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[[de:41edo]]
[[de:41edo]]
{{Infobox ET
{{Infobox ET
| Prime factorization = 41
| Subgroup = 2.3.5.7.11.13.19
| Step size = 29.268
| Step size = 29.268
| Fifth type = [[schismic]] 24\41 702.44¢
| Fifth type = 24\41 702.44¢
| Common uses =
| Important MOS =
| Example composition =
| Score =
}}
}}


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== Theory ==
== Theory ==


{| class="wikitable" style="text-align:center;"
! colspan="2" |
! prime 2
! prime 3
! prime 5
! prime 7
! prime 11
! prime 13
! prime 17
! prime 19
|-
! rowspan="2" |Error
! absolute (¢)
| 0.0
|  +0.48
|  -5.8
|  -3.0
|  +4.8
|  +8.3
|  +12.1
|  -4.8
|-
! relative (%)
| 0.0
|  +1.7
|  -20
|  -10
|  +16
|  +28
|  +41
|  -17
|-
! colspan="2" |[[Patent val|nearest edomapping]]
|41
|24
|13
|33
|19
|29
|4
|10
|-
! colspan="2" |[[fifthspan]]
| 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.


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41-ET forms the foundation of the [http://www.h-pi.com/theory/huntsystem1.html H-System], which uses the scale degrees of 41-ET as the basic [[13-limit]] intervals requiring fine tuning +/- 1 [http://www.h-pi.com/theory/huntsystem2.html average JND] from the 41-ET circle in [[205edo]]. 41-ET is also used by the [[The Kite Guitar|Kite Guitar]], see below in "Instruments".
41-ET forms the foundation of the [http://www.h-pi.com/theory/huntsystem1.html H-System], which uses the scale degrees of 41-ET as the basic [[13-limit]] intervals requiring fine tuning +/- 1 [http://www.h-pi.com/theory/huntsystem2.html average JND] from the 41-ET circle in [[205edo]]. 41-ET is also used by the [[The Kite Guitar|Kite Guitar]], see below in "Instruments".


41edo is the 13th [[prime_numbers|prime]] edo, following [[37edo]] and coming before [[43edo]].
41edo is the 13th [[prime_numbers|prime]] edo, following [[37edo]] and coming before [[43edo]]


== Intervals ==
== Intervals ==
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=== Selected just intervals ===
=== Selected just intervals ===
{| class="wikitable" style="text-align:center;"
! colspan="2" |
! prime 2
! prime 3
! prime 5
! prime 7
! prime 11
! prime 13
! prime 17
! prime 19
|-
! rowspan="2" |Error
! absolute (¢)
| 0.0
| +0.48
| -5.8
| -3.0
| +4.8
| +8.3
| +12.1
| -4.8
|-
! relative (%)
| 0.0
| +1.7
| -19.9
| -10.2
| +16.3
| +28.2
| +41.4
| -16.5
|-
! colspan="2" |[[fifthspan]]
| 0
| +1
| -8
| -14
| -18
| +20
| +7
| -3
|}


The following table shows how [[15-odd-limit intervals]] are represented in 41edo. Prime harmonics are in '''bold'''.  
The following table shows how [[15-odd-limit intervals]] are represented in 41edo. Prime harmonics are in '''bold'''.  
Retrieved from "https://en.xen.wiki/w/41edo"