17edo: Difference between revisions

Comma table: no need for multiple name columns since most of them are blank
I've edited the interval table to separate note names using sharps-and-flats only from ups-and-downs notation, and filled in several enharmonic equivalent spelling.
Line 25: Line 25:
{| class="wikitable center-all right-1 right-2 left-3 left-7"
{| class="wikitable center-all right-1 right-2 left-3 left-7"
|-
|-
! Degree
! Edo steps
! Cents
! Cents
! Names of Intervals
! colspan="2" | Names of Intervals
! colspan="3" | [[Ups and Downs Notation]]
! Note Name
! [[Ups and Downs Notation]]
! Approximate Ratios*
! Approximate Ratios*
! Temperament(s) generated
! Temperament(s) generated
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| 0.00
| 0.00
| Unison
| Unison
| unison
| P1
| P1
| C
| C
| C
| 1/1
| 1/1
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| 70.59
| 70.59
| Super Unison/Minor Second
| Super Unison/Minor Second
| minor 2nd
| m2
| m2
| Db
| Db <br> (B#)
| ^C
| [[25/24]], [[26/25]], [[33/32]], [[24/23]]
| [[25/24]], [[26/25]], [[33/32]], [[24/23]]
|  
|  
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| 141.18
| 141.18
| Augmented Unison/Neutral Second
| Augmented Unison/Neutral Second
| mid 2nd
| ~2
| ~2
| C#
| vD
| vD
| [[13/12]], [[12/11]], [[14/13]], [[25/23]]
| [[13/12]], [[12/11]], [[14/13]], [[25/23]]
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| 211.76
| 211.76
| Major Second/Sub Third
| Major Second/Sub Third
| major 2nd
| M2
| M2
| D
| D
| D
| [[9/8]], [[8/7]], [[28/25]], [[25/22]], [[26/23]]
| [[9/8]], [[8/7]], [[28/25]], [[25/22]], [[26/23]]
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| 282.35
| 282.35
| Minor Third/Super Second
| Minor Third/Super Second
| minor 3rd
| m3
| m3
| Eb
| Eb
| ^D
| [[13/11]], [[7/6]]
| [[13/11]], [[7/6]]
| [[Huxley]]/[[Chromatic pairs#Lovecraft|Lovecraft]]
| [[Huxley]]/[[Chromatic pairs#Lovecraft|Lovecraft]]
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| 352.94
| 352.94
| Augmented Second/Neutral Third/ <br> Diminished Fourth
| Augmented Second/Neutral Third/ <br> Diminished Fourth
| mid 3rd
| ~3
| ~3
| D# <br> (Fb)
| vE
| vE
| [[11/9]], [[16/13]], [[28/23]]
| [[11/9]], [[16/13]], [[28/23]]
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| 423.53
| 423.53
| Major Third/Sub Fourth
| Major Third/Sub Fourth
| major 3rd
| M3
| M3
| E
| E
| E
| [[32/25]], [[9/7]], [[14/11]], [[33/26]], [[23/18]]
| [[32/25]], [[9/7]], [[14/11]], [[33/26]], [[23/18]]
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| 494.12
| 494.12
| Perfect Fourth
| Perfect Fourth
| perfect 4th
| P4
| P4
| F
| F
| F
| [[4/3]]
| [[4/3]]
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| 564.71
| 564.71
| Super Fourth/Diminshed Fifth
| Super Fourth/Diminshed Fifth
| up 4th, mid 4th, <br> diminished 5th
| ^4, ~4, <br> d5
| ^4, ~4, <br> d5
| ^F, Gb
| Gb <br> (E#)
| ^F
| [[11/8]], [[18/13]], [[32/23]]
| [[11/8]], [[18/13]], [[32/23]]
| [[Progress]]
| [[Progress]]
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| 635.29
| 635.29
| Augmented Fourth/Sub Fifth
| Augmented Fourth/Sub Fifth
| augmented 4th, <br> down 5th, mid 5th
| A4, <br> v5, ~5
| A4, <br> v5, ~5
| F#, vG
| F#
| vG
| [[16/11]], [[13/9]], [[23/16]]
| [[16/11]], [[13/9]], [[23/16]]
| Progress
| Progress
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| 705.88
| 705.88
| Perfect Fifth
| Perfect Fifth
| perfect 5th
| P5
| P5
| G
| G
| G
| [[3/2]]
| [[3/2]]
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| 776.47
| 776.47
| Super Fifth/Minor Sixth
| Super Fifth/Minor Sixth
| minor 6th
| m6
| m6
| Ab
| Ab
| ^G
| [[25/16]], [[14/9]], [[11/7]], [[52/33]], [[36/23]]
| [[25/16]], [[14/9]], [[11/7]], [[52/33]], [[36/23]]
| Skwares
| Skwares
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| 847.06
| 847.06
| Augmented Fifth/Neutral Sixth/ <br> Diminished Seventh
| Augmented Fifth/Neutral Sixth/ <br> Diminished Seventh
| mid 6th
| ~6
| ~6
| G#
| vA
| vA
| [[13/8]], [[18/11]], [[23/14]]
| [[13/8]], [[18/11]], [[23/14]]
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| 917.65
| 917.65
| Major Sixth/Sub Seventh
| Major Sixth/Sub Seventh
| major 6th
| M6
| M6
| A
| A
| A
| [[17/10]], [[22/13]],[[12/7]]
| [[17/10]], [[22/13]],[[12/7]]
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| 988.24
| 988.24
| Minor Seventh/Super Sixth
| Minor Seventh/Super Sixth
| minor 7th
| m7
| m7
| Bb
| Bb
| ^A
| [[16/9]], [[7/4]], [[25/14]], [[44/25]], [[23/13]]
| [[16/9]], [[7/4]], [[25/14]], [[44/25]], [[23/13]]
| Machine
| Machine
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| 1058.82
| 1058.82
| Augmented Sixth/Neutral Seventh/ <br> Diminished Octave
| Augmented Sixth/Neutral Seventh/ <br> Diminished Octave
| mid 7th
| ~7
| ~7
| A# <br> (Cb)
| vB
| vB
| [[11/6]], [[24/13]], [[13/7]], [[46/25]]
| [[11/6]], [[24/13]], [[13/7]], [[46/25]]
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| 1129.41
| 1129.41
| Major Seventh/Sub Octave
| Major Seventh/Sub Octave
| major 7th
| M7
| M7
| B
| B
| B
| [[25/13]], [[48/25]], [[64/33]], [[23/12]]
| [[25/13]], [[48/25]], [[64/33]], [[23/12]]
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| 1200.00
| 1200.00
| Perfect Octave
| Perfect Octave
| octave
| P8
| P8
| C
| C
| C
| [[2/1]]
| [[2/1]]
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|}
|}
<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
In 17edo, ups and downs can respectively be substituted with half-sharps and half-flats,
since sharps and flats each span two edo steps.
Using half-sharps and half-flats may be preferable for compatibility with the ups-and-downs notation in [[34edo]],
in which and up or down respectively constitute a quarter-sharp or quarter-flat.


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: