17edo: Difference between revisions
m →Rank-2 temperaments: +links |
→Intervals: we found that listing some enharmonics is helpful for real-time playing instruction. Also clarify about + and d |
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| Line 86: | Line 86: | ||
! Edosteps | ! Edosteps | ||
! Cents | ! Cents | ||
! colspan="2" | Extended [[circle-of-fifths notation]] | ! colspan="2" | Extended [[circle-of-fifths notation]] * | ||
! colspan="3" | [[Ups and Downs Notation]] | ! colspan="3" | [[Ups and Downs Notation]] | ||
! Approximate | ! Approximate Ratios† | ||
|- | |- | ||
| 0 | | 0 | ||
| Line 101: | Line 101: | ||
| 1 | | 1 | ||
| 70.59 | | 70.59 | ||
| Minor 2nd | | Minor 2nd<br>(Semiaugmented 1sn) | ||
| Eb | | Eb<br>(D+) | ||
| minor 2nd | | minor 2nd | ||
| m2 | | m2 | ||
| Line 110: | Line 110: | ||
| 2 | | 2 | ||
| 141.18 | | 141.18 | ||
| Neutral 2nd | | Augmented 1sn<br>(Neutral 2nd) | ||
| Ed | | D#<br>(Ed) | ||
| mid 2nd | | mid 2nd | ||
| ~2 | | ~2 | ||
| Line 137: | Line 137: | ||
| 5 | | 5 | ||
| 352.94 | | 352.94 | ||
| Neutral 3rd | | Diminished 4th<br>(Neutral 3rd) | ||
| F+ | | Gb<br>(F+) | ||
| mid 3rd | | mid 3rd | ||
| ~3 | | ~3 | ||
| Line 146: | Line 146: | ||
| 6 | | 6 | ||
| 423.53 | | 423.53 | ||
| Major 3rd | | Major 3rd<br>(Semidiminished 4th) | ||
| F# | | F#<br>(Gd) | ||
| major 3rd | | major 3rd | ||
| M3 | | M3 | ||
| Line 164: | Line 164: | ||
| 8 | | 8 | ||
| 564.71 | | 564.71 | ||
| Diminshed 5th | | Diminshed 5th<br>(Semiaugmented 4th) | ||
| G+ | | Ab<br>(G+) | ||
| mid 4th, <br>diminished 5th | | mid 4th, <br>diminished 5th | ||
| ~4, d5 | | ~4, d5 | ||
| Line 173: | Line 173: | ||
| 9 | | 9 | ||
| 635.29 | | 635.29 | ||
| Augmented 4th | | Augmented 4th<br>(Semidiminished 5th) | ||
| Ad | | G#<br>(Ad) | ||
| augmented 4th, <br>mid 5th | | augmented 4th, <br>mid 5th | ||
| A4, ~5 | | A4, ~5 | ||
| Line 191: | Line 191: | ||
| 11 | | 11 | ||
| 776.47 | | 776.47 | ||
| Minor 6th | | Minor 6th<br>(Semiaugmented 5th) | ||
| Bb | | Bb<br>(A+) | ||
| minor 6th | | minor 6th | ||
| m6 | | m6 | ||
| Line 200: | Line 200: | ||
| 12 | | 12 | ||
| 847.06 | | 847.06 | ||
| Neutral 6th | | Augmented 5th<br>(Neutral 6th) | ||
| Bd | | A#<br>(Bd) | ||
| mid 6th | | mid 6th | ||
| ~6 | | ~6 | ||
| Line 214: | Line 214: | ||
| M6 | | M6 | ||
| B | | B | ||
| [[17/10]], [[22/13]],[[12/7]] | | [[17/10]], [[22/13]], [[12/7]] | ||
|- | |- | ||
| 14 | | 14 | ||
| Line 227: | Line 227: | ||
| 15 | | 15 | ||
| 1058.82 | | 1058.82 | ||
| Neutral 7th | | Diminished 8ve<br>(Neutral 7th) | ||
| C+ | | Db<br>(C+) | ||
| mid 7th | | mid 7th | ||
| ~7 | | ~7 | ||
| Line 236: | Line 236: | ||
| 16 | | 16 | ||
| 1129.41 | | 1129.41 | ||
| Major 7th | | Major 7th<br>(Semidiminished 8ve) | ||
| C# | | C#<br>(Dd) | ||
| major 7th | | major 7th | ||
| M7 | | M7 | ||
| Line 252: | Line 252: | ||
| [[2/1]] | | [[2/1]] | ||
|} | |} | ||
<nowiki>*</nowiki> | <nowiki>*</nowiki> Half-sharps and half-flats (denoted "+" and "d", respectively) can be used to alter the note by a single step, 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 an up or down respectively constitute a quarter-sharp or quarter-flat. | ||
† Ratios based on treating 17edo as a 2.3.7.11.13.23.25 subgroup temperament. | |||
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: | ||