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| ja = 17平均律
| ja = 17平均律
}}
}}
=<span style="color: #1300ff;">17 tone equal temperament</span>=
__FORCETOC__
__FORCETOC__


'''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|13edo]] and coming before [[19edo|19edo]].
'''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 [[SeventeenTonePianoProject|SeventeenTonePianoProject]]: [[SeventeenTheory|SeventeenTheory]].
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 Solfege]]. [[17edo_tetrachords|17edo tetrachords]]. [http://microtonalismo.com/proyecto-xvii Proyect 17-Perú]
[[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; [[27edt|27edt]] (a variant of 17edo in which the octaves are flattened by ~2.5 cents) is a good alternative. Another one is [[44ed6|44ed6]].
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 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.
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]] [[Ups_and_Downs_Notation|notation]]
! 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;" | [[25/24|25/24]], [[26/25|26/25]], [[33/32|33/32]]
| 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;" | [[13/12|13/12]], [[12/11|12/11]], [[14/13|14/13]]
| style="text-align:center;" | [[13/12]], [[12/11]], [[14/13]]
| | [[Bleu|Bleu]]
| | [[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;" | [[9/8|9/8]], [[25/22|25/22]], [[8/7|8/7]], [[28/25|28/25]]
| style="text-align:center;" | [[9/8]], [[25/22]], [[8/7]], [[28/25]]
| | [[Machine|Machine]]
| | [[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;" | [[13/11|13/11]], [[7/6|7/6]]
| style="text-align:center;" | [[13/11]], [[7/6]]
| | [[Huxley|Huxley]]
| | [[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;" | [[11/9|11/9]], [[16/13|16/13]]
| style="text-align:center;" | [[11/9]], [[16/13]]
| | [[maqamic|Maqamic]]/[[Hemif|hemif]]
| | [[Maqamic]]/[[Hemif]]
|-
|-
| | 6
| | 6
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| style="text-align:center;" | M3
| style="text-align:center;" | M3
| style="text-align:center;" | E
| style="text-align:center;" | E
| style="text-align:center;" | [[32/25|32/25]], [[33/26|33/26]], [[9/7|9/7]], [[14/11|14/11]]
| style="text-align:center;" | [[32/25]], [[33/26]], [[9/7]], [[14/11]]
| | [[Skwares|Skwares]]
| | [[Skwares]]
|-
|-
| | 7
| | 7
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| style="text-align:center;" | P4
| style="text-align:center;" | P4
| style="text-align:center;" | F
| style="text-align:center;" | F
| style="text-align:center;" | [[4/3|4/3]]
| style="text-align:center;" | [[4/3]]
| | [[Supra|Supra]]
| | [[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;" | [[11/8|11/8]], 18/13
| style="text-align:center;" | [[11/8]], [[18/13]]
| | [[Progress|Progress]]
| | [[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;" | [[16/11|16/11]], 13/9, [[23/16|23/16]]
| 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;" | [[3/2|3/2]]
| 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, [[11/7|11/7]]
| 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;" | [[13/8|13/8]], 18/11
| 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;" | [[17/10|17/10]], [[22/13|22/13]],[[12/7|12/7]]
| 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;" | [[16/9|16/9]], 7/4, 25/14
| 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;" | [[11/6|11/6]], 24/13, [[13/7|13/7]]
| 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;" | [[2/1|2/1]]
| 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's_color_notation|color notation]], qualities can be loosely associated with colors:
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;" | [[18/13|18/13]], [[13/9|13/9]]
| style="text-align:center;" | [[18/13]], [[13/9]]
| style="text-align:center;" | 1.324
| style="text-align:center;" | 1.324
|-
|-
| style="text-align:center;" | [[13/12|13/12]], [[24/13|24/13]]
| style="text-align:center;" | [[13/12]], [[24/13]]
| style="text-align:center;" | 2.604
| style="text-align:center;" | 2.604
|-
|-
| style="text-align:center;" | [[4/3|4/3]], [[3/2|3/2]]
| style="text-align:center;" | [[4/3]], [[3/2]]
| style="text-align:center;" | 3.927
| style="text-align:center;" | 3.927
|-
|-
| style="text-align:center;" | [[11/9|11/9]], [[18/11|18/11]]
| style="text-align:center;" | [[11/9]], [[18/11]]
| style="text-align:center;" | 5.533
| style="text-align:center;" | 5.533
|-
|-
| style="text-align:center;" | [[14/11|14/11]], [[11/7|11/7]]
| style="text-align:center;" | [[14/11]], [[11/7]]
| style="text-align:center;" | 6.021
| style="text-align:center;" | 6.021
|-
|-
| style="text-align:center;" | [[16/13|16/13]], [[13/8|13/8]]
| style="text-align:center;" | [[16/13]], [[13/8]]
| style="text-align:center;" | 6.531
| style="text-align:center;" | 6.531
|-
|-
| style="text-align:center;" | [[13/11|13/11]], [[22/13|22/13]]
| style="text-align:center;" | [[13/11]], [[22/13]]
| style="text-align:center;" | 6.857
| style="text-align:center;" | 6.857
|-
|-
| style="text-align:center;" | [[9/8|9/8]], [[16/9|16/9]]
| style="text-align:center;" | [[9/8]], [[16/9]]
| style="text-align:center;" | 7.855
| style="text-align:center;" | 7.855
|-
|-
| style="text-align:center;" | [[12/11|12/11]], [[11/6|11/6]]
| style="text-align:center;" | [[12/11]], [[11/6]]
| style="text-align:center;" | 9.461
| style="text-align:center;" | 9.461
|-
|-
| style="text-align:center;" | [[9/7|9/7]], [[14/9|14/9]]
| style="text-align:center;" | [[9/7]], [[14/9]]
| style="text-align:center;" | 11.555
| style="text-align:center;" | 11.555
|-
|-
| style="text-align:center;" | [[14/13|14/13]], [[13/7|13/7]]
| style="text-align:center;" | [[14/13]], [[13/7]]
| style="text-align:center;" | 12.878
| style="text-align:center;" | 12.878
|-
|-
| style="text-align:center;" | [[11/8|11/8]], [[16/11|16/11]]
| style="text-align:center;" | [[11/8]], [[16/11]]
| style="text-align:center;" | 13.388
| style="text-align:center;" | 13.388
|-
|-
| style="text-align:center;" | [[7/6|7/6]], [[12/7|12/7]]
| style="text-align:center;" | [[7/6]], [[12/7]]
| style="text-align:center;" | 15.482
| style="text-align:center;" | 15.482
|-
|-
| style="text-align:center;" | [[7/5|7/5]], [[10/7|10/7]]
| style="text-align:center;" | [[7/5]], [[10//7]]
| style="text-align:center;" | 17.806
| style="text-align:center;" | 17.806
|-
|-
| style="text-align:center;" | [[8/7|8/7]], [[7/4|7/4]]
| style="text-align:center;" | [[8/7]], [[7/4|]
| style="text-align:center;" | 19.409
| style="text-align:center;" | 19.409
|-
|-
| style="text-align:center;" | [[15/14|15/14]], [[28/15|28/15]]
| style="text-align:center;" | [[15/14]], [[28/15]]
| style="text-align:center;" | 21.734
| style="text-align:center;" | 21.734
|-
|-
| style="text-align:center;" | [[11/10|11/10]], [[20/11|20/11]]
| style="text-align:center;" | [[11/10]], [[20/11]]
| style="text-align:center;" | 23.828
| style="text-align:center;" | 23.828
|-
|-
| style="text-align:center;" | [[15/11|15/11]], [[22/15|22/15]]
| style="text-align:center;" | [[15/11]], [[22/15]]
| style="text-align:center;" | 27.755
| style="text-align:center;" | 27.755
|-
|-
| style="text-align:center;" | [[10/9|10/9]], [[9/5|9/5]]
| style="text-align:center;" | [[10/9]], [[9/5]]
| style="text-align:center;" | 29.361
| style="text-align:center;" | 29.361
|-
|-
| style="text-align:center;" | [[16/15|16/15]], [[15/8|15/8]]
| style="text-align:center;" | [[16/15]], [[15/8]]
| style="text-align:center;" | 29.445
| style="text-align:center;" | 29.445
|-
|-
| style="text-align:center;" | [[13/10|13/10]], [[20/13|20/13]]
| style="text-align:center;" | [[13/10]], [[20/13]]
| style="text-align:center;" | 30.685
| style="text-align:center;" | 30.685
|-
|-
| style="text-align:center;" | [[6/5|6/5]], [[5/3|5/3]]
| style="text-align:center;" | [[6/5]], [[5/3]]
| style="text-align:center;" | 33.288
| style="text-align:center;" | 33.288
|-
|-
| style="text-align:center;" | [[5/4|5/4]], [[8/5|8/5]]
| style="text-align:center;" | [[5/4]], [[8/5]]
| style="text-align:center;" | 33.373
| style="text-align:center;" | 33.373
|-
|-
| style="text-align:center;" | [[15/13|15/13]], [[26/15|26/15]]
| 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;" | [[18/13|18/13]], [[13/9|13/9]]
| style="text-align:center;" | [[18/13]], [[13/9]]
| style="text-align:center;" | 1.324
| style="text-align:center;" | 1.324
|-
|-
| style="text-align:center;" | [[13/12|13/12]], [[24/13|24/13]]
| style="text-align:center;" | [[13/12]], [[24/13]]
| style="text-align:center;" | 2.604
| style="text-align:center;" | 2.604
|-
|-
| style="text-align:center;" | [[4/3|4/3]], [[3/2|3/2]]
| style="text-align:center;" | [[4/3]], [[3/2]]
| style="text-align:center;" | 3.927
| style="text-align:center;" | 3.927
|-
|-
| style="text-align:center;" | [[11/9|11/9]], [[18/11|18/11]]
| style="text-align:center;" | [[11/9]], [[18/11]]
| style="text-align:center;" | 5.533
| style="text-align:center;" | 5.533
|-
|-
| style="text-align:center;" | [[14/11|14/11]], [[11/7|11/7]]
| style="text-align:center;" | [[14/11]], [[11/7]]
| style="text-align:center;" | 6.021
| style="text-align:center;" | 6.021
|-
|-
| style="text-align:center;" | [[16/13|16/13]], [[13/8|13/8]]
| style="text-align:center;" | [[16/13]], [[13/8]]
| style="text-align:center;" | 6.531
| style="text-align:center;" | 6.531
|-
|-
| style="text-align:center;" | [[13/11|13/11]], [[22/13|22/13]]
| style="text-align:center;" | [[13/11]], [[22/13]]
| style="text-align:center;" | 6.857
| style="text-align:center;" | 6.857
|-
|-
| style="text-align:center;" | [[9/8|9/8]], [[16/9|16/9]]
| style="text-align:center;" | [[9/8]], [[16/9]]
| style="text-align:center;" | 7.855
| style="text-align:center;" | 7.855
|-
|-
| style="text-align:center;" | [[12/11|12/11]], [[11/6|11/6]]
| style="text-align:center;" | [[12/11]], [[11/6]]
| style="text-align:center;" | 9.461
| style="text-align:center;" | 9.461
|-
|-
| style="text-align:center;" | [[9/7|9/7]], [[14/9|14/9]]
| style="text-align:center;" | [[9/7]], [[14/9]]
| style="text-align:center;" | 11.555
| style="text-align:center;" | 11.555
|-
|-
| style="text-align:center;" | [[14/13|14/13]], [[13/7|13/7]]
| style="text-align:center;" | [[14/13]], [[13/7]]
| style="text-align:center;" | 12.878
| style="text-align:center;" | 12.878
|-
|-
| style="text-align:center;" | [[11/8|11/8]], [[16/11|16/11]]
| style="text-align:center;" | [[11/8]], [[16/11]]
| style="text-align:center;" | 13.388
| style="text-align:center;" | 13.388
|-
|-
| style="text-align:center;" | [[7/6|7/6]], [[12/7|12/7]]
| style="text-align:center;" | [[7/6]], [[12/7]]
| style="text-align:center;" | 15.482
| style="text-align:center;" | 15.482
|-
|-
| style="text-align:center;" | [[8/7|8/7]], [[7/4|7/4]]
| style="text-align:center;" | [[8/7]], [[7/4]]
| style="text-align:center;" | 19.409
| style="text-align:center;" | 19.409
|-
|-
| style="text-align:center;" | [[16/15|16/15]], [[15/8|15/8]]
| style="text-align:center;" | [[16/15]], [[15/8]]
| style="text-align:center;" | 29.445
| style="text-align:center;" | 29.445
|-
|-
| style="text-align:center;" | [[5/4|5/4]], [[8/5|8/5]]
| style="text-align:center;" | [[5/4]], [[8/5]]
| style="text-align:center;" | 33.373
| style="text-align:center;" | 33.373
|-
|-
| style="text-align:center;" | [[15/13|15/13]], [[26/15|26/15]]
| style="text-align:center;" | [[15/13]], [[26/15]]
| style="text-align:center;" | 35.976
| style="text-align:center;" | 35.976
|-
|-
| style="text-align:center;" | [[6/5|6/5]], [[5/3|5/3]]
| style="text-align:center;" | [[6/5]], [[5/3]]
| style="text-align:center;" | 37.300
| style="text-align:center;" | 37.300
|-
|-
| style="text-align:center;" | [[13/10|13/10]], [[20/13|20/13]]
| style="text-align:center;" | [[13/10]], [[20/13]]
| style="text-align:center;" | 39.904
| style="text-align:center;" | 39.904
|-
|-
| style="text-align:center;" | [[10/9|10/9]], [[9/5|9/5]]
| style="text-align:center;" | [[10/9]], [[9/5]]
| style="text-align:center;" | 41.227
| style="text-align:center;" | 41.227
|-
|-
| style="text-align:center;" | [[15/11|15/11]], [[22/15|22/15]]
| style="text-align:center;" | [[15/11]], [[22/15]]
| style="text-align:center;" | 42.833
| style="text-align:center;" | 42.833
|-
|-
| style="text-align:center;" | [[11/10|11/10]], [[20/11|20/11]]
| style="text-align:center;" | [[11/10]], [[20/11]]
| style="text-align:center;" | 46.760
| style="text-align:center;" | 46.760
|-
|-
| style="text-align:center;" | [[15/14|15/14]], [[28/15|28/15]]
| style="text-align:center;" | [[15/14]], [[28/15]]
| style="text-align:center;" | 48.855
| style="text-align:center;" | 48.855
|-
|-
| style="text-align:center;" | [[7/5|7/5]], [[10/7|10/7]]
| 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 [[Comma|comma]]s. (Note: This assumes [[val|val]] &lt; 17 27 39 48 59 63 |, cent values ​​rounded to 5 digits.)
17 EDO [[tempering_out|tempers out]] the following [[comma]]s. (Note: This assumes [[val]] &lt; 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>
| |<nowiki> | 27 -17 </nowiki>&gt;
| | {{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
| |<nowiki> |-3 -1 2</nowiki>&gt;
| | {{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
| |<nowiki> | -15 8 1 </nowiki>&gt;
| | {{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
| |<nowiki> | 6 -2 0 -1 </nowiki>&gt;
| | {{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
| |<nowiki> | 0 -5 1 2 </nowiki>&gt;
| | {{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
| |<nowiki> | 6 3 -1 -3 </nowiki>&gt;
| | {{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
Line 517: Line 515:
|-
|-
| style="text-align:center;" |  
| style="text-align:center;" |  
| |<nowiki> | -6 -8 2 5 </nowiki>&gt;
| | {{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
Line 524: Line 522:
|-
|-
| style="text-align:center;" | 99/98
| style="text-align:center;" | 99/98
| |<nowiki> | -1 2 0 -2 1 </nowiki>&gt;
| | {{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
Line 531: Line 529:
|-
|-
| style="text-align:center;" | 896/891
| style="text-align:center;" | 896/891
| |<nowiki> | 7 -4 0 1 -1 </nowiki>&gt;
| | {{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
Line 538: Line 536:
|-
|-
| style="text-align:center;" | 243/242
| style="text-align:center;" | 243/242
| |<nowiki> | -1 5 0 0 -2 </nowiki>&gt;
| | {{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
Line 545: Line 543:
|-
|-
| style="text-align:center;" | 385/384
| style="text-align:center;" | 385/384
| |<nowiki> | -7 -1 1 1 1 </nowiki>&gt;
| | {{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
Line 551: Line 549:
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
| style="text-align:center;" | <span style="display: block; text-align: center;">525/512</span>
| style="text-align:center;" | 525/512
| | <span style="display: block; text-align: left;"><nowiki>| -9 1 2 1 </nowiki>&gt;</span>
| | {{Monzo | -9 1 2 1 }}
| style="text-align:right;" | 43.408
| style="text-align:right;" | 43.408
| style="text-align:center;" | <span style="display: block; text-align: center;">Avicennma</span>
| 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=
<ul><li>[[Otonal_17|Otonal 17]]</li><li>[https://web.archive.org/web/20140215081520/http://microtonalismo.com/proyecto-xvii Blues Peruvian 17edo]</li><li>[[17edo_neutral_scale|17edo neutral scale]]</li><li>[[Scorp|Scorp]]</li><li>[[Screamapillar|Screamapillar]]</li><li>[[Hydra|Hydra]]</li><li>[[MOS_scales_of_17edo|MOS scales of 17edo]] (horograms)</li></ul>
* [[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)


[[List_of_17edo_rank_two_temperaments_by_badness|List of 17edo rank two temperaments by badness]]
=Temperaments=
 
* [[List of 17edo rank two temperaments by badness]]
[[List_of_edo-distinct_17c_rank_two_temperaments|List of edo-distinct 17c rank two temperaments]]
* [[List of edo-distinct 17c rank two temperaments]]


=Music=
=Music=
 
==Scores==
==Compositions==
* [http://home.snafu.de/djwolf/PreludeIn17tet.pdf Prelude] (PDF) by [[Daniel Wolf]]
<ul><li>[https://soundcloud.com/overtoneshock/demanding-two-faces-17-edo Demanding Two Faces] (xen-pop) by [https://soundcloud.com/overtoneshock Stephen Weigel]</li><li>[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]</li><li>[http://home.snafu.de/djwolf/PreludeIn17tet.pdf Prelude] by [[Daniel_Wolf|Daniel Wolf]]</li><li>[http://www.georghajdu.de/heptadecatonic_drops.html Heptadecatonic Drops] by Georg Hajdu</li><li>[http://www.georghajdu.de/63.html?&L=1%20 Klangmoraste] by Georg Hajdu</li><li>[http://www.microtonalismo.com/proyecto-xvii Charles Loli 17edo] music for guitar heptadecatonic (2001) and armony inductive microtonaly (1993)</li><li>[http://microtonalismo.com/ microtonalismo] Heptadecatonic Peruvian</li><li>[[Multiverse|Multiverse]] by [[JacobBarton|Jacob Barton]]</li></ul>
* [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==
<ul><li>[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]]</li><li><span style=""><span style=""><span style="">''[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]</li><li><span style=""><span style=""><span style="">''[https://soundcloud.com/aaron-krister-johnson/adagio-for-margo Adagio for Margo]'' </span></span> </span> by [http://www.untwelve.org/board Aaron Krister Johnson]</li><li><span style=""><span style=""><span style="">''[http://home.comcast.net/~teamouse/Transformation.mp3 Transformation]'' </span></span> </span> by [http://home.comcast.net/%7Eteamouse/ Herman Miller]</li><li><span style=""><span style=""><span style="">''[http://www.emcollective.org/chris/items/17tet/17waltz.mp3 Waltz]'' </span></span> </span> by Christopher Bailey</li><li><span style=""><span style=""><span style="">''[http://www.emcollective.org/chris/items/17Chorus/17tppp4_lostfound.mp3 Lostfound]'' </span></span> </span> by Christopher Bailey</li><li>excerpt from <span style=""><span style=""><span style="">''[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] .</li><li><span style=""><span style=""><span style="">''[http://www.h-pi.com/mp3/17ET.mp3 Two-Part Invention in 17ET]'' </span></span></span> by Aaron Andrew Hunt</li><li>''[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]</li><li>''[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]</li><li><span style="">''[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)</li><li><span style="">''[http://micro.soonlabel.com/gene_ward_smith/Others/Igs/First%20Impressions.mp3 First Impressions]'' </span> by Igliashon Jones</li><li>[http://micro.soonlabel.com/gene_ward_smith/Others/Igs/I%20Insist.mp3 I Insist] by Igliashon Jones</li><li>''[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</li><li>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]].</li><li>[http://www.archive.org/search.php?query=subject%3A%2217-edo%22 17edo] - 17edo-tagged compositions on www.archive.org</li><li>[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 &amp; voice.</li><li>[http://soundclick.com/share?songid=8839073 stringfinger it everybean] by Andrew Heathwaite (composed 2008, recorded 2010).</li><li>[http://soundclick.com/share?songid=8839069 cat feet belly] by Andrew Heathwaite (composed 2008, recorded 2010).</li><li><span style=""><span style=""><span style="">''[http://www.youtube.com/watch?v=a9N_T6LNDaE 17 Tone Jam]'' </span></span></span> by Marmalade Man</li><li>[http://www.youtube.com/results?search_query=17edo&search=tag youtube videos tagged with 17edo]</li><li>[http://chrisvaisvil.com/?p=784 On the Shores of the Dead Sea blog] <span style=""><span style=""><span style="">''[http://www.youtube.com/watch?v=D39MVFhb0Ho video of On the Shores of the Dead Sea]'' </span></span> </span> by [[Chris_Vaisvil|Chris Vaisvil]]</li><li>[http://chrisvaisvil.com/?p=466 Only in Disneyland 17 blog] edo guitar solo <span style=""><span style=""><span style="">''[http://micro.soonlabel.com/17-ET/daily20110205-17et-disneyland.mp3 play Only in Disneyland]'' </span></span> </span> by [[Chris_Vaisvil|Chris Vaisvil]]</li><li>[http://chrisvaisvil.com/?p=460 17 Reasons I Hate the Blues blog] <span style=""><span style=""><span style="">''[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|Chris Vaisvil]]</li><li>[http://chrisvaisvil.com/?p=422 Klingon Opera Overture blog] <span style=""><span style=""><span style="">''[http://micro.soonlabel.com/17-ET/daily20110109-albino-17et.mp3 play Klingon Opera Overture]'' </span></span> </span> by [[Chris_Vaisvil|Chris Vaisvil]]</li><li>[http://chrisvaisvil.com/?p=298 Seventeen Selfless Notes blog] <span style=""><span style=""><span style="">''[http://micro.soonlabel.com/17-ET/if20101028selfless.mp3 play Seventeen Selfless Notes]'' </span></span> </span> by [[Chris_Vaisvil|Chris Vaisvil]]</li><li>[http://chrisvaisvil.com/?p=76 17ET Jazz blog] <span style=""><span style=""><span style="">''[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)</li><li>[http://chrisvaisvil.com/?p=742 17 Pink Tuxedos blog] <span style=""><span style=""><span style="">''[http://micro.soonlabel.com/17-ET/daily20110416-17_pink-tuxes.mp3 play 17 Pink Tuxedos]'' </span></span></span> by [[Chris_Vaisvil|Chris Vaisvil]]</li><li>[http://chrisvaisvil.com/?p=706 Devil in the Deep Blue Sea blog] <span style=""><span style=""><span style="">''[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).</li><li>[http://chrisvaisvil.com/?p=585 Seventeen Years in the Sixties blog] <span style=""><span style=""><span style="">''[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|Chris Vaisvil]]</li><li>[http://chrisvaisvil.com/?p=699 CT Scan blog] <span style=""><span style=""><span style="">''[http://www.youtube.com/watch?v=ZEEuytYwtbo play video CT Scan]'' </span></span></span> by Chris Vaisvil</li><li>[http://chrisvaisvil.com/?p=470 Fish and a Grenade blog] <span style=""><span style=""><span style="">''[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</li><li>[http://chrisvaisvil.com/?p=550 Seventeen Unsteady Hands blog] <span style=""><span style=""><span style="">''[http://www.youtube.com/watch?v=rAKHCqBNhfc play video of performance of Seventeen Unsteady Hands]'' </span></span></span> by Chris Vaisvil</li><li>[http://chrisvaisvil.com/?p=38 The Pond blog] by Chris Vaisvil and <span style=""><span style=""><span style="">''[http://www.youtube.com/watch?v=25sC3_uheyA video version of The Pond with Japanese Garden]'' </span></span></span></li><li><span style="">[http://chrisvaisvil.com/?p=305 Graveyard blog] </span><span style=""><span style=""><span style="">''[http://micro.soonlabel.com/17-ET/if20101028-graveyard.mp3 play Graveyard]'' </span></span> </span> by Chris Vaisvil</li><li><span style=""><span style=""><span style="">''[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]</li><li><span style=""><span style="">''[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] =&gt; [http://chrisvaisvil.com/?p=1439 more on composition]</li><li><span style=""><span style="">''[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] =&gt; [http://chrisvaisvil.com/?p=1427 more on composition]</li><li>[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]</li><li>[http://webzoom.freewebs.com/ralphjarzombek/micro7(17tet).mp3 Micro7] by Ralph Jarzombek</li><li>[http://micro.soonlabel.com/17-ET/20161125_linn_speactral_17.MP3 Flying Into O'Hare] by [[Chris_Vaisvil|Chris Vaisvil]]</li><li>[https://drive.google.com/drive/folders/0BwsXD8q2VCYUM0tRdDNhVzNhcHM Helas, pitié] by Alex Ness (in 17edo with stretched octaves)</li></ul>
* [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 &amp; 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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* [http://chrisvaisvil.com/?p=436 17 note per octave conversion from a "standard" stratocastor copy] - conversion by Brad Smith
* [http://chrisvaisvil.com/?p=436 17 note per octave conversion from a "standard" Stratocaster copy] - conversion by Brad Smith


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[[File:17P1050829r.JPG|alt=17P1050829r.JPG|17P1050829r.JPG]]

Revision as of 18:29, 9 December 2018


17 tone equal temperament, or 17-EDO, divides the octave in 17 equal steps, each 70.588 cents in size. It is the seventh prime EDO, following 13edo and coming before 19edo.

Theory

An introduction to 17-EDO theory, through the eyes of the SeventeenTonePianoProject: SeventeenTheory.

Another introduction into 17-EDO theory: The 17-tone Puzzle [dead link] by George Secor.

17edo Solfege. 17edo tetrachords. 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; 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.

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 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

Degree Cents Names of Intervals ups and downs notation Approximate Ratios* Temperament(s)generated
0 0 Unison unison P1 C 1/1
1 70.59 Super Unison/Minor Second minor 2nd m2 Db 25/24, 26/25, 33/32
2 141.18 Augmented Unison/Neutral Second mid 2nd ~2 Dv 13/12, 12/11, 14/13 Bleu
3 211.765 Major Second/Sub Third major 2nd M2 D 9/8, 25/22, 8/7, 28/25 Machine
4 282.35 Minor Third/Super Second minor 3rd m3 Eb 13/11, 7/6 Huxley
5 352.94 Augmented Second/Neutral Third/

Diminished Fourth

mid 3rd ~3 Ev 11/9, 16/13 Maqamic/Hemif
6 423.53 Major Third/Sub Fourth major 3rd M3 E 32/25, 33/26, 9/7, 14/11 Skwares
7 494.11 Perfect Fourth perfect 4th P4 F 4/3 Supra
8 564.71 Super FourthDiminished Fifth up 4th,

diminished 5th

^4, d5 F^, Gb 11/8, 18/13 Progress
9 635.29 Augmented Fourth/Sub Fifth augmented 4th,

down 5th

A4, v5 F#, Gv 16/11, 13/9, 23/16 Progress
10 705.88 Perfect Fifth perfect 5th P5 G 3/2 Supra
11 776.47 Super Fifth/Minor Sixth minor 6th m6 Ab 25/16, 14/9, 11/7 Skwares
12 847.06 Augmented Fifth/Neutral Sixth/

Diminished Seventh

mid 6th ~6 Av 13/8, 18/11 Maqamic/hemif
13 917.65 Major Sixth/Sub Seventh major 6th M6 A 17/10, 22/13,12/7 Huxley
14 988.235 Minor Seventh/Super Sixth minor 7th m7 Bb 16/9, 7/4, 25/14 Machine
15 1058.82 Augmented Sixth/Neutral Seventh/

Diminished Octave

mid 7th ~7 Bv 11/6, 24/13, 13/7 Bleu
16 1129.41 Major Seventh/Sub Octave major 7th M7 B 25/13, 48/25, 64/33
17 1200 Perfect Octave octave P8 C 2/1

*Ratios based on treating 17edo as a 2.3.7.11.13.25 subgroup

Combining ups and downs notation with Kite's color notation, qualities can be loosely associated with colors:

quality color monzo format examples
minor zo {a, b, 0, 1} 7/6, 7/4
" fourthward wa {a, b}, b < -1 32/27, 16/9
mid ilo {a, b, 0, 0, 1} 11/9, 11/6
" lu {a, b, 0, 0, -1} 12/11, 18/11
major fifthward wa {a, b}, b > 1 9/8, 27/16
" ru {a, b, 0, -1} 9/7, 12/7

Chord Names

All 17edo chords can be named using ups and downs. Here are the zo, ilo and ru triads:

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 Ev G C~ C mid
ru 14:18:27 0-6-10 C E G C C major or C

0-4-9 = C Eb Gv = Cm(v5) = C minor down-five

0-5-9 = C Ev G = 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

0-5-10-14 = 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 Ups and Downs Notation - Chord names in other EDOs.

Selected just intervals by error

The following table shows how some prominent just intervals are represented in 17edo (ordered by absolute error).

Best direct mapping, even if inconsistent

Interval, complement Error (abs., in cents)
18/13, 13/9 1.324
13/12, 24/13 2.604
4/3, 3/2 3.927
11/9, 18/11 5.533
14/11, 11/7 6.021
16/13, 13/8 6.531
13/11, 22/13 6.857
9/8, 16/9 7.855
12/11, 11/6 9.461
9/7, 14/9 11.555
14/13, 13/7 12.878
11/8, 16/11 13.388
7/6, 12/7 15.482
7/5, 10//7 17.806
8/7, [[7/4|] 19.409
15/14, 28/15 21.734
11/10, 20/11 23.828
15/11, 22/15 27.755
10/9, 9/5 29.361
16/15, 15/8 29.445
13/10, 20/13 30.685
6/5, 5/3 33.288
5/4, 8/5 33.373
15/13, 26/15 34.612

Patent val mapping

Interval, complement Error (abs., in cents)
18/13, 13/9 1.324
13/12, 24/13 2.604
4/3, 3/2 3.927
11/9, 18/11 5.533
14/11, 11/7 6.021
16/13, 13/8 6.531
13/11, 22/13 6.857
9/8, 16/9 7.855
12/11, 11/6 9.461
9/7, 14/9 11.555
14/13, 13/7 12.878
11/8, 16/11 13.388
7/6, 12/7 15.482
8/7, 7/4 19.409
16/15, 15/8 29.445
5/4, 8/5 33.373
15/13, 26/15 35.976
6/5, 5/3 37.300
13/10, 20/13 39.904
10/9, 9/5 41.227
15/11, 22/15 42.833
11/10, 20/11 46.760
15/14, 28/15 48.855
7/5, 10/7 52.782

alt : Your browser has no SVG support.

17ed2-001.svg

Commas

17 EDO tempers out the following commas. (Note: This assumes val < 17 27 39 48 59 63 |, cent values ​​rounded to 5 digits.)

Comma Monzo Value (Cents) Name 1 Name 2 Name 3
[27 -17⟩ 66.765 17-Comma
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
525/512 [-9 1 2 1⟩ 43.408 Avicennma 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.

Scales

Temperaments

Music

Scores

Sound files

Instruments

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