41edo: Difference between revisions
m State the primality in infobox |
ET parameter name, cleanup |
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| Prime factorization = 41 (prime) | | Prime factorization = 41 (prime) | ||
| Step size = 29.268¢ | | Step size = 29.268¢ | ||
| Fifth | | Fifth = 24\41 = 702.44¢ | ||
| Major 2nd = 7\41 = 205¢ | | Major 2nd = 7\41 = 205¢ | ||
| Minor 2nd = 3\41 = 88¢ | | Minor 2nd = 3\41 = 88¢ | ||
| Line 13: | Line 13: | ||
== Theory == | == Theory == | ||
{| class="wikitable | {| class="wikitable center-all" | ||
! colspan="2" | | ! colspan="2" | <!-- empty cell --> | ||
! prime 2 | ! prime 2 | ||
! prime 3 | ! prime 3 | ||
| Line 24: | Line 24: | ||
! prime 19 | ! prime 19 | ||
|- | |- | ||
! rowspan="2" |Error | ! rowspan="2" | Error | ||
! absolute (¢) | ! absolute (¢) | ||
| 0.0 | | 0.0 | ||
| | | +0.5 | ||
| | | -5.8 | ||
| | | -3.0 | ||
| | | +4.8 | ||
| | | +8.3 | ||
| | | +12.1 | ||
| | | -4.8 | ||
|- | |- | ||
! relative (%) | ! relative (%) | ||
| | | 0 | ||
| | | +2 | ||
| | | -20 | ||
| | | -10 | ||
| | | +16 | ||
| | | +28 | ||
| | | +41 | ||
| | | -17 | ||
|- | |- | ||
! colspan="2" |[[ | ! colspan="2" | [[nearest edomapping]] | ||
|41 | | 41 | ||
|24 | | 24 | ||
|13 | | 13 | ||
|33 | | 33 | ||
|19 | | 19 | ||
|29 | | 29 | ||
|4 | | 4 | ||
|10 | | 10 | ||
|- | |- | ||
! colspan="2" |[[fifthspan]] | ! colspan="2" | [[fifthspan]] | ||
| 0 | | 0 | ||
| | | +1 | ||
| | | -8 | ||
| | | -14 | ||
| | | -18 | ||
| | | +20 | ||
| | | +7 | ||
| | | -3 | ||
|} | |} | ||
41-ET can be seen as a tuning of the [[Schismatic_family#Garibaldi|Garibaldi temperament]] [[#cite_note-1|[1]]] , [[#cite_note-2|[2]]] , [[#cite_note-3|[3]]] the [[Magic_family|Magic temperament]] [[#cite_note-4|[4]]] and the [[Superkleismic|superkleismic (41&26) temperament]]. It is the second smallest equal temperament (after [[29edo]]) whose perfect fifth is closer to just intonation than that of [[12edo|12-ET]], and is the seventh [[The_Riemann_Zeta_Function_and_Tuning#Zeta EDO lists|zeta integral edo]] after 31; it is not, however, a [[The_Riemann_Zeta_Function_and_Tuning#Zeta EDO lists|zeta gap edo]]. This has to do with the fact that it can deal with the [[11-limit]] fairly well, and the [[13-limit]] perhaps close enough for government work, though its [[13/10]] is 14 cents sharp. Various 13-limit [[magic extensions]] are supported by 41: 13-limit magic, and less successfully necromancy and witchcraft, all merge into one in 41edo tuning. The 41f val provides a superb tuning for sorcery, giving a less-complex version of the 13-limit, and the 41ef val likewise works well for telepathy; telepathy and sorcery merging into one however not in 41edo but in 22edo. | 41-ET can be seen as a tuning of the [[Schismatic_family#Garibaldi|Garibaldi temperament]] [[#cite_note-1|[1]]] , [[#cite_note-2|[2]]] , [[#cite_note-3|[3]]] the [[Magic_family|Magic temperament]] [[#cite_note-4|[4]]] and the [[Superkleismic|superkleismic (41&26) temperament]]. It is the second smallest equal temperament (after [[29edo]]) whose perfect fifth is closer to just intonation than that of [[12edo|12-ET]], and is the seventh [[The_Riemann_Zeta_Function_and_Tuning#Zeta EDO lists|zeta integral edo]] after 31; it is not, however, a [[The_Riemann_Zeta_Function_and_Tuning#Zeta EDO lists|zeta gap edo]]. This has to do with the fact that it can deal with the [[11-limit]] fairly well, and the [[13-limit]] perhaps close enough for government work, though its [[13/10]] is 14 cents sharp. Various 13-limit [[magic extensions]] are supported by 41: 13-limit magic, and less successfully necromancy and witchcraft, all merge into one in 41edo tuning. The 41f val provides a superb tuning for sorcery, giving a less-complex version of the 13-limit, and the 41ef val likewise works well for telepathy; telepathy and sorcery merging into one however not in 41edo but in 22edo. | ||