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17edo: Difference between revisions

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autopatrolled, Sysops
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TallKite (talk | contribs)
autopatrolled, Sysops
4,194 edits
Deleted the "25/24et" cents column (1201.43 cents per 8ve) because it is confusingly close to the usual 1200/8ve cents
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__FORCETOC__
__FORCETOC__


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


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{| class="wikitable"
{| class="wikitable"
|-
|-
! rowspan="2" | Degree
! Degree
! colspan="2" | Cents
! Cents
! rowspan="2" | Names of Intervals
! Names of Intervals
! colspan="3" rowspan="2" | [[Ups and Downs Notation|ups and downs notation]]
! colspan="3" | [[Ups and Downs Notation|ups and downs notation]]
! rowspan="2" | Approximate Ratios*
! Approximate Ratios*
! rowspan="2" | Temperament(s)generated
! Temperament(s)generated
|-
!Pure octave
!25/24et
|-
|-
| colspan="3" | 0
| 0
|0
| | Unison
| | Unison
| style="text-align:center;" | unison
| style="text-align:center;" | unison
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| | 1
| | 1
| | 70.59
| | 70.59
|70.67
| | Super Unison/Minor Second
| | Super Unison/Minor Second
| style="text-align:center;" | minor 2nd
| style="text-align:center;" | minor 2nd
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| | 2
| | 2
| | 141.18
| | 141.18
|141.345
| | Augmented Unison/Neutral Second
| | Augmented Unison/Neutral Second
| style="text-align:center;" | mid 2nd
| style="text-align:center;" | mid 2nd
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| | 3
| | 3
| | 211.765
| | 211.765
|212.02
| | Major Second/Sub Third
| | Major Second/Sub Third
| style="text-align:center;" | major 2nd
| style="text-align:center;" | major 2nd
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| | 4
| | 4
| | 282.35
| | 282.35
|282.69
| | Minor Third/Super Second
| | Minor Third/Super Second
| style="text-align:center;" | minor 3rd
| style="text-align:center;" | minor 3rd
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| | 5
| | 5
| | 352.94
| | 352.94
|353.36
| | Augmented Second/Neutral Third/
| | Augmented Second/Neutral Third/
Diminished Fourth
Diminished Fourth
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| | 6
| | 6
| | 423.53
| | 423.53
|424.035
| | Major Third/Sub Fourth
| | Major Third/Sub Fourth
| style="text-align:center;" | major 3rd
| style="text-align:center;" | major 3rd
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| | 7
| | 7
| | 494.12
| | 494.12
|494.71
| | Perfect Fourth
| | Perfect Fourth
| style="text-align:center;" | perfect 4th
| style="text-align:center;" | perfect 4th
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| | 8
| | 8
| | 564.71
| | 564.71
|565.38
| |Super Fourth/Diminshed Fifth
| |Super Fourth/Diminshed Fifth
| style="text-align:center;" | up 4th,
| style="text-align:center;" | up 4th,
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| | 9
| | 9
| | 635.29
| | 635.29
|636.05
| | Augmented Fourth/Sub Fifth
| | Augmented Fourth/Sub Fifth
| style="text-align:center;" | augmented 4th,
| style="text-align:center;" | augmented 4th,
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| | 10
| | 10
| | 705.88
| | 705.88
|706.72
| | Perfect Fifth
| | Perfect Fifth
| style="text-align:center;" | perfect 5th
| style="text-align:center;" | perfect 5th
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| | 11
| | 11
| | 776.47
| | 776.47
|777.4
| | Super Fifth/Minor Sixth
| | Super Fifth/Minor Sixth
| style="text-align:center;" | minor 6th
| style="text-align:center;" | minor 6th
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| | 12
| | 12
| | 847.06
| | 847.06
|848.07
| | Augmented Fifth/Neutral Sixth/
| | Augmented Fifth/Neutral Sixth/
Diminished Seventh
Diminished Seventh
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| | 13
| | 13
| | 917.65
| | 917.65
|918.74
| | Major Sixth/Sub Seventh
| | Major Sixth/Sub Seventh
| style="text-align:center;" | major 6th
| style="text-align:center;" | major 6th
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| | 14
| | 14
| | 988.235
| | 988.235
|989.41
| | Minor Seventh/Super Sixth
| | Minor Seventh/Super Sixth
| style="text-align:center;" | minor 7th
| style="text-align:center;" | minor 7th
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| | 15
| | 15
| | 1058.82
| | 1058.82
|1060.09
| | Augmented Sixth/Neutral Seventh/
| | Augmented Sixth/Neutral Seventh/
Diminished Octave
Diminished Octave
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| | 16
| | 16
| | 1129.41
| | 1129.41
|1130.76
| | Major Seventh/Sub Octave
| | Major Seventh/Sub Octave
| style="text-align:center;" | major 7th
| style="text-align:center;" | major 7th
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| | 17
| | 17
| | 1200
| | 1200
|1201.43
| | Perfect Octave
| | Perfect Octave
| style="text-align:center;" | octave
| style="text-align:center;" | octave
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| style="text-align:center;" | 2.604
| style="text-align:center;" | 2.604
|-
|-
| style="text-align:center;" | [[4/3]], [[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]], [[18/11]]
| style="text-align:center;" | [[11/9]], [[18/11]]
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| style="text-align:center;" | 6.021
| style="text-align:center;" | 6.021
|-
|-
| style="text-align:center;" | [[16/13]], [[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]], [[22/13]]
| style="text-align:center;" | [[13/11]], [[22/13]]
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| style="text-align:center;" | 12.878
| style="text-align:center;" | 12.878
|-
|-
| style="text-align:center;" | [[11/8]], [[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]], [[12/7]]
| style="text-align:center;" | [[7/6]], [[12/7]]
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| style="text-align:center;" | 17.806
| style="text-align:center;" | 17.806
|-
|-
| style="text-align:center;" | [[8/7]], [[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]], [[28/15]]
| style="text-align:center;" | [[15/14]], [[28/15]]
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| style="text-align:center;" | 33.288
| style="text-align:center;" | 33.288
|-
|-
| style="text-align:center;" | [[5/4]], [[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]], [[26/15]]
| style="text-align:center;" | [[15/13]], [[26/15]]
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| style="text-align:center;" | 2.604
| style="text-align:center;" | 2.604
|-
|-
| style="text-align:center;" | [[4/3]], [[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]], [[18/11]]
| style="text-align:center;" | [[11/9]], [[18/11]]
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| style="text-align:center;" | 6.021
| style="text-align:center;" | 6.021
|-
|-
| style="text-align:center;" | [[16/13]], [[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]], [[22/13]]
| style="text-align:center;" | [[13/11]], [[22/13]]
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| style="text-align:center;" | 12.878
| style="text-align:center;" | 12.878
|-
|-
| style="text-align:center;" | [[11/8]], [[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]], [[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]], [[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]], [[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]], [[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]], [[26/15]]
| style="text-align:center;" | [[15/13]], [[26/15]]
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