22ed5: Difference between revisions
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''' ( | {{Infobox ET}} | ||
'''[[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|15EDT]] and every second step of [[19edo|19EDO]], but with the 5/1 rather than 2/1 or 3/1 being just. | |||
== Intervals == | |||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
| Line 51: | Line 53: | ||
| | 1013.2050 | | | 1013.2050 | ||
| | 70/39 | | | 70/39 | ||
| | | | | -4.4 cents from [[9/5]] | ||
|- | |- | ||
| | 9 | | | 9 | ||
| Line 60: | Line 62: | ||
| | 10 | | | 10 | ||
| | 1266.5062 | | | 1266.5062 | ||
| | | | | [[26/25|52/25]], 160/77 | ||
| | | | | | ||
|- | |- | ||
| Line 70: | Line 72: | ||
| | 12 | | | 12 | ||
| | 1519.8075 | | | 1519.8075 | ||
| | | | | [[77/64|77/32]], 125/52 | ||
| | | | | | ||
|- | |- | ||
| Line 76: | Line 78: | ||
| | 1646.4581 | | | 1646.4581 | ||
| | [[22/17|44/17]] | | | [[22/17|44/17]] | ||
| | | | | -7.8 cents from [[13/5]] | ||
|- | |- | ||
| | 14 | | | 14 | ||
| Line 96: | Line 98: | ||
| | 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 113: | ||
| | 2533.0125 | | | 2533.0125 | ||
| | 95/22 | | | 95/22 | ||
| | | | | +48.5 cents from [[21/20|21/5]] | ||
|- | |- | ||
| | 21 | | | 21 | ||
| | 2659.6631 | | | 2659.6631 | ||
| | 65/14 | | | 65/14 | ||
| | | | | +17.7 cents from [[23/20|23/5]] | ||
|- | |- | ||
| | 22 | | | 22 | ||
| Line 124: | Line 126: | ||
|} | |} | ||
== | == Harmonics == | ||
{{Harmonics in equal | |||
| steps = 22 | |||
| num = 5 | |||
| denom = 1 | |||
}} | |||
{{Harmonics in equal | |||
| steps = 22 | |||
| num = 5 | |||
| denom = 1 | |||
| start = 12 | |||
| collapsed = 1 | |||
}} | |||
== 22ED5 as a generator == | |||
22ED5 can also be thought of as a generator of the 19-limit [[Hemimean clan #Mowglic|mowglic temperament]], which tempers out 351/350, 476/475, 495/494, 513/512, 540/539, and 1701/1690, which is an extension of the [[Syntonic–enneadecal equivalence continuum|mowgli temperament]]. This temperament is supported by [[19edo|19EDO]], [[161edo|161EDO]], and [[180edo|180EDO]] among others. | |||
[[Category: | [[Category:Hyperpyth]] | ||
{{todo|expand}} | |||