17edo: Difference between revisions
Added: "17-tone equal temperament" --> 17-EDO music by benyamind. |
Move temperament measures to RTT properties section |
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[[File:17edo Sagittal.png|800px]] | [[File:17edo Sagittal.png|800px]] | ||
== Chord | == Chord names == | ||
All 17edo chords can be named using ups and downs. Here are the zo, ilo and ru triads: | All 17edo chords can be named using ups and downs. Here are the zo, ilo and ru triads: | ||
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0-5-10-15 = C vE G vB = C~7 = C mid-seven | 0-5-10-15 = C vE G vB = C~7 = C mid-seven | ||
For a more complete list, see [[Ups and Downs Notation# | For a more complete list, see [[Ups and Downs Notation #Chords and Chord Progressions]]. | ||
== | == JI approximation == | ||
=== 15-odd-limit mappings === | |||
The following table shows how [[15-odd-limit intervals]] are represented in 17edo (ordered by absolute error). Prime harmonics are in '''bold'''; inconsistent intervals are in ''italic''. | The following table shows how [[15-odd-limit intervals]] are represented in 17edo (ordered by absolute error). Prime harmonics are in '''bold'''; inconsistent intervals are in ''italic''. | ||
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|} | |} | ||
=== Selected 13-limit intervals === | |||
[[File:17ed2-001.svg|alt=alt : Your browser has no SVG support.]] | [[File:17ed2-001.svg|alt=alt : Your browser has no SVG support.]] | ||
== Scales == | == Scales == | ||
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17edo is very close to a circle of seventeen [[25/24]] chromatic semitones: (25/24)^17 is only 1.43131 cents sharp of an octave. This means that if you can tune seventeen 25/24's accurately (by say, tuning 5/4 up, 3/2 down and 5/4 up, taking care to minimize the error at each step), you have a shot at approximating 17edo within melodic just noticeable difference. | 17edo is very close to a circle of seventeen [[25/24]] chromatic semitones: (25/24)^17 is only 1.43131 cents sharp of an octave. This means that if you can tune seventeen 25/24's accurately (by say, tuning 5/4 up, 3/2 down and 5/4 up, taking care to minimize the error at each step), you have a shot at approximating 17edo within melodic just noticeable difference. | ||
== Commas == | == Regular temperament properties == | ||
{| class="wikitable center-4 center-5 center-6" | |||
! rowspan="2" | Subgroup | |||
! rowspan="2" | [[Comma list]] | |||
! rowspan="2" | [[Mapping]] | |||
! rowspan="2" | Optimal<br>8ve stretch (¢) | |||
! colspan="2" | Tuning error | |||
|- | |||
! [[TE error|Absolute]] (¢) | |||
! [[TE simple badness|Relative]] (%) | |||
|- | |||
| 2.3 | |||
| {{monzo| 27 -17 }} | |||
| [{{val| 17 27 }}] | |||
| -1.24 | |||
| 1.24 | |||
| 1.76 | |||
|- | |||
| 2.3.7 | |||
| 64/63, 17496/16807 | |||
| [{{val| 17 27 48 }}] | |||
| -3.13 | |||
| 2.85 | |||
| 4.05 | |||
|- | |||
| 2.3.7.11 | |||
| 64/63, 99/98, 243/242 | |||
| [{{val| 17 27 48 59 }}] | |||
| -3.31 | |||
| 2.49 | |||
| 3.54 | |||
|- | |||
| 2.3.7.11.13 | |||
| 64/63, 78/77, 99/98, 144/143 | |||
| [{{val| 17 27 48 59 63 }}] | |||
| -3.00 | |||
| 2.31 | |||
| 3.28 | |||
|} | |||
17et is lower in relative error than any previous equal temperaments in the no-5 11- and 13-limit. The next ETs better in these subgroups are 41 and 207, respectively. | |||
=== Commas === | |||
17 EDO [[tempers out]] the following [[comma]]s. (Note: This assumes [[val]] {{val| 17 27 39 48 59 63 }}, cent values rounded to 5 digits.) | 17 EDO [[tempers out]] the following [[comma]]s. (Note: This assumes [[val]] {{val| 17 27 39 48 59 63 }}, cent values rounded to 5 digits.) | ||
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Note that despite their relatively large size, the 17-comma, the avicennma and the chromatic semitone are all tempered out by the 13-limit patent val, as stated. | Note that despite their relatively large size, the 17-comma, the avicennma and the chromatic semitone are all tempered out by the 13-limit patent val, as stated. | ||
=== Rank-2 temperaments === | |||
=== Rank- | |||
* [[List of 17edo rank two temperaments by badness]] | * [[List of 17edo rank two temperaments by badness]] | ||
* [[List of edo-distinct 17c rank two temperaments]] | * [[List of edo-distinct 17c rank two temperaments]] | ||
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* Pathological [[squares]] 3L11s 11211121112 (6\17, 1\1) | * Pathological [[squares]] 3L11s 11211121112 (6\17, 1\1) | ||
* [[lovecraft]] 4L5s 313131311 (4\17, 1\1) | * [[lovecraft]] 4L5s 313131311 (4\17, 1\1) | ||
*Pathological [[1L 13s]] 4 1 1 1 1 1 1 1 1 1 1 1 1 (1\17, 1\1) | * Pathological [[1L 13s]] 4 1 1 1 1 1 1 1 1 1 1 1 1 (1\17, 1\1) | ||
*Pathological [[1L 13s|1L 14s]] 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 (1\17, 1\1) | * Pathological [[1L 13s|1L 14s]] 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 (1\17, 1\1) | ||
*Pathological [[2L 13s]] 2 1 1 1 1 1 1 1 2 1 1 1 1 1 1 (8\17, 1\1) | * Pathological [[2L 13s]] 2 1 1 1 1 1 1 1 2 1 1 1 1 1 1 (8\17, 1\1) | ||
*Pathological 1L 15s 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 (1\17, 1\1) | * Pathological 1L 15s 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 (1\17, 1\1) | ||
== Introductory materials == | == Introductory materials == | ||
* [[File:17edo_1MC.mp3|270px]] 17-edo example composition by [[User:Schrodingasdawg|Schrodingasdawg]] ([[File:17edo_1MC_score.pdf|score]]) | * [[File:17edo_1MC.mp3|270px]] 17-edo example composition by [[User:Schrodingasdawg|Schrodingasdawg]] ([[File:17edo_1MC_score.pdf|score]]) | ||
* [[SeventeenTheory]], an introduction to 17-EDO theory, through the eyes of the [[SeventeenTonePianoProject]]. | * [[SeventeenTheory]], an introduction to 17-EDO theory, through the eyes of the [[SeventeenTonePianoProject]]. | ||
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[[Category:Pythagorean]] | [[Category:Pythagorean]] | ||
[[Category:Teentuning]] | [[Category:Teentuning]] | ||
{{todo| cleanup }} | |||