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__FORCETOC__
__FORCETOC__


==Theory==
== Theory ==
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]].
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]].


Line 22: Line 22:
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.
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 ==


{| class="wikitable"
{| class="wikitable center-all right-1 right-2 left-3"
|-
|-
! Degree
! Degree
Line 34: Line 34:
|-
|-
| 0
| 0
|0
| 0.00
| | Unison
| Unison
| style="text-align:center;" | unison
| unison
| style="text-align:center;" | P1
| P1
| style="text-align:center;" | C
| C
| style="text-align:center;" | 1/1
| 1/1
| |  
|  
|-
|-
| | 1
| 1
| | 70.59
| 70.59
| | Super Unison/Minor Second
| Super Unison/Minor Second
| style="text-align:center;" | minor 2nd
| minor 2nd
| style="text-align:center;" | m2
| m2
| style="text-align:center;" | Db
| Db
| style="text-align:center;" | [[25/24]], [[26/25]], [[33/32]]
| [[25/24]], [[26/25]], [[33/32]]
| |  
|  
|-
|-
| | 2
| 2
| | 141.18
| 141.18
| | Augmented Unison/Neutral Second
| Augmented Unison/Neutral Second
| style="text-align:center;" | mid 2nd
| mid 2nd
| style="text-align:center;" | ~2
| ~2
| style="text-align:center;" | vD
| vD
| style="text-align:center;" | [[13/12]], [[12/11]], [[14/13]], [[25/23]]
| [[13/12]], [[12/11]], [[14/13]], [[25/23]]
| | [[Bleu]]
| [[Bleu]]
|-
|-
| | 3
| 3
| | 211.765
| 211.76
| | Major Second/Sub Third
| Major Second/Sub Third
| style="text-align:center;" | major 2nd
| major 2nd
| style="text-align:center;" | M2
| M2
| style="text-align:center;" | D
| D
| style="text-align:center;" | [[9/8]], [[25/22]], [[8/7]], [[28/25]], [[25/22]], [[26/23]]
| [[9/8]], [[25/22]], [[8/7]], [[28/25]], [[25/22]], [[26/23]]
| | [[Machine]]
| [[Machine]]
|-
|-
| | 4
| 4
| | 282.35
| 282.35
| | Minor Third/Super Second
| Minor Third/Super Second
| style="text-align:center;" | minor 3rd
| minor 3rd
| style="text-align:center;" | m3
| m3
| style="text-align:center;" | Eb
| Eb
| style="text-align:center;" | [[13/11]], [[7/6]]
| [[13/11]], [[7/6]]
| | [[Huxley]]
| [[Huxley]]
|-
|-
| | 5
| 5
| | 352.94
| 352.94
| | Augmented Second/Neutral Third/
| Augmented Second/Neutral Third/ <br> Diminished Fourth
Diminished Fourth
| mid 3rd
| style="text-align:center;" | mid 3rd
| ~3
| style="text-align:center;" | ~3
| vE
| style="text-align:center;" | vE
| [[11/9]], [[16/13]]
| style="text-align:center;" | [[11/9]], [[16/13]]
| [[Maqamic]]/[[Hemif]]
| | [[Maqamic]]/[[Hemif]]
|-
|-
| | 6
| 6
| | 423.53
| 423.53
| | Major Third/Sub Fourth
| Major Third/Sub Fourth
| style="text-align:center;" | major 3rd
| major 3rd
| style="text-align:center;" | M3
| M3
| style="text-align:center;" | E
| E
| style="text-align:center;" | [[32/25]], [[33/26]], [[9/7]], [[14/11]], [[23/18]]
| [[32/25]], [[33/26]], [[9/7]], [[14/11]], [[23/18]]
| | [[Skwares]]
| [[Skwares]]
|-
|-
| | 7
| 7
| | 494.12
| 494.12
| | Perfect Fourth
| Perfect Fourth
| style="text-align:center;" | perfect 4th
| perfect 4th
| style="text-align:center;" | P4
| P4
| style="text-align:center;" | F
| F
| style="text-align:center;" | [[4/3]]
| [[4/3]]
| | [[Supra]]
| [[Supra]]
|-
|-
| | 8
| 8
| | 564.71
| 564.71
| |Super Fourth/Diminshed Fifth
| Super Fourth/Diminshed Fifth
| style="text-align:center;" | up 4th, mid 4th,
| up 4th, mid 4th, <br> diminished 5th
diminished 5th
| ^4, ~4, <br> d5
| style="text-align:center;" | ^4, ~4
| ^F, Gb
d5
| [[11/8]], [[18/13]]
| style="text-align:center;" | ^F, Gb
| [[Progress]]
| style="text-align:center;" | [[11/8]], [[18/13]]
| | [[Progress]]
|-
|-
| | 9
| 9
| | 635.29
| 635.29
| | Augmented Fourth/Sub Fifth
| Augmented Fourth/Sub Fifth
| style="text-align:center;" | augmented 4th,
| augmented 4th, <br> down 5th, mid 5th
down 5th, mid 5th
| A4, <br> v5, ~5
| style="text-align:center;" | A4,  
| F#, vG
v5, ~5
| [[16/11]], [[13/9]], [[23/16]]
| style="text-align:center;" | F#, vG
| Progress
| style="text-align:center;" | [[16/11]], [[13/9]], [[23/16]]
| | Progress
|-
|-
| | 10
| 10
| | 705.88
| 705.88
| | Perfect Fifth
| Perfect Fifth
| style="text-align:center;" | perfect 5th
| perfect 5th
| style="text-align:center;" | P5
| P5
| style="text-align:center;" | G
| G
| style="text-align:center;" | [[3/2]]
| [[3/2]]
| | Supra
| Supra
|-
|-
| | 11
| 11
| | 776.47
| 776.47
| | Super Fifth/Minor Sixth
| Super Fifth/Minor Sixth
| style="text-align:center;" | minor 6th
| minor 6th
| style="text-align:center;" | m6
| m6
| style="text-align:center;" | Ab
| Ab
| style="text-align:center;" | [[25/16]], [[14/9]], [[11/7]]
| [[25/16]], [[14/9]], [[11/7]]
| | Skwares
| Skwares
|-
|-
| | 12
| 12
| | 847.06
| 847.06
| | Augmented Fifth/Neutral Sixth/
| Augmented Fifth/Neutral Sixth/ <br> Diminished Seventh
Diminished Seventh
| mid 6th
| style="text-align:center;" | mid 6th
| ~6
| style="text-align:center;" | ~6
| vA
| style="text-align:center;" | vA
| [[13/8]], [[18/11]], [[23/14]]
| style="text-align:center;" | [[13/8]], [[18/11]], [[23/14]]
| Maqamic/hemif
| | Maqamic/hemif
|-
|-
| | 13
| 13
| | 917.65
| 917.65
| | Major Sixth/Sub Seventh
| Major Sixth/Sub Seventh
| style="text-align:center;" | major 6th
| major 6th
| style="text-align:center;" | M6
| M6
| style="text-align:center;" | A
| A
| style="text-align:center;" | [[17/10]], [[22/13]],[[12/7]]
| [[17/10]], [[22/13]],[[12/7]]
| | Huxley
| Huxley
|-
|-
| | 14
| 14
| | 988.235
| 988.24
| | Minor Seventh/Super Sixth
| Minor Seventh/Super Sixth
| style="text-align:center;" | minor 7th
| minor 7th
| style="text-align:center;" | m7
| m7
| style="text-align:center;" | Bb
| Bb
| style="text-align:center;" | [[16/9]], [[7/4]], [[25/14]], [[23/13]]
| [[16/9]], [[7/4]], [[25/14]], [[23/13]]
| | Machine
| Machine
|-
|-
| | 15
| 15
| | 1058.82
| 1058.82
| | Augmented Sixth/Neutral Seventh/
| Augmented Sixth/Neutral Seventh/ <br> Diminished Octave
Diminished Octave
| mid 7th
| style="text-align:center;" | mid 7th
| ~7
| style="text-align:center;" | ~7
| vB
| style="text-align:center;" | vB
| [[11/6]], [[24/13]], [[13/7]]
| style="text-align:center;" | [[11/6]], [[24/13]], [[13/7]]
| Bleu
| | Bleu
|-
|-
| | 16
| 16
| | 1129.41
| 1129.41
| | Major Seventh/Sub Octave
| Major Seventh/Sub Octave
| style="text-align:center;" | major 7th
| major 7th
| style="text-align:center;" | M7
| M7
| style="text-align:center;" | B
| B
| style="text-align:center;" | [[25/13]], [[48/25]], [[64/33]], [[23/12]]
| [[25/13]], [[48/25]], [[64/33]], [[23/12]]
| |
|
|-
|-
| | 17
| 17
| | 1200
| 1200.00
| | Perfect Octave
| Perfect Octave
| style="text-align:center;" | octave
| octave
| style="text-align:center;" | P8
| P8
| style="text-align:center;" | C
| C
| style="text-align:center;" | [[2/1]]
| [[2/1]]
| |  
|  
|}
|}
<nowiki>*</nowiki>Ratios based on treating 17edo as a 2.3.7.11.13.23.25 subgroup
<nowiki>*</nowiki>Ratios based on treating 17edo as a 2.3.7.11.13.23.25 subgroup
Line 206: Line 199:
Combining ups and downs notation with [[color notation]], qualities can be loosely associated with colors:
Combining ups and downs notation with [[color notation]], qualities can be loosely associated with colors:


{| class="wikitable"
{| class="wikitable center-all"
! quality
! color
! monzo format
! examples
|-
|-
! | quality
| minor
! | color
| zo
! | monzo format
| {a, b, 0, 1}
! | examples
| 7/6, 7/4
|-
|-
| style="text-align:center;" | minor
| "
| style="text-align:center;" | zo
| fourthward wa
| style="text-align:center;" | {a, b, 0, 1}
| {a, b}, b &lt; -1
| style="text-align:center;" | 7/6, 7/4
| 32/27, 16/9
|-
|-
| style="text-align:center;" | "
| mid
| style="text-align:center;" | fourthward wa
| ilo
| style="text-align:center;" | {a, b}, b &lt; -1
| {a, b, 0, 0, 1}
| style="text-align:center;" | 32/27, 16/9
| 11/9, 11/6
|-
|-
| style="text-align:center;" | mid
| "
| style="text-align:center;" | ilo
| lu
| style="text-align:center;" | {a, b, 0, 0, 1}
| {a, b, 0, 0, -1}
| style="text-align:center;" | 11/9, 11/6
| 12/11, 18/11
|-
|-
| style="text-align:center;" | "
| major
| style="text-align:center;" | lu
| fifthward wa
| style="text-align:center;" | {a, b, 0, 0, -1}
| {a, b}, b &gt; 1
| style="text-align:center;" | 12/11, 18/11
| 9/8, 27/16
|-
|-
| style="text-align:center;" | major
| "
| style="text-align:center;" | fifthward wa
| ru
| style="text-align:center;" | {a, b}, b &gt; 1
| {a, b, 0, -1}
| style="text-align:center;" | 9/8, 27/16
| 9/7, 12/7
|-
| style="text-align:center;" | "
| style="text-align:center;" | ru
| style="text-align:center;" | {a, b, 0, -1}
| style="text-align:center;" | 9/7, 12/7
|}
|}


=Chord Names=
== Chord Names ==


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


{| class="wikitable"
{| class="wikitable center-all"
|-
|-
! | [[Kite's color notation|color of the 3rd]]
! [[Kite's color notation|color of the 3rd]]
! | JI chord
! JI chord
! | notes as edosteps
! notes as edosteps
! | notes of C chord
! notes of C chord
! | written name
! written name
! | spoken name
! spoken name
|-
|-
| style="text-align:center;" | zo
| zo
| style="text-align:center;" | 6:7:9
| 6:7:9
| style="text-align:center;" | 0-4-10
| 0-4-10
| style="text-align:center;" | C Eb G
| C Eb G
| style="text-align:center;" | Cm
| Cm
| style="text-align:center;" | C minor
| C minor
|-
|-
| style="text-align:center;" | ilo
| ilo
| style="text-align:center;" | 18:22:27
| 18:22:27
| style="text-align:center;" | 0-5-10
| 0-5-10
| style="text-align:center;" | C vE G
| C vE G
| style="text-align:center;" | C~
| C~
| style="text-align:center;" | C mid
| C mid
|-
|-
| style="text-align:center;" | ru
| ru
| style="text-align:center;" | 14:18:21
| 14:18:21
| style="text-align:center;" | 0-6-10
| 0-6-10
| style="text-align:center;" | C E G
| C E G
| style="text-align:center;" | C
| C
| style="text-align:center;" | C major or C
| C major or C
|}
|}


Line 297: Line 289:
For a more complete list, see [[Ups and Downs Notation#Chords and Chord Progressions|Ups and Downs Notation - Chords and Chord Progressions]].
For a more complete list, see [[Ups and Downs Notation#Chords and Chord Progressions|Ups and Downs Notation - Chords and Chord Progressions]].


=Selected just intervals by error=
== Selected just intervals by error ==
{| class="wikitable" style="text-align:center;"
{| class="wikitable center-all"
!
!
!prime 2
! prime 2
!prime 3
! prime 3
!prime 5
! prime 5
!prime 7
! prime 7
!prime 11
! prime 11
!prime 13
! prime 13
|-
|-
!error
! error
|0¢
| 0¢
| +3.93¢
| +3.93¢
| -33.4¢
| -33.4¢
Line 315: Line 307:
| +6.5¢
| +6.5¢
|-
|-
![[fifthspan]]
! [[fifthspan]]
|0
| 0
| +1
| +1
| -8
| -8
Line 325: Line 317:
The following table shows how [[Just-24|some prominent just intervals]] are represented in 17edo (ordered by absolute error).
The following table shows how [[Just-24|some prominent just intervals]] are represented in 17edo (ordered by absolute error).


===Best direct mapping, even if inconsistent===
=== Best direct mapping, even if inconsistent ===


{| class="wikitable sortable" style="text-align:center;"  
{| class="wikitable sortable center-1 right-2"
|-
|-
! class=unsortable | Interval, complement
! class=unsortable | Interval, <br> complement
! Error (abs., in [[cent]]s)
! Abs. error <br> (in [[cent]]s)
|-
|-
| [[18/13]], [[13/9]]
| [[18/13]], [[13/9]]
Line 338: Line 330:
| 2.604
| 2.604
|-
|-
| '''[[4/3]], [[3/2]]'''
| [[4/3]], [[3/2]]
| 3.927
| 3.927
|-
|-
Line 347: Line 339:
| 6.021
| 6.021
|-
|-
| '''[[16/13]], [[13/8]]'''
| [[16/13]], [[13/8]]
| 6.531'''
| 6.531
|-
|-
| [[13/11]], [[22/13]]
| [[13/11]], [[22/13]]
Line 365: Line 357:
| 12.878
| 12.878
|-
|-
| '''[[11/8]], [[16/11]]'''
| [[11/8]], [[16/11]]
| 13.388'''
| 13.388
|-
|-
| [[7/6]], [[12/7]]
| [[7/6]], [[12/7]]
Line 374: Line 366:
| 17.806
| 17.806
|-
|-
| '''[[8/7]], [[7/4]]'''
| [[8/7]], [[7/4]]
| '''19.409'''
| 19.409
|-
|-
| [[15/14]], [[28/15]]
| [[15/14]], [[28/15]]
Line 398: Line 390:
| 33.288
| 33.288
|-
|-
| '''[[5/4]], [[8/5]]'''
| [[5/4]], [[8/5]]
| '''33.373'''
| 33.373
|-
|-
| [[15/13]], [[26/15]]
| [[15/13]], [[26/15]]
Line 405: Line 397:
|}
|}


===Patent val mapping===
=== Patent val mapping ===


{| class="wikitable"
{| class="wikitable center-1 right-2"
|-
|-
| | '''Interval, complement'''
! Interval, <br> complement
| | '''Error (abs., in [[cent]]s)'''
! Abs. error <br> (in [[cent]]s)
|-
|-
| style="text-align:center;" | [[18/13]], [[13/9]]
| [[18/13]], [[13/9]]
| style="text-align:center;" | 1.324
| 1.324
|-
|-
| style="text-align:center;" | [[13/12]], [[24/13]]
| [[13/12]], [[24/13]]
| style="text-align:center;" | 2.604
| 2.604
|-
|-
| style="text-align:center;" | '''[[4/3]], [[3/2]]'''
| '''[[4/3]], [[3/2]]'''
| style="text-align:center;" | '''3.927'''
| '''3.927'''
|-
|-
| style="text-align:center;" | [[11/9]], [[18/11]]
| [[11/9]], [[18/11]]
| style="text-align:center;" | 5.533
| 5.533
|-
|-
| style="text-align:center;" | [[14/11]], [[11/7]]
| [[14/11]], [[11/7]]
| style="text-align:center;" | 6.021
| 6.021
|-
|-
| style="text-align:center;" | '''[[16/13]], [[13/8]]'''
| '''[[16/13]], [[13/8]]'''
| style="text-align:center;" | '''6.531'''
| '''6.531'''
|-
|-
| style="text-align:center;" | [[13/11]], [[22/13]]
| [[13/11]], [[22/13]]
| style="text-align:center;" | 6.857
| 6.857
|-
|-
| style="text-align:center;" | [[9/8]], [[16/9]]
| [[9/8]], [[16/9]]
| style="text-align:center;" | 7.855
| 7.855
|-
|-
| style="text-align:center;" | [[12/11]], [[11/6]]
| [[12/11]], [[11/6]]
| style="text-align:center;" | 9.461
| 9.461
|-
|-
| style="text-align:center;" | [[9/7]], [[14/9]]
| [[9/7]], [[14/9]]
| style="text-align:center;" | 11.555
| 11.555
|-
|-
| style="text-align:center;" | [[14/13]], [[13/7]]
| [[14/13]], [[13/7]]
| style="text-align:center;" | 12.878
| 12.878
|-
|-
| style="text-align:center;" | '''[[11/8]], [[16/11]]'''
| '''[[11/8]], [[16/11]]'''
| style="text-align:center;" | '''13.388'''
| '''13.388'''
|-
|-
| style="text-align:center;" | [[7/6]], [[12/7]]
| [[7/6]], [[12/7]]
| style="text-align:center;" | 15.482
| 15.482
|-
|-
| style="text-align:center;" | '''[[8/7]], [[7/4]]'''
| '''[[8/7]], [[7/4]]'''
| style="text-align:center;" | '''19.409'''
| '''19.409'''
|-
|-
| style="text-align:center;" | [[16/15]], [[15/8]]
| [[16/15]], [[15/8]]
| style="text-align:center;" | 29.445
| 29.445
|-
|-
| style="text-align:center;" | '''[[5/4]], [[8/5]]'''
| '''[[5/4]], [[8/5]]'''
| style="text-align:center;" | '''33.373'''
| '''33.373'''
|-
|-
| style="text-align:center;" | [[15/13]], [[26/15]]
| [[15/13]], [[26/15]]
| style="text-align:center;" | 35.976
| 35.976
|-
|-
| style="text-align:center;" | [[6/5]], [[5/3]]
| [[6/5]], [[5/3]]
| style="text-align:center;" | 37.300
| 37.300
|-
|-
| style="text-align:center;" | [[13/10]], [[20/13]]
| [[13/10]], [[20/13]]
| style="text-align:center;" | 39.904
| 39.904
|-
|-
| style="text-align:center;" | [[10/9]], [[9/5]]
| [[10/9]], [[9/5]]
| style="text-align:center;" | 41.227
| 41.227
|-
|-
| style="text-align:center;" | [[15/11]], [[22/15]]
| [[15/11]], [[22/15]]
| style="text-align:center;" | 42.833
| 42.833
|-
|-
| style="text-align:center;" | [[11/10]], [[20/11]]
| [[11/10]], [[20/11]]
| style="text-align:center;" | 46.760
| 46.760
|-
|-
| style="text-align:center;" | [[15/14]], [[28/15]]
| [[15/14]], [[28/15]]
| style="text-align:center;" | 48.855
| 48.855
|-
|-
| style="text-align:center;" | [[7/5]], [[10/7]]
| [[7/5]], [[10/7]]
| style="text-align:center;" | 52.782
| 52.782
|}
|}


Line 489: Line 481:
[[:File:17ed2-001.svg|17ed2-001.svg]]
[[:File:17ed2-001.svg|17ed2-001.svg]]


=Commas=
== Commas ==
17 EDO [[tempering out|tempers out]] the following [[comma]]s. (Note: This assumes [[val]] {{val| 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]] {{val| 17 27 39 48 59 63 }}, cent values ​​rounded to 5 digits.)


{| class="wikitable"
{| class="wikitable center-all left-2 right-3"
|-
|-
! | Comma
! Comma
! | Monzo
! Monzo
! | Cents
! Cents
![[Color notation/Temperament Names|Color Name]]
! [[Color notation/Temperament Names|Color Name]]
! | Name 1
! Name 1
! | Name 2
! Name 2
! | Name 3
! Name 3
|-
|-
| style="text-align:center;" | <span style="display: block; text-align: center;"></span>
|  
| | {{Monzo | 27 -17 }}
| {{Monzo | 27 -17 }}
| style="text-align:right;" | 66.765
| 66.765
| style="text-align:center;" |Sasawa
| Sasawa
| | <span style="display: block; text-align: center;">17-Comma</span>
| 17-Comma
| style="text-align:center;" |  
|  
| |  
|  
|-
|-
| style="text-align:center;" | 25/24
| 25/24
| | {{Monzo | -3 -1 2 }}
| {{Monzo | -3 -1 2 }}
| style="text-align:right;" | 70.762
| 70.762
| style="text-align:center;" |Yoyo
| Yoyo
| | Chromatic semitone
| Chromatic semitone
| style="text-align:center;" | Dicot comma
| Dicot comma
| |  
|  
|-
|-
| style="text-align:center;" | 32805/32768
| 32805/32768
| | {{Monzo | -15 8 1 }}
| {{Monzo | -15 8 1 }}
| style="text-align:right;" | 1.9537
| 1.9537
| style="text-align:center;" |Layo
| Layo
| style="text-align:center;" | Schisma
| Schisma
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
|-
|-
| style="text-align:center;" | 525/512
| 525/512
| | {{Monzo | -9 1 2 1 }}
| {{Monzo | -9 1 2 1 }}
| style="text-align:right;" | 43.408
| 43.408
| style="text-align:center;" |Zoyoyo
| Zoyoyo
| style="text-align:center;" | Avicennma
| Avicennma
| style="text-align:center;" | Avicennma's Enharmonic Diesis
| Avicennma's Enharmonic Diesis
| style="text-align:center;" |  
|  
|-
|-
| style="text-align:center;" | 64/63
| 64/63
| | {{Monzo | 6 -2 0 -1 }}
| {{Monzo | 6 -2 0 -1 }}
| style="text-align:right;" | 27.264
| 27.264
| style="text-align:center;" |Ru
| Ru
| style="text-align:center;" | Septimal Comma
| Septimal Comma
| style="text-align:center;" | Archytas' Comma
| Archytas' Comma
| style="text-align:center;" | Leipziger Komma
| Leipziger Komma
|-
|-
| style="text-align:center;" | 245/243
| 245/243
| | {{Monzo | 0 -5 1 2 }}
| {{Monzo | 0 -5 1 2 }}
| style="text-align:right;" | 14.191
| 14.191
| style="text-align:center;" |Zozoyo
| Zozoyo
| style="text-align:center;" | Sensamagic
| Sensamagic
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
|-
|-
| style="text-align:center;" | 1728/1715
| 1728/1715
| | {{Monzo | 6 3 -1 -3 }}
| {{Monzo | 6 3 -1 -3 }}
| style="text-align:right;" | 13.074
| 13.074
| style="text-align:center;" |Triru-agu
| Triru-agu
| style="text-align:center;" | Orwellisma
| Orwellisma
| style="text-align:center;" | Orwell Comma
| Orwell Comma
| style="text-align:center;" |  
|  
|-
|-
| style="text-align:center;" |  
|  
| | {{Monzo | -6 -8 2 5 }}
| {{Monzo | -6 -8 2 5 }}
| style="text-align:right;" | 1.1170
| 1.1170
| style="text-align:center;" |Quinzo-ayoyo
| Quinzo-ayoyo
| style="text-align:center;" | Wizma
| Wizma
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
|-
|-
| style="text-align:center;" | 99/98
| 99/98
| | {{Monzo | -1 2 0 -2 1 }}
| {{Monzo | -1 2 0 -2 1 }}
| style="text-align:right;" | 17.576
| 17.576
| style="text-align:center;" |Loruru
| Loruru
| style="text-align:center;" | Mothwellsma
| Mothwellsma
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
|-
|-
| style="text-align:center;" | 896/891
| 896/891
| | {{Monzo | 7 -4 0 1 -1 }}
| {{Monzo | 7 -4 0 1 -1 }}
| style="text-align:right;" | 9.6880
| 9.6880
| style="text-align:center;" |Saluzo
| Saluzo
| style="text-align:center;" | Pentacircle
| Pentacircle
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
|-
|-
| style="text-align:center;" | 243/242
| 243/242
| | {{Monzo | -1 5 0 0 -2 }}
| {{Monzo| -1 5 0 0 -2 }}
| style="text-align:right;" | 7.1391
| 7.1391
| style="text-align:center;" |Lulu
| Lulu
| style="text-align:center;" | Rastma
| Rastma
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
|-
|-
| style="text-align:center;" | 385/384
| 385/384
| | {{Monzo | -7 -1 1 1 1 }}
| {{Monzo| -7 -1 1 1 1 }}
| style="text-align:right;" | 4.5026
| 4.5026
| style="text-align:center;" |Lozoyo
| Lozoyo
| style="text-align:center;" | Keenanisma
| Keenanisma
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
|}
|}


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.
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=
== Scales ==
* [[Otonal 17]]
* [[Otonal 17]]
* [https://web.archive.org/web/20140215081520/http://microtonalismo.com/proyecto-xvii Blues Peruvian 17edo]
* [https://web.archive.org/web/20140215081520/http://microtonalismo.com/proyecto-xvii Blues Peruvian 17edo]
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* [[MOS scales of 17edo]] (horograms)
* [[MOS scales of 17edo]] (horograms)


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


=Music=
== Music ==
==Scores==
=== Scores ===
* [http://home.snafu.de/djwolf/PreludeIn17tet.pdf Prelude] (PDF) by [[Daniel Wolf]]
* [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/heptadecatonic-drops/ Heptadecatonic Drops] by [http://georghajdu.de/biography/ Georg Hajdu]
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* [http://christopherbaileymusic.com/walrus/v/#../../kitwo245m45n698th139rwebm845MQPxiF82J7WovYNRLK6klyq456/balladei.pdf Balladei] by [http://christopherbaileymusic.com/quick-bio/ Christopher Bailey]
* [http://christopherbaileymusic.com/walrus/v/#../../kitwo245m45n698th139rwebm845MQPxiF82J7WovYNRLK6klyq456/balladei.pdf Balladei] by [http://christopherbaileymusic.com/quick-bio/ Christopher Bailey]


==Sound files==
=== Sound files ===
* [https://youtu.be/aU8RmEeXap8 Arm's Length by Diamond Doll (xen-pop)]
* [https://youtu.be/aU8RmEeXap8 Arm's Length by Diamond Doll (xen-pop)]
* [https://themercurytree.bandcamp.com/album/spidermilk Spidermilk] (prog album) by [https://themercurytree.bandcamp.com/ The Mercury Tree]
* [https://themercurytree.bandcamp.com/album/spidermilk Spidermilk] (prog album) by [https://themercurytree.bandcamp.com/ The Mercury Tree]
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** ''Flying Into O'Hare'': [http://chrisvaisvil.com/?p=6909 blog] | [http://micro.soonlabel.com/17-ET/20161125_linn_speactral_17.MP3 MP3]
** ''Flying Into O'Hare'': [http://chrisvaisvil.com/?p=6909 blog] | [http://micro.soonlabel.com/17-ET/20161125_linn_speactral_17.MP3 MP3]


=Instruments=
== Instruments ==
* '''[http://www.microtonalismo.com/proyecto-xvii Guitar Heptadecatonic from Peruvian - Charles Loli and Antonio Huamani]''' {{forbidden}}
* '''[http://www.microtonalismo.com/proyecto-xvii Guitar Heptadecatonic from Peruvian - Charles Loli and Antonio Huamani]''' {{forbidden}}
  {{External image| http://sphotos.ak.fbcdn.net/hphotos-ak-snc4/hs883.snc4/71639_167001659983806_100000219181856_601995_1526184_n.jpg {{dead link}} }}
  {{External image| http://sphotos.ak.fbcdn.net/hphotos-ak-snc4/hs883.snc4/71639_167001659983806_100000219181856_601995_1526184_n.jpg {{dead link}} }}
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