22ed5: Difference between revisions
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Created page with "'''Division of the 5th harmonic into 22 equal parts''' (22ed5) is a good hyperpyth tuning. The step size about 126.6506 cents. It is similar to 15edt and every..." Tags: Mobile edit Mobile web edit |
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'''[[Ed5|Division of the 5th harmonic]] into 22 equal parts''' (22ed5) is a good [[hyperpyth | '''[[Ed5|Division of the 5th harmonic]] into 22 equal parts''' (22ed5) is a good [[hyperpyth]] tuning. The step size about 126.6506 cents. It is compared to [[15edt]] and every second step of [[19edo]], but with the 5/1 rather than 2/1 or 3/1 being just. | ||
{| class="wikitable" | {| class="wikitable" | ||
| Line 51: | Line 51: | ||
| | 1013.2050 | | | 1013.2050 | ||
| | 70/39 | | | 70/39 | ||
| | | | | -4.4 cents from [[9/5]] | ||
|- | |- | ||
| | 9 | | | 9 | ||
| Line 76: | Line 76: | ||
| | 1646.4581 | | | 1646.4581 | ||
| | [[22/17|44/17]] | | | [[22/17|44/17]] | ||
| | | | | -7.8 cents from [[13/5]] | ||
|- | |- | ||
| | 14 | | | 14 | ||
| Line 96: | Line 96: | ||
| | 2153.0606 | | | 2153.0606 | ||
| | [[26/15|52/15]] | | | [[26/15|52/15]] | ||
| | | | | +34.4 cents from [[17/10|17/5]] | ||
|- | |- | ||
| | 18 | | | 18 | ||
| | 2279.7112 | | | 2279.7112 | ||
| | [[28/15|56/15]] | | | [[28/15|56/15]] | ||
| | | | | -31.5 cents from [[19/10|19/5]] | ||
|- | |- | ||
| | 19 | | | 19 | ||
| Line 111: | Line 111: | ||
| | 2533.0125 | | | 2533.0125 | ||
| | 95/22 | | | 95/22 | ||
| | | | | +48.5 cents from [[21/20|21/5]] | ||
|- | |- | ||
| | 21 | | | 21 | ||
| Line 125: | Line 125: | ||
==22ed5 as a generator== | ==22ed5 as a generator== | ||
22ed5 can also be thought of as a generator of the 19-limit [[15edt|mowgli temperament]], which tempers out 351/350, 476/475, 495/494, 969/968, 1445/1444, and 1701/1690, which is a cluster temperament with nine clusters of notes in an octave. This temperament is supported by [[19edo]] and [[ | 22ed5 can also be thought of as a generator of the 19-limit [[15edt|mowgli temperament]], which tempers out 351/350, 476/475, 495/494, 969/968, 1445/1444, and 1701/1690, which is a cluster temperament with nine clusters of notes in an octave. This temperament is supported by [[19edo]], [[161edo]], and [[180edo]] among others. | ||
[[Category:Ed5]] | [[Category:Ed5]] | ||
[[Category:Edonoi]] | [[Category:Edonoi]] | ||
Revision as of 11:15, 17 January 2019
Division of the 5th harmonic into 22 equal parts (22ed5) is a good hyperpyth tuning. The step size about 126.6506 cents. It is compared to 15edt and every second step of 19edo, but with the 5/1 rather than 2/1 or 3/1 being just.
| degree | cents value | corresponding JI intervals |
comments |
|---|---|---|---|
| 0 | 0.0000 | exact 1/1 | |
| 1 | 126.6506 | 14/13 | |
| 2 | 253.3012 | 22/19 | |
| 3 | 379.9519 | 56/45 | |
| 4 | 506.6025 | 75/56 | |
| 5 | 633.2531 | 75/52 | |
| 6 | 759.9037 | ||
| 7 | 886.5544 | 5/3 | |
| 8 | 1013.2050 | 70/39 | -4.4 cents from 9/5 |
| 9 | 1139.8556 | 85/44 | |
| 10 | 1266.5062 | ||
| 11 | 1393.1569 | 38/17, 85/38 | |
| 12 | 1519.8075 | ||
| 13 | 1646.4581 | 44/17 | -7.8 cents from 13/5 |
| 14 | 1773.1087 | 39/14 | |
| 15 | 1899.7593 | 3/1 | |
| 16 | 2026.4100 | ||
| 17 | 2153.0606 | 52/15 | +34.4 cents from 17/5 |
| 18 | 2279.7112 | 56/15 | -31.5 cents from 19/5 |
| 19 | 2406.3618 | 225/56 | |
| 20 | 2533.0125 | 95/22 | +48.5 cents from 21/5 |
| 21 | 2659.6631 | 65/14 | |
| 22 | 2786.3137 | exact 5/1 | just major third plus two octaves |
22ed5 as a generator
22ed5 can also be thought of as a generator of the 19-limit mowgli temperament, which tempers out 351/350, 476/475, 495/494, 969/968, 1445/1444, and 1701/1690, which is a cluster temperament with nine clusters of notes in an octave. This temperament is supported by 19edo, 161edo, and 180edo among others.