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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | {{interwiki |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | | de = 17-EDO |
| : This revision was by author [[User:TallKite|TallKite]] and made on <tt>2017-11-11 19:07:22 UTC</tt>.<br>
| | | en = 17edo |
| : The original revision id was <tt>621462079</tt>.<br>
| | | es = 17 EDO |
| : The revision comment was: <tt></tt><br>
| | | ja = 17平均律 |
| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
| | }} |
| <h4>Original Wikitext content:</h4>
| | {{Infobox ET}} |
| <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html"><span style="display: block; text-align: right;"><span style="color: #1300ff;">[[xenharmonie/17edo|Deutsch]] - [[17平均律|日本語]]</span>
| | {{ED intro}} |
| </span>
| | {{Wikipedia|17 equal temperament}} |
| =<span style="color: #1300ff;">17 tone equal temperament</span>=
| |
| [[toc]]
| |
| **17-EDO** divides the octave in 17 equal steps, each 70.588 [[cent|cents]] in size. It is the seventh [[prime numbers|prime]] edo, following [[13edo]] and coming before [[19edo]].
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| ==Theory== | | == Theory == |
| An introduction to 17-EDO theory, through the eyes of the [[SeventeenTonePianoProject]]: [[SeventeenTheory]].
| | 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. |
| Another introduction into 17-EDO theory: [[http://xenharmony.wikispaces.com/space/showimage/17puzzle.pdf|The 17-tone Puzzle]] by George Secor.
| |
| [[17edo Solfege]]. [[17edo tetrachords]]. [[http://microtonalismo.com/proyecto-xvii|Proyect 17-Perú]] | |
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| 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]].
| | 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]]. |
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| 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. | | === 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. |
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| 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 famous [[https://en.wikipedia.org/wiki/Mu_chord|mu major 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.
| | 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. |
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| =Intervals=
| | 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. |
| ||~ Degree ||~ Cents ||~ Names of
| |
| Intervals ||||||~ [[Ups and Downs Notation|ups and downs ]][[Ups and Downs Notation|notation]] ||~ Approximate
| |
| Ratios* ||~ Temperament(s)
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| generated || | |
| || 0 || 0 || Unison ||= unison ||= P1 ||= C ||= 1/1 || ||
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| || 1 || 70.59 || Super Unison/
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| Minor Second ||= minor 2nd ||= m2 ||= Db ||= [[25_24|25/24]], [[26_25|26/25]], [[33_32|33/32]] || ||
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| || 2 || 141.18 || Augmented Unison/
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| Neutral Second ||= mid 2nd ||= ~2 ||= Dv ||= [[13_12|13/12]], [[12_11|12/11]], [[14_13|14/13]] || [[Bleu]] ||
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| || 3 || 211.765 || Major Second/
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| Sub Third ||= major 2nd ||= M2 ||= D ||= [[9_8|9/8]], [[25_22|25/22]], [[8_7|8/7]], [[28_25|28/25]] || [[Machine]] ||
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| || 4 || 282.35 || Minor Third/
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| Super Second ||= minor 3rd ||= m3 ||= Eb ||= [[13_11|13/11]], [[75_64|75/64]], [[7_6|7/6]] || [[Huxley]] ||
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| || 5 || 352.94 || Augmented Second/
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| Neutral Third/
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| Diminished Fourth ||= mid 3rd ||= ~3 ||= Ev ||= [[11_9|11/9]], [[16_13|16/13]] || [[Maqamic]]/[[hemif]] ||
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| || 6 || 423.53 || Major Third/
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| Sub Fourth ||= major 3rd ||= M3 ||= E ||= [[32_25|32/25]], [[33_26|33/26]], [[9_7|9/7]], [[14_11|14/11]], [[51_40|51/40]] || [[Skwares]] ||
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| || 7 || 494.11 || Perfect Fourth ||= perfect 4th ||= P4 ||= F ||= [[4_3|4/3]] || [[Supra]] ||
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| || 8 || 564.71 || Super Fourth
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| Diminished Fifth ||= up 4th,
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| diminished 5th ||= ^4, d5 ||= F^, Gb ||= [[11_8|11/8]], 18/13 || [[Progress]] ||
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| || 9 || 635.29 || Augmented Fourth/
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| Sub Fifth ||= augmented 4th,
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| down 5th ||= A4, v5 ||= F#, Gv ||= [[16_11|16/11]], 13/9, [[23_16|23/16]] || Progress ||
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| || 10 || 705.88 || Perfect Fifth ||= perfect 5th ||= P5 ||= G ||= [[3_2|3/2]] || Supra ||
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| || 11 || 776.47 || Super Fifth/
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| Minor Sixth ||= minor 6th ||= m6 ||= Ab ||= 25/16, 52/33, 14/9, [[11_7|11/7]] || Skwares ||
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| || 12 || 847.06 || Augmented Fifth/
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| Neutral Sixth/
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| Diminished Seventh ||= mid 6th ||= ~6 ||= Av ||= [[13_8|13/8]], 18/11 || Maqamic/hemif ||
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| || 13 || 917.65 || Major Sixth/
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| Sub Seventh ||= major 6th ||= M6 ||= A ||= [[17_10|17/10]], [[22_13|22/13]], 128/75, [[12_7|12/7]] || Huxley ||
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| || 14 || 988.235 || Minor Seventh/
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| Super Sixth ||= minor 7th ||= m7 ||= Bb ||= [[16_9|16/9]], 44/25, 7/4, 25/14 || Machine ||
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| || 15 || 1058.82 || Augmented Sixth/
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| Neutral Seventh/
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| Diminished Octave ||= mid 7th ||= ~7 ||= Bv ||= [[11_6|11/6]], 24/13, [[13_7|13/7]] || Bleu ||
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| || 16 || 1129.41 || Major Seventh/
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| Sub Octave ||= major 7th ||= M7 ||= B ||= 25/13, 48/25, 64/33 || ||
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| || 17 || 1200 || Perfect Octave ||= octave ||= P8 ||= C ||= [[2_1|2/1]] || ||
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| Combining ups and downs notation with [[Kite's color notation|color notation]], qualities can be loosely associated with colors:
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| ||~ quality ||~ color ||~ monzo format ||~ examples ||
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| ||= minor ||= blue ||= {a, b, 0, 1} ||= 7/6, 7/4 ||
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| ||= " ||= fourthward white ||= {a, b}, b < -1 ||= 32/27, 16/9 ||
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| ||= mid ||= jade ||= {a, b, 0, 0, 1} ||= 11/9, 11/6 ||
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| ||= " ||= amber ||= {a, b, 0, 0, -1} ||= 12/11, 18/11 ||
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| ||= major ||= fifthward white ||= {a, b}, b > 1 ||= 9/8, 27/16 ||
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| ||= " ||= red ||= {a, b, 0, -1} ||= 9/7, 12/7 ||
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| =Chord Names=
| | Because the 5th harmonic is not well approximated, using timbres with attenuated 5th harmonics (and its multiples) may reduce audible beating. |
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| All 17edo chords can be named using ups and downs. Here are the blue, jade and red triads:
| | === Odd harmonics === |
| ||~ color of the 3rd ||~ JI chord ||~ notes as edosteps ||~ notes of C chord ||~ written name ||~ spoken name ||
| | {{Harmonics in equal|17|intervals=odd|columns=11}} |
| ||= blue ||= 6:7:9 ||= 0-4-10 ||= C Eb G ||= Cm ||= C minor ||
| | {{Harmonics in equal|17|intervals=odd|columns=12|start=12|collapsed=true|title=Approximation of odd harmonics in 17edo (continued)}} |
| ||= jade ||= 18:22:27 ||= 0-5-10 ||= C Ev G ||= C~ ||= C mid || | |
| ||= red ||= 14:18:27 ||= 0-6-10 ||= C E G ||= C ||= C major or C || | |
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| 0-4-9 = C Eb Gv = Cm(v5) = C minor down-five | | === Subsets and supersets === |
| 0-5-9 = C Ev G = C~(v5) = C mid down-five | | 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. |
| 0-6-11 = C E G^ = C(^5) = C up-five | | |
| | [[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 == |
| | {{See also| 17edo solfege }} |
| | |
| | {| class="wikitable center-all right-2 left-3" |
| | |- |
| | ! # |
| | ! Cents |
| | ! Approximate ratios<ref group="note">{{sg|limit=2.3.25.7.11.13.85.23 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)}} |
| | |- |
| | | 0 |
| | | 0.0 |
| | | [[1/1]] |
| | | Unison |
| | | D |
| | | unison |
| | | P1 |
| | | D |
| | | unison |
| | | P1 |
| | | D |
| | |- |
| | | 1 |
| | | 70.6 |
| | | [[24/23]], [[25/24]], [[26/25]], [[27/26]], [[28/27]] |
| | | Minor 2nd<br>(Semiaugmented 1sn) |
| | | Eb<br>(Dt) |
| | | up unison, <br>minor 2nd |
| | | ^1, m2 |
| | | Eb |
| | | uber unison, <br>minor 2nd |
| | | U1, m2 |
| | | UD, Eb |
| | |- |
| | | 2 |
| | | 141.2 |
| | | [[12/11]], [[13/12]], [[14/13]], [[25/23]] |
| | | Augmented 1sn<br>(Neutral 2nd) |
| | | D#<br>(Ed) |
| | | augmented 1sn, <br>mid 2nd |
| | | A1, ~2 |
| | | vE |
| | | neutral 2nd |
| | | N2 |
| | | UEb, uE |
| | |- |
| | | 3 |
| | | 211.8 |
| | | [[8/7]], [[9/8]], [[17/15]], [[25/22]], [[26/23]] |
| | | Major 2nd |
| | | E |
| | | major 2nd |
| | | M2 |
| | | E |
| | | major 2nd |
| | | M2 |
| | | E |
| | |- |
| | | 4 |
| | | 282.4 |
| | | [[7/6]], [[13/11]], [[20/17]] |
| | | Minor 3rd |
| | | F |
| | | minor 3rd |
| | | m3 |
| | | F |
| | | minor 3rd |
| | | m3 |
| | | F |
| | |- |
| | | 5 |
| | | 352.9 |
| | | [[11/9]], [[27/22]], [[16/13]], [[39/32]] |
| | | Diminished 4th<br>(Neutral 3rd) |
| | | Gb<br>(Ft) |
| | | mid 3rd |
| | | ~3 |
| | | ^F |
| | | neutral 3rd |
| | | N3 |
| | | UF, uF# |
| | |- |
| | | 6 |
| | | 423.5 |
| | | [[9/7]], [[14/11]], [[23/18]], [[32/25]], [[51/40]] |
| | | Major 3rd<br>(Semidiminished 4th) |
| | | F#<br>(Gd) |
| | | major 3rd |
| | | M3 |
| | | F# |
| | | major 3rd |
| | | M3 |
| | | F# |
| | |- |
| | | 7 |
| | | 494.1 |
| | | [[4/3]], [[21/16]], [[85/64]] |
| | | Perfect 4th |
| | | G |
| | | perfect 4th |
| | | P4 |
| | | G |
| | | perfect 4th |
| | | P4 |
| | | G |
| | |- |
| | | 8 |
| | | 564.7 |
| | | [[11/8]], [[18/13]], [[25/18]], [[32/23]] |
| | | Diminished 5th<br>(Semiaugmented 4th) |
| | | Ab<br>(Gt) |
| | | mid 4th, <br>diminished 5th |
| | | ~4, d5 |
| | | ^G, Ab |
| | | uber 4th/<br>neutral 4th |
| | | U4/N4 |
| | | UG |
| | |- |
| | | 9 |
| | | 635.3 |
| | | [[13/9]], [[16/11]], [[23/16]], [[36/25]] |
| | | Augmented 4th<br>(Semidiminished 5th) |
| | | G#<br>(Ad) |
| | | augmented 4th, <br>mid 5th |
| | | A4, ~5 |
| | | G#, vA |
| | | unter 5th/<br>neutral 5th |
| | | u5/N5 |
| | | uA |
| | |- |
| | | 10 |
| | | 705.9 |
| | | [[3/2]], [[32/21]], [[128/85]] |
| | | Perfect 5th |
| | | A |
| | | perfect 5th |
| | | P5 |
| | | A |
| | | perfect 5th |
| | | P5 |
| | | A |
| | |- |
| | | 11 |
| | | 776.5 |
| | | [[11/7]], [[14/9]], [[25/16]], [[36/23]], [[80/51]] |
| | | Minor 6th<br>(Semiaugmented 5th) |
| | | Bb<br>(At) |
| | | minor 6th |
| | | m6 |
| | | Bb |
| | | minor 6th |
| | | m6 |
| | | Bb |
| | |- |
| | | 12 |
| | | 847.1 |
| | | [[13/8]], [[18/11]], [[44/27]], [[64/39]] |
| | | Augmented 5th<br>(Neutral 6th) |
| | | A#<br>(Bd) |
| | | mid 6th |
| | | ~6 |
| | | vB |
| | | neutral 6th |
| | | N6 |
| | | UBb, uB |
| | |- |
| | | 13 |
| | | 917.6 |
| | | [[12/7]], [[17/10]], [[22/13]] |
| | | Major 6th |
| | | B |
| | | major 6th |
| | | M6 |
| | | B |
| | | major 6th |
| | | M6 |
| | | B |
| | |- |
| | | 14 |
| | | 988.2 |
| | | [[7/4]], [[16/9]], [[23/13]], [[30/17]], [[44/25]] |
| | | Minor 7th |
| | | C |
| | | minor 7th |
| | | m7 |
| | | C |
| | | minor 7th |
| | | m7 |
| | | C |
| | |- |
| | | 15 |
| | | 1058.8 |
| | | [[11/6]], [[13/7]], [[24/13]], [[46/25]] |
| | | Diminished 8ve<br>(Neutral 7th) |
| | | Db<br>(Ct) |
| | | mid 7th |
| | | ~7 |
| | | ^C |
| | | neutral 7th |
| | | N7 |
| | | UC, uC# |
| | |- |
| | | 16 |
| | | 1129.4 |
| | | [[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# |
| | | major 7th,<br>unter octave |
| | | M7, u8 |
| | | C#, uD |
| | |- |
| | | 17 |
| | | 1200.0 |
| | | [[2/1]] |
| | | Octave |
| | | D |
| | | octave |
| | | P8 |
| | | D |
| | | octave |
| | | P8 |
| | | D |
| | |} |
| | <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: |
| | |
| | {| class="wikitable center-all" |
| | |- |
| | ! Quality |
| | ! Color |
| | ! Monzo format |
| | ! Examples |
| | |- |
| | | rowspan="2" | minor |
| | | zo |
| | | (a, b, 0, 1) |
| | | 7/6, 7/4 |
| | |- |
| | | fourthward wa |
| | | (a, b), b < -1 |
| | | 32/27, 16/9 |
| | |- |
| | | rowspan="2" | mid |
| | | ilo |
| | | (a, b, 0, 0, 1) |
| | | 11/9, 11/6 |
| | |- |
| | | lu |
| | | (a, b, 0, 0, -1) |
| | | 12/11, 18/11 |
| | |- |
| | | rowspan="2" | major |
| | | fifthward wa |
| | | (a, b), b > 1 |
| | | 9/8, 27/16 |
| | |- |
| | | ru |
| | | (a, b, 0, -1) |
| | | 9/7, 12/7 |
| | |} |
| | |
| | All 17edo chords can be named using ups and downs. Here are the zo, ilo and ru triads: |
| | |
| | {| class="wikitable center-all" |
| | |- |
| | ! [[Color notation|Color of the 3rd]] |
| | ! JI chord |
| | ! Notes as edosteps |
| | ! Notes of C chord |
| | ! Written name |
| | ! Spoken name |
| | |- |
| | | zo |
| | | 6:7:9 |
| | | 0-4-10 |
| | | C Eb G |
| | | Cm |
| | | C minor |
| | |- |
| | | ilo |
| | | 18:22:27 |
| | | 0-5-10 |
| | | C vE G |
| | | C~ |
| | | C mid |
| | |- |
| | | ru |
| | | 14:18:21 |
| | | 0-6-10 |
| | | C E G |
| | | C |
| | | C major or C |
| | |} |
| | |
| | Alterations are always enclosed in parentheses, additions never are. An up, down or mid immediately after the chord root affects the 3rd, 6th, 7th, and/or the 11th (every other note of a stacked-3rds chord 6-1-3-5-7-9-11-13). |
| | |
| | 0-4-9 = C Eb vG = Cm(v5) = C minor down-five |
| | |
| | 0-5-9 = C vE vG = C~(v5) = C mid down-five |
| | |
| | 0-6-11 = C E ^G = C(^5) = C up-five |
|
| |
|
| 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 Ev G Bb = C7(~3) = C seven mid-three
| |
| 0-6-10-15 = C E G Bv = C,~7 = C mid seven
| |
| 0-5-10-15 = C Ev G Bv = C.~7 = C dot mid seven
| |
|
| |
|
| For a more complete list, see [[xenharmonic/Ups and Downs Notation#Chord%20names%20in%20other%20EDOs|Ups and Downs Notation - Chord names in other EDOs]]. | | 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 |
| | |
| | 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. |
| | |
| | ==== 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: |
| | |
| | [[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" |
| | |- |
| | ! # |
| | ! Cents |
| | ! Note |
| | ! Name |
| | ! Associated ratios |
| | |- |
| | | 0 |
| | | 0.0 |
| | | D |
| | | Perfect 1sn |
| | | 1/1 |
| | |- |
| | | 1 |
| | | 70.6 |
| | | D# |
| | | Augmented 1sn |
| | | 33/32 |
| | |- |
| | | 2 |
| | | 141.2 |
| | | Eb |
| | | Minor 2nd |
| | | 12/11 |
| | |- |
| | | 3 |
| | | 211.8 |
| | | E |
| | | Major 2nd |
| | | 9/8 |
| | |- |
| | | 4 |
| | | 282.4 |
| | | Fb |
| | | Diminished 3rd |
| | | 32/27 |
| | |- |
| | | 5 |
| | | 352.9 |
| | | F |
| | | Perfect 3rd |
| | | 11/9, 27/22 |
| | |- |
| | | 6 |
| | | 423.5 |
| | | F# |
| | | Augmented 3rd |
| | | 81/64 |
| | |- |
| | | 7 |
| | | 494.1 |
| | | G |
| | | Minor 4th |
| | | 4/3 |
| | |- |
| | | 8 |
| | | 564.7 |
| | | G# |
| | | Major 4th |
| | | 11/8 |
| | |- |
| | | 9 |
| | | 635.3 |
| | | Ab |
| | | Minor 5th |
| | | 16/11 |
| | |- |
| | | 10 |
| | | 705.9 |
| | | A |
| | | Major 5th |
| | | 3/2 |
| | |- |
| | | 11 |
| | | 776.5 |
| | | Bb |
| | | Diminished 6th |
| | | 128/81 |
| | |- |
| | | 12 |
| | | 847.1 |
| | | B |
| | | Perfect 6th |
| | | 18/11, 44/27 |
| | |- |
| | | 13 |
| | | 917.6 |
| | | B# |
| | | Augmented 6th |
| | | 27/16 |
| | |- |
| | | 14 |
| | | 988.2 |
| | | Cb |
| | | Minor 7th |
| | | 16/9 |
| | |- |
| | | 15 |
| | | 1058.8 |
| | | C |
| | | Major 7th |
| | | 11/6 |
| | |- |
| | | 16 |
| | | 1129.4 |
| | | Db |
| | | Diminished 8ve |
| | | 64/33 |
| | |- |
| | | 17 |
| | | 1200.0 |
| | | D |
| | | Perfect 8ve |
| | | 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. |
|
| |
|
| =Selected just intervals by error= | | == Regular temperament properties == |
| The following table shows how [[Just-24|some prominent just intervals]] are represented in 17edo (ordered by absolute error).
| | {| class="wikitable center-4 center-5 center-6" |
| || **Interval, complement** || **Error (abs., in [[cent|cents]])** || | | ! rowspan="2" | [[Subgroup]] |
| ||= [[18_13|18/13]], [[13_9|13/9]] ||= 1.324 ||
| | ! rowspan="2" | [[Comma list]] |
| ||= [[13_12|13/12]], [[24_13|24/13]] ||= 2.604 ||
| | ! rowspan="2" | [[Mapping]] |
| ||= [[4_3|4/3]], [[3_2|3/2]] ||= 3.927 ||
| | ! rowspan="2" | Optimal<br>8ve stretch (¢) |
| ||= [[11_9|11/9]], [[18_11|18/11]] ||= 5.533 ||
| | ! colspan="2" | Tuning error |
| ||= [[14_11|14/11]], [[11_7|11/7]] ||= 6.021 || | | |- |
| ||= [[16_13|16/13]], [[13_8|13/8]] ||= 6.531 || | | ! [[TE error|Absolute]] (¢) |
| ||= [[13_11|13/11]], [[22_13|22/13]] ||= 6.857 || | | ! [[TE simple badness|Relative]] (%) |
| ||= [[9_8|9/8]], [[16_9|16/9]] ||= 7.855 || | | |- |
| ||= [[12_11|12/11]], [[11_6|11/6]] ||= 9.461 || | | | 2.3 |
| ||= [[9_7|9/7]], [[14_9|14/9]] ||= 11.555 || | | | {{Monzo| 27 -17 }} |
| ||= [[14_13|14/13]], [[13_7|13/7]] ||= 12.878 || | | | {{Mapping| 17 27 }} |
| ||= [[11_8|11/8]], [[16_11|16/11]] ||= 13.388 || | | | −1.24 |
| ||= [[7_6|7/6]], [[12_7|12/7]] ||= 15.482 || | | | 1.24 |
| ||= [[7_5|7/5]], [[10_7|10/7]] ||= 17.806 || | | | 1.76 |
| ||= [[8_7|8/7]], [[7_4|7/4]] ||= 19.409 || | | |- |
| ||= [[15_14|15/14]], [[28_15|28/15]] ||= 21.734 || | | | 2.3.7 |
| ||= [[11_10|11/10]], [[20_11|20/11]] ||= 23.828 || | | | 64/63, 17496/16807 |
| ||= [[15_11|15/11]], [[22_15|22/15]] ||= 27.755 || | | | {{Mapping| 17 27 48 }} |
| ||= [[10_9|10/9]], [[9_5|9/5]] ||= 29.361 ||
| | | −3.13 |
| ||= [[16_15|16/15]], [[15_8|15/8]] ||= 29.445 || | | | 2.85 |
| ||= [[13_10|13/10]], [[20_13|20/13]] ||= 30.685 || | | | 4.05 |
| ||= [[6_5|6/5]], [[5_3|5/3]] ||= 33.288 || | | |- |
| ||= [[5_4|5/4]], [[8_5|8/5]] ||= 33.373 ||
| | | 2.3.7.11 |
| ||= [[15_13|15/13]], [[26_15|26/15]] ||= 34.612 ||
| | | 64/63, 99/98, 243/242 |
| | | {{Mapping| 17 27 48 59 }} |
| | | −3.31 |
| | | 2.49 |
| | | 3.54 |
| | |- |
| | | 2.3.7.11.13 |
| | | 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. |
|
| |
|
| [[media type="custom" key="24810186"]]
| | === Uniform maps === |
| [[file:17ed2-001.svg]]
| | {{Uniform map|edo=17}} |
|
| |
|
| =Commas= | | === Commas === |
| 17 EDO [[tempering out|tempers out]] the following [[comma]]s. (Note: This assumes [[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.) |
| ||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||~ Name 3 ||
| |
| ||= <span style="display: block; text-align: center;">
| |
| </span> || | 27 -17 > ||> 66.765 || <span style="display: block; text-align: center;">17-Comma</span> ||= || ||
| |
| ||= 25/24 || |-3 -1 2> ||> 70.762 || Chromatic semitone ||= Dicot comma || ||
| |
| ||= 32805/32768 ||< | -15 8 1 > ||> 1.9537 ||= Schisma ||= ||= ||
| |
| ||= 64/63 ||< | 6 -2 0 -1 > ||> 27.264 ||= Septimal Comma ||= Archytas' Comma ||= Leipziger Komma ||
| |
| ||= 245/243 ||< | 0 -5 1 2 > ||> 14.191 ||= Sensamagic ||= ||= ||
| |
| ||= 1728/1715 ||< | 6 3 -1 -3 > ||> 13.074 ||= Orwellisma ||= Orwell Comma ||= ||
| |
| ||= ||< | -6 -8 2 5 > ||> 1.1170 ||= Wizma ||= ||= ||
| |
| ||= 99/98 ||< | -1 2 0 -2 1 > ||> 17.576 ||= Mothwellsma ||= ||= ||
| |
| ||= 896/891 ||< | 7 -4 0 1 -1 > ||> 9.6880 ||= Pentacircle ||= ||= ||
| |
| ||= 243/242 ||< | -1 5 0 0 -2 > ||> 7.1391 ||= Rastma ||= ||= ||
| |
| ||= 385/384 ||< | -7 -1 1 1 1 > ||> 4.5026 ||= Keenanisma ||= ||= ||
| |
| ||= <span style="display: block; text-align: center;">525/512</span> ||< <span style="display: block; text-align: left;">| -9 1 2 1 ></span> ||> 43.408 ||= <span style="display: block; text-align: center;">Avicennma</span> ||= Avicennma's Enharmonic Diesis ||= ||
| |
|
| |
|
| 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. | | {| 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]] |
| | |- |
| | | 5 |
| | | [[25/24]] |
| | | {{Monzo| -3 -1 2 }} |
| | | 70.76 |
| | | Yoyo |
| | | Dicot comma |
| | |- |
| | | 5 |
| | | [[32805/32768]] |
| | | {{Monzo| -15 8 1 }} |
| | | 1.95 |
| | | Layo |
| | | Schisma |
| | |- |
| | | 7 |
| | | [[64/63]] |
| | | {{Monzo| 6 -2 0 -1 }} |
| | | 27.26 |
| | | Ru |
| | | Septimal comma |
| | |- |
| | | 7 |
| | | [[525/512]] |
| | | {{Monzo| -9 1 2 1 }} |
| | | 43.41 |
| | | Lazoyoyo |
| | | Avicennma |
| | |- |
| | | 7 |
| | | [[245/243]] |
| | | {{Monzo| 0 -5 1 2 }} |
| | | 14.19 |
| | | Zozoyo |
| | | Sensamagic comma |
| | |- |
| | | 7 |
| | | [[1728/1715]] |
| | | {{Monzo| 6 3 -1 -3 }} |
| | | 13.07 |
| | | Triru-agu |
| | | 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 |
| | | <abbr title="420175/419904">(12 digits)</abbr> |
| | | {{Monzo| -6 -8 2 5 }} |
| | | 1.12 |
| | | Quinzo-ayoyo |
| | | [[Wizma]] |
| | |- |
| | | 11 |
| | | [[45/44]] |
| | | {{Monzo| -2 2 1 0 -1 }} |
| | | 38.91 |
| | | Luyo |
| | | Cake comma |
| | |- |
| | | 11 |
| | | [[99/98]] |
| | | {{Monzo| -1 2 0 -2 1 }} |
| | | 17.58 |
| | | Loruru |
| | | Mothwellsma |
| | |- |
| | | 11 |
| | | [[896/891]] |
| | | {{Monzo| 7 -4 0 1 -1 }} |
| | | 9.69 |
| | | Saluzo |
| | | Pentacircle comma |
| | |- |
| | | 11 |
| | | [[243/242]] |
| | | {{Monzo| -1 5 0 0 -2 }} |
| | | 7.14 |
| | | Lulu |
| | | Rastma, neutral thirds comma |
| | |- |
| | | 11 |
| | | [[385/384]] |
| | | {{Monzo| -7 -1 1 1 1 }} |
| | | 4.50 |
| | | Lozoyo |
| | | 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 |
| | | [[1352/1331]] |
| | | {{Monzo| 3 0 0 0 -3 2 }} |
| | | 27.10 |
| | | Bithotrilu |
| | | Lovecraft comma |
| | |- |
| | | 13 |
| | | [[2197/2187]] |
| | | {{Monzo| 0 -7 0 0 0 3 }} |
| | | 7.90 |
| | | Satritho |
| | | 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 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. |
|
| |
|
| =Scales= | | === Rank-2 temperaments === |
| * [[Otonal 17]]
| | * [[List of 17edo rank two temperaments by badness]] |
| * [[http://www.microtonalismo.com/proyecto-xvii|Blues Peruvian 17edo]]
| | * [[List of edo-distinct 17c rank two temperaments]] |
| * [[17edo neutral scale]] | | * [[List of edo-distinct 17et rank two temperaments]] |
| * [[Scorp]] | | * [[List of edo-distinct 17et no-fives rank two temperaments]] |
| * [[Screamapillar]] | |
| * [[Hydra]] | |
| * [[MOS scales of 17edo]] (horograms)
| |
|
| |
|
| [[List of 17edo rank two temperaments by badness]]
| | {| class="wikitable center-all right-3 left-5" |
| [[List of edo-distinct 17c rank two temperaments]] | | |+ style="font-size: 105%;" | Table of rank-2 temperaments by generator |
| | |- |
| | ! Periods<br>per 8ve |
| | ! Generator |
| | ! Cents |
| | ! Associated<br>ratio |
| | ! Temperament |
| | |- |
| | | 1 |
| | | 2\17 |
| | | 141.18 |
| | | 13/12 |
| | | [[Bleu]] / [[progression]] (17c) / [[glacier]] |
| | |- |
| | | 1 |
| | | 3\17 |
| | | 211.76 |
| | | 8/7~9/8 |
| | | [[Machine]] |
| | |- |
| | | 1 |
| | | 3\17 |
| | | 211.76 |
| | | 26/23 |
| | | [[Shoal|Shoal (trivial tuning)]] |
| | |- |
| | | 1 |
| | | 4\17 |
| | | 282.35 |
| | | 13/11 |
| | | [[Huxley]] / [[lovecraft]] / [[subklei]] (17c) |
| | |- |
| | | 1 |
| | | 5\17 |
| | | 352.94 |
| | | 11/9 |
| | | [[Suhajira]] / [[neutrominant]] (17c) / [[beatles]] (17c) / [[dichotic]] (17) <br>[[Hemif]] / [[mohamaq]] (17c) / [[salsa]] (17) |
| | |- |
| | | 1 |
| | | 6\17 |
| | | 423.53 |
| | | 9/7 |
| | | [[Skwares]] / [[squares]] (17c) / [[sentinel]] (17) / [[sidi]] (17) |
| | |- |
| | | 1 |
| | | 7\17 |
| | | 494.12 |
| | | 4/3 |
| | | [[Archy]] / [[supra]] / [[quasisuper]] (17c) / [[dominant (temperament)|dominant]] (17c) / [[superpyth]] (17) / [[schism]] (17)<br>[[Fiventeen]] |
| | |- |
| | | 1 |
| | | 8\17 |
| | | 564.71 |
| | | 7/5 |
| | | [[Lee]] / [[liese]] (17c) / [[pycnic]] (17)<br>[[Progress]] (17c) |
| | |} |
|
| |
|
| =Music= | | == Octave stretch or compression == |
| ==Compositions==
| | 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. |
| * [[@https://soundcloud.com/overtoneshock/demanding-two-faces-17-edo|Demanding Two Faces]] (xen-pop) by [[https://soundcloud.com/overtoneshock|Stephen Weigel]]
| |
| * [[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]]
| |
| * [[http://home.snafu.de/djwolf/PreludeIn17tet.pdf|Prelude]] by [[Daniel Wolf]]
| |
| * [[http://www.georghajdu.de/heptadecatonic_drops.html|Heptadecatonic Drops]] by Georg Hajdu
| |
| * [[http://www.georghajdu.de/63.html?&L=1%20|Klangmoraste]] by Georg Hajdu
| |
| * [[http://www.microtonalismo.com/proyecto-xvii|Charles Loli 17edo]] music for guitar heptadecatonic (2001) and armony inductive microtonaly (1993)
| |
| * [[http://microtonalismo.com/|microtonalismo]] Heptadecatonic Peruvian
| |
| * [[Multiverse]] by [[JacobBarton|Jacob Barton]]
| |
|
| |
|
| ==Sound files== | | == Scales == |
| * [[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[[@xenharmonic/Chris Vaisvil| Chris Vaisvil]] | | * [[Antipental blues]]: 4 3 1 2 4 3 |
| * <span class="ymp-btn-page-play ymp-media-3ece313d36e9307c749e0e3549ece422"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">//[[https://soundcloud.com/aaron-krister-johnson/puhlops-and-lauguas-big-adventure|Puhlops and Laugua's Big Adventure]]// </span></span> </span> by [[http://www.untwelve.org/board||Aaron Krister Johnson]]
| | * [https://web.archive.org/web/20140215081520/http://microtonalismo.com/proyecto-xvii Blues Peruvian]: 4 3 1 1 1 4 3 |
| * <span class="ymp-btn-page-play ymp-media-3ece313d36e9307c749e0e3549ece422"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">//[[https://soundcloud.com/aaron-krister-johnson/adagio-for-margo|Adagio for Margo]]// </span></span> </span> by [[http://www.untwelve.org/board|Aaron Krister Johnson]] | | * [[Hydra]]: 3 3 1 1 2 3 2 1 1 |
| * <span class="ymp-btn-page-play ymp-media-cd2c0c4934993e036385ed158d0617c4"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">//[[http://home.comcast.net/~teamouse/Transformation.mp3|Transformation]]// </span></span> </span> by [[http://home.comcast.net/%7Eteamouse/|Herman Miller]]
| | * [[Maqam|Husayni]] Ascending: 2 2 3 3 2 2 3 |
| * <span class="ymp-btn-page-play ymp-media-c31e19054d7ac007c7b9b339babdd228"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">//[[http://www.emcollective.org/chris/items/17tet/17waltz.mp3|Waltz]]// </span></span> </span> by Christopher Bailey
| | * [[Otonal 17]]: 3 2 3 2 2 2 3 |
| * <span class="ymp-btn-page-play ymp-media-817b931db5b9d03733d0439eb4c5b365"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">//[[http://www.emcollective.org/chris/items/17Chorus/17tppp4_lostfound.mp3|Lostfound]]// </span></span> </span> by Christopher Bailey
| | * [[Scorp]]: 3 2 3 1 3 2 3 |
| * excerpt from <span class="ymp-btn-page-play ymp-media-2de29bc81b3c87ba3015583ebe32228c"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">//[[http://music.columbia.edu/~chris/sounds/balladei_exc.mp3|Balladei]]// </span></span> </span> (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/ref=sr_1_19/105-0183009-3913216?ie=UTF8&s=music&qid=1184598550&sr=1-19|here]] .
| | * [[Screamapillar]]: 3 3 2 2 3 3 1 |
| * <span class="ymp-btn-page-play ymp-media-60b300d674b6179dec2e49769bcd92d2"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">//[[http://www.h-pi.com/mp3/17ET.mp3|Two-Part Invention in 17ET]]// </span></span></span> by Aaron Andrew Hunt | | * sLmLs: 2 5 3 5 2 |
| * //[[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]]
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| * //[[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]]
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| * <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">//[[http://micro.soonlabel.com/gene_ward_smith/Others/Igs/City%20Of%20The%20Asleep%20-%2017-A%20Calamitous%20Simultaneity.mp3|A Calamitous Simultaneity]]// </span> by Igliashon Jones (17edo and 22edo)
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| * <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">//[[http://micro.soonlabel.com/gene_ward_smith/Others/Igs/First%20Impressions.mp3|First Impressions]]// </span> 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]]// and //[[http://archive.org/download/EtudeNo2For2PianosIn17EqualTemperament/EtudeNo2ForTwoPianosIn17edo.mp3|Etude no2 for 2 Pianos in 17 Equal Temperament]]// Jon Lyle Smith
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| * 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]]. | |
| * [[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 & voice.
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| * [[http://soundclick.com/share?songid=8839073|stringfinger it everybean]] by Andrew Heathwaite (composed 2008, recorded 2010).
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| * [[http://soundclick.com/share?songid=8839069|cat feet belly]] by Andrew Heathwaite (composed 2008, recorded 2010).
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| * <span class="ymp-btn-page-play ymp-media-c1117aea0d7479a1907922962588a201"><span class="ywp-page-play-pause ywp-page-video ywp-link-hover"><span class="ywp-page-play-pause ywp-page-video ywp-link-hover ywp-page-img-link">//[[http://www.youtube.com/watch?v=a9N_T6LNDaE|17 Tone Jam]]// </span></span></span> by Marmalade Man
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| * [[http://www.youtube.com/results?search_query=17edo&search=tag|youtube videos tagged with 17edo]]
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| * [[@http://chrisvaisvil.com/?p=784|On the Shores of the Dead Sea blog]] <span class="ymp-btn-page-play ymp-media-58c0d564107bea8b718066b4a846e9a4"><span class="ywp-page-play-pause ywp-page-video ywp-link-hover"><span class="ywp-page-play-pause ywp-page-video ywp-link-hover ywp-page-img-link">//[[http://www.youtube.com/watch?v=D39MVFhb0Ho|video of On the Shores of the Dead Sea]]// </span></span> </span> by [[Chris Vaisvil]] | |
| * [[@http://chrisvaisvil.com/?p=466|Only in Disneyland 17 blog]] edo guitar solo <span class="ymp-btn-page-play ymp-media-ed57956200d2220e2dd400299c6c9d82"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">//[[http://micro.soonlabel.com/17-ET/daily20110205-17et-disneyland.mp3|play Only in Disneyland]]// </span></span> </span> by [[Chris Vaisvil]] | |
| * [[@http://chrisvaisvil.com/?p=460|17 Reasons I Hate the Blues blog]] <span class="ymp-btn-page-play ymp-media-b9bb77ee97249899bce1c2e34b7ca029"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">//[[http://micro.soonlabel.com/17-ET/daily20110125b-17-reasons-I-hate-the-blues.mp3|play 17 Reasons I Hate the Blues]]// </span></span> </span> by [[Chris Vaisvil]]
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| * [[@http://chrisvaisvil.com/?p=422|Klingon Opera Overture blog]] <span class="ymp-btn-page-play ymp-media-1270ddd333612c93cd386aaa93b59aba"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">//[[http://micro.soonlabel.com/17-ET/daily20110109-albino-17et.mp3|play Klingon Opera Overture]]// </span></span> </span> by [[Chris Vaisvil]]
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| * [[@http://chrisvaisvil.com/?p=298|Seventeen Selfless Notes blog]] <span class="ymp-btn-page-play ymp-media-835371d8b0e3022bd14b58e3c0a6175a"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">//[[http://micro.soonlabel.com/17-ET/if20101028selfless.mp3|play Seventeen Selfless Notes]]// </span></span> </span> by [[Chris Vaisvil]]
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| * [[@http://chrisvaisvil.com/?p=76|17ET Jazz blog]] <span class="ymp-btn-page-play ymp-media-b4292082727ce51de4e72ce8e860e140"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">//[[http://micro.soonlabel.com/17-ET/60x60-4001-1-ver2.mp3|play 17et Jazz]]// </span></span></span> by[[Chris Vaisvil| Chris Vaisvil]] (60 x 60 winner)
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| * [[http://chrisvaisvil.com/?p=742|17 Pink Tuxedos blog]] <span class="ymp-btn-page-play ymp-media-20284c23c4ce5614c44285891a72b2b9"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">//[[http://micro.soonlabel.com/17-ET/daily20110416-17_pink-tuxes.mp3|play 17 Pink Tuxedos]]// </span></span></span> by [[Chris Vaisvil]]
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| * [[http://chrisvaisvil.com/?p=706|Devil in the Deep Blue Sea blog]] <span class="ymp-btn-page-play ymp-media-2b49237889b140316b82293bc4e5743c"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">//[[http://micro.soonlabel.com/17-ET/daily20110401-17-2-devil_in_the_deep_blue_sea.mp3|play Devil in the Deep Blue sea]]// </span></span></span> blues collaboration between The Two Regs (vocals / lyrics) and Norm Harris (percussion) and Chris Vaisvil (17 note per octave electric guitar and fretless bass). | |
| * [[http://chrisvaisvil.com/?p=585|Seventeen Years in the Sixties blog]] <span class="ymp-btn-page-play ymp-media-e59982cb3a388488ca0ccb733e7439e7"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">//[[http://micro.soonlabel.com/17-ET/daily20110318-seventeen-years-in-the-sixties.mp3|play Seventeen Years in the Sixties]]// </span></span></span> by [[Chris Vaisvil]]
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| * [[@http://chrisvaisvil.com/?p=699|CT Scan blog]] <span class="ymp-btn-page-play ymp-media-6c6c5ec192c22569d28c8dd09467c623"><span class="ywp-page-play-pause ywp-page-video ywp-link-hover"><span class="ywp-page-play-pause ywp-page-video ywp-link-hover ywp-page-img-link">//[[http://www.youtube.com/watch?v=ZEEuytYwtbo|play video CT Scan]]// </span></span></span> by Chris Vaisvil
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| * [[http://chrisvaisvil.com/?p=470|Fish and a Grenade blog]] <span class="ymp-btn-page-play ymp-media-d882886a0b66279c7c3aa180aacb7339"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">//[[http://micro.soonlabel.com/17-ET/daily20110208-17-a-fish-and-a-grenade.mp3|play Fish and a Grenade]]// </span></span></span> (parental advisory language) by Chris Vaisvil
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| * [[@http://chrisvaisvil.com/?p=550|Seventeen Unsteady Hands blog]] <span class="ymp-btn-page-play ymp-media-0623ec5592a422ce10eddb210d094b60"><span class="ywp-page-play-pause ywp-page-video ywp-link-hover"><span class="ywp-page-play-pause ywp-page-video ywp-link-hover ywp-page-img-link">//[[http://www.youtube.com/watch?v=rAKHCqBNhfc|play video of performance of Seventeen Unsteady Hands]]// </span></span></span> by Chris Vaisvil
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| * [[http://chrisvaisvil.com/?p=38|The Pond blog]] by Chris Vaisvil and <span class="ymp-btn-page-play ymp-media-ad53e2e57d0cedd582013ae5cdd29164"><span class="ywp-page-play-pause ywp-page-video ywp-link-hover"><span class="ywp-page-play-pause ywp-page-video ywp-link-hover ywp-page-img-link">//[[@http://www.youtube.com/watch?v=25sC3_uheyA|video version of The Pond with Japanese Garden ]]// </span></span></span>
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| * <span class="ymp-btn-page-play ymp-media-ad53e2e57d0cedd582013ae5cdd29164">[[@http://chrisvaisvil.com/?p=305|Graveyard blog]] </span><span class="ymp-btn-page-play ymp-media-7a8cb8e49c18c67a2ea8b60d80c25b21"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">//[[http://micro.soonlabel.com/17-ET/if20101028-graveyard.mp3|play Graveyard]]// </span></span> </span> by Chris Vaisvil
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| * <span class="ymp-btn-page-play ymp-media-e13a9b281483c4b0a10ba321bb7cc2b4"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">//[[http://micro.soonlabel.com/17-ET/daily20110713_q49_17_brass_voice_choirs.mp3|For Brass and Voice Choirs in 17 edo]]// </span></span></span> by [[@http://chrisvaisvil.com/|Chris Vaisvil ]] [[@http://chrisvaisvil.com/?p=1039|more on the composition]]
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| * <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">//[[http://micro.soonlabel.com/17-ET/daily20111015-fungi.mp3|And I Became One With My Per Fungi]]// </span></span> by [[@http://chrisvaisvil.com/|Chris Vaisvil]] => [[@http://chrisvaisvil.com/?p=1439|more on composition]]
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| * <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">//[[http://micro.soonlabel.com/17-ET/20111014-STE-002-counter-intuitive.mp3|counterintuitive (17 edo guitar solo)]]// </span></span> by [[@http://www.chrisvaisvil.com/|Chris Vaisvil]] => [[@http://chrisvaisvil.com/?p=1427|more on composition]]
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| * [[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/no-love|Gregory Sanchez]]
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| * [[http://webzoom.freewebs.com/ralphjarzombek/micro7(17tet).mp3|Micro7]] by Ralph Jarzombek
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| * [[http://micro.soonlabel.com/17-ET/20161125_linn_speactral_17.MP3|Flying Into O'Hare]] by [[Chris Vaisvil]]
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| * [[@https://drive.google.com/drive/folders/0BwsXD8q2VCYUM0tRdDNhVzNhcHM|Helas, pitié]] by Alex Ness (in 17edo with stretched octaves)
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|
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|
| =Instruments= | | === MOS scales === |
| * ====**[[http://www.microtonalismo.com/proyecto-xvii|Guitar Heptadecatonic from Peruvian - Charles Loli and Antonio Huamani]]**====
| | {{Main| MOS scales of 17edo }} |
| > ====[[image:http://sphotos.ak.fbcdn.net/hphotos-ak-snc4/hs883.snc4/71639_167001659983806_100000219181856_601995_1526184_n.jpg width="706" height="249"]]====
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|
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| * ====**[[http://www.microtonalismo.com/proyecto-xvii|Bass Heptadecatonic from Peruvian - Charles Loli and Antonio Huamani]]**==== | | * diatonic ([[leapfrog]]/[[archy]]) [[5L 2s]] 3 3 3 1 3 3 1 (10\17, 1\1) |
| > ====[[image:http://sphotos.ak.fbcdn.net/hphotos-ak-ash2/hs382.ash2/66019_167001006650538_100000219181856_601987_48585_n.jpg width="689" height="256"]]==== | | * [[neutrominant]] [[3L 4s]] 3 2 3 2 3 2 2 (5\17, 1\1) (''dedicated article: [[17edo neutral scale]]'') |
| | * [[neutrominant]] [[7L 3s]] 2 2 2 1 2 2 1 2 2 1 (5\17, 1\1) |
| | * [[squares]] [[3L 5s]] 1 1 4 1 4 1 4 (6\17, 1\1) |
| | * [[squares]] [[3L 8s]] 1 3 1 1 3 1 1 3 (6\17, 1\1) |
| | * lovecraft [[4L 5s]] 3 1 3 1 3 1 3 1 1 (4\17, 1\1) |
|
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|
| * [[@http://chrisvaisvil.com/?p=436|17 note per octave conversion from a "standard" stratocastor copy]] - conversion by Brad Smith | | === Well temperaments === |
| | * [[Secor wt17|George Secor's 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]] |
|
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|
| [[image:17P1050829r.JPG]][[media type="custom" key="23473418"]]</pre></div>
| | {{Todo|expand scales list}} |
| <h4>Original HTML content:</h4>
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| <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>17edo</title></head><body><span style="display: block; text-align: right;"><span style="color: #1300ff;"><a class="wiki_link" href="http://xenharmonie.wikispaces.com/17edo">Deutsch</a> - <a class="wiki_link" href="/17%E5%B9%B3%E5%9D%87%E5%BE%8B">日本語</a></span><br />
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| </span><br />
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| <!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc0"><a name="x17 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:2 --><span style="color: #1300ff;">17 tone equal temperament</span></h1>
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| <!-- ws:start:WikiTextTocRule:32:&lt;img id=&quot;wikitext@@toc@@normal&quot; class=&quot;WikiMedia WikiMediaToc&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/normal?w=225&amp;h=100&quot;/&gt; --><div id="toc"><h1 class="nopad">Table of Contents</h1><!-- ws:end:WikiTextTocRule:32 --><!-- ws:start:WikiTextTocRule:33: --><div style="margin-left: 1em;"><a href="#x17 tone equal temperament">17 tone equal temperament</a></div>
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| <!-- ws:end:WikiTextTocRule:33 --><!-- ws:start:WikiTextTocRule:34: --><div style="margin-left: 2em;"><a href="#x17 tone equal temperament-Theory">Theory</a></div>
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| <!-- ws:end:WikiTextTocRule:34 --><!-- ws:start:WikiTextTocRule:35: --><div style="margin-left: 1em;"><a href="#Intervals">Intervals</a></div>
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| <!-- ws:end:WikiTextTocRule:35 --><!-- ws:start:WikiTextTocRule:36: --><div style="margin-left: 1em;"><a href="#Chord Names">Chord Names</a></div>
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| <!-- ws:end:WikiTextTocRule:36 --><!-- ws:start:WikiTextTocRule:37: --><div style="margin-left: 1em;"><a href="#Selected just intervals by error">Selected just intervals by error</a></div>
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| <!-- ws:end:WikiTextTocRule:37 --><!-- ws:start:WikiTextTocRule:38: --><div style="margin-left: 1em;"><a href="#Commas">Commas</a></div>
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| <!-- ws:end:WikiTextTocRule:38 --><!-- ws:start:WikiTextTocRule:39: --><div style="margin-left: 1em;"><a href="#Scales">Scales</a></div>
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| <!-- ws:end:WikiTextTocRule:39 --><!-- ws:start:WikiTextTocRule:40: --><div style="margin-left: 1em;"><a href="#Music">Music</a></div>
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| <!-- ws:end:WikiTextTocRule:40 --><!-- ws:start:WikiTextTocRule:41: --><div style="margin-left: 2em;"><a href="#Music-Compositions">Compositions</a></div>
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| <!-- ws:end:WikiTextTocRule:41 --><!-- ws:start:WikiTextTocRule:42: --><div style="margin-left: 2em;"><a href="#Music-Sound files">Sound files</a></div>
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| <!-- ws:end:WikiTextTocRule:42 --><!-- ws:start:WikiTextTocRule:43: --><div style="margin-left: 1em;"><a href="#Instruments">Instruments</a></div>
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| <!-- ws:end:WikiTextTocRule:43 --><!-- ws:start:WikiTextTocRule:44: --><div style="margin-left: 4em;"><a href="#Instruments---Guitar Heptadecatonic from Peruvian - Charles Loli and Antonio Huamani">Guitar Heptadecatonic from Peruvian - Charles Loli and Antonio Huamani</a></div>
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| <!-- ws:end:WikiTextTocRule:44 --><!-- ws:start:WikiTextTocRule:45: --><div style="margin-left: 4em;"><a href="#toc12"></a></div>
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| <!-- ws:end:WikiTextTocRule:45 --><!-- ws:start:WikiTextTocRule:46: --><div style="margin-left: 4em;"><a href="#Instruments---Bass Heptadecatonic from Peruvian - Charles Loli and Antonio Huamani">Bass Heptadecatonic from Peruvian - Charles Loli and Antonio Huamani</a></div>
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| <!-- ws:end:WikiTextTocRule:46 --><!-- ws:start:WikiTextTocRule:47: --><div style="margin-left: 4em;"><a href="#toc14"></a></div>
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| <!-- ws:end:WikiTextTocRule:47 --><!-- ws:start:WikiTextTocRule:48: --></div>
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| <!-- ws:end:WikiTextTocRule:48 --><strong>17-EDO</strong> divides the octave in 17 equal steps, each 70.588 <a class="wiki_link" href="/cent">cents</a> in size. It is the seventh <a class="wiki_link" href="/prime%20numbers">prime</a> edo, following <a class="wiki_link" href="/13edo">13edo</a> and coming before <a class="wiki_link" href="/19edo">19edo</a>.<br />
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| <br />
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| <!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc1"><a name="x17 tone equal temperament-Theory"></a><!-- ws:end:WikiTextHeadingRule:4 -->Theory</h2>
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| An introduction to 17-EDO theory, through the eyes of the <a class="wiki_link" href="/SeventeenTonePianoProject">SeventeenTonePianoProject</a>: <a class="wiki_link" href="/SeventeenTheory">SeventeenTheory</a>.<br />
| |
| Another introduction into 17-EDO theory: <a class="wiki_link_ext" href="http://xenharmony.wikispaces.com/space/showimage/17puzzle.pdf" rel="nofollow">The 17-tone Puzzle</a> by George Secor.<br />
| |
| <a class="wiki_link" href="/17edo%20Solfege">17edo Solfege</a>. <a class="wiki_link" href="/17edo%20tetrachords">17edo tetrachords</a>. <a class="wiki_link_ext" href="http://microtonalismo.com/proyecto-xvii" rel="nofollow">Proyect 17-Perú</a><br />
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| <br />
| |
| 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; <a class="wiki_link" href="/27edt">27edt</a> (a variant of 17edo in which the octaves are flattened by ~2.5 cents) is a good alternative. Another one is <a class="wiki_link" href="/44ed6">44ed6</a>.<br />
| |
| <br />
| |
| 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.<br />
| |
| <br />
| |
| 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 famous <a class="wiki_link_ext" href="https://en.wikipedia.org/wiki/Mu_chord" rel="nofollow">mu major chord</a> 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.<br />
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| <br />
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| <!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc2"><a name="Intervals"></a><!-- ws:end:WikiTextHeadingRule:6 -->Intervals</h1>
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|
| |
|
| |
|
| <table class="wiki_table">
| | == Instruments == |
| <tr>
| | === Fretted String Instruments === |
| <th>Degree<br />
| | * [http://chrisvaisvil.com/?p=436 17 note per octave conversion from a "standard" Stratocaster copy] - conversion by Brad Smith |
| </th>
| |
| <th>Cents<br />
| |
| </th>
| |
| <th>Names of<br />
| |
| Intervals<br />
| |
| </th>
| |
| <th colspan="3"><a class="wiki_link" href="/Ups%20and%20Downs%20Notation">ups and downs </a><a class="wiki_link" href="/Ups%20and%20Downs%20Notation">notation</a><br />
| |
| </th>
| |
| <th>Approximate<br />
| |
| Ratios*<br />
| |
| </th>
| |
| <th>Temperament(s)<br />
| |
| generated<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td>0<br />
| |
| </td>
| |
| <td>0<br />
| |
| </td>
| |
| <td>Unison<br />
| |
| </td>
| |
| <td style="text-align: center;">unison<br />
| |
| </td>
| |
| <td style="text-align: center;">P1<br />
| |
| </td>
| |
| <td style="text-align: center;">C<br />
| |
| </td>
| |
| <td style="text-align: center;">1/1<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>1<br />
| |
| </td>
| |
| <td>70.59<br />
| |
| </td>
| |
| <td>Super Unison/<br />
| |
| Minor Second<br />
| |
| </td>
| |
| <td style="text-align: center;">minor 2nd<br />
| |
| </td>
| |
| <td style="text-align: center;">m2<br />
| |
| </td>
| |
| <td style="text-align: center;">Db<br />
| |
| </td>
| |
| <td style="text-align: center;"><a class="wiki_link" href="/25_24">25/24</a>, <a class="wiki_link" href="/26_25">26/25</a>, <a class="wiki_link" href="/33_32">33/32</a><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>2<br />
| |
| </td>
| |
| <td>141.18<br />
| |
| </td>
| |
| <td>Augmented Unison/<br />
| |
| Neutral Second<br />
| |
| </td>
| |
| <td style="text-align: center;">mid 2nd<br />
| |
| </td>
| |
| <td style="text-align: center;">~2<br />
| |
| </td>
| |
| <td style="text-align: center;">Dv<br />
| |
| </td>
| |
| <td style="text-align: center;"><a class="wiki_link" href="/13_12">13/12</a>, <a class="wiki_link" href="/12_11">12/11</a>, <a class="wiki_link" href="/14_13">14/13</a><br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/Bleu">Bleu</a><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>3<br />
| |
| </td>
| |
| <td>211.765<br />
| |
| </td>
| |
| <td>Major Second/<br />
| |
| Sub Third<br />
| |
| </td>
| |
| <td style="text-align: center;">major 2nd<br />
| |
| </td>
| |
| <td style="text-align: center;">M2<br />
| |
| </td>
| |
| <td style="text-align: center;">D<br />
| |
| </td>
| |
| <td style="text-align: center;"><a class="wiki_link" href="/9_8">9/8</a>, <a class="wiki_link" href="/25_22">25/22</a>, <a class="wiki_link" href="/8_7">8/7</a>, <a class="wiki_link" href="/28_25">28/25</a><br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/Machine">Machine</a><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>4<br />
| |
| </td>
| |
| <td>282.35<br />
| |
| </td>
| |
| <td>Minor Third/<br />
| |
| Super Second<br />
| |
| </td>
| |
| <td style="text-align: center;">minor 3rd<br />
| |
| </td>
| |
| <td style="text-align: center;">m3<br />
| |
| </td>
| |
| <td style="text-align: center;">Eb<br />
| |
| </td>
| |
| <td style="text-align: center;"><a class="wiki_link" href="/13_11">13/11</a>, <a class="wiki_link" href="/75_64">75/64</a>, <a class="wiki_link" href="/7_6">7/6</a><br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/Huxley">Huxley</a><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>5<br />
| |
| </td>
| |
| <td>352.94<br />
| |
| </td>
| |
| <td>Augmented Second/<br />
| |
| Neutral Third/<br />
| |
| Diminished Fourth<br />
| |
| </td>
| |
| <td style="text-align: center;">mid 3rd<br />
| |
| </td>
| |
| <td style="text-align: center;">~3<br />
| |
| </td>
| |
| <td style="text-align: center;">Ev<br />
| |
| </td>
| |
| <td style="text-align: center;"><a class="wiki_link" href="/11_9">11/9</a>, <a class="wiki_link" href="/16_13">16/13</a><br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/Maqamic">Maqamic</a>/<a class="wiki_link" href="/hemif">hemif</a><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>6<br />
| |
| </td>
| |
| <td>423.53<br />
| |
| </td>
| |
| <td>Major Third/<br />
| |
| Sub Fourth<br />
| |
| </td>
| |
| <td style="text-align: center;">major 3rd<br />
| |
| </td>
| |
| <td style="text-align: center;">M3<br />
| |
| </td>
| |
| <td style="text-align: center;">E<br />
| |
| </td>
| |
| <td style="text-align: center;"><a class="wiki_link" href="/32_25">32/25</a>, <a class="wiki_link" href="/33_26">33/26</a>, <a class="wiki_link" href="/9_7">9/7</a>, <a class="wiki_link" href="/14_11">14/11</a>, <a class="wiki_link" href="/51_40">51/40</a><br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/Skwares">Skwares</a><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>7<br />
| |
| </td>
| |
| <td>494.11<br />
| |
| </td>
| |
| <td>Perfect Fourth<br />
| |
| </td>
| |
| <td style="text-align: center;">perfect 4th<br />
| |
| </td>
| |
| <td style="text-align: center;">P4<br />
| |
| </td>
| |
| <td style="text-align: center;">F<br />
| |
| </td>
| |
| <td style="text-align: center;"><a class="wiki_link" href="/4_3">4/3</a><br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/Supra">Supra</a><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>8<br />
| |
| </td>
| |
| <td>564.71<br />
| |
| </td>
| |
| <td>Super Fourth<br />
| |
| Diminished Fifth<br />
| |
| </td>
| |
| <td style="text-align: center;">up 4th,<br />
| |
| diminished 5th<br />
| |
| </td>
| |
| <td style="text-align: center;">^4, d5<br />
| |
| </td>
| |
| <td style="text-align: center;">F^, Gb<br />
| |
| </td>
| |
| <td style="text-align: center;"><a class="wiki_link" href="/11_8">11/8</a>, 18/13<br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/Progress">Progress</a><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>9<br />
| |
| </td>
| |
| <td>635.29<br />
| |
| </td>
| |
| <td>Augmented Fourth/<br />
| |
| Sub Fifth<br />
| |
| </td>
| |
| <td style="text-align: center;">augmented 4th,<br />
| |
| down 5th<br />
| |
| </td>
| |
| <td style="text-align: center;">A4, v5<br />
| |
| </td>
| |
| <td style="text-align: center;">F#, Gv<br />
| |
| </td>
| |
| <td style="text-align: center;"><a class="wiki_link" href="/16_11">16/11</a>, 13/9, <a class="wiki_link" href="/23_16">23/16</a><br />
| |
| </td>
| |
| <td>Progress<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>10<br />
| |
| </td>
| |
| <td>705.88<br />
| |
| </td>
| |
| <td>Perfect Fifth<br />
| |
| </td>
| |
| <td style="text-align: center;">perfect 5th<br />
| |
| </td>
| |
| <td style="text-align: center;">P5<br />
| |
| </td>
| |
| <td style="text-align: center;">G<br />
| |
| </td>
| |
| <td style="text-align: center;"><a class="wiki_link" href="/3_2">3/2</a><br />
| |
| </td>
| |
| <td>Supra<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>11<br />
| |
| </td>
| |
| <td>776.47<br />
| |
| </td>
| |
| <td>Super Fifth/<br />
| |
| Minor Sixth<br />
| |
| </td>
| |
| <td style="text-align: center;">minor 6th<br />
| |
| </td>
| |
| <td style="text-align: center;">m6<br />
| |
| </td>
| |
| <td style="text-align: center;">Ab<br />
| |
| </td>
| |
| <td style="text-align: center;">25/16, 52/33, 14/9, <a class="wiki_link" href="/11_7">11/7</a><br />
| |
| </td>
| |
| <td>Skwares<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>12<br />
| |
| </td>
| |
| <td>847.06<br />
| |
| </td>
| |
| <td>Augmented Fifth/<br />
| |
| Neutral Sixth/<br />
| |
| Diminished Seventh<br />
| |
| </td>
| |
| <td style="text-align: center;">mid 6th<br />
| |
| </td>
| |
| <td style="text-align: center;">~6<br />
| |
| </td>
| |
| <td style="text-align: center;">Av<br />
| |
| </td>
| |
| <td style="text-align: center;"><a class="wiki_link" href="/13_8">13/8</a>, 18/11<br />
| |
| </td>
| |
| <td>Maqamic/hemif<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>13<br />
| |
| </td>
| |
| <td>917.65<br />
| |
| </td>
| |
| <td>Major Sixth/<br />
| |
| Sub Seventh<br />
| |
| </td>
| |
| <td style="text-align: center;">major 6th<br />
| |
| </td>
| |
| <td style="text-align: center;">M6<br />
| |
| </td>
| |
| <td style="text-align: center;">A<br />
| |
| </td>
| |
| <td style="text-align: center;"><a class="wiki_link" href="/17_10">17/10</a>, <a class="wiki_link" href="/22_13">22/13</a>, 128/75, <a class="wiki_link" href="/12_7">12/7</a><br />
| |
| </td>
| |
| <td>Huxley<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>14<br />
| |
| </td>
| |
| <td>988.235<br />
| |
| </td>
| |
| <td>Minor Seventh/<br />
| |
| Super Sixth<br />
| |
| </td>
| |
| <td style="text-align: center;">minor 7th<br />
| |
| </td>
| |
| <td style="text-align: center;">m7<br />
| |
| </td>
| |
| <td style="text-align: center;">Bb<br />
| |
| </td>
| |
| <td style="text-align: center;"><a class="wiki_link" href="/16_9">16/9</a>, 44/25, 7/4, 25/14<br />
| |
| </td>
| |
| <td>Machine<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>15<br />
| |
| </td>
| |
| <td>1058.82<br />
| |
| </td>
| |
| <td>Augmented Sixth/<br />
| |
| Neutral Seventh/<br />
| |
| Diminished Octave<br />
| |
| </td>
| |
| <td style="text-align: center;">mid 7th<br />
| |
| </td>
| |
| <td style="text-align: center;">~7<br />
| |
| </td>
| |
| <td style="text-align: center;">Bv<br />
| |
| </td>
| |
| <td style="text-align: center;"><a class="wiki_link" href="/11_6">11/6</a>, 24/13, <a class="wiki_link" href="/13_7">13/7</a><br />
| |
| </td>
| |
| <td>Bleu<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>16<br />
| |
| </td>
| |
| <td>1129.41<br />
| |
| </td>
| |
| <td>Major Seventh/<br />
| |
| Sub Octave<br />
| |
| </td>
| |
| <td style="text-align: center;">major 7th<br />
| |
| </td>
| |
| <td style="text-align: center;">M7<br />
| |
| </td>
| |
| <td style="text-align: center;">B<br />
| |
| </td>
| |
| <td style="text-align: center;">25/13, 48/25, 64/33<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>17<br />
| |
| </td>
| |
| <td>1200<br />
| |
| </td>
| |
| <td>Perfect Octave<br />
| |
| </td>
| |
| <td style="text-align: center;">octave<br />
| |
| </td>
| |
| <td style="text-align: center;">P8<br />
| |
| </td>
| |
| <td style="text-align: center;">C<br />
| |
| </td>
| |
| <td style="text-align: center;"><a class="wiki_link" href="/2_1">2/1</a><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| Combining ups and downs notation with <a class="wiki_link" href="/Kite%27s%20color%20notation">color notation</a>, qualities can be loosely associated with colors:<br />
| | [[File:17P1050829r.JPG|alt=17P1050829r.JPG|17P1050829r.JPG]] |
|
| |
|
| | * 17edo soprano Harmony ukulele with a 3D printed fretboard - conversion by [[User:Tristanbay|Tristan Bay]] |
|
| |
|
| <table class="wiki_table">
| | [[File:17edo soprano ukulele with 3D printed fretboard.jpg|frameless|640x640px]] |
| <tr>
| |
| <th>quality<br />
| |
| </th>
| |
| <th>color<br />
| |
| </th>
| |
| <th>monzo format<br />
| |
| </th>
| |
| <th>examples<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">minor<br />
| |
| </td>
| |
| <td style="text-align: center;">blue<br />
| |
| </td>
| |
| <td style="text-align: center;">{a, b, 0, 1}<br />
| |
| </td>
| |
| <td style="text-align: center;">7/6, 7/4<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">&quot;<br />
| |
| </td>
| |
| <td style="text-align: center;">fourthward white<br />
| |
| </td>
| |
| <td style="text-align: center;">{a, b}, b &lt; -1<br />
| |
| </td>
| |
| <td style="text-align: center;">32/27, 16/9<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">mid<br />
| |
| </td>
| |
| <td style="text-align: center;">jade<br />
| |
| </td>
| |
| <td style="text-align: center;">{a, b, 0, 0, 1}<br />
| |
| </td>
| |
| <td style="text-align: center;">11/9, 11/6<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">&quot;<br />
| |
| </td>
| |
| <td style="text-align: center;">amber<br />
| |
| </td>
| |
| <td style="text-align: center;">{a, b, 0, 0, -1}<br />
| |
| </td>
| |
| <td style="text-align: center;">12/11, 18/11<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">major<br />
| |
| </td>
| |
| <td style="text-align: center;">fifthward white<br />
| |
| </td>
| |
| <td style="text-align: center;">{a, b}, b &gt; 1<br />
| |
| </td>
| |
| <td style="text-align: center;">9/8, 27/16<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">&quot;<br />
| |
| </td>
| |
| <td style="text-align: center;">red<br />
| |
| </td>
| |
| <td style="text-align: center;">{a, b, 0, -1}<br />
| |
| </td>
| |
| <td style="text-align: center;">9/7, 12/7<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| <br />
| | === Keyboards === |
| <!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc3"><a name="Chord Names"></a><!-- ws:end:WikiTextHeadingRule:8 -->Chord Names</h1>
| | [[Lumatone mapping for 17edo|Lumatone mappings for 17edo]] are available. |
| <br />
| |
| All 17edo chords can be named using ups and downs. Here are the blue, jade and red triads:<br />
| |
|
| |
|
| | 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. |
|
| |
|
| <table class="wiki_table">
| | [[File:Strisoboard_piano2a_s.jpg|frameless]] |
| <tr>
| |
| <th>color of the 3rd<br />
| |
| </th>
| |
| <th>JI chord<br />
| |
| </th>
| |
| <th>notes as edosteps<br />
| |
| </th>
| |
| <th>notes of C chord<br />
| |
| </th>
| |
| <th>written name<br />
| |
| </th>
| |
| <th>spoken name<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">blue<br />
| |
| </td>
| |
| <td style="text-align: center;">6:7:9<br />
| |
| </td>
| |
| <td style="text-align: center;">0-4-10<br />
| |
| </td>
| |
| <td style="text-align: center;">C Eb G<br />
| |
| </td>
| |
| <td style="text-align: center;">Cm<br />
| |
| </td>
| |
| <td style="text-align: center;">C minor<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">jade<br />
| |
| </td>
| |
| <td style="text-align: center;">18:22:27<br />
| |
| </td>
| |
| <td style="text-align: center;">0-5-10<br />
| |
| </td>
| |
| <td style="text-align: center;">C Ev G<br />
| |
| </td>
| |
| <td style="text-align: center;">C~<br />
| |
| </td>
| |
| <td style="text-align: center;">C mid<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">red<br />
| |
| </td>
| |
| <td style="text-align: center;">14:18:27<br />
| |
| </td>
| |
| <td style="text-align: center;">0-6-10<br />
| |
| </td>
| |
| <td style="text-align: center;">C E G<br />
| |
| </td>
| |
| <td style="text-align: center;">C<br />
| |
| </td>
| |
| <td style="text-align: center;">C major or C<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| <br />
| | 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]]: |
| 0-4-9 = C Eb Gv = Cm(v5) = C minor down-five<br />
| |
| 0-5-9 = C Ev G = C~(v5) = C mid down-five<br />
| |
| 0-6-11 = C E G^ = C(^5) = C up-five<br />
| |
| <br />
| |
| 0-4-10-14 = C Eb G Bb = Cm7 = C minor seven<br />
| |
| 0-5-10-14 = C Ev G Bb = C7(~3) = C seven mid-three<br />
| |
| 0-6-10-15 = C E G Bv = C,~7 = C mid seven<br />
| |
| 0-5-10-15 = C Ev G Bv = C.~7 = C dot mid seven<br />
| |
| <br />
| |
| For a more complete list, see <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation#Chord%20names%20in%20other%20EDOs">Ups and Downs Notation - Chord names in other EDOs</a>.<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:10:&lt;h1&gt; --><h1 id="toc4"><a name="Selected just intervals by error"></a><!-- ws:end:WikiTextHeadingRule:10 -->Selected just intervals by error</h1>
| |
| The following table shows how <a class="wiki_link" href="/Just-24">some prominent just intervals</a> are represented in 17edo (ordered by absolute error).<br />
| |
|
| |
|
| | * [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) |
|
| |
|
| <table class="wiki_table">
| | == Music == |
| <tr>
| | {{Main| 17edo/Music }} |
| <td><strong>Interval, complement</strong><br />
| | {{Catrel|17edo tracks}} |
| </td>
| |
| <td><strong>Error (abs., in <a class="wiki_link" href="/cent">cents</a>)</strong><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><a class="wiki_link" href="/18_13">18/13</a>, <a class="wiki_link" href="/13_9">13/9</a><br />
| |
| </td>
| |
| <td style="text-align: center;">1.324<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><a class="wiki_link" href="/13_12">13/12</a>, <a class="wiki_link" href="/24_13">24/13</a><br />
| |
| </td>
| |
| <td style="text-align: center;">2.604<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><a class="wiki_link" href="/4_3">4/3</a>, <a class="wiki_link" href="/3_2">3/2</a><br />
| |
| </td>
| |
| <td style="text-align: center;">3.927<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><a class="wiki_link" href="/11_9">11/9</a>, <a class="wiki_link" href="/18_11">18/11</a><br />
| |
| </td>
| |
| <td style="text-align: center;">5.533<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><a class="wiki_link" href="/14_11">14/11</a>, <a class="wiki_link" href="/11_7">11/7</a><br />
| |
| </td>
| |
| <td style="text-align: center;">6.021<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><a class="wiki_link" href="/16_13">16/13</a>, <a class="wiki_link" href="/13_8">13/8</a><br />
| |
| </td>
| |
| <td style="text-align: center;">6.531<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><a class="wiki_link" href="/13_11">13/11</a>, <a class="wiki_link" href="/22_13">22/13</a><br />
| |
| </td>
| |
| <td style="text-align: center;">6.857<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><a class="wiki_link" href="/9_8">9/8</a>, <a class="wiki_link" href="/16_9">16/9</a><br />
| |
| </td>
| |
| <td style="text-align: center;">7.855<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><a class="wiki_link" href="/12_11">12/11</a>, <a class="wiki_link" href="/11_6">11/6</a><br />
| |
| </td>
| |
| <td style="text-align: center;">9.461<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><a class="wiki_link" href="/9_7">9/7</a>, <a class="wiki_link" href="/14_9">14/9</a><br />
| |
| </td>
| |
| <td style="text-align: center;">11.555<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><a class="wiki_link" href="/14_13">14/13</a>, <a class="wiki_link" href="/13_7">13/7</a><br />
| |
| </td>
| |
| <td style="text-align: center;">12.878<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><a class="wiki_link" href="/11_8">11/8</a>, <a class="wiki_link" href="/16_11">16/11</a><br />
| |
| </td>
| |
| <td style="text-align: center;">13.388<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><a class="wiki_link" href="/7_6">7/6</a>, <a class="wiki_link" href="/12_7">12/7</a><br />
| |
| </td>
| |
| <td style="text-align: center;">15.482<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><a class="wiki_link" href="/7_5">7/5</a>, <a class="wiki_link" href="/10_7">10/7</a><br />
| |
| </td>
| |
| <td style="text-align: center;">17.806<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><a class="wiki_link" href="/8_7">8/7</a>, <a class="wiki_link" href="/7_4">7/4</a><br />
| |
| </td>
| |
| <td style="text-align: center;">19.409<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><a class="wiki_link" href="/15_14">15/14</a>, <a class="wiki_link" href="/28_15">28/15</a><br />
| |
| </td>
| |
| <td style="text-align: center;">21.734<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><a class="wiki_link" href="/11_10">11/10</a>, <a class="wiki_link" href="/20_11">20/11</a><br />
| |
| </td>
| |
| <td style="text-align: center;">23.828<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><a class="wiki_link" href="/15_11">15/11</a>, <a class="wiki_link" href="/22_15">22/15</a><br />
| |
| </td>
| |
| <td style="text-align: center;">27.755<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><a class="wiki_link" href="/10_9">10/9</a>, <a class="wiki_link" href="/9_5">9/5</a><br />
| |
| </td>
| |
| <td style="text-align: center;">29.361<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><a class="wiki_link" href="/16_15">16/15</a>, <a class="wiki_link" href="/15_8">15/8</a><br />
| |
| </td>
| |
| <td style="text-align: center;">29.445<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><a class="wiki_link" href="/13_10">13/10</a>, <a class="wiki_link" href="/20_13">20/13</a><br />
| |
| </td>
| |
| <td style="text-align: center;">30.685<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><a class="wiki_link" href="/6_5">6/5</a>, <a class="wiki_link" href="/5_3">5/3</a><br />
| |
| </td>
| |
| <td style="text-align: center;">33.288<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><a class="wiki_link" href="/5_4">5/4</a>, <a class="wiki_link" href="/8_5">8/5</a><br />
| |
| </td>
| |
| <td style="text-align: center;">33.373<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><a class="wiki_link" href="/15_13">15/13</a>, <a class="wiki_link" href="/26_15">26/15</a><br />
| |
| </td>
| |
| <td style="text-align: center;">34.612<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| <br />
| | ; [https://www.youtube.com/playlist?list=PLWB50RFxjvduT6F1Mwu0CmPa41LBRdXf5 YouTube playlist of 17edo pieces] |
| <!-- ws:start:WikiTextMediaRule:0:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/custom/24810186?h=0&amp;w=0&quot; class=&quot;WikiMedia WikiMediaCustom&quot; id=&quot;wikitext@@media@@type=&amp;quot;custom&amp;quot; key=&amp;quot;24810186&amp;quot;&quot; title=&quot;Custom Media&quot;/&gt; --><object id="example" type="image/svg+xml" data="http://xenharmonic.wikispaces.com/file/view/17ed2-001.svg">alt : Your browser has no SVG support.</object><!-- ws:end:WikiTextMediaRule:0 --><br />
| | ; [https://www.youtube.com/results?search_query=17edo&search=tag YouTube videos tagged with 17edo] |
| <!-- ws:start:WikiTextFileRule:992:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file/17ed2-001.svg?h=52&amp;w=320&quot; class=&quot;WikiFile&quot; id=&quot;wikitext@@file@@17ed2-001.svg&quot; title=&quot;File: 17ed2-001.svg&quot; width=&quot;320&quot; height=&quot;52&quot; /&gt; --><div class="objectEmbed"><a href="/file/view/17ed2-001.svg/480990638/17ed2-001.svg" onclick="ws.common.trackFileLink('/file/view/17ed2-001.svg/480990638/17ed2-001.svg');"><img src="http://www.wikispaces.com/i/mime/32/empty.png" height="32" width="32" alt="17ed2-001.svg" /></a><div><a href="/file/view/17ed2-001.svg/480990638/17ed2-001.svg" onclick="ws.common.trackFileLink('/file/view/17ed2-001.svg/480990638/17ed2-001.svg');" class="filename" title="17ed2-001.svg">17ed2-001.svg</a><br /><ul><li><a href="/file/detail/17ed2-001.svg">Details</a></li><li><a href="/file/view/17ed2-001.svg/480990638/17ed2-001.svg">Download</a></li><li style="color: #666">19 KB</li></ul></div></div><!-- ws:end:WikiTextFileRule:992 --><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:12:&lt;h1&gt; --><h1 id="toc5"><a name="Commas"></a><!-- ws:end:WikiTextHeadingRule:12 -->Commas</h1>
| |
| 17 EDO <a class="wiki_link" href="/tempering%20out">tempers out</a> the following <a class="wiki_link" href="/comma">comma</a>s. (Note: This assumes <a class="wiki_link" href="/val">val</a> &lt; 17 27 39 48 59 63 |, cent values rounded to 5 digits.)<br />
| |
|
| |
|
| | ; 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 |
| | --> |
|
| |
|
| <table class="wiki_table">
| | == Introductory Materials == |
| <tr>
| | * [[SeventeenTheory]], an introduction to 17edo theory, through the eyes of the [[SeventeenTonePianoProject]]. |
| <th>Comma<br />
| | * [http://anaphoria.com/Secor17puzzle.pdf The 17-tone Puzzle] by George Secor, another introduction into 17edo theory. |
| </th>
| | * [[17edo tetrachords]] |
| <th>Monzo<br />
| | * [http://microtonalismo.com/proyecto-xvii Proyect 17-Perú] {{forbidden}} |
| </th>
| |
| <th>Value (Cents)<br />
| |
| </th>
| |
| <th>Name 1<br />
| |
| </th>
| |
| <th>Name 2<br />
| |
| </th>
| |
| <th>Name 3<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><span style="display: block; text-align: center;"><br />
| |
| </span><br />
| |
| </td>
| |
| <td>| 27 -17 &gt;<br />
| |
| </td>
| |
| <td style="text-align: right;">66.765<br />
| |
| </td>
| |
| <td><span style="display: block; text-align: center;">17-Comma</span><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">25/24<br />
| |
| </td>
| |
| <td>|-3 -1 2&gt;<br />
| |
| </td>
| |
| <td style="text-align: right;">70.762<br />
| |
| </td>
| |
| <td>Chromatic semitone<br />
| |
| </td>
| |
| <td style="text-align: center;">Dicot comma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">32805/32768<br />
| |
| </td>
| |
| <td style="text-align: left;">| -15 8 1 &gt;<br />
| |
| </td>
| |
| <td style="text-align: right;">1.9537<br />
| |
| </td>
| |
| <td style="text-align: center;">Schisma<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">64/63<br />
| |
| </td>
| |
| <td style="text-align: left;">| 6 -2 0 -1 &gt;<br />
| |
| </td>
| |
| <td style="text-align: right;">27.264<br />
| |
| </td>
| |
| <td style="text-align: center;">Septimal Comma<br />
| |
| </td>
| |
| <td style="text-align: center;">Archytas' Comma<br />
| |
| </td>
| |
| <td style="text-align: center;">Leipziger Komma<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">245/243<br />
| |
| </td>
| |
| <td style="text-align: left;">| 0 -5 1 2 &gt;<br />
| |
| </td>
| |
| <td style="text-align: right;">14.191<br />
| |
| </td>
| |
| <td style="text-align: center;">Sensamagic<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">1728/1715<br />
| |
| </td>
| |
| <td style="text-align: left;">| 6 3 -1 -3 &gt;<br />
| |
| </td>
| |
| <td style="text-align: right;">13.074<br />
| |
| </td>
| |
| <td style="text-align: center;">Orwellisma<br />
| |
| </td>
| |
| <td style="text-align: center;">Orwell Comma<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: left;">| -6 -8 2 5 &gt;<br />
| |
| </td>
| |
| <td style="text-align: right;">1.1170<br />
| |
| </td>
| |
| <td style="text-align: center;">Wizma<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">99/98<br />
| |
| </td>
| |
| <td style="text-align: left;">| -1 2 0 -2 1 &gt;<br />
| |
| </td>
| |
| <td style="text-align: right;">17.576<br />
| |
| </td>
| |
| <td style="text-align: center;">Mothwellsma<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">896/891<br />
| |
| </td>
| |
| <td style="text-align: left;">| 7 -4 0 1 -1 &gt;<br />
| |
| </td>
| |
| <td style="text-align: right;">9.6880<br />
| |
| </td>
| |
| <td style="text-align: center;">Pentacircle<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">243/242<br />
| |
| </td>
| |
| <td style="text-align: left;">| -1 5 0 0 -2 &gt;<br />
| |
| </td>
| |
| <td style="text-align: right;">7.1391<br />
| |
| </td>
| |
| <td style="text-align: center;">Rastma<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">385/384<br />
| |
| </td>
| |
| <td style="text-align: left;">| -7 -1 1 1 1 &gt;<br />
| |
| </td>
| |
| <td style="text-align: right;">4.5026<br />
| |
| </td>
| |
| <td style="text-align: center;">Keenanisma<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><span style="display: block; text-align: center;">525/512</span><br />
| |
| </td>
| |
| <td style="text-align: left;"><span style="display: block; text-align: left;">| -9 1 2 1 &gt;</span><br />
| |
| </td>
| |
| <td style="text-align: right;">43.408<br />
| |
| </td>
| |
| <td style="text-align: center;"><span style="display: block; text-align: center;">Avicennma</span><br />
| |
| </td>
| |
| <td style="text-align: center;">Avicennma's Enharmonic Diesis<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| <br />
| | [[Category:Teentuning]] |
| 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.<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:14:&lt;h1&gt; --><h1 id="toc6"><a name="Scales"></a><!-- ws:end:WikiTextHeadingRule:14 -->Scales</h1>
| |
| <ul><li><a class="wiki_link" href="/Otonal%2017">Otonal 17</a></li><li><a class="wiki_link_ext" href="http://www.microtonalismo.com/proyecto-xvii" rel="nofollow">Blues Peruvian 17edo</a></li><li><a class="wiki_link" href="/17edo%20neutral%20scale">17edo neutral scale</a></li><li><a class="wiki_link" href="/Scorp">Scorp</a></li><li><a class="wiki_link" href="/Screamapillar">Screamapillar</a></li><li><a class="wiki_link" href="/Hydra">Hydra</a></li><li><a class="wiki_link" href="/MOS%20scales%20of%2017edo">MOS scales of 17edo</a> (horograms)</li></ul><br />
| |
| <a class="wiki_link" href="/List%20of%2017edo%20rank%20two%20temperaments%20by%20badness">List of 17edo rank two temperaments by badness</a><br />
| |
| <a class="wiki_link" href="/List%20of%20edo-distinct%2017c%20rank%20two%20temperaments">List of edo-distinct 17c rank two temperaments</a><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:16:&lt;h1&gt; --><h1 id="toc7"><a name="Music"></a><!-- ws:end:WikiTextHeadingRule:16 -->Music</h1>
| |
| <!-- ws:start:WikiTextHeadingRule:18:&lt;h2&gt; --><h2 id="toc8"><a name="Music-Compositions"></a><!-- ws:end:WikiTextHeadingRule:18 -->Compositions</h2>
| |
| <ul><li><a class="wiki_link_ext" href="https://soundcloud.com/overtoneshock/demanding-two-faces-17-edo" rel="nofollow" target="_blank">Demanding Two Faces</a> (xen-pop) by <a class="wiki_link_ext" href="https://soundcloud.com/overtoneshock" rel="nofollow">Stephen Weigel</a></li><li><a class="wiki_link_ext" href="https://soundcloud.com/overtoneshock/where-were-you-during-the-apocalypse-17-edo" rel="nofollow">Where were you at the Apocalypse?</a> (xen-pop) by <a class="wiki_link_ext" href="https://soundcloud.com/overtoneshock" rel="nofollow">Stephen Weigel</a></li><li><a class="wiki_link_ext" href="http://home.snafu.de/djwolf/PreludeIn17tet.pdf" rel="nofollow">Prelude</a> by <a class="wiki_link" href="/Daniel%20Wolf">Daniel Wolf</a></li><li><a class="wiki_link_ext" href="http://www.georghajdu.de/heptadecatonic_drops.html" rel="nofollow">Heptadecatonic Drops</a> by Georg Hajdu</li><li><a class="wiki_link_ext" href="http://www.georghajdu.de/63.html?&amp;L=1%20" rel="nofollow">Klangmoraste</a> by Georg Hajdu</li><li><a class="wiki_link_ext" href="http://www.microtonalismo.com/proyecto-xvii" rel="nofollow">Charles Loli 17edo</a> music for guitar heptadecatonic (2001) and armony inductive microtonaly (1993)</li><li><a class="wiki_link_ext" href="http://microtonalismo.com/" rel="nofollow">microtonalismo</a> Heptadecatonic Peruvian</li><li><a class="wiki_link" href="/Multiverse">Multiverse</a> by <a class="wiki_link" href="/JacobBarton">Jacob Barton</a></li></ul><br />
| |
| <!-- ws:start:WikiTextHeadingRule:20:&lt;h2&gt; --><h2 id="toc9"><a name="Music-Sound files"></a><!-- ws:end:WikiTextHeadingRule:20 -->Sound files</h2>
| |
| <ul><li><a class="wiki_link_ext" href="http://chrisvaisvil.com/shanidar-cave-17-edo/" rel="nofollow">Shanidar Cave</a> 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<a class="wiki_link" href="http://xenharmonic.wikispaces.com/Chris%20Vaisvil" target="_blank"> Chris Vaisvil</a></li><li><span class="ymp-btn-page-play ymp-media-3ece313d36e9307c749e0e3549ece422"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><em><a class="wiki_link_ext" href="https://soundcloud.com/aaron-krister-johnson/puhlops-and-lauguas-big-adventure" rel="nofollow">Puhlops and Laugua's Big Adventure</a></em> </span></span> </span> by <a class="wiki_link_ext" href="http://www.untwelve.org/board" rel="nofollow">|Aaron Krister Johnson</a></li><li><span class="ymp-btn-page-play ymp-media-3ece313d36e9307c749e0e3549ece422"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><em><a class="wiki_link_ext" href="https://soundcloud.com/aaron-krister-johnson/adagio-for-margo" rel="nofollow">Adagio for Margo</a></em> </span></span> </span> by <a class="wiki_link_ext" href="http://www.untwelve.org/board" rel="nofollow">Aaron Krister Johnson</a></li><li><span class="ymp-btn-page-play ymp-media-cd2c0c4934993e036385ed158d0617c4"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><em><a class="wiki_link_ext" href="http://home.comcast.net/~teamouse/Transformation.mp3" rel="nofollow">Transformation</a></em> </span></span> </span> by <a class="wiki_link_ext" href="http://home.comcast.net/%7Eteamouse/" rel="nofollow">Herman Miller</a></li><li><span class="ymp-btn-page-play ymp-media-c31e19054d7ac007c7b9b339babdd228"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><em><a class="wiki_link_ext" href="http://www.emcollective.org/chris/items/17tet/17waltz.mp3" rel="nofollow">Waltz</a></em> </span></span> </span> by Christopher Bailey</li><li><span class="ymp-btn-page-play ymp-media-817b931db5b9d03733d0439eb4c5b365"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><em><a class="wiki_link_ext" href="http://www.emcollective.org/chris/items/17Chorus/17tppp4_lostfound.mp3" rel="nofollow">Lostfound</a></em> </span></span> </span> by Christopher Bailey</li><li>excerpt from <span class="ymp-btn-page-play ymp-media-2de29bc81b3c87ba3015583ebe32228c"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><em><a class="wiki_link_ext" href="http://music.columbia.edu/~chris/sounds/balladei_exc.mp3" rel="nofollow">Balladei</a></em> </span></span> </span> (in 17, 29 and 12) by <a class="wiki_link_ext" href="http://music.columbia.edu/%7Echris/" rel="nofollow">Christopher Bailey</a> , CD available <a class="wiki_link_ext" href="http://www.amazon.com/Christopher-Bailey-Shiau-Uen-Jacob-Rhodebeck/dp/B000TDZSAU/ref=sr_1_19/105-0183009-3913216?ie=UTF8&amp;s=music&amp;qid=1184598550&amp;sr=1-19" rel="nofollow">here</a> .</li><li><span class="ymp-btn-page-play ymp-media-60b300d674b6179dec2e49769bcd92d2"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><em><a class="wiki_link_ext" href="http://www.h-pi.com/mp3/17ET.mp3" rel="nofollow">Two-Part Invention in 17ET</a></em> </span></span></span> by Aaron Andrew Hunt</li><li><em><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/McGowan/MSND-Ovtr.mp3" rel="nofollow">Overture to A Midsummer Night's Dream</a></em> by <a class="wiki_link_ext" href="http://azuma-asobi.com/" rel="nofollow">Rick McGowan</a></li><li><em><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/McGowan/FairyLullaby-1.mp3" rel="nofollow">Fairy Lullaby from A Midsummer Night's Dream</a></em> by <a class="wiki_link_ext" href="http://azuma-asobi.com/" rel="nofollow">Rick McGowan</a></li><li><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><em><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Igs/City%20Of%20The%20Asleep%20-%2017-A%20Calamitous%20Simultaneity.mp3" rel="nofollow">A Calamitous Simultaneity</a></em> </span> by Igliashon Jones (17edo and 22edo)</li><li><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><em><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Igs/First%20Impressions.mp3" rel="nofollow">First Impressions</a></em> </span> by Igliashon Jones</li><li><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Igs/I%20Insist.mp3" rel="nofollow" target="_blank">I Insist</a> by Igliashon Jones</li><li><em><a class="wiki_link_ext" href="http://archive.org/download/EtudeNo1For2PianosIn17EqualTemperament/EtudeForTwoPianosIn17edo.mp3" rel="nofollow">Etude no1 for 2 Pianos in 17 Equal Temperament</a></em> and <em><a class="wiki_link_ext" href="http://archive.org/download/EtudeNo2For2PianosIn17EqualTemperament/EtudeNo2ForTwoPianosIn17edo.mp3" rel="nofollow">Etude no2 for 2 Pianos in 17 Equal Temperament</a></em> Jon Lyle Smith</li><li>A number of compositions from <a class="wiki_link_ext" href="http://www.archive.org/details/seventeenTPP_01" rel="nofollow">seventeen-tone piano project phase I</a> , <a class="wiki_link" href="/SeventeenTPPPhaseTwo">seventeen-tone piano project phase II</a>, <a class="wiki_link" href="/SeventeenTPPPhaseThree">seventeen-tone piano project phase III</a>.</li><li><a class="wiki_link_ext" href="http://www.archive.org/search.php?query=subject%3A%2217-edo%22" rel="nofollow">17edo</a> - 17edo-tagged compositions on www.archive.org</li><li><a class="wiki_link_ext" href="http://soundclick.com/share?songid=8839072" rel="nofollow">sing a blue</a> by Andrew Heathwaite (composed 2008, recorded 2010). This and the other pieces below by Andrew for cümbüş, steel tubes &amp; voice.</li><li><a class="wiki_link_ext" href="http://soundclick.com/share?songid=8839073" rel="nofollow">stringfinger it everybean</a> by Andrew Heathwaite (composed 2008, recorded 2010).</li><li><a class="wiki_link_ext" href="http://soundclick.com/share?songid=8839069" rel="nofollow">cat feet belly</a> by Andrew Heathwaite (composed 2008, recorded 2010).</li><li><span class="ymp-btn-page-play ymp-media-c1117aea0d7479a1907922962588a201"><span class="ywp-page-play-pause ywp-page-video ywp-link-hover"><span class="ywp-page-play-pause ywp-page-video ywp-link-hover ywp-page-img-link"><em><a class="wiki_link_ext" href="http://www.youtube.com/watch?v=a9N_T6LNDaE" rel="nofollow">17 Tone Jam</a></em> </span></span></span> by Marmalade Man</li><li><a class="wiki_link_ext" href="http://www.youtube.com/results?search_query=17edo&amp;search=tag" rel="nofollow">youtube videos tagged with 17edo</a></li><li><a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=784" rel="nofollow" target="_blank">On the Shores of the Dead Sea blog</a> <span class="ymp-btn-page-play ymp-media-58c0d564107bea8b718066b4a846e9a4"><span class="ywp-page-play-pause ywp-page-video ywp-link-hover"><span class="ywp-page-play-pause ywp-page-video ywp-link-hover ywp-page-img-link"><em><a class="wiki_link_ext" href="http://www.youtube.com/watch?v=D39MVFhb0Ho" rel="nofollow">video of On the Shores of the Dead Sea</a></em> </span></span> </span> by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a></li><li><a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=466" rel="nofollow" target="_blank">Only in Disneyland 17 blog</a> edo guitar solo <span class="ymp-btn-page-play ymp-media-ed57956200d2220e2dd400299c6c9d82"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><em><a class="wiki_link_ext" href="http://micro.soonlabel.com/17-ET/daily20110205-17et-disneyland.mp3" rel="nofollow">play Only in Disneyland</a></em> </span></span> </span> by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a></li><li><a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=460" rel="nofollow" target="_blank">17 Reasons I Hate the Blues blog</a> <span class="ymp-btn-page-play ymp-media-b9bb77ee97249899bce1c2e34b7ca029"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><em><a class="wiki_link_ext" href="http://micro.soonlabel.com/17-ET/daily20110125b-17-reasons-I-hate-the-blues.mp3" rel="nofollow">play 17 Reasons I Hate the Blues</a></em> </span></span> </span> by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a></li><li><a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=422" rel="nofollow" target="_blank">Klingon Opera Overture blog</a> <span class="ymp-btn-page-play ymp-media-1270ddd333612c93cd386aaa93b59aba"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><em><a class="wiki_link_ext" href="http://micro.soonlabel.com/17-ET/daily20110109-albino-17et.mp3" rel="nofollow">play Klingon Opera Overture</a></em> </span></span> </span> by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a></li><li><a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=298" rel="nofollow" target="_blank">Seventeen Selfless Notes blog</a> <span class="ymp-btn-page-play ymp-media-835371d8b0e3022bd14b58e3c0a6175a"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><em><a class="wiki_link_ext" href="http://micro.soonlabel.com/17-ET/if20101028selfless.mp3" rel="nofollow">play Seventeen Selfless Notes</a></em> </span></span> </span> by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a></li><li><a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=76" rel="nofollow" target="_blank">17ET Jazz blog</a> <span class="ymp-btn-page-play ymp-media-b4292082727ce51de4e72ce8e860e140"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><em><a class="wiki_link_ext" href="http://micro.soonlabel.com/17-ET/60x60-4001-1-ver2.mp3" rel="nofollow">play 17et Jazz</a></em> </span></span></span> by<a class="wiki_link" href="/Chris%20Vaisvil"> Chris Vaisvil</a> (60 x 60 winner)</li><li><a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=742" rel="nofollow">17 Pink Tuxedos blog</a> <span class="ymp-btn-page-play ymp-media-20284c23c4ce5614c44285891a72b2b9"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><em><a class="wiki_link_ext" href="http://micro.soonlabel.com/17-ET/daily20110416-17_pink-tuxes.mp3" rel="nofollow">play 17 Pink Tuxedos</a></em> </span></span></span> by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a></li><li><a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=706" rel="nofollow">Devil in the Deep Blue Sea blog</a> <span class="ymp-btn-page-play ymp-media-2b49237889b140316b82293bc4e5743c"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><em><a class="wiki_link_ext" href="http://micro.soonlabel.com/17-ET/daily20110401-17-2-devil_in_the_deep_blue_sea.mp3" rel="nofollow">play Devil in the Deep Blue sea</a></em> </span></span></span> blues collaboration between The Two Regs (vocals / lyrics) and Norm Harris (percussion) and Chris Vaisvil (17 note per octave electric guitar and fretless bass).</li><li><a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=585" rel="nofollow">Seventeen Years in the Sixties blog</a> <span class="ymp-btn-page-play ymp-media-e59982cb3a388488ca0ccb733e7439e7"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><em><a class="wiki_link_ext" href="http://micro.soonlabel.com/17-ET/daily20110318-seventeen-years-in-the-sixties.mp3" rel="nofollow">play Seventeen Years in the Sixties</a></em> </span></span></span> by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a></li><li><a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=699" rel="nofollow" target="_blank">CT Scan blog</a> <span class="ymp-btn-page-play ymp-media-6c6c5ec192c22569d28c8dd09467c623"><span class="ywp-page-play-pause ywp-page-video ywp-link-hover"><span class="ywp-page-play-pause ywp-page-video ywp-link-hover ywp-page-img-link"><em><a class="wiki_link_ext" href="http://www.youtube.com/watch?v=ZEEuytYwtbo" rel="nofollow">play video CT Scan</a></em> </span></span></span> by Chris Vaisvil</li><li><a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=470" rel="nofollow">Fish and a Grenade blog</a> <span class="ymp-btn-page-play ymp-media-d882886a0b66279c7c3aa180aacb7339"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><em><a class="wiki_link_ext" href="http://micro.soonlabel.com/17-ET/daily20110208-17-a-fish-and-a-grenade.mp3" rel="nofollow">play Fish and a Grenade</a></em> </span></span></span> (parental advisory language) by Chris Vaisvil</li><li><a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=550" rel="nofollow" target="_blank">Seventeen Unsteady Hands blog</a> <span class="ymp-btn-page-play ymp-media-0623ec5592a422ce10eddb210d094b60"><span class="ywp-page-play-pause ywp-page-video ywp-link-hover"><span class="ywp-page-play-pause ywp-page-video ywp-link-hover ywp-page-img-link"><em><a class="wiki_link_ext" href="http://www.youtube.com/watch?v=rAKHCqBNhfc" rel="nofollow">play video of performance of Seventeen Unsteady Hands</a></em> </span></span></span> by Chris Vaisvil</li><li><a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=38" rel="nofollow">The Pond blog</a> by Chris Vaisvil and <span class="ymp-btn-page-play ymp-media-ad53e2e57d0cedd582013ae5cdd29164"><span class="ywp-page-play-pause ywp-page-video ywp-link-hover"><span class="ywp-page-play-pause ywp-page-video ywp-link-hover ywp-page-img-link"><em><a class="wiki_link_ext" href="http://www.youtube.com/watch?v=25sC3_uheyA" rel="nofollow" target="_blank">video version of The Pond with Japanese Garden </a></em> </span></span></span></li><li><span class="ymp-btn-page-play ymp-media-ad53e2e57d0cedd582013ae5cdd29164"><a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=305" rel="nofollow" target="_blank">Graveyard blog</a> </span><span class="ymp-btn-page-play ymp-media-7a8cb8e49c18c67a2ea8b60d80c25b21"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><em><a class="wiki_link_ext" href="http://micro.soonlabel.com/17-ET/if20101028-graveyard.mp3" rel="nofollow">play Graveyard</a></em> </span></span> </span> by Chris Vaisvil</li><li><span class="ymp-btn-page-play ymp-media-e13a9b281483c4b0a10ba321bb7cc2b4"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><em><a class="wiki_link_ext" href="http://micro.soonlabel.com/17-ET/daily20110713_q49_17_brass_voice_choirs.mp3" rel="nofollow">For Brass and Voice Choirs in 17 edo</a></em> </span></span></span> by <a class="wiki_link_ext" href="http://chrisvaisvil.com/" rel="nofollow" target="_blank">Chris Vaisvil </a> <a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=1039" rel="nofollow" target="_blank">more on the composition</a></li><li><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><em><a class="wiki_link_ext" href="http://micro.soonlabel.com/17-ET/daily20111015-fungi.mp3" rel="nofollow">And I Became One With My Per Fungi</a></em> </span></span> by <a class="wiki_link_ext" href="http://chrisvaisvil.com/" rel="nofollow" target="_blank">Chris Vaisvil</a> =&gt; <a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=1439" rel="nofollow" target="_blank">more on composition</a></li><li><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><em><a class="wiki_link_ext" href="http://micro.soonlabel.com/17-ET/20111014-STE-002-counter-intuitive.mp3" rel="nofollow">counterintuitive (17 edo guitar solo)</a></em> </span></span> by <a class="wiki_link_ext" href="http://www.chrisvaisvil.com/" rel="nofollow" target="_blank">Chris Vaisvil</a> =&gt; <a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=1427" rel="nofollow" target="_blank">more on composition</a></li><li><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Sanchez/No_Love_by_Gregory_Sanchez_1_on_SoundCloud___Hear_the_world_s_sounds.mp3" rel="nofollow">No Love</a> by <a class="wiki_link_ext" href="https://soundcloud.com/gregory-sanchez-2/no-love" rel="nofollow">Gregory Sanchez</a></li><li><a class="wiki_link_ext" href="http://webzoom.freewebs.com/ralphjarzombek/micro7(17tet).mp3" rel="nofollow">Micro7</a> by Ralph Jarzombek</li><li><a class="wiki_link_ext" href="http://micro.soonlabel.com/17-ET/20161125_linn_speactral_17.MP3" rel="nofollow">Flying Into O'Hare</a> by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a></li><li><a class="wiki_link_ext" href="https://drive.google.com/drive/folders/0BwsXD8q2VCYUM0tRdDNhVzNhcHM" rel="nofollow" target="_blank">Helas, pitié</a> by Alex Ness (in 17edo with stretched octaves)</li></ul><br />
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| <!-- ws:start:WikiTextHeadingRule:22:&lt;h1&gt; --><h1 id="toc10"><a name="Instruments"></a><!-- ws:end:WikiTextHeadingRule:22 -->Instruments</h1>
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| <ul><li><!-- ws:start:WikiTextHeadingRule:24:&lt;h4&gt; --><h4 id="toc11"><a name="Instruments---Guitar Heptadecatonic from Peruvian - Charles Loli and Antonio Huamani"></a><!-- ws:end:WikiTextHeadingRule:24 --><strong><a class="wiki_link_ext" href="http://www.microtonalismo.com/proyecto-xvii" rel="nofollow">Guitar Heptadecatonic from Peruvian - Charles Loli and Antonio Huamani</a></strong></h4>
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| <!-- ws:start:WikiTextHeadingRule:26:&lt;h4&gt; --><h4 id="toc12"><!-- ws:end:WikiTextHeadingRule:26 --><!-- ws:start:WikiTextRemoteImageRule:990:&lt;img src=&quot;http://sphotos.ak.fbcdn.net/hphotos-ak-snc4/hs883.snc4/71639_167001659983806_100000219181856_601995_1526184_n.jpg&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 249px; width: 706px;&quot; /&gt; --><img src="http://sphotos.ak.fbcdn.net/hphotos-ak-snc4/hs883.snc4/71639_167001659983806_100000219181856_601995_1526184_n.jpg" alt="external image 71639_167001659983806_100000219181856_601995_1526184_n.jpg" title="external image 71639_167001659983806_100000219181856_601995_1526184_n.jpg" style="height: 249px; width: 706px;" /><!-- ws:end:WikiTextRemoteImageRule:990 --></h4>
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| <ul><li><!-- ws:start:WikiTextHeadingRule:28:&lt;h4&gt; --><h4 id="toc13"><a name="Instruments---Bass Heptadecatonic from Peruvian - Charles Loli and Antonio Huamani"></a><!-- ws:end:WikiTextHeadingRule:28 --><strong><a class="wiki_link_ext" href="http://www.microtonalismo.com/proyecto-xvii" rel="nofollow">Bass Heptadecatonic from Peruvian - Charles Loli and Antonio Huamani</a></strong></h4>
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| <!-- ws:start:WikiTextHeadingRule:30:&lt;h4&gt; --><h4 id="toc14"><!-- ws:end:WikiTextHeadingRule:30 --><!-- ws:start:WikiTextRemoteImageRule:991:&lt;img src=&quot;http://sphotos.ak.fbcdn.net/hphotos-ak-ash2/hs382.ash2/66019_167001006650538_100000219181856_601987_48585_n.jpg&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 256px; width: 689px;&quot; /&gt; --><img src="http://sphotos.ak.fbcdn.net/hphotos-ak-ash2/hs382.ash2/66019_167001006650538_100000219181856_601987_48585_n.jpg" alt="external image 66019_167001006650538_100000219181856_601987_48585_n.jpg" title="external image 66019_167001006650538_100000219181856_601987_48585_n.jpg" style="height: 256px; width: 689px;" /><!-- ws:end:WikiTextRemoteImageRule:991 --></h4>
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| <ul><li><a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=436" rel="nofollow" target="_blank">17 note per octave conversion from a &quot;standard&quot; stratocastor copy</a> - conversion by Brad Smith</li></ul><br />
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