48ed5: Difference between revisions
Created page with "'''Division of the 5th harmonic into 48 equal parts''' (48ed5) is related to the semimiracle temperament. The step size is about 58.0482 cents. It is simil..." |
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'''Division of the 5th harmonic into 48 equal parts''' (48ed5) is related to the [[Gamelismic clan|semimiracle temperament]]. The step size is about 58.0482 cents. It is similar to every third step of [[62edo]], but with the 5/1 rather than the 2/1 being just. This tuning has a meantone fifth as the number of divisions of the 5th harmonic is multiple of 4. | {{Infobox ET}} | ||
'''[[Ed5|Division of the 5th harmonic]] into 48 equal parts''' (48ed5) is related to the [[Gamelismic clan|semimiracle temperament]]. The step size is about 58.0482 cents. It is similar to every third step of [[62edo]], but with the 5/1 rather than the 2/1 being just. This tuning has a meantone fifth as the number of divisions of the 5th harmonic is multiple of 4. | |||
{| class="wikitable" | == Intervals == | ||
{| class="wikitable mw-collapsible" | |||
|+ Intervals of 48ed5 | |||
|- | |- | ||
! | degree | ! | degree | ||
| Line 253: | Line 256: | ||
| | just major third plus two octaves | | | just major third plus two octaves | ||
|} | |} | ||
== Harmonics == | |||
{{Harmonics in equal | |||
| steps = 48 | |||
| num = 5 | |||
| denom = 1 | |||
}} | |||
{{Harmonics in equal | |||
| steps = 48 | |||
| num = 5 | |||
| denom = 1 | |||
| start = 12 | |||
| collapsed = 1 | |||
}} | |||
==48ed5 as a generator== | ==48ed5 as a generator== | ||
48ed5 can also be thought of as a [[generator]] of the 23-limit temperament which tempers out 169/168, 225/224, 243/242, 286/285, 385/384, 598/595, and 1445/1444 which is a [[cluster temperament]] with 21 clusters of notes in an octave. The large chroma interval between adjacent notes in each cluster is very versatile, representing 77/75 ~ 39/38 ~ 165/161 ~ 253/247 ~ 169/165 ~ 128/125 ~ 306/299 ~ 45/44 ~ 136/133 ~ 46/45 ~ 608/595 ~ 1292/1265 ~ 49/48 ~ 50/49 ~ 352/345 ~ 55/54 ~ 56/55 ~ 64/63 all tempered together. This temperament is supported by [[62edo]], [[82edo]] (82gh val), and [[144edo]] (144f val). | 48ed5 can also be thought of as a [[generator]] of the 23-limit temperament which tempers out 169/168, 225/224, 243/242, 286/285, 385/384, 598/595, and 1445/1444 which is a [[cluster temperament]] with 21 clusters of notes in an octave. The large chroma interval between adjacent notes in each cluster is very versatile, representing 77/75 ~ 39/38 ~ 165/161 ~ 253/247 ~ 169/165 ~ 128/125 ~ 306/299 ~ 45/44 ~ 136/133 ~ 46/45 ~ 608/595 ~ 1292/1265 ~ 49/48 ~ 50/49 ~ 352/345 ~ 55/54 ~ 56/55 ~ 64/63 all tempered together. This temperament is supported by [[62edo]], [[82edo]] (82gh val), and [[144edo]] (144f val). | ||
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