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17edo: Difference between revisions

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→Intervals: improve interval organisation and remove the most extremely questionable interpretations
m →Intervals: sort intervals by complexity. Normalize subgroups to HNF
Line 52: Line 52:
| 1
| 1
| 70.59
| 70.59
| [[28/27]], [[27/26]], [[26/25]], [[25/24]], [[24/23]]
| [[24/23]], [[25/24]], [[26/25]], [[27/26]], [[28/27]]
| Minor 2nd<br>(Semiaugmented 1sn)
| Minor 2nd<br>(Semiaugmented 1sn)
| Eb<br>(Dt)
| Eb<br>(Dt)
Line 58: Line 58:
| ^1, m2
| ^1, m2
| Eb
| Eb
| uber unison,  
| uber unison, <br>minor 2nd
minor 2nd
| U1, m2
| U1, m2
| UD, Eb
| UD, Eb
Line 67: Line 66:
| 2
| 2
| 141.18
| 141.18
| [[14/13]], [[13/12]], [[25/23]], [[12/11]]
| [[12/11]], [[13/12]], [[14/13]], [[25/23]]
| Augmented 1sn<br>(Neutral 2nd)
| Augmented 1sn<br>(Neutral 2nd)
| D#<br>(Ed)
| D#<br>(Ed)
Line 81: Line 80:
| 3
| 3
| 211.76
| 211.76
| [[9/8]], [[26/23]], [[17/15]], [[25/22]], [[8/7]]
| [[8/7]], [[9/8]], [[17/15]], [[25/22]], [[26/23]]
| Major 2nd
| Major 2nd
| E
| E
Line 95: Line 94:
| 4
| 4
| 282.35
| 282.35
| [[7/6]], [[20/17]], [[13/11]]
| [[7/6]], [[13/11]], [[20/17]]
| Minor 3rd
| Minor 3rd
| F
| F
Line 109: Line 108:
| 5
| 5
| 352.94
| 352.94
| [[11/9]], [[27/22]], [[16/13]]
| [[11/9]], [[27/22]], [[16/13]], [[39/32]]
| Diminished 4th<br>(Neutral 3rd)
| Diminished 4th<br>(Neutral 3rd)
| Gb<br>(Ft)
| Gb<br>(Ft)
Line 123: Line 122:
| 6
| 6
| 423.53
| 423.53
| [[14/11]], [[51/40]], [[23/18]], [[32/25]], [[9/7]]
| [[9/7]], [[14/11]], [[23/18]], [[32/25]], [[51/40]]
| Major 3rd<br>(Semidiminished 4th)
| Major 3rd<br>(Semidiminished 4th)
| F#<br>(Gd)
| F#<br>(Gd)
Line 137: Line 136:
| 7
| 7
| 494.12
| 494.12
| [[21/16]], [[85/64]], [[4/3]]
| [[4/3]], [[21/16]], [[85/64]]
| Perfect 4th
| Perfect 4th
| G
| G
Line 157: Line 156:
| ~4, d5
| ~4, d5
| ^G, Ab
| ^G, Ab
| uber 4th/
| uber 4th/<br>neutral 4th
neutral 4th
| U4/N4
| U4/N4
| UG
| UG
Line 166: Line 164:
| 9
| 9
| 635.29
| 635.29
| [[23/16]], [[36/25]], [[13/9]], [[16/11]]
| [[13/9]], [[16/11]], [[23/16]], [[36/25]]
| Augmented 4th<br>(Semidiminished 5th)
| Augmented 4th<br>(Semidiminished 5th)
| G#<br>(Ad)
| G#<br>(Ad)
Line 172: Line 170:
| A4, ~5
| A4, ~5
| G#, vA
| G#, vA
| unter 5th/
| unter 5th/<br>neutral 5th
neutral 5th
| u5/N5
| u5/N5
| uA
| uA
Line 181: Line 178:
| 10
| 10
| 705.88
| 705.88
| [[3/2]], [[128/85]], [[32/21]]
| [[3/2]], [[32/21]], [[128/85]]
| Perfect 5th
| Perfect 5th
| A
| A
Line 195: Line 192:
| 11
| 11
| 776.47
| 776.47
| [[14/9]], [[25/16]], [[36/23]], [[80/51]], [[11/7]]
| [[11/7]], [[14/9]], [[25/16]], [[36/23]], [[80/51]]
| Minor 6th<br>(Semiaugmented 5th)
| Minor 6th<br>(Semiaugmented 5th)
| Bb<br>(At)
| Bb<br>(At)
Line 209: Line 206:
| 12
| 12
| 847.06
| 847.06
| [[13/8]], [[44/27]], [[18/11]]
| [[13/8]], [[18/11]], [[44/27]], [[64/39]]
| Augmented 5th<br>(Neutral 6th)
| Augmented 5th<br>(Neutral 6th)
| A#<br>(Bd)
| A#<br>(Bd)
Line 223: Line 220:
| 13
| 13
| 917.65
| 917.65
| [[17/10]], [[22/13]], [[12/7]]
| [[12/7]], [[17/10]], [[22/13]]
| Major 6th
| Major 6th
| B
| B
Line 237: Line 234:
| 14
| 14
| 988.24
| 988.24
| [[7/4]], [[44/25]], [[30/17]], [[23/13]], [[16/9]]
| [[7/4]], [[16/9]], [[23/13]], [[30/17]], [[44/25]]
| Minor 7th
| Minor 7th
| C
| C
Line 251: Line 248:
| 15
| 15
| 1058.82
| 1058.82
| [[11/6]], [[46/25]], [[24/13]], [[13/7]]
| [[11/6]], [[13/7]], [[24/13]], [[46/25]]
| Diminished 8ve<br>(Neutral 7th)
| Diminished 8ve<br>(Neutral 7th)
| Db<br>(Ct)
| Db<br>(Ct)
Line 265: Line 262:
| 16
| 16
| 1129.41
| 1129.41
| [[23/12]], [[48/25]], [[25/13]], [[52/27]], [[27/14]]
| [[23/12]], [[25/13]], [[27/14]], [[48/25]], [[52/27]]
| Major 7th<br>(Semidiminished 8ve)
| Major 7th<br>(Semidiminished 8ve)
| C#<br>(Dd)
| C#<br>(Dd)
Line 271: Line 268:
| M7, v8
| M7, v8
| C#
| C#
| major 7th,
| major 7th,<br>unter octave
unter octave
| M7, u8
| M7, u8
| C#, uD
| C#, uD
Line 293: Line 289:
|}
|}


<nowiki>*</nowiki> Ratios based on treating 17edo as a 2.3.17/5.7.11.13.23.25 subgroup temperament.  
<nowiki>*</nowiki> Ratios based on treating 17edo as a 2.3.25.7.11.13.85.23-subgroup temperament.  


† Half-sharps and half-flats (denoted "t" and "d", respectively) can be used to alter the note by a single step, since sharps and flats each span two edosteps. Using half-sharps and half-flats may be preferable for compatibility with the ups-and-downs notation in [[34edo]], in which an up or down respectively constitute a quarter-sharp or quarter-flat.
† Half-sharps and half-flats (denoted "t" and "d", respectively) can be used to alter the note by a single step, since sharps and flats each span two edosteps. Using half-sharps and half-flats may be preferable for compatibility with the ups-and-downs notation in [[34edo]], in which an up or down respectively constitute a quarter-sharp or quarter-flat.
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