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. |
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| 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" | ||
|- | |- | ||
! | ! Edo steps | ||
! Cents | ! Cents | ||
! Names of Intervals | ! colspan="2" | Names of Intervals | ||
! | ! Note Name | ||
! [[Ups and Downs Notation]] | |||
! Approximate Ratios* | ! Approximate Ratios* | ||
! Temperament(s) generated | ! Temperament(s) generated | ||
| Line 35: | Line 36: | ||
| 0.00 | | 0.00 | ||
| Unison | | Unison | ||
| P1 | | P1 | ||
| C | |||
| C | | C | ||
| 1/1 | | 1/1 | ||
| Line 44: | Line 45: | ||
| 70.59 | | 70.59 | ||
| Super Unison/Minor Second | | Super Unison/Minor Second | ||
| m2 | | m2 | ||
| Db | | Db <br> (B#) | ||
| ^C | |||
| [[25/24]], [[26/25]], [[33/32]], [[24/23]] | | [[25/24]], [[26/25]], [[33/32]], [[24/23]] | ||
| | | | ||
| Line 53: | Line 54: | ||
| 141.18 | | 141.18 | ||
| Augmented Unison/Neutral Second | | Augmented Unison/Neutral Second | ||
| ~2 | | ~2 | ||
| C# | |||
| vD | | vD | ||
| [[13/12]], [[12/11]], [[14/13]], [[25/23]] | | [[13/12]], [[12/11]], [[14/13]], [[25/23]] | ||
| Line 62: | Line 63: | ||
| 211.76 | | 211.76 | ||
| Major Second/Sub Third | | Major Second/Sub Third | ||
| 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]] | ||
| Line 71: | Line 72: | ||
| 282.35 | | 282.35 | ||
| Minor Third/Super Second | | Minor Third/Super Second | ||
| m3 | | m3 | ||
| Eb | | Eb | ||
| ^D | |||
| [[13/11]], [[7/6]] | | [[13/11]], [[7/6]] | ||
| [[Huxley]]/[[Chromatic pairs#Lovecraft|Lovecraft]] | | [[Huxley]]/[[Chromatic pairs#Lovecraft|Lovecraft]] | ||
| Line 80: | Line 81: | ||
| 352.94 | | 352.94 | ||
| Augmented Second/Neutral Third/ <br> Diminished Fourth | | Augmented Second/Neutral Third/ <br> Diminished Fourth | ||
| ~3 | | ~3 | ||
| D# <br> (Fb) | |||
| vE | | vE | ||
| [[11/9]], [[16/13]], [[28/23]] | | [[11/9]], [[16/13]], [[28/23]] | ||
| Line 89: | Line 90: | ||
| 423.53 | | 423.53 | ||
| Major Third/Sub Fourth | | Major Third/Sub Fourth | ||
| 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]] | ||
| Line 98: | Line 99: | ||
| 494.12 | | 494.12 | ||
| Perfect Fourth | | Perfect Fourth | ||
| P4 | | P4 | ||
| F | |||
| F | | F | ||
| [[4/3]] | | [[4/3]] | ||
| Line 107: | Line 108: | ||
| 564.71 | | 564.71 | ||
| Super Fourth/Diminshed Fifth | | Super Fourth/Diminshed Fifth | ||
| ^4, ~4, <br> d5 | | ^4, ~4, <br> d5 | ||
| ^F | | Gb <br> (E#) | ||
| ^F | |||
| [[11/8]], [[18/13]], [[32/23]] | | [[11/8]], [[18/13]], [[32/23]] | ||
| [[Progress]] | | [[Progress]] | ||
| Line 116: | Line 117: | ||
| 635.29 | | 635.29 | ||
| Augmented Fourth/Sub Fifth | | Augmented Fourth/Sub Fifth | ||
| A4, <br> v5, ~5 | | A4, <br> v5, ~5 | ||
| F# | | F# | ||
| vG | |||
| [[16/11]], [[13/9]], [[23/16]] | | [[16/11]], [[13/9]], [[23/16]] | ||
| Progress | | Progress | ||
| Line 125: | Line 126: | ||
| 705.88 | | 705.88 | ||
| Perfect Fifth | | Perfect Fifth | ||
| P5 | | P5 | ||
| G | |||
| G | | G | ||
| [[3/2]] | | [[3/2]] | ||
| Line 134: | Line 135: | ||
| 776.47 | | 776.47 | ||
| Super Fifth/Minor Sixth | | Super Fifth/Minor Sixth | ||
| 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 | ||
| Line 143: | Line 144: | ||
| 847.06 | | 847.06 | ||
| Augmented Fifth/Neutral Sixth/ <br> Diminished Seventh | | Augmented Fifth/Neutral Sixth/ <br> Diminished Seventh | ||
| ~6 | | ~6 | ||
| G# | |||
| vA | | vA | ||
| [[13/8]], [[18/11]], [[23/14]] | | [[13/8]], [[18/11]], [[23/14]] | ||
| Line 152: | Line 153: | ||
| 917.65 | | 917.65 | ||
| Major Sixth/Sub Seventh | | Major Sixth/Sub Seventh | ||
| M6 | | M6 | ||
| A | |||
| A | | A | ||
| [[17/10]], [[22/13]],[[12/7]] | | [[17/10]], [[22/13]],[[12/7]] | ||
| Line 161: | Line 162: | ||
| 988.24 | | 988.24 | ||
| Minor Seventh/Super Sixth | | Minor Seventh/Super Sixth | ||
| 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 | ||
| Line 170: | Line 171: | ||
| 1058.82 | | 1058.82 | ||
| Augmented Sixth/Neutral Seventh/ <br> Diminished Octave | | Augmented Sixth/Neutral Seventh/ <br> Diminished Octave | ||
| ~7 | | ~7 | ||
| A# <br> (Cb) | |||
| vB | | vB | ||
| [[11/6]], [[24/13]], [[13/7]], [[46/25]] | | [[11/6]], [[24/13]], [[13/7]], [[46/25]] | ||
| Line 179: | Line 180: | ||
| 1129.41 | | 1129.41 | ||
| Major Seventh/Sub Octave | | Major Seventh/Sub Octave | ||
| M7 | | M7 | ||
| B | |||
| B | | B | ||
| [[25/13]], [[48/25]], [[64/33]], [[23/12]] | | [[25/13]], [[48/25]], [[64/33]], [[23/12]] | ||
| Line 188: | Line 189: | ||
| 1200.00 | | 1200.00 | ||
| Perfect Octave | | Perfect Octave | ||
| P8 | | P8 | ||
| C | |||
| C | | C | ||
| [[2/1]] | | [[2/1]] | ||
| Line 195: | Line 196: | ||
|} | |} | ||
<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: | ||