17edo: Difference between revisions
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'''17-EDO''' divides the octave in 17 equal steps, each 70.588 [[cent | '''17 tone equal temperament''', or '''17-EDO''', divides the octave in 17 equal steps, each 70.588 [[cent]]s in size. It is the seventh [[prime_numbers|prime]] [[EDO]], following [[13edo]] and coming before [[19edo]]. | ||
==Theory== | ==Theory== | ||
An introduction to 17-EDO theory, through the eyes of the [[ | An introduction to 17-EDO theory, through the eyes of the [[SeventeenTonePianoProject]]: [[SeventeenTheory]]. | ||
Another introduction into 17-EDO theory: [http://xenharmony.wikispaces.com/space/showimage/17puzzle.pdf The 17-tone Puzzle] by George Secor. | Another introduction into 17-EDO theory: [http://xenharmony.wikispaces.com/space/showimage/17puzzle.pdf The 17-tone Puzzle] {{dead link}} by George Secor. | ||
[[ | [[17edo Solfege]]. [[17edo tetrachords]]. [http://microtonalismo.com/proyecto-xvii Proyect 17-Perú] {{forbidden}} | ||
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; [[ | 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]]. | ||
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 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. | ||
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 | Instead, the tonic chords of 17-EDO could be considered to be the tetrad 6:7:8:9 and its utonal inversion, the former of which is a subminor chord with added fourth, and the latter a supermajor chord with added second (resembling the [https://en.wikipedia.org/wiki/Mu_chord mu chord] of Steely Dan fame). These are realized in 17-EDO as 0-4-7-10 and 0-3-6-10, respectively. Both of these have distinct moods, and are stable and consonant, if somewhat more sophisticated than their classic 5-limit counterparts. To this group we could also add the 0-3-7-10 (which is a sus4 with added second, or sus2 with added fourth). These three chords comprise the three ways to divide the 17-EDO perfect fifth into two whole tones and one subminor third. Chromatic alterations of them also exist, for example, the 0-3-7-10 chord may be altered to 0-2-7-10 (which approximates 12:13:16:18) or 0-3-8-10 (which approximates 8:9:11:12). The 0-3-8-10 chord is impressive-sounding, resembling a sus4 but with even more tension; it resolves quite nicely to 0-3-6-10. | ||
=Intervals= | =Intervals= | ||
| Line 31: | Line 29: | ||
! | Cents | ! | Cents | ||
! | Names of Intervals | ! | Names of Intervals | ||
! colspan="3" | [[Ups_and_Downs_Notation|ups and downs | ! colspan="3" | [[Ups_and_Downs_Notation|ups and downs notation]] | ||
! | Approximate Ratios* | ! | Approximate Ratios* | ||
! | Temperament(s)generated | ! | Temperament(s)generated | ||
| Line 50: | Line 48: | ||
| style="text-align:center;" | m2 | | style="text-align:center;" | m2 | ||
| style="text-align:center;" | Db | | style="text-align:center;" | Db | ||
| style="text-align:center;" | [[ | | style="text-align:center;" | [[25/24]], [[26/25]], [[33/32]] | ||
| | | | | | ||
|- | |- | ||
| Line 59: | Line 57: | ||
| style="text-align:center;" | ~2 | | style="text-align:center;" | ~2 | ||
| style="text-align:center;" | Dv | | style="text-align:center;" | Dv | ||
| style="text-align:center;" | [[ | | style="text-align:center;" | [[13/12]], [[12/11]], [[14/13]] | ||
| | [[ | | | [[Bleu]] | ||
|- | |- | ||
| | 3 | | | 3 | ||
| Line 68: | Line 66: | ||
| style="text-align:center;" | M2 | | style="text-align:center;" | M2 | ||
| style="text-align:center;" | D | | style="text-align:center;" | D | ||
| style="text-align:center;" | [[ | | style="text-align:center;" | [[9/8]], [[25/22]], [[8/7]], [[28/25]] | ||
| | [[ | | | [[Machine]] | ||
|- | |- | ||
| | 4 | | | 4 | ||
| Line 77: | Line 75: | ||
| style="text-align:center;" | m3 | | style="text-align:center;" | m3 | ||
| style="text-align:center;" | Eb | | style="text-align:center;" | Eb | ||
| style="text-align:center;" | [[ | | style="text-align:center;" | [[13/11]], [[7/6]] | ||
| | [[ | | | [[Huxley]] | ||
|- | |- | ||
| | 5 | | | 5 | ||
| Line 87: | Line 85: | ||
| style="text-align:center;" | ~3 | | style="text-align:center;" | ~3 | ||
| style="text-align:center;" | Ev | | style="text-align:center;" | Ev | ||
| style="text-align:center;" | [[ | | style="text-align:center;" | [[11/9]], [[16/13]] | ||
| | [[ | | | [[Maqamic]]/[[Hemif]] | ||
|- | |- | ||
| | 6 | | | 6 | ||
| Line 96: | Line 94: | ||
| style="text-align:center;" | M3 | | style="text-align:center;" | M3 | ||
| style="text-align:center;" | E | | style="text-align:center;" | E | ||
| style="text-align:center;" | [[ | | style="text-align:center;" | [[32/25]], [[33/26]], [[9/7]], [[14/11]] | ||
| | [[ | | | [[Skwares]] | ||
|- | |- | ||
| | 7 | | | 7 | ||
| Line 105: | Line 103: | ||
| style="text-align:center;" | P4 | | style="text-align:center;" | P4 | ||
| style="text-align:center;" | F | | style="text-align:center;" | F | ||
| style="text-align:center;" | [[ | | style="text-align:center;" | [[4/3]] | ||
| | [[ | | | [[Supra]] | ||
|- | |- | ||
| | 8 | | | 8 | ||
| Line 115: | Line 113: | ||
| style="text-align:center;" | ^4, d5 | | style="text-align:center;" | ^4, d5 | ||
| style="text-align:center;" | F^, Gb | | style="text-align:center;" | F^, Gb | ||
| style="text-align:center;" | [[ | | style="text-align:center;" | [[11/8]], [[18/13]] | ||
| | [[ | | | [[Progress]] | ||
|- | |- | ||
| | 9 | | | 9 | ||
| Line 125: | Line 123: | ||
| style="text-align:center;" | A4, v5 | | style="text-align:center;" | A4, v5 | ||
| style="text-align:center;" | F#, Gv | | style="text-align:center;" | F#, Gv | ||
| style="text-align:center;" | [[ | | style="text-align:center;" | [[16/11]], [[13/9]], [[23/16]] | ||
| | Progress | | | Progress | ||
|- | |- | ||
| Line 134: | Line 132: | ||
| style="text-align:center;" | P5 | | style="text-align:center;" | P5 | ||
| style="text-align:center;" | G | | style="text-align:center;" | G | ||
| style="text-align:center;" | [[ | | style="text-align:center;" | [[3/2]] | ||
| | Supra | | | Supra | ||
|- | |- | ||
| Line 143: | Line 141: | ||
| style="text-align:center;" | m6 | | style="text-align:center;" | m6 | ||
| style="text-align:center;" | Ab | | style="text-align:center;" | Ab | ||
| style="text-align:center;" | 25/16, 14/9, [[ | | style="text-align:center;" | [[25/16]], [[14/9]], [[11/7]] | ||
| | Skwares | | | Skwares | ||
|- | |- | ||
| Line 153: | Line 151: | ||
| style="text-align:center;" | ~6 | | style="text-align:center;" | ~6 | ||
| style="text-align:center;" | Av | | style="text-align:center;" | Av | ||
| style="text-align:center;" | [[ | | style="text-align:center;" | [[13/8]], [[18/11]] | ||
| | Maqamic/hemif | | | Maqamic/hemif | ||
|- | |- | ||
| Line 162: | Line 160: | ||
| style="text-align:center;" | M6 | | style="text-align:center;" | M6 | ||
| style="text-align:center;" | A | | style="text-align:center;" | A | ||
| style="text-align:center;" | [[ | | style="text-align:center;" | [[17/10]], [[22/13]],[[12/7]] | ||
| | Huxley | | | Huxley | ||
|- | |- | ||
| Line 171: | Line 169: | ||
| style="text-align:center;" | m7 | | style="text-align:center;" | m7 | ||
| style="text-align:center;" | Bb | | style="text-align:center;" | Bb | ||
| style="text-align:center;" | [[ | | style="text-align:center;" | [[16/9]], [[7/4]], [[25/14]] | ||
| | Machine | | | Machine | ||
|- | |- | ||
| Line 181: | Line 179: | ||
| style="text-align:center;" | ~7 | | style="text-align:center;" | ~7 | ||
| style="text-align:center;" | Bv | | style="text-align:center;" | Bv | ||
| style="text-align:center;" | [[ | | style="text-align:center;" | [[11/6]], [[24/13]], [[13/7]] | ||
| | Bleu | | | Bleu | ||
|- | |- | ||
| Line 190: | Line 188: | ||
| style="text-align:center;" | M7 | | style="text-align:center;" | M7 | ||
| style="text-align:center;" | B | | style="text-align:center;" | B | ||
| style="text-align:center;" | 25/13, 48/25, 64/33 | | style="text-align:center;" | [[25/13]], [[48/25]], [[64/33]] | ||
| | | | | | ||
|- | |- | ||
| Line 199: | Line 197: | ||
| style="text-align:center;" | P8 | | style="text-align:center;" | P8 | ||
| style="text-align:center;" | C | | style="text-align:center;" | C | ||
| style="text-align:center;" | [[ | | style="text-align:center;" | [[2/1]] | ||
| | | | | | ||
|} | |} | ||
<nowiki>*</nowiki>Ratios based on treating 17edo as a 2.3.7.11.13.25 subgroup | <nowiki>*</nowiki>Ratios based on treating 17edo as a 2.3.7.11.13.25 subgroup | ||
Combining ups and downs notation with [[Kite' | Combining ups and downs notation with [[Kite's color notation]], qualities can be loosely associated with colors: | ||
{| class="wikitable" | {| class="wikitable" | ||
| Line 305: | Line 303: | ||
| | '''Error (abs., in [[cent|cents]])''' | | | '''Error (abs., in [[cent|cents]])''' | ||
|- | |- | ||
| style="text-align:center;" | [[ | | style="text-align:center;" | [[18/13]], [[13/9]] | ||
| style="text-align:center;" | 1.324 | | style="text-align:center;" | 1.324 | ||
|- | |- | ||
| style="text-align:center;" | [[ | | style="text-align:center;" | [[13/12]], [[24/13]] | ||
| style="text-align:center;" | 2.604 | | style="text-align:center;" | 2.604 | ||
|- | |- | ||
| style="text-align:center;" | [[ | | style="text-align:center;" | [[4/3]], [[3/2]] | ||
| style="text-align:center;" | 3.927 | | style="text-align:center;" | 3.927 | ||
|- | |- | ||
| style="text-align:center;" | [[ | | style="text-align:center;" | [[11/9]], [[18/11]] | ||
| style="text-align:center;" | 5.533 | | style="text-align:center;" | 5.533 | ||
|- | |- | ||
| style="text-align:center;" | [[ | | style="text-align:center;" | [[14/11]], [[11/7]] | ||
| style="text-align:center;" | 6.021 | | style="text-align:center;" | 6.021 | ||
|- | |- | ||
| style="text-align:center;" | [[ | | style="text-align:center;" | [[16/13]], [[13/8]] | ||
| style="text-align:center;" | 6.531 | | style="text-align:center;" | 6.531 | ||
|- | |- | ||
| style="text-align:center;" | [[ | | style="text-align:center;" | [[13/11]], [[22/13]] | ||
| style="text-align:center;" | 6.857 | | style="text-align:center;" | 6.857 | ||
|- | |- | ||
| style="text-align:center;" | [[ | | style="text-align:center;" | [[9/8]], [[16/9]] | ||
| style="text-align:center;" | 7.855 | | style="text-align:center;" | 7.855 | ||
|- | |- | ||
| style="text-align:center;" | [[ | | style="text-align:center;" | [[12/11]], [[11/6]] | ||
| style="text-align:center;" | 9.461 | | style="text-align:center;" | 9.461 | ||
|- | |- | ||
| style="text-align:center;" | [[ | | style="text-align:center;" | [[9/7]], [[14/9]] | ||
| style="text-align:center;" | 11.555 | | style="text-align:center;" | 11.555 | ||
|- | |- | ||
| style="text-align:center;" | [[ | | style="text-align:center;" | [[14/13]], [[13/7]] | ||
| style="text-align:center;" | 12.878 | | style="text-align:center;" | 12.878 | ||
|- | |- | ||
| style="text-align:center;" | [[ | | style="text-align:center;" | [[11/8]], [[16/11]] | ||
| style="text-align:center;" | 13.388 | | style="text-align:center;" | 13.388 | ||
|- | |- | ||
| style="text-align:center;" | [[ | | style="text-align:center;" | [[7/6]], [[12/7]] | ||
| style="text-align:center;" | 15.482 | | style="text-align:center;" | 15.482 | ||
|- | |- | ||
| style="text-align:center;" | [[ | | style="text-align:center;" | [[7/5]], [[10//7]] | ||
| style="text-align:center;" | 17.806 | | style="text-align:center;" | 17.806 | ||
|- | |- | ||
| style="text-align:center;" | [[ | | style="text-align:center;" | [[8/7]], [[7/4|] | ||
| style="text-align:center;" | 19.409 | | style="text-align:center;" | 19.409 | ||
|- | |- | ||
| style="text-align:center;" | [[ | | style="text-align:center;" | [[15/14]], [[28/15]] | ||
| style="text-align:center;" | 21.734 | | style="text-align:center;" | 21.734 | ||
|- | |- | ||
| style="text-align:center;" | [[ | | style="text-align:center;" | [[11/10]], [[20/11]] | ||
| style="text-align:center;" | 23.828 | | style="text-align:center;" | 23.828 | ||
|- | |- | ||
| style="text-align:center;" | [[ | | style="text-align:center;" | [[15/11]], [[22/15]] | ||
| style="text-align:center;" | 27.755 | | style="text-align:center;" | 27.755 | ||
|- | |- | ||
| style="text-align:center;" | [[ | | style="text-align:center;" | [[10/9]], [[9/5]] | ||
| style="text-align:center;" | 29.361 | | style="text-align:center;" | 29.361 | ||
|- | |- | ||
| style="text-align:center;" | [[ | | style="text-align:center;" | [[16/15]], [[15/8]] | ||
| style="text-align:center;" | 29.445 | | style="text-align:center;" | 29.445 | ||
|- | |- | ||
| style="text-align:center;" | [[ | | style="text-align:center;" | [[13/10]], [[20/13]] | ||
| style="text-align:center;" | 30.685 | | style="text-align:center;" | 30.685 | ||
|- | |- | ||
| style="text-align:center;" | [[ | | style="text-align:center;" | [[6/5]], [[5/3]] | ||
| style="text-align:center;" | 33.288 | | style="text-align:center;" | 33.288 | ||
|- | |- | ||
| style="text-align:center;" | [[ | | style="text-align:center;" | [[5/4]], [[8/5]] | ||
| style="text-align:center;" | 33.373 | | style="text-align:center;" | 33.373 | ||
|- | |- | ||
| style="text-align:center;" | [[ | | style="text-align:center;" | [[15/13]], [[26/15]] | ||
| style="text-align:center;" | 34.612 | | style="text-align:center;" | 34.612 | ||
|} | |} | ||
| Line 385: | Line 383: | ||
| | '''Error (abs., in [[cent|cents]])''' | | | '''Error (abs., in [[cent|cents]])''' | ||
|- | |- | ||
| style="text-align:center;" | [[ | | style="text-align:center;" | [[18/13]], [[13/9]] | ||
| style="text-align:center;" | 1.324 | | style="text-align:center;" | 1.324 | ||
|- | |- | ||
| style="text-align:center;" | [[ | | style="text-align:center;" | [[13/12]], [[24/13]] | ||
| style="text-align:center;" | 2.604 | | style="text-align:center;" | 2.604 | ||
|- | |- | ||
| style="text-align:center;" | [[ | | style="text-align:center;" | [[4/3]], [[3/2]] | ||
| style="text-align:center;" | 3.927 | | style="text-align:center;" | 3.927 | ||
|- | |- | ||
| style="text-align:center;" | [[ | | style="text-align:center;" | [[11/9]], [[18/11]] | ||
| style="text-align:center;" | 5.533 | | style="text-align:center;" | 5.533 | ||
|- | |- | ||
| style="text-align:center;" | [[ | | style="text-align:center;" | [[14/11]], [[11/7]] | ||
| style="text-align:center;" | 6.021 | | style="text-align:center;" | 6.021 | ||
|- | |- | ||
| style="text-align:center;" | [[ | | style="text-align:center;" | [[16/13]], [[13/8]] | ||
| style="text-align:center;" | 6.531 | | style="text-align:center;" | 6.531 | ||
|- | |- | ||
| style="text-align:center;" | [[ | | style="text-align:center;" | [[13/11]], [[22/13]] | ||
| style="text-align:center;" | 6.857 | | style="text-align:center;" | 6.857 | ||
|- | |- | ||
| style="text-align:center;" | [[ | | style="text-align:center;" | [[9/8]], [[16/9]] | ||
| style="text-align:center;" | 7.855 | | style="text-align:center;" | 7.855 | ||
|- | |- | ||
| style="text-align:center;" | [[ | | style="text-align:center;" | [[12/11]], [[11/6]] | ||
| style="text-align:center;" | 9.461 | | style="text-align:center;" | 9.461 | ||
|- | |- | ||
| style="text-align:center;" | [[ | | style="text-align:center;" | [[9/7]], [[14/9]] | ||
| style="text-align:center;" | 11.555 | | style="text-align:center;" | 11.555 | ||
|- | |- | ||
| style="text-align:center;" | [[ | | style="text-align:center;" | [[14/13]], [[13/7]] | ||
| style="text-align:center;" | 12.878 | | style="text-align:center;" | 12.878 | ||
|- | |- | ||
| style="text-align:center;" | [[ | | style="text-align:center;" | [[11/8]], [[16/11]] | ||
| style="text-align:center;" | 13.388 | | style="text-align:center;" | 13.388 | ||
|- | |- | ||
| style="text-align:center;" | [[ | | style="text-align:center;" | [[7/6]], [[12/7]] | ||
| style="text-align:center;" | 15.482 | | style="text-align:center;" | 15.482 | ||
|- | |- | ||
| style="text-align:center;" | [[ | | style="text-align:center;" | [[8/7]], [[7/4]] | ||
| style="text-align:center;" | 19.409 | | style="text-align:center;" | 19.409 | ||
|- | |- | ||
| style="text-align:center;" | [[ | | style="text-align:center;" | [[16/15]], [[15/8]] | ||
| style="text-align:center;" | 29.445 | | style="text-align:center;" | 29.445 | ||
|- | |- | ||
| style="text-align:center;" | [[ | | style="text-align:center;" | [[5/4]], [[8/5]] | ||
| style="text-align:center;" | 33.373 | | style="text-align:center;" | 33.373 | ||
|- | |- | ||
| style="text-align:center;" | [[ | | style="text-align:center;" | [[15/13]], [[26/15]] | ||
| style="text-align:center;" | 35.976 | | style="text-align:center;" | 35.976 | ||
|- | |- | ||
| style="text-align:center;" | [[ | | style="text-align:center;" | [[6/5]], [[5/3]] | ||
| style="text-align:center;" | 37.300 | | style="text-align:center;" | 37.300 | ||
|- | |- | ||
| style="text-align:center;" | [[ | | style="text-align:center;" | [[13/10]], [[20/13]] | ||
| style="text-align:center;" | 39.904 | | style="text-align:center;" | 39.904 | ||
|- | |- | ||
| style="text-align:center;" | [[ | | style="text-align:center;" | [[10/9]], [[9/5]] | ||
| style="text-align:center;" | 41.227 | | style="text-align:center;" | 41.227 | ||
|- | |- | ||
| style="text-align:center;" | [[ | | style="text-align:center;" | [[15/11]], [[22/15]] | ||
| style="text-align:center;" | 42.833 | | style="text-align:center;" | 42.833 | ||
|- | |- | ||
| style="text-align:center;" | [[ | | style="text-align:center;" | [[11/10]], [[20/11]] | ||
| style="text-align:center;" | 46.760 | | style="text-align:center;" | 46.760 | ||
|- | |- | ||
| style="text-align:center;" | [[ | | style="text-align:center;" | [[15/14]], [[28/15]] | ||
| style="text-align:center;" | 48.855 | | style="text-align:center;" | 48.855 | ||
|- | |- | ||
| style="text-align:center;" | [[ | | style="text-align:center;" | [[7/5]], [[10/7]] | ||
| style="text-align:center;" | 52.782 | | style="text-align:center;" | 52.782 | ||
|} | |} | ||
| Line 463: | Line 461: | ||
=Commas= | =Commas= | ||
17 EDO [[tempering_out|tempers out]] the following [[ | 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.) | ||
{| class="wikitable" | {| class="wikitable" | ||
| Line 475: | Line 473: | ||
|- | |- | ||
| style="text-align:center;" | <span style="display: block; text-align: center;"></span> | | style="text-align:center;" | <span style="display: block; text-align: center;"></span> | ||
| | | | | {{Monzo | 27 -17 }} | ||
| style="text-align:right;" | 66.765 | | style="text-align:right;" | 66.765 | ||
| | <span style="display: block; text-align: center;">17-Comma</span> | | | <span style="display: block; text-align: center;">17-Comma</span> | ||
| Line 482: | Line 480: | ||
|- | |- | ||
| style="text-align:center;" | 25/24 | | style="text-align:center;" | 25/24 | ||
| | | | | {{Monzo | -3 -1 2 }} | ||
| style="text-align:right;" | 70.762 | | style="text-align:right;" | 70.762 | ||
| | Chromatic semitone | | | Chromatic semitone | ||
| Line 489: | Line 487: | ||
|- | |- | ||
| style="text-align:center;" | 32805/32768 | | style="text-align:center;" | 32805/32768 | ||
| | | | | {{Monzo | -15 8 1 }} | ||
| style="text-align:right;" | 1.9537 | | style="text-align:right;" | 1.9537 | ||
| style="text-align:center;" | Schisma | | style="text-align:center;" | Schisma | ||
| Line 496: | Line 494: | ||
|- | |- | ||
| style="text-align:center;" | 64/63 | | style="text-align:center;" | 64/63 | ||
| | | | | {{Monzo | 6 -2 0 -1 }} | ||
| style="text-align:right;" | 27.264 | | style="text-align:right;" | 27.264 | ||
| style="text-align:center;" | Septimal Comma | | style="text-align:center;" | Septimal Comma | ||
| Line 503: | Line 501: | ||
|- | |- | ||
| style="text-align:center;" | 245/243 | | style="text-align:center;" | 245/243 | ||
| | | | | {{Monzo | 0 -5 1 2 }} | ||
| style="text-align:right;" | 14.191 | | style="text-align:right;" | 14.191 | ||
| style="text-align:center;" | Sensamagic | | style="text-align:center;" | Sensamagic | ||
| Line 510: | Line 508: | ||
|- | |- | ||
| style="text-align:center;" | 1728/1715 | | style="text-align:center;" | 1728/1715 | ||
| | | | | {{Monzo | 6 3 -1 -3 }} | ||
| style="text-align:right;" | 13.074 | | style="text-align:right;" | 13.074 | ||
| style="text-align:center;" | Orwellisma | | style="text-align:center;" | Orwellisma | ||
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|- | |- | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| | | | | {{Monzo | -6 -8 2 5 }} | ||
| style="text-align:right;" | 1.1170 | | style="text-align:right;" | 1.1170 | ||
| style="text-align:center;" | Wizma | | style="text-align:center;" | Wizma | ||
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|- | |- | ||
| style="text-align:center;" | 99/98 | | style="text-align:center;" | 99/98 | ||
| | | | | {{Monzo | -1 2 0 -2 1 }} | ||
| style="text-align:right;" | 17.576 | | style="text-align:right;" | 17.576 | ||
| style="text-align:center;" | Mothwellsma | | style="text-align:center;" | Mothwellsma | ||
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|- | |- | ||
| style="text-align:center;" | 896/891 | | style="text-align:center;" | 896/891 | ||
| | | | | {{Monzo | 7 -4 0 1 -1 }} | ||
| style="text-align:right;" | 9.6880 | | style="text-align:right;" | 9.6880 | ||
| style="text-align:center;" | Pentacircle | | style="text-align:center;" | Pentacircle | ||
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|- | |- | ||
| style="text-align:center;" | 243/242 | | style="text-align:center;" | 243/242 | ||
| | | | | {{Monzo | -1 5 0 0 -2 }} | ||
| style="text-align:right;" | 7.1391 | | style="text-align:right;" | 7.1391 | ||
| style="text-align:center;" | Rastma | | style="text-align:center;" | Rastma | ||
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|- | |- | ||
| style="text-align:center;" | 385/384 | | style="text-align:center;" | 385/384 | ||
| | | | | {{Monzo | -7 -1 1 1 1 }} | ||
| style="text-align:right;" | 4.5026 | | style="text-align:right;" | 4.5026 | ||
| style="text-align:center;" | Keenanisma | | style="text-align:center;" | Keenanisma | ||
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| style="text-align:center;" | | | style="text-align:center;" | | ||
|- | |- | ||
| style="text-align:center;" | | | style="text-align:center;" | 525/512 | ||
| | | | | {{Monzo | -9 1 2 1 }} | ||
| style="text-align:right;" | 43.408 | | style="text-align:right;" | 43.408 | ||
| style="text-align:center;" | | | style="text-align:center;" | Avicennma | ||
| style="text-align:center;" | Avicennma's Enharmonic Diesis | | style="text-align:center;" | Avicennma's Enharmonic Diesis | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 562: | Line 560: | ||
=Scales= | =Scales= | ||
* [[Otonal 17]] | |||
* [https://web.archive.org/web/20140215081520/http://microtonalismo.com/proyecto-xvii Blues Peruvian 17edo] | |||
* [[17edo neutral scale]] | |||
* [[Scorp]] | |||
* [[Screamapillar]] | |||
* [[Hydra]] | |||
* [[MOS scales of 17edo]] (horograms) | |||
[[ | =Temperaments= | ||
* [[List of 17edo rank two temperaments by badness]] | |||
[[ | * [[List of edo-distinct 17c rank two temperaments]] | ||
=Music= | =Music= | ||
==Scores== | |||
== | * [http://home.snafu.de/djwolf/PreludeIn17tet.pdf Prelude] (PDF) by [[Daniel Wolf]] | ||
* [http://georghajdu.de/compositions/heptadecatonic-drops/ Heptadecatonic Drops] by [http://georghajdu.de/biography/ Georg Hajdu] | |||
* [http://georghajdu.de/compositions/klangmoraste/ Klangmoraste] by Georg Hajdu | |||
* [http://www.microtonalismo.com/proyecto-xvii Charles Loli 17edo] {{forbidden}} music for guitar heptadecatonic (2001) and armony inductive microtonaly (1993) | |||
* [http://microtonalismo.com/ microtonalismo] Heptadecatonic Peruvian | |||
* [[Multiverse]] by [[JacobBarton|Jacob Barton]] | |||
* [http://christopherbaileymusic.com/walrus/v/#../../kitwo245m45n698th139rwebm845MQPxiF82J7WovYNRLK6klyq456/balladei.pdf Balladei] by [http://christopherbaileymusic.com/quick-bio/ Christopher Bailey] | |||
==Sound files== | ==Sound files== | ||
* [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://chrisvaisvil.com/shanidar-cave-17-edo/ Shanidar Cave] is a piece in 17 edo that features an electric 17 edo guitar and what is essentially an electric tanpura which ends up making this a sort of fusion of middle eastern and Indian music in a sense. by[[Chris_Vaisvil| Chris Vaisvil]] | |||
* ''[https://soundcloud.com/aaron-krister-johnson/puhlops-and-lauguas-big-adventure Puhlops and Laugua's Big Adventure]'' by [http://www.untwelve.org/board |Aaron Krister Johnson] | |||
* ''[https://soundcloud.com/aaron-krister-johnson/adagio-for-margo Adagio for Margo]'' by [http://www.untwelve.org/board Aaron Krister Johnson] | |||
* ''[http://home.comcast.net/~teamouse/Transformation.mp3 Transformation]'' by [http://home.comcast.net/%7Eteamouse/ Herman Miller] {{dead link}} | |||
* ''[https://christopherbailey.bandcamp.com/track/waltz-in-17-tone-equal-tuning-2006 Waltz]'' by Christopher Bailey | |||
* ''Lost & Found Things #2'' [https://soundcloud.com/zipzappoozoo/lost-and-found-things-2 (studio)] [https://soundcloud.com/zipzappoozoo/lost_found_live (live)] by Christopher Bailey | |||
* ''[https://soundcloud.com/zipzappoozoo/balladei-live-christopher-bailey Balladei (live)]'' (in 17, 29 and 12) by [http://music.columbia.edu/%7Echris/ Christopher Bailey] , CD available [http://www.amazon.com/Christopher-Bailey-Shiau-Uen-Jacob-Rhodebeck/dp/B000TDZSAU/ here] . | |||
* ''[http://www.h-pi.com/mp3/17ET.mp3 Two-Part Invention in 17ET]'' {{dead link}} by Aaron Andrew Hunt | |||
* ''[http://micro.soonlabel.com/gene_ward_smith/Others/McGowan/MSND-Ovtr.mp3 Overture to A Midsummer Night's Dream]'' by [http://azuma-asobi.com/ Rick McGowan] | |||
* ''[http://micro.soonlabel.com/gene_ward_smith/Others/McGowan/FairyLullaby-1.mp3 Fairy Lullaby from A Midsummer Night's Dream]'' by [http://azuma-asobi.com/ Rick McGowan] | |||
* ''[http://micro.soonlabel.com/gene_ward_smith/Others/Igs/City%20Of%20The%20Asleep%20-%2017-A%20Calamitous%20Simultaneity.mp3 A Calamitous Simultaneity]'' by Igliashon Jones (17edo and 22edo) | |||
* ''[http://micro.soonlabel.com/gene_ward_smith/Others/Igs/First%20Impressions.mp3 First Impressions]'' 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]'' {{dead link}} and ''[http://archive.org/download/EtudeNo2For2PianosIn17EqualTemperament/EtudeNo2ForTwoPianosIn17edo.mp3 Etude no2 for 2 Pianos in 17 Equal Temperament]'' {{dead link}} by Jon Lyle Smith | |||
* A number of compositions from [http://www.archive.org/details/seventeenTPP_01 seventeen-tone piano project phase I] , [[SeventeenTPPPhaseTwo|seventeen-tone piano project phase II]], [[SeventeenTPPPhaseThree|seventeen-tone piano project phase III]]. | |||
<!-- currently redundant: | |||
* [http://www.archive.org/search.php?query=subject%3A%2217-edo%22 17edo] - 17edo-tagged compositions on www.archive.org | |||
--> | |||
* [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. | |||
* [http://soundclick.com/share?songid=8839073 stringfinger it everybean] by Andrew Heathwaite (composed 2008, recorded 2010). | |||
* [http://soundclick.com/share?songid=8839069 cat feet belly] by Andrew Heathwaite (composed 2008, recorded 2010). | |||
* ''[http://www.youtube.com/watch?v=a9N_T6LNDaE 17 Tone Jam]'' by Marmalade Man | |||
* [http://www.youtube.com/results?search_query=17edo&search=tag youtube videos tagged with 17edo] | |||
* [http://micro.soonlabel.com/gene_ward_smith/Others/Sanchez/No_Love_by_Gregory_Sanchez_1_on_SoundCloud___Hear_the_world_s_sounds.mp3 No Love] by [https://soundcloud.com/gregory-sanchez-2 Gregory Sanchez] | |||
* [http://webzoom.freewebs.com/ralphjarzombek/micro7(17tet).mp3 Micro7] by Ralph Jarzombek | |||
* [https://drive.google.com/drive/folders/0BwsXD8q2VCYUM0tRdDNhVzNhcHM Helas, pitié] by Alex Ness (in 17edo with stretched octaves) | |||
* by [[Chris Vaisvil]]: | |||
** ''On the Shores of the Dead Sea'': [http://chrisvaisvil.com/?p=784 blog] | [http://www.youtube.com/watch?v=D39MVFhb0Ho video] | |||
** ''Only in Disneyland'': [http://chrisvaisvil.com/?p=466 blog] | [http://micro.soonlabel.com/17-ET/daily20110205-17et-disneyland.mp3 MP3] (guitar solo) | |||
** ''17 Reasons I Hate the Blues'': [http://chrisvaisvil.com/?p=460 blog] | [http://micro.soonlabel.com/17-ET/daily20110125b-17-reasons-I-hate-the-blues.mp3 MP3 ] | |||
** ''Klingon Opera Overture'': [http://chrisvaisvil.com/?p=422 blog] | [http://micro.soonlabel.com/17-ET/daily20110109-albino-17et.mp3 MP3] | |||
** ''Seventeen Selfless Notes'': [http://chrisvaisvil.com/?p=298 blog] | [http://micro.soonlabel.com/17-ET/if20101028selfless.mp3 MP3 ] | |||
** ''17et Jazz'': [http://chrisvaisvil.com/?p=76 blog] | [http://micro.soonlabel.com/17-ET/60x60-4001-1-ver2.mp3 MP3] (60 x 60 winner) | |||
** ''17 Pink Tuxedos'': [http://chrisvaisvil.com/?p=742 blog] | [http://micro.soonlabel.com/17-ET/daily20110416-17_pink-tuxes.mp3 MP3] | |||
** ''Devil in the Deep Blue Sea'': [http://chrisvaisvil.com/?p=706 blog] | [http://micro.soonlabel.com/17-ET/daily20110401-17-2-devil_in_the_deep_blue_sea.mp3 MP3] (blues collaboration between The Two Regs (vocals / lyrics) and Norm Harris (percussion) and Chris Vaisvil (17 note per octave electric guitar and fretless bass)) | |||
** ''Seventeen Years in the Sixties'': [http://chrisvaisvil.com/?p=585 blog] | [http://micro.soonlabel.com/17-ET/daily20110318-seventeen-years-in-the-sixties.mp3 MP3] | |||
** ''CT Scan'': [http://chrisvaisvil.com/?p=699 blog] | [http://www.youtube.com/watch?v=ZEEuytYwtbo MP3] | |||
** ''Fish and a Grenade'': [http://chrisvaisvil.com/?p=470 blog] | [http://micro.soonlabel.com/17-ET/daily20110208-17-a-fish-and-a-grenade.mp3 MP3] (parental advisory: language) | |||
** ''Seventeen Unsteady Hands'': [http://chrisvaisvil.com/?p=550 blog] | [http://www.youtube.com/watch?v=rAKHCqBNhfc video of performance] | |||
** ''The Pond'': [http://chrisvaisvil.com/?p=38 blog] | [http://www.youtube.com/watch?v=25sC3_uheyA video] | |||
** ''Graveyard'': [http://chrisvaisvil.com/?p=305 blog] | [http://micro.soonlabel.com/17-ET/if20101028-graveyard.mp3 MP3] | |||
** ''For Brass and Voice Choirs in 17 edo'': [http://chrisvaisvil.com/?p=1039 blog] | [http://micro.soonlabel.com/17-ET/daily20110713_q49_17_brass_voice_choirs.mp3 MP3] | |||
** ''And I Became One With My Pet Fungi'': [http://chrisvaisvil.com/?p=1439 blog] | [http://micro.soonlabel.com/17-ET/daily20111015-fungi.mp3 MP3] | |||
** ''Counterintuitive'': [http://chrisvaisvil.com/?p=1427 blog] | [http://micro.soonlabel.com/17-ET/20111014-STE-002-counter-intuitive.mp3 MP3] (guitar solo) | |||
** ''Flying Into O'Hare'': [http://chrisvaisvil.com/?p=6909 blog] | [http://micro.soonlabel.com/17-ET/20161125_linn_speactral_17.MP3 MP3] | |||
=Instruments= | =Instruments= | ||
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{{External image| http://sphotos.ak.fbcdn.net/hphotos-ak-ash2/hs382.ash2/66019_167001006650538_100000219181856_601987_48585_n.jpg {{dead link}} }} | {{External image| http://sphotos.ak.fbcdn.net/hphotos-ak-ash2/hs382.ash2/66019_167001006650538_100000219181856_601987_48585_n.jpg {{dead link}} }} | ||
* [http://chrisvaisvil.com/?p=436 17 note per octave conversion from a "standard" | * [http://chrisvaisvil.com/?p=436 17 note per octave conversion from a "standard" Stratocaster copy] - conversion by Brad Smith | ||
[[File:17P1050829r.JPG|alt=17P1050829r.JPG|17P1050829r.JPG]] | [[File:17P1050829r.JPG|alt=17P1050829r.JPG|17P1050829r.JPG]] | ||