28/27]], [[33/32]], [[24/23]]
| UD, Eb
|-
|-
| 2
| 2
| 141.18
| 141.2
| [[12/11]], [[13/12]], [[14/13]], [[25/23]]
| Augmented 1sn<br>(Neutral 2nd)
| Augmented 1sn<br>(Neutral 2nd)
| D#<br>(Ed)
| D#<br>(Ed)
| augmented 1sn,
| augmented 1sn, <br>mid 2nd
mid 2nd
| A1, ~2
| A1, ~2
| vE
| vE
| minor 2nd
| neutral 2nd
| Eb
| N2
| [[13/12]], [[12/11]], [[14/13]], [[25/23]]
| 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 78: Line 89:
| E
| E
| major 2nd
| major 2nd
| M2
| E
| E
| [[9/8]], [[8/7]], [[28/25]], [[25/22]], [[26/23]]
|-
|-
| 4
| 4
| 282.35
| 282.4
| [[7/6]], [[13/11]], [[20/17]]
| Minor 3rd
| Minor 3rd
| F
| F
Line 88: Line 100:
| m3
| m3
| F
| F
| diminished 3rd
| minor 3rd
| Fb
| m3
| [[13/11]], [[7/6]]
| F
|-
|-
| 5
| 5
| 352.94
| 352.9
| [[11/9]], [[27/22]], [[16/13]], [[39/32]]
| Diminished 4th<br>(Neutral 3rd)
| Diminished 4th<br>(Neutral 3rd)
| Gb<br>(F+)
| Gb<br>(Ft)
| mid 3rd
| mid 3rd
| ~3
| ~3
| ^F
| ^F
| perfect 3rd
| neutral 3rd
| F
| N3
| [[11/9]], [[16/13]], [[28/23]]
| UF, uF#
|-
|-
| 6
| 6
| 423.53
| 423.5
| [[9/7]], [[14/11]], [[23/18]], [[32/25]], [[51/40]]
| Major 3rd<br>(Semidiminished 4th)
| Major 3rd<br>(Semidiminished 4th)
| F#<br>(Gd)
| F#<br>(Gd)
Line 110: Line 124:
| M3
| M3
| F#
| F#
| augmented 3rd
| major 3rd
| 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 121: Line 136:
| P4
| P4
| G
| G
| minor 4th
| perfect 4th
| P4
| G
| G
| [[4/3]], [[21/16]]
|-
|-
| 8
| 8
| 564.71
| 564.7
| Diminshed 5th<br>(Semiaugmented 4th)
| [[11/8]], [[18/13]], [[25/18]], [[32/23]]
| Ab<br>(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
| major 4th
| uber 4th/<br>neutral 4th
| G#
| U4/N4
| [[11/8]], [[18/13]], [[32/23]]
| UG
|-
|-
| 9
| 9
| 635.29
| 635.3
| [[13/9]], [[16/11]], [[23/16]], [[36/25]]
| Augmented 4th<br>(Semidiminished 5th)
| Augmented 4th<br>(Semidiminished 5th)
| G#<br>(Ad)
| G#<br>(Ad)
Line 143: Line 160:
| A4, ~5
| A4, ~5
| G#, vA
| G#, vA
| minor 5th
| unter 5th/<br>neutral 5th
| Ab
| u5/N5
| [[16/11]], [[13/9]], [[23/16]]
| uA
|-
|-
| 10
| 10
| 705.88
| 705.9
| [[3/2]], [[32/21]], [[128/85]]
| Perfect 5th
| Perfect 5th
| A
| A
Line 154: Line 172:
| P5
| P5
| A
| A
| major 5th
| perfect 5th
| P5
| A
| A
| [[3/2]], [[32/21]]
|-
|-
| 11
| 11
| 776.47
| 776.5
| [[11/7]], [[14/9]], [[25/16]], [[36/23]], [[80/51]]
| Minor 6th<br>(Semiaugmented 5th)
| Minor 6th<br>(Semiaugmented 5th)
| Bb<br>(A+)
| Bb<br>(At)
| minor 6th
| minor 6th
| m6
| m6
| Bb
| Bb
| diminished 6th
| minor 6th
| m6
| Bb
| Bb
| [[25/16]], [[14/9]], [[11/7]], [[52/33]], [[36/23]]
|-
|-
| 12
| 12
| 847.06
| 847.1
| [[13/8]], [[18/11]], [[44/27]], [[64/39]]
| Augmented 5th<br>(Neutral 6th)
| Augmented 5th<br>(Neutral 6th)
| A#<br>(Bd)
| A#<br>(Bd)
Line 176: Line 196:
| ~6
| ~6
| vB
| vB
| perfect 6th
| neutral 6th
| B
| N6
| [[13/8]], [[18/11]], [[23/14]]
| UBb, uB
|-
|-
| 13
| 13
| 917.65
| 917.6
| [[12/7]], [[17/10]], [[22/13]]
| Major 6th
| Major 6th
| B
| B
Line 187: Line 208:
| M6
| M6
| B
| B
| augmented 6th
| major 6th
| B#
| M6
| [[17/10]], [[22/13]], [[12/7]]
| B
|-
|-
| 14
| 14
| 988.24
| 988.2
| [[7/4]], [[16/9]], [[23/13]], [[30/17]], [[44/25]]
| Minor 7th
| Minor 7th
| C
| C
Line 199: Line 221:
| C
| C
| minor 7th
| minor 7th
| Cb
| m7
| [[16/9]], [[7/4]], [[25/14]], [[44/25]], [[23/13]]
| C
|-
|-
| 15
| 15
| 1058.82
| 1058.8
| [[11/6]], [[13/7]], [[24/13]], [[46/25]]
| Diminished 8ve<br>(Neutral 7th)
| Diminished 8ve<br>(Neutral 7th)
| Db<br>(C+)
| Db<br>(Ct)
| mid 7th
| mid 7th
| ~7
| ~7
| ^C
| ^C
| major 7th
| neutral 7th
| C
| N7
| [[11/6]], [[24/13]], [[13/7]], [[46/25]]
| UC, uC#
|-
|-
| 16
| 16
| 1129.41
| 1129.4
| [[23/12]], [[25/13]], [[27/14]], [[48/25]], [[52/27]]
| Major 7th<br>(Semidiminished 8ve)
| Major 7th<br>(Semidiminished 8ve)
| C#<br>(Dd)
| C#<br>(Dd)
| major 7th,
| major 7th,<br>down 8ve
down 8ve
| M7, v8
| M7, v8
| C#
| C#
| diminshed 8ve
| major 7th,<br>unter octave
| [[21/11]], [[25/13]], [[48/25]], [[27/14]], [[64/33]], [[23/12]]
| M7, u8
| C#, uD
|-
|-
| 17
| 17
| 1200.00
| 1200.0
| [[2/1]]
| Octave
| Octave
| D
| D
Line 232: Line 257:
| D
| D
| octave
| octave
| P8
| D
| D
| [[2/1]]
|}
|}
<nowiki>*</nowiki> Half-sharps and half-flats (denoted "+" and "d", respectively) can be used to alter the note by a single step, 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.
<references group="note" />
 
† Ratios based on treating 17edo as a 2.3.7.11.13.23.25 subgroup temperament.


=== 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
! Quality
! monzo format
! Color
! examples
! Monzo format
! Examples
|-
|-
| rowspan="2" | minor
| rowspan="2" | minor
Line 253: Line 278:
|-
|-
| fourthward wa
| fourthward wa
| (a, b), b &lt; -1
| (a, b), b < -1
| 32/27, 16/9
| 32/27, 16/9
|-
|-
Line 267: Line 292:
| rowspan="2" | 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
|-
|-
Line 274: Line 299:
| 9/7, 12/7
| 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:
Line 281: 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 326: 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 ==
== Notation ==
=== Sagittal ===
=== 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.
 
==== 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:
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]]
[[File:17edo Sagittal.png|800px]]


== JI approximation ==
=== 3L 4s (mosh) notation ===
=== 15-odd-limit interval mappings ===
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 ♭.  
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-all mw-collapsible mw-collapsed"
{| class="wikitable center-all right-2 left-4 left-5 mw-collapsible mw-collapsed"
|+style=white-space:nowrap| 15-odd-limit intervals by direct approximation (even if inconsistent)
|-
|-
! class="unsortable" | Interval, complement
! #
! Error (abs, [[Cent|¢]])
! Cents
! Error (rel, [[Relative cent|%]])
! Note
! Name
! Associated ratios
|-
|-
| [[18/13]], [[13/9]]
| 0
| 1.324
| 0.0
| 1.9
| D
| Perfect 1sn
| 1/1
|-
|-
| [[13/12]], [[24/13]]
| 1
| 2.604
| 70.6
| 3.7
| D#
| Augmented 1sn
| 33/32
|-
|-
| '''[[4/3]], [[3/2]]'''
| 2
| '''3.927'''
| 141.2
| '''5.6'''
| Eb
| Minor 2nd
| 12/11
|-
|-
| [[11/9]], [[18/11]]
| 3
| 5.533
| 211.8
| 7.8
| E
| Major 2nd
| 9/8
|-
|-
| [[14/11]], [[11/7]]
| 4
| 6.021
| 282.4
| 8.5
| Fb
| Diminished 3rd
| 32/27
|-
|-
| '''[[16/13]], [[13/8]]'''
| 5
| '''6.531'''
| 352.9
| '''9.3'''
| F
| Perfect 3rd
| 11/9, 27/22
|-
|-
| [[13/11]], [[22/13]]
| 6
| 6.857
| 423.5
| 9.7
| F#
| Augmented 3rd
| 81/64
|-
|-
| [[9/8]], [[16/9]]
| 7
| 7.855
| 494.1
| 11.1
| G
| Minor 4th
| 4/3
|-
|-
| [[12/11]], [[11/6]]
| 8
| 9.461
| 564.7
| 13.4
| G#
| Major 4th
| 11/8
|-
|-
| [[9/7]], [[14/9]]
| 9
| 11.555
| 635.3
| 16.4
| Ab
| Minor 5th
| 16/11
|-
|-
| [[14/13]], [[13/7]]
| 10
| 12.878
| 705.9
| 18.2
| A
| Major 5th
| 3/2
|-
|-
| '''[[11/8]], [[16/11]]'''
| 11
| '''13.388'''
| 776.5
| '''19.0'''
| Bb
| Diminished 6th
| 128/81
|-
|-
| [[7/6]], [[12/7]]
| 12
| 15.482
| 847.1
| 21.0
| B
| Perfect 6th
| 18/11, 44/27
|-
|-
| ''[[7/5]], [[10/7]]''
| 13
| ''17.806''
| 917.6
| ''25.2''
| B#
| Augmented 6th
| 27/16
|-
|-
| '''[[8/7]], [[7/4]]'''
| 14
| '''19.409'''
| 988.2
| '''27.5'''
| Cb
| Minor 7th
| 16/9
|-
|-
| ''[[15/14]], [[28/15]]''
| 15
| ''21.734''
| 1058.8
| ''30.8''
| C
| Major 7th
| 11/6
|-
|-
| ''[[11/10]], [[20/11]]''
| 16
| ''23.828''
| 1129.4
| ''33.8''
| Db
| Diminished 8ve
| 64/33
|-
|-
| ''[[15/11]], [[22/15]]''
| 17
| ''27.755''
| 1200.0
| ''39.3''
| D
|-
| Perfect 8ve
| ''[[10/9]], [[9/5]]''
| 2/1
| ''29.361''
| ''41.6''
|-
| [[16/15]], [[15/8]]
| 29.445
| 41.7
|-
| ''[[13/10]], [[20/13]]''
| ''30.685''
| ''43.5''
|-
| ''[[6/5]], [[5/3]]''
| ''33.288''
| ''47.2''
|-
| '''[[5/4]], [[8/5]]'''
| '''33.373'''
| '''47.3'''
|-
| ''[[15/13]], [[26/15]]''
| ''34.612''
| ''49.0''
|}
|}
{{15-odd-limit|17}}
 
== 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 ===
=== Selected 13-limit intervals ===
Line 447: Line 508:


== Tuning 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 461: 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 469: 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 476: 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 483: 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 doing better in these subgroups are 41 and 207, respectively.
=== Uniform maps ===
{{Uniform map|edo=17}}


=== Commas ===
=== Commas ===
17et [[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
| [[64/63]]
| {{Monzo| 6 -2 0 -1 }}
| 27.26
| Ru
| Septimal comma
|-
|-
| 7
| 7
| [[525/512]]
| [[525/512]]
| {{Monzo | -9 1 2 1 }}
| {{Monzo| -9 1 2 1 }}
| 43.408
| 43.41
| Lazoyoyo
| Lazoyoyo
| Avicennma, Avicennma's enharmonic diesis
| Avicennma
|-
| 7
| [[64/63]]
| {{Monzo | 6 -2 0 -1 }}
| 27.264
| Ru
| Septimal comma, Archytas' comma, Leipziger Komma
|-
|-
| 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 568: 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 ===
Line 611: Line 786:


{| 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 622: Line 798:
| 141.18
| 141.18
| 13/12
| 13/12
| [[Bleu]] / [[progression]] (17c)
| [[Bleu]] / [[progression]] (17c) / [[glacier]]
|-
|-
| 1
| 1
Line 629: 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 634: Line 816:
| 282.35
| 282.35
| 13/11
| 13/11
| [[Huxley]]{{clarify}}<br>[[Lovecraft]]
| [[Huxley]] / [[lovecraft]] / [[subklei]] (17c)
|-
|-
| 1
| 1
Line 640: 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 652: 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 660: 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}}
* [[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.
== Instruments ==
* [[17edo tetrachords]]
=== Fretted String Instruments ===
* [http://microtonalismo.com/proyecto-xvii Proyect 17-Perú] {{forbidden}}
* [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]]
 
* 17edo soprano Harmony ukulele with a 3D printed fretboard - conversion by [[User:Tristanbay|Tristan Bay]]


== Music ==
[[File:17edo soprano ukulele with 3D printed fretboard.jpg|frameless|640x640px]]
{{See also|:Category:17edo tracks}}


=== Scores ===
=== Keyboards ===
; [[Christopher Bailey]] ([http://christopherbaileymusic.com/quick-bio/ site])
[[Lumatone mapping for 17edo|Lumatone mappings for 17edo]] are available.
* [http://christopherbaileymusic.com/walrus/v/#../../kitwo245m45n698th139rwebm845MQPxiF82J7WovYNRLK6klyq456/balladei.pdf ''Balladei'']


; [[Daniel Wolf]]
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.
* [http://home.snafu.de/djwolf/PreludeIn17tet.pdf ''Prelude''] (PDF)


; [[Georg Hajdu]] ([http://georghajdu.de/biography/ site])
[[File:Strisoboard_piano2a_s.jpg|frameless]]
* [http://georghajdu.de/compositions/heptadecatonic-drops/ ''Heptadecatonic Drops'']
* [http://georghajdu.de/compositions/klangmoraste/ ''Klangmoraste'']


; [[User:Inthar|Inthar]]
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]]:
* [[:File:Locrian Suite Sarabande Score.pdf|''Sarabande from the Locrian Suite'']]


; [[Jacob Barton]]
* [https://www.youtube.com/watch?v=2B14mttkavA ''Take This Stone (17-TET microtonal cover)''] (2025)
* ''[[Multiverse]]''
* [https://www.youtube.com/watch?v=nboggmtayk0 ''DIY microtonal piano - 17 notes per octave''] (2026)


; [[Microtonalismo]] ([http://microtonalismo.com/ site])
== Music ==
* [http://www.microtonalismo.com/proyecto-xvii Charles Loli 17edo]{{dead link}} music for guitar heptadecatonic (2001) and armony inductive microtonally (1993)
{{Main| 17edo/Music }}
* Heptadecatonic Peruvian{{clarify}}
{{Catrel|17edo tracks}}


=== 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://www.youtube.com/results?search_query=17edo&search=tag YouTube videos tagged with 17edo]
Line 731: Line 910:
-->
-->


; [[Aaron Andrew Hunt]]
== Introductory Materials ==
* [http://www.h-pi.com/mp3/17ET.mp3 ''Two-Part Invention in 17ET'']{{dead link}}
* [[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.  
; [[Aaron Krister Johnson]] ([http://www.untwelve.org/board site])
* [[17edo tetrachords]]
* [https://soundcloud.com/aaron-krister-johnson/puhlops-and-lauguas-big-adventure ''Puhlops and Laugua's Big Adventure'']
* [http://microtonalismo.com/proyecto-xvii Proyect 17-Perú] {{forbidden}}
* [https://soundcloud.com/aaron-krister-johnson/adagio-for-margo ''Adagio for Margo'']
 
; [[Alex Ness]]
* [https://drive.google.com/drive/folders/0BwsXD8q2VCYUM0tRdDNhVzNhcHM ''Helas, pitié''] in 17edo with stretched octaves
 
; [[Andrew Heathwaite]]
* [https://soundclick.com/share?songid=8839072 ''sing a blue''] (composed 2008, recorded 2010). This and the other pieces below by Andrew for cümbüş, steel tubes &amp; voice.
* [https://soundclick.com/share?songid=8839073 ''stringfinger it everybean''] (composed 2008, recorded 2010)
* [https://soundclick.com/share?songid=8839069 ''cat feet belly''] (composed 2008, recorded 2010)
 
; [[Beheld]]
* [https://www.youtube.com/watch?v=y_rOW1e4vg8 ''Radiant vibe'']
 
; [[benyamind]]
* [https://youtu.be/vISyCcogrOs ''Yandan Sin Imi Utra'']
 
; [[Chris Vaisvil]]
* [http://chrisvaisvil.com/shanidar-cave-17-edo/ ''Shanidar Cave''], a piece in 17edo that features an electric 17edo 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
* ''On the Shores of the Dead Sea'': [http://chrisvaisvil.com/?p=784 blog] | [https://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] | [https://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] | [https://www.youtube.com/watch?v=rAKHCqBNhfc video of performance]
* ''The Pond'': [http://chrisvaisvil.com/?p=38 blog] | [https://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]
 
; [[Christopher Bailey]] ([http://music.columbia.edu/%7Echris/ site])
* [https://christopherbailey.bandcamp.com/track/waltz-in-17-tone-equal-tuning-2006 ''Waltz'']
* ''Lost & Found Things #2'' [https://soundcloud.com/zipzappoozoo/lost-and-found-things-2 (studio)] [https://soundcloud.com/zipzappoozoo/lost_found_live (live)]
* [https://soundcloud.com/zipzappoozoo/balladei-live-christopher-bailey ''Balladei'' (live)], in 17edo, 29edo and 12edo ([https://www.amazon.com/Christopher-Bailey-Shiau-Uen-Jacob-Rhodebeck/dp/B000TDZSAU/ CD]).
 
; [[Diamond Doll]] (Xen-Pop)
* ''Arm's Length'' [https://open.spotify.com/track/7gMaNtFZBpnuOvncJnoF05?si=7304c25ad72f447e Spotify], [https://youtu.be/aU8RmEeXap8 YouTube Link], [https://helloitsdiamonddoll.bandcamp.com/track/arms-length Bandcamp Link]
 
; [[User:Francium|Francium]]
* [https://www.youtube.com/watch?v=YV039SK8wZc ''peaceful walk on flowers'']
* [https://www.youtube.com/watch?v=OXqfQ-3kQuA ''Jam with Kam'']
 
; [[Gregory Sanchez]] ([https://soundcloud.com/gregory-sanchez-2 site])
* [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'']
 
; [[Herman Miller]] ([http://home.comcast.net/%7Eteamouse/ site]{{dead link}})
* [http://home.comcast.net/~teamouse/Transformation.mp3 ''Transformation'']
 
; [[Igliashon Jones]]
* [http://micro.soonlabel.com/gene_ward_smith/Others/Igs/City%20Of%20The%20Asleep%20-%2017-A%20Calamitous%20Simultaneity.mp3 ''A Calamitous Simultaneity''] in 17edo and 22edo
* [http://micro.soonlabel.com/gene_ward_smith/Others/Igs/First%20Impressions.mp3 ''First Impressions'']{{dead link}}
* [http://micro.soonlabel.com/gene_ward_smith/Others/Igs/I%20Insist.mp3 ''I Insist'']{{dead link}}
 
; [[Jon Lyle Smith]]
* [https://archive.org/download/EtudeNo1For2PianosIn17EqualTemperament/EtudeForTwoPianosIn17edo.mp3 ''Etude no1 for 2 Pianos in 17 Equal Temperament'']{{dead link}}
* [https://archive.org/download/EtudeNo2For2PianosIn17EqualTemperament/EtudeNo2ForTwoPianosIn17edo.mp3 ''Etude no2 for 2 Pianos in 17 Equal Temperament'']{{dead link}}
 
; [[User:Jutomi|Jutomi]]
* [https://soundcloud.com/user-455564099/march-of-the-mushrooms ''March of the Mushrooms'']
 
; [[Marmalade Man]]
* [https://www.youtube.com/watch?v=a9N_T6LNDaE ''17 Tone Jam'']
 
; [[Nick, The NRG]]
* [https://www.youtube.com/watch?v=3VnpyWrgpv8 ''Full Moon Light'']
* [https://www.youtube.com/watch?v=tt7B9PisjTM ''Lofi Hip Hop Beet'']
 
; [[Ralph Jarzombek]]
* [http://webzoom.freewebs.com/ralphjarzombek/micro7(17tet).mp3 ''Micro7'']
 
; [[Rick McGowan]]
* [https://web.archive.org/web/20161013092841/http://azuma-asobi.com/Music/MSND-Ovtr.mp3 "Overture" to ''A Midsummer Night's Dream'']
* [https://web.archive.org/web/20161013092841/http://azuma-asobi.com/Music/FairyLullaby-1.mp3 "Fairy Lullaby" from ''A Midsummer Night's Dream'']
 
; [[Stephen Weigel]] ([https://soundcloud.com/overtoneshock site])
* [https://soundcloud.com/overtoneshock/demanding-two-faces-17-edo ''Demanding Two Faces''] (xen-pop)
* [https://soundcloud.com/overtoneshock/where-were-you-during-the-apocalypse-17-edo Where were you at the Apocalypse?] (xen-pop)
 
; [[The Mercury Tree]] ([https://themercurytree.bandcamp.com/ site])
* [https://themercurytree.bandcamp.com/album/spidermilk ''Spidermilk''] (prog album)
 
== Instruments ==
* '''[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}} }}
 
* [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]]
 
== See also ==
* [[Lumatone mapping for 17edo]]


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[[Category:Listen]]
[[Category:Prime EDO]]
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[[Category:Teentuning]]
[[Category:Teentuning]]
Retrieved from "https://en.xen.wiki/w/17edo"