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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
Line 618: Line 618:
| [[17496/16807]]
| [[17496/16807]]
| {{Monzo| 3 7 0 -5 }}
| {{Monzo| 3 7 0 -5 }}
| 69.555
| 69.56
| Quinru
| Quinru
| Bleu comma
| Bleu comma
Line 625: Line 625:
| [[19683/19208]]
| [[19683/19208]]
| {{Monzo| -3 9 0 -4 }}
| {{Monzo| -3 9 0 -4 }}
| 42.291
| 42.29
| Laquadru
| Laquadru
| Skwares comma
| Skwares comma
Line 632: Line 632:
| <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 639: 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 646: 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 653: 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 660: 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 667: 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
Line 674: Line 674:
| [[40/39]]
| [[40/39]]
| {{Monzo| 3 -1 1 0 0 -1 }}
| {{Monzo| 3 -1 1 0 0 -1 }}
| 43.831
| 43.83
| Thuyo
| Thuyo
| Unintendo comma
| Unintendo comma
Line 681: Line 681:
| [[65/64]]
| [[65/64]]
| {{Monzo| -6 0 1 0 0 1 }}
| {{Monzo| -6 0 1 0 0 1 }}
| 26.841
| 26.84
| Thoyo
| Thoyo
| Wilsorma
| Wilsorma
Line 688: Line 688:
| [[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 695: 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 702: 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 709: 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 716: 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 723: 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 730: 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 737: 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
Line 744: Line 744:
| [[162/161]]
| [[162/161]]
| {{Monzo| 1 4 0 -1 0 0 0 0 -1 }}
| {{Monzo| 1 4 0 -1 0 0 0 0 -1 }}
| 10.720
| 10.72
| Twethuru
| Twethuru
| Minor kirnbergerisma
| Minor kirnbergerisma
Line 751: Line 751:
| [[208/207]]
| [[208/207]]
| {{Monzo| 4 -2 0 0 0 1 0 0 -1 }}
| {{Monzo| 4 -2 0 0 0 1 0 0 -1 }}
| 8.3433
| 8.34
| Twethutho
| Twethutho
| Vicetone comma
| Vicetone comma
Line 758: Line 758:
| [[253/252]]
| [[253/252]]
| {{Monzo| -2 -2 0 -1 1 0 0 0 1 }}
| {{Monzo| -2 -2 0 -1 1 0 0 0 1 }}
| 6.8564
| 6.86
| Twetholoru
| Twetholoru
| Middle neutravicema
| Middle neutravicema
Line 765: Line 765:
| [[529/528]]
| [[529/528]]
| {{Monzo| -4 -1 0 0 -1 0 0 0 2 }}
| {{Monzo| -4 -1 0 0 -1 0 0 0 2 }}
| 3.2758
| 3.28
| Bitwetho-alu
| Bitwetho-alu
| Preziosisma
| Preziosisma
Line 772: Line 772:
| [[736/729]]
| [[736/729]]
| {{Monzo| 5 -6 0 0 0 0 0 0 1 }}
| {{Monzo| 5 -6 0 0 0 0 0 0 1 }}
| 16.544
| 16.54
| Satwetho
| Satwetho
| 23-limit Tenney/Cage comma (HEJI)
| 23-limit Tenney/Cage comma (HEJI)
Line 860: 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 882: 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"