Chain-of-fifths notation: Difference between revisions
The correct term should be diatonic semitone and chromatic semitone |
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EDOs that are best supported by this system are those whose fifth does not deviate too much from the pure fifth [[3/2]] (702 cent) and that can be represented by only one ring of fifths. 24edo, as a counter-example to this, contains two rings. If we as well demand that whole tones (2*P5 - P8), diatonic semitones (3*P8 - 5*P5), and chromatic semitones (shifts caused by one accidental, 7*P5 - 4*P8), use a positive number of steps, we lose all EDOs below 12 EDO and also {{EDOs| 13, 16, 18, and 23 }}. | EDOs that are best supported by this system are those whose fifth does not deviate too much from the pure fifth [[3/2]] (702 cent) and that can be represented by only one ring of fifths. 24edo, as a counter-example to this, contains two rings. If we as well demand that whole tones (2*P5 - P8), diatonic semitones (3*P8 - 5*P5), and chromatic semitones (shifts caused by one accidental, 7*P5 - 4*P8), use a positive number of steps, we lose all EDOs below 12 EDO and also {{EDOs| 13, 16, 18, and 23 }}. | ||
EDOs up to 100 are listed in the following table. The unit (if not stated otherwise) is ''steps'' of the corresponding EDO which is given in the first column of each row. | == EDOs up to 100 == | ||
EDOs up to 100 are listed in the following table. The unit (if not stated otherwise) is ''steps'' of the corresponding EDO which is given in the first column of each row. The list contains only those EDOs whose all degrees can be reached by fifth steps. | |||
{| class="wikitable center-all" | {| class="wikitable center-all" | ||
| Line 163: | Line 165: | ||
| 58 || +1.1 ( +8.9%) || 17 || 7 || 10 | | 58 || +1.1 ( +8.9%) || 17 || 7 || 10 | ||
|} | |} | ||
== See also == | |||
* [[Alternative symbols for ups and downs notation]] -- system that supports sub-circles | |||
* [[User:Xenwolf/cofn]] -- sortable table with more intervals (all fifths within the interval [4\7, 3\5]) | |||
[[Category:Notation]] | [[Category:Notation]] | ||
[[Category:Method]] | [[Category:Method]] | ||
Revision as of 15:34, 19 November 2020
The circle-of-fifths notation is suitable to open up the variety of tones of a selection of EDOs and regular temperaments of fifth generator. The principle is based on one of the intervals taking over the role of the fifth of the traditional classical notation system (in 12-EDO or the meantone tuning). The classical notation system uses seven root notes and accidentals (♯, ♭ and their multiples) to sharpen and flatten these root notes by the same amount (which is an octave-reduced stack of 7 fifths).
EDOs that are best supported by this system are those whose fifth does not deviate too much from the pure fifth 3/2 (702 cent) and that can be represented by only one ring of fifths. 24edo, as a counter-example to this, contains two rings. If we as well demand that whole tones (2*P5 - P8), diatonic semitones (3*P8 - 5*P5), and chromatic semitones (shifts caused by one accidental, 7*P5 - 4*P8), use a positive number of steps, we lose all EDOs below 12 EDO and also 13, 16, 18, and 23.
EDOs up to 100
EDOs up to 100 are listed in the following table. The unit (if not stated otherwise) is steps of the corresponding EDO which is given in the first column of each row. The list contains only those EDOs whose all degrees can be reached by fifth steps.
| Octave/ Edo |
Fifth | Fifth-detuning abs(¢), rel(%) |
Whole tone |
Diatonic semitone |
Chromatic semitone |
|---|---|---|---|---|---|
| 12 | 7 | -2.0 ( -2.0%) | 2 | 1 | 1 |
| 17 | 10 | +3.9 ( +5.6%) | 3 | 1 | 2 |
| 19 | 11 | -7.2 (-11.4%) | 3 | 2 | 1 |
| 22 | 13 | +7.1 (+13.1%) | 4 | 1 | 3 |
| 26 | 15 | -9.6 (-20.9%) | 4 | 3 | 1 |
| 27 | 16 | +9.2 (+20.6%) | 5 | 1 | 4 |
| 29 | 17 | +1.5 ( +3.6%) | 5 | 2 | 3 |
| 31 | 18 | -5.2 (-13.4%) | 5 | 3 | 2 |
| 32 | 19 | +10.5 (+28.1%) | 6 | 1 | 5 |
| 33 | 19 | -11.0 (-30.4%) | 5 | 4 | 1 |
| 37 | 22 | +11.6 (+35.6%) | 7 | 1 | 6 |
| 39 | 23 | +5.7 (+18.6%) | 7 | 2 | 5 |
| 40 | 23 | -12.0 (-39.9%) | 6 | 5 | 1 |
| 41 | 24 | +0.5 ( +1.7%) | 7 | 3 | 4 |
| 42 | 25 | +12.3 (+43.2%) | 8 | 1 | 7 |
| 43 | 25 | -4.3 (-15.3%) | 7 | 4 | 3 |
| 45 | 26 | -8.6 (-32.3%) | 7 | 5 | 2 |
| 46 | 27 | +2.4 ( +9.2%) | 8 | 3 | 5 |
| 47 | 27 | -12.6 (-49.3%) | 7 | 6 | 1 |
| 49 | 29 | +8.2 (+33.7%) | 9 | 2 | 7 |
| 50 | 29 | -6.0 (-24.8%) | 8 | 5 | 3 |
| 53 | 31 | -0.1 ( -0.3%) | 9 | 4 | 5 |
| 55 | 32 | -3.8 (-17.3%) | 9 | 5 | 4 |
| 56 | 33 | +5.2 (+24.2%) | 10 | 3 | 7 |
| 59 | 35 | +9.9 (+48.7%) | 11 | 2 | 9 |
| 61 | 36 | +6.2 (+31.7%) | 11 | 3 | 8 |
| 63 | 37 | +2.8 (+14.7%) | 11 | 4 | 7 |
| 64 | 37 | -8.2 (-43.8%) | 10 | 7 | 3 |
| 65 | 38 | -0.4 ( -2.3%) | 11 | 5 | 6 |
| 67 | 39 | -3.4 (-19.2%) | 11 | 6 | 5 |
| 69 | 40 | -6.3 (-36.2%) | 11 | 7 | 4 |
| 70 | 41 | +0.9 ( +5.3%) | 12 | 5 | 7 |
| 71 | 42 | +7.9 (+46.8%) | 13 | 3 | 10 |
| 73 | 43 | +4.9 (+29.8%) | 13 | 4 | 9 |
| 74 | 43 | -4.7 (-28.7%) | 12 | 7 | 5 |
| 75 | 44 | +2.0 (+12.8%) | 13 | 5 | 8 |
| 77 | 45 | -0.7 ( -4.2%) | 13 | 6 | 7 |
| 79 | 46 | -3.2 (-21.2%) | 13 | 7 | 6 |
| 80 | 47 | +3.0 (+20.3%) | 14 | 5 | 9 |
| 81 | 47 | -5.7 (-38.2%) | 13 | 8 | 5 |
| 83 | 49 | +6.5 (+44.8%) | 15 | 4 | 11 |
| 88 | 51 | -6.5 (-47.7%) | 14 | 9 | 5 |
| 89 | 52 | -0.8 ( -6.2%) | 15 | 7 | 8 |
| 90 | 53 | +4.7 (+35.3%) | 16 | 5 | 11 |
| 91 | 53 | -3.1 (-23.2%) | 15 | 8 | 7 |
| 94 | 55 | +0.2 ( +1.4%) | 16 | 7 | 9 |
| 95 | 56 | +5.4 (+42.9%) | 17 | 5 | 12 |
| 97 | 57 | +3.2 (+25.9%) | 17 | 6 | 11 |
| 98 | 57 | -4.0 (-32.6%) | 16 | 9 | 7 |
| 99 | 58 | +1.1 ( +8.9%) | 17 | 7 | 10 |
See also
- Alternative symbols for ups and downs notation -- system that supports sub-circles
- User:Xenwolf/cofn -- sortable table with more intervals (all fifths within the interval [4\7, 3\5])