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17edo: Difference between revisions

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=== Commas ===
=== Commas ===
17et [[tempering out|tempers out]] the following [[comma]]s. (Note: This assumes [[patent val]] {{val| 17 27 39 48 59 63 69 72 77}}, cent values ​​rounded to 5 digits.)
17et [[tempering out|tempers out]] the following [[comma]]s. (Note: This assumes [[patent val]] {{val| 17 27 39 48 59 63 69 72 77}}, cent values ​​rounded to 1/100 of a cent.)


{| class="commatable wikitable center-all left-3 right-4 left-6"
{| class="commatable wikitable center-all left-3 right-4 left-6"
Line 569: Line 569:
| <abbr title="134217728/129140163">(18 digits)</abbr>
| <abbr title="134217728/129140163">(18 digits)</abbr>
| {{Monzo| 27 -17 }}
| {{Monzo| 27 -17 }}
| 66.765
| 66.76
| Sasawa
| Sasawa
| [[Gothic comma]]
| [[Gothic comma]]
Line 576: Line 576:
| [[25/24]]
| [[25/24]]
| {{Monzo| -3 -1 2 }}
| {{Monzo| -3 -1 2 }}
| 70.762
| 70.76
| Yoyo
| Yoyo
| Dicot comma
| Dicot comma
Line 583: Line 583:
| [[32805/32768]]
| [[32805/32768]]
| {{Monzo| -15 8 1 }}
| {{Monzo| -15 8 1 }}
| 1.9537
| 1.95
| Layo
| Layo
| Schisma
| Schisma
Line 590: Line 590:
| [[64/63]]
| [[64/63]]
| {{Monzo| 6 -2 0 -1 }}
| {{Monzo| 6 -2 0 -1 }}
| 27.264
| 27.26
| Ru
| Ru
| Septimal comma
| Septimal comma
Line 597: Line 597:
| [[525/512]]
| [[525/512]]
| {{Monzo| -9 1 2 1 }}
| {{Monzo| -9 1 2 1 }}
| 43.408
| 43.41
| Lazoyoyo
| Lazoyoyo
| Avicennma
| Avicennma
Line 604: Line 604:
| [[245/243]]
| [[245/243]]
| {{Monzo| 0 -5 1 2 }}
| {{Monzo| 0 -5 1 2 }}
| 14.191
| 14.19
| Zozoyo
| Zozoyo
| Sensamagic comma
| Sensamagic comma
Line 611: Line 611:
| [[1728/1715]]
| [[1728/1715]]
| {{Monzo| 6 3 -1 -3 }}
| {{Monzo| 6 3 -1 -3 }}
| 13.074
| 13.07
| Triru-agu
| Triru-agu
| Orwellisma
| Orwellisma
|-
| 7
| [[17496/16807]]
| {{Monzo| 3 7 0 -5 }}
| 69.56
| Quinru
| Bleu comma
|-
| 7
| [[19683/19208]]
| {{Monzo| -3 9 0 -4 }}
| 42.29
| Laquadru
| Skwares comma
|-
|-
| 7
| 7
| <abbr title="420175/419904">(12 digits)</abbr>
| <abbr title="420175/419904">(12 digits)</abbr>
| {{Monzo| -6 -8 2 5 }}
| {{Monzo| -6 -8 2 5 }}
| 1.1170
| 1.12
| Quinzo-ayoyo
| Quinzo-ayoyo
| [[Wizma]]
| [[Wizma]]
Line 625: Line 639:
| [[45/44]]
| [[45/44]]
| {{Monzo| -2 2 1 0 -1 }}
| {{Monzo| -2 2 1 0 -1 }}
| 38.906
| 38.91
| Luyo
| Luyo
| Cake comma
| Cake comma
Line 632: Line 646:
| [[99/98]]
| [[99/98]]
| {{Monzo| -1 2 0 -2 1 }}
| {{Monzo| -1 2 0 -2 1 }}
| 17.576
| 17.58
| Loruru
| Loruru
| Mothwellsma
| Mothwellsma
Line 639: Line 653:
| [[896/891]]
| [[896/891]]
| {{Monzo| 7 -4 0 1 -1 }}
| {{Monzo| 7 -4 0 1 -1 }}
| 9.6880
| 9.69
| Saluzo
| Saluzo
| Pentacircle comma
| Pentacircle comma
Line 646: Line 660:
| [[243/242]]
| [[243/242]]
| {{Monzo| -1 5 0 0 -2 }}
| {{Monzo| -1 5 0 0 -2 }}
| 7.1391
| 7.14
| Lulu
| Lulu
| Rastma, neutral thirds comma
| Rastma, neutral thirds comma
Line 653: Line 667:
| [[385/384]]
| [[385/384]]
| {{Monzo| -7 -1 1 1 1 }}
| {{Monzo| -7 -1 1 1 1 }}
| 4.5026
| 4.50
| Lozoyo
| Lozoyo
| Keenanisma
| Keenanisma
|-
| 13
| [[40/39]]
| {{Monzo| 3 -1 1 0 0 -1 }}
| 43.83
| Thuyo
| Unintendo comma
|-
| 13
| [[65/64]]
| {{Monzo| -6 0 1 0 0 1 }}
| 26.84
| Thoyo
| Wilsorma
|-
|-
| 13
| 13
| [[78/77]]
| [[78/77]]
| {{Monzo| 1 1 0 -1 -1 1 }}
| {{Monzo| 1 1 0 -1 -1 1 }}
| 22.339
| 22.34
| Tholuru
| Tholuru
| Negustma
| Negustma
Line 667: Line 695:
| [[144/143]]
| [[144/143]]
| {{Monzo| 4 2 0 0 -1 -1 }}
| {{Monzo| 4 2 0 0 -1 -1 }}
| 12.064
| 12.06
| Thulu
| Thulu
| Grossma
| Grossma
Line 674: Line 702:
| [[169/168]]
| [[169/168]]
| {{Monzo| -3 -1 0 -1 0 2 }}
| {{Monzo| -3 -1 0 -1 0 2 }}
| 10.274
| 10.27
| Thothoru
| Thothoru
| Buzurgisma, dhanvantarisma
| Buzurgisma, dhanvantarisma
Line 681: Line 709:
| [[352/351]]
| [[352/351]]
| [5 -3 0 0 1 -1⟩
| [5 -3 0 0 1 -1⟩
| 4.9253
| 4.93
| Thulo
| Thulo
| Major minthma
| Major minthma
Line 688: Line 716:
| [[364/363]]
| [[364/363]]
| {{Monzo| 2 -1 0 1 -2 1 }}
| {{Monzo| 2 -1 0 1 -2 1 }}
| 4.7627
| 4.76
| Tholuluzo
| Tholuluzo
| Minor minthma
| Minor minthma
Line 695: Line 723:
| [[512/507]]
| [[512/507]]
| {{Monzo| 9 -1 0 0 0 -2 }}
| {{Monzo| 9 -1 0 0 0 -2 }}
| 16.990
| 16.99
| Thuthu
| Thuthu
| Tridecimal neutral thirds comma
| Tridecimal neutral thirds comma
Line 702: Line 730:
| [[1352/1331]]
| [[1352/1331]]
| {{Monzo| 3 0 0 0 -3 2 }}
| {{Monzo| 3 0 0 0 -3 2 }}
| 27.101
| 27.10
| Bithotrilu
| Bithotrilu
| Lovecraft comma
| Lovecraft comma
Line 709: Line 737:
| [[2197/2187]]
| [[2197/2187]]
| {{Monzo| 0 -7 0 0 0 3 }}
| {{Monzo| 0 -7 0 0 0 3 }}
| 7.8980
| 7.90
| Satritho
| Satritho
| Threedie
| Threedie
|-
| 23
| [[162/161]]
| {{Monzo| 1 4 0 -1 0 0 0 0 -1 }}
| 10.72
| Twethuru
| Minor kirnbergerisma
|-
|-
| 23
| 23
| [[208/207]]
| [[208/207]]
| [4 -2 0 0 0 1 0 0 -1⟩
| {{Monzo| 4 -2 0 0 0 1 0 0 -1 }}
| 8.343
| 8.34
| Twethutho 2nd
| Twethutho
| Vicetone comma
| 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" />
<references group="note" />
Note that despite their relatively large size, the 17-comma, the avicennma and the chromatic semitone are all tempered out by the patent val, the latter two due to 17edo's inaccurate prime 5.
Note that due to the inaccurate prime 5, the rather large commas [[25/24]], [[525/512]], [[45/44]], and [[40/39]] are all tempered out by 17edo's patent val.


=== Rank-2 temperaments ===
=== Rank-2 temperaments ===
Line 804: Line 860:


* diatonic ([[leapfrog]]/[[archy]]) [[5L&nbsp;2s]] 3 3 3 1 3 3 1 (10\17, 1\1)
* diatonic ([[leapfrog]]/[[archy]]) [[5L&nbsp;2s]] 3 3 3 1 3 3 1 (10\17, 1\1)
* [[neutrominant]] [[3L&nbsp;4s]] 3 2 3 2 3 2 2 (5\17, 1\1)
* [[neutrominant]] [[3L&nbsp;4s]] 3 2 3 2 3 2 2 (5\17, 1\1) (''dedicated article: [[17edo neutral scale]]'')
* [[neutrominant]] [[7L&nbsp;3s]] 2 2 2 1 2 2 1 2 2 1 (5\17, 1\1)
* [[neutrominant]] [[7L&nbsp;3s]] 2 2 2 1 2 2 1 2 2 1 (5\17, 1\1)
* [[squares]] [[3L&nbsp;5s]] 1 1 4 1 4 1 4 (6\17, 1\1)
* [[squares]] [[3L&nbsp;5s]] 1 1 4 1 4 1 4 (6\17, 1\1)
Line 826: Line 882:


[[File:17edo soprano ukulele with 3D printed fretboard.jpg|frameless|640x640px]]
[[File:17edo soprano ukulele with 3D printed fretboard.jpg|frameless|640x640px]]
Keyboards have also been built for 17edo &mdash; see [[Stephen Weigel]]'s [https://www.youtube.com/watch?v=2B14mttkavA ''Take This Stone (17-TET microtonal cover)''] (2025).


=== Keyboards ===
=== Keyboards ===
[[Lumatone mapping for 17edo|Lumatone mappings for 17edo]] are available.
[[Lumatone mapping for 17edo|Lumatone mappings for 17edo]] are available.
The Striso Board can be tuned in many ways, but as it has 17 notes per octave and is organised in a circle of fifths based layout, it works particularly well with 17edo, letting you play far wider stretches of notes than a standard keyboard.
[[File:Strisoboard_piano2a_s.jpg|frameless]]
It is possible to rebuild some standard MIDI keyboards to have 17 note per octave by combining parts from multiple keyboards, as with the finished product shown in the following videos by [[Stephen Weigel]] and [[Chris Vaisvil]]:
* [https://www.youtube.com/watch?v=2B14mttkavA ''Take This Stone (17-TET microtonal cover)''] (2025)
* [https://www.youtube.com/watch?v=nboggmtayk0 ''DIY microtonal piano - 17 notes per octave''] (2026)


== Music ==
== Music ==
Retrieved from "https://en.xen.wiki/w/17edo"