28ed5: Difference between revisions
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{{Main| Quindromeda family }} | {{Main| Quindromeda family }} | ||
28ed5 can also be thought of as a [[generator]] of the 2.3.5.17.19 [[subgroup temperament]] which tempers out 1216/1215, 1445/1444, and 6144/6137, which is a [[cluster temperament]] with 12 clusters of notes in an octave (''quindromeda'' temperament). This temperament is supported by {{Val list| 12 | 28ed5 can also be thought of as a [[generator]] of the 2.3.5.17.19 [[subgroup temperament]] which tempers out 1216/1215, 1445/1444, and 6144/6137, which is a [[cluster temperament]] with 12 clusters of notes in an octave (''quindromeda'' temperament). This temperament is supported by {{Val list| 12, 169, 181, 193, 205, 217, 229 }}, and [[241edo|241]] EDOs. | ||
Equating 225/224 with 256/255 leads ''[[quintakwai]]'' (12&193), which tempers out 400/399 (also equating 20/19 and 21/20) in the 2.3.5.7.17.19 subgroup, and 361/360 with 400/399 leads ''[[quintagar]]'' (12&217), which tempers out 476/475 (also equating 19/17 with 28/25) in the 2.3.5.7.17.19 subgroup. | Equating 225/224 with 256/255 leads ''[[quintakwai]]'' (12&193), which tempers out 400/399 (also equating 20/19 and 21/20) in the 2.3.5.7.17.19 subgroup, and 361/360 with 400/399 leads ''[[quintagar]]'' (12&217), which tempers out 476/475 (also equating 19/17 with 28/25) in the 2.3.5.7.17.19 subgroup. | ||
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* [[42ed11|42ED11]] - relative ED11 | * [[42ed11|42ED11]] - relative ED11 | ||
* [[18/17s equal temperament|AS18/17]] - relative [[AS|ambitonal sequence]] | * [[18/17s equal temperament|AS18/17]] - relative [[AS|ambitonal sequence]] | ||
== External links == | |||
* [https://sevish.com/scaleworkshop/index.htm?name=28ed5&data=99.5112040666012%0A199.0224081332025%0A298.5336121998037%0A398.0448162664050%0A497.5560203330062%0A597.0672243996075%0A696.5784284662087%0A796.0896325328099%0A895.6008365994112%0A995.1120406660124%0A1094.6232447326137%0A1194.1344487992149%0A1293.6456528658162%0A1393.1568569324174%0A1492.6680609990187%0A1592.1792650656199%0A1691.6904691322211%0A1791.2016731988224%0A1890.7128772654236%0A1990.2240813320249%0A2089.7352853986261%0A2189.2464894652274%0A2288.7576935318286%0A2388.2688975984298%0A2487.7801016650311%0A2587.2913057316323%0A2686.8025097982336%0A2786.3137138648348&freq=220&midi=57&vert=10&horiz=1 Play 28ed5] | |||
[[Category:Ed5]] | [[Category:Ed5]] | ||
[[Category:Edonoi]] | [[Category:Edonoi]] | ||
Revision as of 22:10, 13 March 2022
Division of the 5th harmonic into 28 equal parts (28ED5) is related to 12EDO, but with the 5/1 rather than the 2/1 being just. The octave is about 5.8656 cents compressed and the step size is about 99.5112 cents. This tuning has a meantone fifth as the number of divisions of the 5th harmonic is multiple of 4. This tuning also has the perfect fourth which is more accurate for 4/3 than that of 12EDO, as well as 18/17, 19/16, and 24/17.
| degree | cents value | corresponding JI intervals |
comments |
|---|---|---|---|
| 0 | 0.0000 | exact 1/1 | |
| 1 | 99.5112 | 18/17 | |
| 2 | 199.0224 | 55/49 | |
| 3 | 298.5336 | 19/16 | |
| 4 | 398.0448 | 34/27 | pseudo-5/4 |
| 5 | 497.5560 | 4/3 | |
| 6 | 597.0672 | 24/17 | |
| 7 | 696.5784 | meantone fifth (pseudo-3/2) | |
| 8 | 796.0896 | 19/12 | |
| 9 | 895.6008 | 57/34 | pseudo-5/3 |
| 10 | 995.1120 | 16/9 | |
| 11 | 1094.6232 | 32/17 | |
| 12 | 1194.1344 | 255/128 | pseudo-octave |
| 13 | 1293.6457 | 19/9 | |
| 14 | 1393.1569 | 38/17, 85/38 | meantone major second plus an octave |
| 15 | 1492.6681 | 45/19 | |
| 16 | 1592.1793 | 128/51 | pseudo-5/2 |
| 17 | 1691.6905 | 85/32 | |
| 18 | 1791.2017 | 45/16 | |
| 19 | 1890.7129 | 170/57 | pseudo-3/1 |
| 20 | 1990.2241 | 60/19 | |
| 21 | 2089.7353 | meantone major sixth plus an octave (pseudo-10/3) | |
| 22 | 2189.2465 | 85/24 | |
| 23 | 2288.7577 | 15/4 | |
| 24 | 2388.2689 | 135/34 | pseudo-4/1 |
| 25 | 2487.7801 | 80/19 | |
| 26 | 2587.2913 | 49/11 | |
| 27 | 2686.8025 | 85/18 | |
| 28 | 2786.3137 | exact 5/1 | just major third plus two octaves |
Regular temperaments
28ed5 can also be thought of as a generator of the 2.3.5.17.19 subgroup temperament which tempers out 1216/1215, 1445/1444, and 6144/6137, which is a cluster temperament with 12 clusters of notes in an octave (quindromeda temperament). This temperament is supported by Template:Val list, and 241 EDOs.
Equating 225/224 with 256/255 leads quintakwai (12&193), which tempers out 400/399 (also equating 20/19 and 21/20) in the 2.3.5.7.17.19 subgroup, and 361/360 with 400/399 leads quintagar (12&217), which tempers out 476/475 (also equating 19/17 with 28/25) in the 2.3.5.7.17.19 subgroup.
See also
- 12EDO - relative EDO
- 19ED3 - relative ED3
- 31ED6 - relative ED6
- 34ED7 - relative ED7
- 40ED10 - relative ED10
- 42ED11 - relative ED11
- AS18/17 - relative ambitonal sequence