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| de = 41-EDO
| de = 41-EDO
| en = 41edo
| en = 41edo
| es =  
| es = 41edo
| ja =  
| ja =  
}}
}}
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=== As a tuning of other temperaments ===
=== As a tuning of other temperaments ===
41edo can be seen as a tuning of the [[garibaldi]] temperament, as well as [[miracle]], [[magic]], [[superkleismic]], and multiple temperaments in the [[tetracot family]].  
41edo can be seen as a tuning of the [[magic]] temperament, as well as [[superkleismic]], [[garibaldi]], [[miracle]], and multiple temperaments in the [[tetracot family]].  


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]].
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; however, telepathy and sorcery merge into one not in 41edo but in [[22edo]].


41edo is also a great [[tetracot]] tuning, and works as an alternative to [[34edo]], providing proper approximations to the 7th and 11th harmonic at the cost of the 13th, and supporting [[monkey]], [[bunya]] and [[octacot]] simultaneously. All three of these extend to the [[11-limit]] by way of interpreting the flat [[10/9]] as an [[11/10]] by tempering out [[100/99]]. This equivalence is especially useful in 41edo, wherein this comma-flat whole tone a.k.a. the second of Tetracot[7] can also be more accurately interpreted as [[21/19]]—which is equated with [[32/29]] above [[31/28]] below (both very near)—providing an explanation of the accuracy of primes [[29/1|29]] and [[31/1|31]] so that it is a uniquely good/versatile choice for interpreting the harmony of tetracot.
41edo is also a great [[tetracot]] tuning, and works as an alternative to [[34edo]], providing proper approximations to the 7th and 11th harmonic at the cost of the 13th, and supporting [[monkey]], [[bunya]] and [[octacot]] simultaneously. All three of these extend to the [[11-limit]] by way of interpreting the flat [[10/9]] as an [[11/10]] by tempering out [[100/99]]. This equivalence is especially useful in 41edo, wherein this comma-flat whole tone a.k.a. the second of Tetracot[7] can also be more accurately interpreted as [[21/19]]—which is equated with [[32/29]] above [[31/28]] below (both very near)—providing an explanation of the accuracy of primes [[29/1|29]] and [[31/1|31]] so that it is a uniquely good/versatile choice for interpreting the harmony of tetracot.
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=== Subsets and supersets ===
=== Subsets and supersets ===
41edo is the 13th [[prime edo]], following [[37edo]] and coming before [[43edo]]. It does not contain any nontrivial subset edos, though it contains [[41ed4]].  
41edo is the 13th [[prime edo]], following [[37edo]] and coming before [[43edo]]. It does not contain any nontrivial subset edos, though it essentially contains [[88cET]] as every third step and [[13edt]] as every fifth step.


[[205edo]], which slices each step of 41edo into five, corrects some approximations of 41edo to near-just quality. As such, 41edo forms the foundation of the [http://www.h-pi.com/theory/huntsystem1.html H-System], which uses the scale degrees of 41edo as the basic [[13-limit]] intervals requiring fine tuning ±1 [http://www.h-pi.com/theory/huntsystem2.html average JND] from the 41edo circle in 205edo. Its step of 1\205 is called a ''mem''.
[[205edo]], which slices each step of 41edo into five, corrects some approximations of 41edo to near-just quality. As such, 41edo forms the foundation of the [http://www.h-pi.com/theory/huntsystem1.html H-System], which uses the scale degrees of 41edo as the basic [[13-limit]] intervals requiring fine tuning ±1 [http://www.h-pi.com/theory/huntsystem2.html average JND] from the 41edo circle in 205edo. Its step of 1\205 is called a ''mem''.
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== Intervals ==
== Intervals ==
{{See also| 41edo solfege }}
{| class="wikitable center-1 right-2"
 
{| class="wikitable center-1 right-2 center-5 center-6 center-8 center-9"
|-
|-
! #
! #
! Cents
! Cents
! Approximate ratios*
! Approximate ratios*
! colspan="3" | [[Ups and downs notation]]<br>([[Enharmonic unisons in ups and downs notation|EUs]]: v<sup>4</sup>A1 and ^d2)
! colspan="2" |[[Kite's ups and downs notation|Ups and downs notation]]
! colspan="3" | [[SKULO interval names|SKULO notation]] (K or S = 1, U = 2)
([[Enharmonic unisons in ups and downs notation|EUs]]: v<sup>4</sup>A1 and ^d2)
! [[41edo solfege|Kite's<br>solfege]]
! [[41edo solfege|Andrew's<br>solfege]]
|-
|-
| 0
| 0
| 0.0
| 0.0
| [[1/1]]
| [[1/1]]
| perfect unison
|P1
| P1
| {{UDnote|step=0}}
| D
| perfect unison
| P1
| D
| Da
| Do
|-
|-
| 1
| 1
| 29.3
| 29.3
| [[49/48]], [[50/49]], [[64/63]], [[81/80]]
| [[49/48]], [[50/49]], [[64/63]], [[81/80]]
| up-unison
|^1
| ^1
| {{UDnote|step=1}}
| ^D
| comma-wide unison, super unison
| K1/S1
| KD, SD
| Du
| Di
|-
|-
| 2
| 2
| 58.5
| 58.5
| [[25/24]], [[28/27]], [[33/32]], [[36/35]]
| [[25/24]], [[28/27]], [[33/32]], [[36/35]]
| dup-unison, downminor 2nd
|^^1, vm2
| ^^1, vm2
| {{UDnote|step=2}}
| ^^D, vEb
| subminor 2nd, classic aug unison, uber unison
| sm2, kkA1, U1
| sEb, kkD#, UD
| Fro
| Ro
|-
|-
| 3
| 3
| 87.8
| 87.8
| [[19/18]], [[20/19]], [[21/20]], [[22/21]]
| [[19/18]], [[20/19]], [[21/20]], [[22/21]]
| down-aug 1sn, minor 2nd
|vA1, m2
| vA1, m2
| {{UDnote|step=3}}
| vD#, Eb
|-
| minor 2nd, comma-narrow augmented unison
| 4
| m2, kA1
| 117.1
| Eb, kD#
| Fra
| Rih
|-
| 4
| 117.1
| [[14/13]], [[15/14]], [[16/15]]
| [[14/13]], [[15/14]], [[16/15]]
| augmented 1sn, upminor 2nd
|A1, ^m2
| A1, ^m2
| {{UDnote|step=4}}
| D#, ^Eb
| classic minor 2nd, augmented unison
| Km2, A1
| KEb, D#
| Fru
| Ra
|-
|-
| 5
| 5
| 146.3
| 146.3
| [[12/11]], [[13/12]]
| [[12/11]], [[13/12]]
| mid 2nd
|~2
| ~2
| {{UDnote|step=5}}
| ^D#, vvE
| neutral second, super augmented unison
| N2, SA1
| UEb/uE, sD#
| Ri
| Ru
|-
|-
| 6
| 6
| 175.6
| 175.6
| [[10/9]], [[11/10]], [[21/19]]
| [[10/9]], [[11/10]], [[21/19]]
| downmajor 2nd
|vM2
| vM2
| {{UDnote|step=6}}
| vE
|-
| classic/comma-wide major 2nd
| 7
| kM2
| 204.9
| kE
| Ro
| Reh
|-
| 7
| 204.9
| [[9/8]]
| [[9/8]]
| major 2nd
|M2
| M2
| {{UDnote|step=7}}
| E
| major 2nd
| M2
| E
| Ra
| Re
|-
|-
| 8
| 8
| 234.1
| 234.1
| [[8/7]], [[15/13]]
| [[8/7]], [[15/13]]
| upmajor 2nd
|^M2
| ^M2
| {{UDnote|step=8}}
| ^E
| supermajor 2nd
| SM2
| SE
| Ru
| Ri
|-
|-
| 9
| 9
| 263.4
| 263.4
| [[7/6]], [[22/19]]
| [[7/6]], [[22/19]]
| downminor 3rd
|vm3
| vm3
| {{UDnote|step=9}}
| vF
|-
| subminor 3rd
| 10
| sm3
| 292.7
| sF
| [[13/11]], [[19/16]], [[32/27]]
| No
|m3
| Ma
| {{UDnote|step=10}}
|-
| 10
| 292.7
| [[13/11]], [[19/16]], [[32/27]]
| minor 3rd
| m3
| F
| minor 3rd
| m3
| F
| Na
| Meh
|-
|-
| 11
| 11
| 322.0
| 322.0
| [[6/5]]
| [[6/5]]
| upminor 3rd
|^m3
| ^m3
| {{UDnote|step=11}}
| ^F
| classic minor 3rd
| Km3
| KF
| Nu
| Me
|-
|-
| 12
| 12
| 351.2
| 351.2
| [[11/9]], [[16/13]]
| [[11/9]], [[16/13]]
| mid 3rd
|~3
| ~3
| {{UDnote|step=12}}
| ^^F, vGb
|-
| neutral 3rd, sub diminished 4th
| 13
| N3, sd4
| 380.5
| UF/uF#, sGb
| Mi
| Mu
|-
| 13
| 380.5
| [[5/4]], [[26/21]]
| [[5/4]], [[26/21]]
| downmajor 3rd
|vM3
| vM3
| {{UDnote|step=13}}
| vF#, Gb
| classic major 3rd, diminished 4th
| kM3, d4
| kF#, Gb
| Mo
| Mi
|-
|-
| 14
| 14
| 409.8
| 409.8
| [[14/11]], [[19/15]], [[24/19]]
| [[14/11]], [[19/15]], [[24/19]]
| major 3rd
|M3
| M3
| {{UDnote|step=14}}
| F#, ^Gb
| major 3rd, comma-wide diminished 4th
| M3, Kd4
| F#, KGb
| Ma
| Maa
|-
|-
| 15
| 15
| 439.0
| 439.0
| [[9/7]], [[32/25]]
| [[9/7]], [[32/25]]
| upmajor 3rd
|^M3
| ^M3
| {{UDnote|step=15}}
| ^F#, vvG
|-
| supermajor 3rd, classic diminished 4th
| 16
| SM3, KKd4
| 468.3
| SF#, KKGb
| [[21/16]], [[13/10]]
| Mu
|v4
| Mo
| {{UDnote|step=16}}
|-
| 16
| 468.3
| [[21/16]], [[13/10]]
| down-4th
| v4
| vG
| sub 4th
| s4
| sG
| Fo
| Fe
|-
|-
| 17
| 17
| 497.6
| 497.6
| [[4/3]]
| [[4/3]]
| perfect 4th
|P4
| P4
| {{UDnote|step=17}}
| G
| perfect 4th
| P4
| G
| Fa
| Fa
|-
|-
| 18
| 18
| 526.8
| 526.8
| [[15/11]], [[19/14]], [[27/20]]
| [[15/11]], [[19/14]], [[27/20]]
| up-4th
|^4
| ^4
| {{UDnote|step=18}}
| ^G
|-
| comma-wide 4th
| 19
| K4
| 556.1
| KG
| Fu
| Fih
|-
| 19
| 556.1
| [[11/8]], [[18/13]], [[26/19]]
| [[11/8]], [[18/13]], [[26/19]]
| mid-4th, downdim 5th
|~4, vd5
| ~4, vd5
| {{UDnote|step=19}}
| ^^G, vAb
| uber/neutral 4th, classic augmented 4th
| U4/N4, kkA4
| UG, kkG#
| Fi/Sho
| Fu
|-
|-
| 20
| 20
| 585.4
| 585.4
| [[7/5]], [[45/32]]
| [[7/5]], [[45/32]]
| downaug 4th, dim 5th
|vA4, d5
| vA4, d5
| {{UDnote|step=20}}
| vG#, Ab
| comma-narrow augmented 4th, diminished 5th
| kA4/d5
| kG#, Ab
| Po/Sha
| Fi
|-
|-
| 21
| 21
| 614.6
| 614.6
| [[10/7]], [[64/45]]
| [[10/7]], [[64/45]]
| aug 4th, updim 5th
|A4, ^d5
| A4, ^d5
| {{UDnote|step=21}}
| G#, ^Ab
|-
| augmented 4th, comma-wide diminished 5th
| 22
| A4/Kd5
| 643.9
| G#, KAb
| [[13/9]], [[16/11]], [[19/13]]
| Pa/Shu
|~5, ^A4
| Se
| {{UDnote|step=22}}
|-
| 22
| 643.9
| [[13/9]], [[16/11]], [[19/13]]
| mid-5th, upaug 4th
| ~5, ^A4
| ^G#, vvA
| unter/neutral 5th, classic diminished 5th
| u5/N5, KKd5
| uA, KKAb
| Pu/Si
| Su
|-
|-
| 23
| 23
| 673.2
| 673.2
| [[22/15]], [[28/19]], [[40/27]]
| [[22/15]], [[28/19]], [[40/27]]
| down-5th
|v5
| v5
| {{UDnote|step=23}}
| vA
| comma-narrow 5th
| k5
| kA
| So
| Sih
|-
|-
| 24
| 24
| 702.4
| 702.4
| [[3/2]]
| [[3/2]]
| perfect 5th
|P5
| P5
| {{UDnote|step=24}}
| A
|-
| perfect 5th
| 25
| P5
| 731.7
| A
| Sa
| Sol
|-
| 25
| 731.7
| [[20/13]], [[32/21]]
| [[20/13]], [[32/21]]
| up-5th
|^5
| ^5
| {{UDnote|step=25}}
| ^A
| super 5th
| S5
| SA
| Su
| Si
|-
|-
| 26
| 26
| 761.0
| 761.0
| [[14/9]], [[25/16]]
| [[14/9]], [[25/16]]
| downminor 6th
|vm6
| vm6
| {{UDnote|step=26}}
| ^^A, vBb
| subminor 6th, classic augmented 5th
| sm6
| sBb, kkA#
| Flo
| Lo
|-
|-
| 27
| 27
| 790.2
| 790.2
| [[11/7]], [[19/12]], [[30/19]]
| [[11/7]], [[19/12]], [[30/19]]
| minor 6th
|m6
| m6
| {{UDnote|step=27}}
| vA#, Bb
|-
| minor 6th, comma-narrow augmented 5th
| 28
| m6
| 819.5
| Bb, kA#
| [[8/5]], [[21/13]]
| Fla
|^m6
| Leh
| {{UDnote|step=28}}
|-
| 28
| 819.5
| [[8/5]], [[21/13]]
| upminor 6th
| ^m6
| A#, ^Bb
| classic minor 6th, augmented 5th
| Km6, A5
| KBb, A#
| Flu
| Le
|-
|-
| 29
| 29
| 848.8
| 848.8
| [[13/8]], [[18/11]]
| [[13/8]], [[18/11]]
| mid 6th
|~6
| ~6
| {{UDnote|step=29}}
| ^A#, vvB
| neutral 6th, super augmented 5th
| N6
| UBb/uB, sA#
| Li
| Lu
|-
|-
| 30
| 30
| 878.0
| 878.0
| [[5/3]]
| [[5/3]]
| downmajor 6th
|vM6
| vM6
| {{UDnote|step=30}}
| vB
|-
| classic major 6th
| 31
| kM6
| 907.3
| kB
| Lo
| La
|-
| 31
| 907.3
| [[22/13]], [[27/16]], [[32/19]]
| [[22/13]], [[27/16]], [[32/19]]
| major 6th
|M6
| M6
| {{UDnote|step=31}}
| B
| major 6th
| M6
| B
| La
| Laa
|-
|-
| 32
| 32
| 936.6
| 936.6
| [[12/7]], [[19/11]]
| [[12/7]], [[19/11]]
| upmajor 6th
|^M6
| ^M6
| {{UDnote|step=32}}
| ^B
| supermajor 6th
| SM6
| SB
| Lu
| Li
|-
|-
| 33
| 33
| 965.9
| 965.9
| [[7/4]], [[26/15]]
| [[7/4]], [[26/15]]
| downminor 7th
|vm7
| vm7
| {{UDnote|step=33}}
| vC
|-
| subminor 7th
| 34
| sm7
| 995.1
| sC
| [[16/9]]
| Tho
|m7
| Ta
| {{UDnote|step=34}}
|-
| 34
| 995.1
| [[16/9]]
| minor 7th
| m7
| C
| minor 7th
| m7
| C
| Tha
| Teh
|-
|-
| 35
| 35
| 1024.4
| 1024.4
| [[9/5]], [[20/11]], [[38/21]]
| [[9/5]], [[20/11]], [[38/21]]
| upminor 7th
|^m7
| ^m7
| {{UDnote|step=35}}
| ^C
| classic/comma-wide minor seventh
| Km7
| KC
| Thu
| Te
|-
|-
| 36
| 36
| 1053.7
| 1053.7
| [[11/6]], [[24/13]]
| [[11/6]], [[24/13]]
| mid 7th
|~7
| ~7
| {{UDnote|step=36}}
| ^^C, vDb
|-
| neutral 7th, sub diminished 8ve
| 37
| N7
| 1082.9
| UC/uC#, sDb
| Ti
| Tu
|-
| 37
| 1082.9
| [[13/7]], [[15/8]], [[28/15]]
| [[13/7]], [[15/8]], [[28/15]]
| downmajor 7th
|vM7
| vM7
| {{UDnote|step=37}}
| vC#, Db
| classic major 7th, diminished 8ve
| kM7, d8
| kC#, Db
| To
| Ti
|-
|-
| 38
| 38
| 1112.2
| 1112.2
| [[19/10]], [[21/11]], [[36/19]], [[40/21]]
| [[19/10]], [[21/11]], [[36/19]], [[40/21]]
| major 7th
|M7
| M7
| {{UDnote|step=38}}
| C#, ^Db
| major 7th, comma-wide diminished 8ve
| M7, Kd8
| C#, KDb
| Ta
| Taa
|-
|-
| 39
| 39
| 1141.5
| 1141.5
| [[27/14]], [[35/18]], [[48/25]], [[64/33]]
| [[27/14]], [[35/18]], [[48/25]], [[64/33]]
| upmajor 7th
|^M7
| ^M7
| {{UDnote|step=39}}
| ^C#, vvD
|-
| supermajor 7th, classic dim 8ve, unter 8ve
| 40
| SM7, KKd8, U8
| 1170.7
| SC#, KKDb, u8
| [[49/25]], [[63/32]], [[96/49]], [[160/81]]
| Tu
|v8
| To
| {{UDnote|step=40}}
|-
| 40
| 1170.7
| [[49/25]], [[63/32]], [[96/49]], [[160/81]]
| dim 8ve
| v8
| vD
| comma-narrow 8ve, sub 8ve
| k8/s8
| kD, sD
| Do
| Da
|-
|-
| 41
| 41
| 1200.0
| 1200.0
| [[2/1]]
| [[2/1]]
| perfect 8ve
|P8
| P8
| {{UDnote|step=41}}
| D
| perfect 8ve
| P8
| D
| Da
| Do
|}
|}
<nowiki>*</nowiki> Based on treating 41edo as a 2.3.5.7.11.13.19 subgroup temperament; other approaches are possible.
<nowiki>*</nowiki> Based on treating 41edo as a 2.3.5.7.11.13.19-subgroup temperament; other approaches are possible.


=== Interval quality and chord names in color notation ===
=== Proposed interval names and solfèges ===
Combining ups and downs notation with [[color notation]], qualities can be loosely associated with colors:
{{See also| 41edo solfege }}


{| class="wikitable center-all"
{| class="wikitable center-all right-2 left-3 left-6 mw-collapsible mw-collapsed"
|+ style="white-space: nowrap;" | Table of proposed interval names and solfèges
|-
|-
! Quality
! #
! [[Color notation|Color]]
! Cents
! Monzo format
! colspan="3" | [[Kite's ups and downs notation]]<br>([[Kite's thoughts on enharmonic unisons in ups and downs notation|EUs]]: v<sup>4</sup>A1 and ^d2)
! Examples
! colspan="3" | [[SKULO interval names|SKULO notation]]<br>(K or S = 1, U = 2)
! Kite's<br>solfège
! Andrew's<br>solfège
|-
|-
| downminor
| 0
| zo
| 0.0
| (a, b, 0, 1)
| perfect unison
| 7/6, 7/4
| P1
| D
| perfect unison
| P1
| D
| Da
| Do
|-
|-
| minor
| 1
| fourthward wa
| 29.3
| (a, b) with b < -1
| up-unison
| 32/27, 16/9
| ^1
|-
| ^D
| upminor
| comma-wide unison, super unison
| gu
| K1/S1
| (a, b, -1)
| KD, SD
| 6/5, 9/5
| Du
| Di
|-
| 2
| 58.5
| dup-unison, downminor 2nd
| ^^1, vm2
| ^^D, vEb
| subminor 2nd, classic aug unison, uber unison
| sm2, kkA1, U1
| sEb, kkD#, UD
| Fro
| Ro
|-
| 3
| 87.8
| down-aug 1sn, minor 2nd
| vA1, m2
| vD#, Eb
| minor 2nd, comma-narrow augmented unison
| m2, kA1
| Eb, kD#
| Fra
| Rih
|-
| 4
| 117.1
| augmented 1sn, upminor 2nd
| A1, ^m2
| D#, ^Eb
| classic minor 2nd, augmented unison
| Km2, A1
| KEb, D#
| Fru
| Ra
|-
| 5
| 146.3
| mid 2nd
| ~2
| ^D#, vvE
| neutral second, super augmented unison
| N2, SA1
| UEb/uE, sD#
| Ri
| Ru
|-
| 6
| 175.6
| downmajor 2nd
| vM2
| vE
| classic/comma-wide major 2nd
| kM2
| kE
| Ro
| Reh
|-
| 7
| 204.9
| major 2nd
| M2
| E
| major 2nd
| M2
| E
| Ra
| Re
|-
| 8
| 234.1
| upmajor 2nd
| ^M2
| ^E
| supermajor 2nd
| SM2
| SE
| Ru
| Ri
|-
| 9
| 263.4
| downminor 3rd
| vm3
| vF
| subminor 3rd
| sm3
| sF
| No
| Ma
|-
| 10
| 292.7
| minor 3rd
| m3
| F
| minor 3rd
| m3
| F
| Na
| Meh
|-
| 11
| 322.0
| upminor 3rd
| ^m3
| ^F
| classic minor 3rd
| Km3
| KF
| Nu
| Me
|-
| 12
| 351.2
| mid 3rd
| ~3
| ^^F, vGb
| neutral 3rd, sub diminished 4th
| N3, sd4
| UF/uF#, sGb
| Mi
| Mu
|-
| 13
| 380.5
| downmajor 3rd
| vM3
| vF#, Gb
| classic major 3rd, diminished 4th
| kM3, d4
| kF#, Gb
| Mo
| Mi
|-
| 14
| 409.8
| major 3rd
| M3
| F#, ^Gb
| major 3rd, comma-wide diminished 4th
| M3, Kd4
| F#, KGb
| Ma
| Maa
|-
| 15
| 439.0
| upmajor 3rd
| ^M3
| ^F#, vvG
| supermajor 3rd, classic diminished 4th
| SM3, KKd4
| SF#, KKGb
| Mu
| Mo
|-
| 16
| 468.3
| down-4th
| v4
| vG
| sub 4th
| s4
| sG
| Fo
| Fe
|-
| 17
| 497.6
| perfect 4th
| P4
| G
| perfect 4th
| P4
| G
| Fa
| Fa
|-
| 18
| 526.8
| up-4th
| ^4
| ^G
| comma-wide 4th
| K4
| KG
| Fu
| Fih
|-
| 19
| 556.1
| mid-4th, downdim 5th
| ~4, vd5
| ^^G, vAb
| uber/neutral 4th, classic augmented 4th
| U4/N4, kkA4
| UG, kkG#
| Fi/Sho
| Fu
|-
| 20
| 585.4
| downaug 4th, dim 5th
| vA4, d5
| vG#, Ab
| comma-narrow augmented 4th, diminished 5th
| kA4/d5
| kG#, Ab
| Po/Sha
| Fi
|-
| 21
| 614.6
| aug 4th, updim 5th
| A4, ^d5
| G#, ^Ab
| augmented 4th, comma-wide diminished 5th
| A4/Kd5
| G#, KAb
| Pa/Shu
| Se
|-
| 22
| 643.9
| mid-5th, upaug 4th
| ~5, ^A4
| ^G#, vvA
| unter/neutral 5th, classic diminished 5th
| u5/N5, KKd5
| uA, KKAb
| Pu/Si
| Su
|-
| 23
| 673.2
| down-5th
| v5
| vA
| comma-narrow 5th
| k5
| kA
| So
| Sih
|-
| 24
| 702.4
| perfect 5th
| P5
| A
| perfect 5th
| P5
| A
| Sa
| Sol
|-
| 25
| 731.7
| up-5th
| ^5
| ^A
| super 5th
| S5
| SA
| Su
| Si
|-
| 26
| 761.0
| downminor 6th
| vm6
| ^^A, vBb
| subminor 6th, classic augmented 5th
| sm6
| sBb, kkA#
| Flo
| Lo
|-
| 27
| 790.2
| minor 6th
| m6
| vA#, Bb
| minor 6th, comma-narrow augmented 5th
| m6
| Bb, kA#
| Fla
| Leh
|-
| 28
| 819.5
| upminor 6th
| ^m6
| A#, ^Bb
| classic minor 6th, augmented 5th
| Km6, A5
| KBb, A#
| Flu
| Le
|-
| 29
| 848.8
| mid 6th
| ~6
| ^A#, vvB
| neutral 6th, super augmented 5th
| N6
| UBb/uB, sA#
| Li
| Lu
|-
| 30
| 878.0
| downmajor 6th
| vM6
| vB
| classic major 6th
| kM6
| kB
| Lo
| La
|-
| 31
| 907.3
| major 6th
| M6
| B
| major 6th
| M6
| B
| La
| Laa
|-
| 32
| 936.6
| upmajor 6th
| ^M6
| ^B
| supermajor 6th
| SM6
| SB
| Lu
| Li
|-
| 33
| 965.9
| downminor 7th
| vm7
| vC
| subminor 7th
| sm7
| sC
| Tho
| Ta
|-
| 34
| 995.1
| minor 7th
| m7
| C
| minor 7th
| m7
| C
| Tha
| Teh
|-
| 35
| 1024.4
| upminor 7th
| ^m7
| ^C
| classic/comma-wide minor seventh
| Km7
| KC
| Thu
| Te
|-
| 36
| 1053.7
| mid 7th
| ~7
| ^^C, vDb
| neutral 7th, sub diminished 8ve
| N7
| UC/uC#, sDb
| Ti
| Tu
|-
| 37
| 1082.9
| downmajor 7th
| vM7
| vC#, Db
| classic major 7th, diminished 8ve
| kM7, d8
| kC#, Db
| To
| Ti
|-
| 38
| 1112.2
| major 7th
| M7
| C#, ^Db
| major 7th, comma-wide diminished 8ve
| M7, Kd8
| C#, KDb
| Ta
| Taa
|-
| 39
| 1141.5
| upmajor 7th
| ^M7
| ^C#, vvD
| supermajor 7th, classic dim 8ve, unter 8ve
| SM7, KKd8, U8
| SC#, KKDb, u8
| Tu
| To
|-
| 40
| 1170.7
| dim 8ve
| v8
| vD
| comma-narrow 8ve, sub 8ve
| k8/s8
| kD, sD
| Do
| Da
|-
| 41
| 1200.0
| perfect 8ve
| P8
| D
| perfect 8ve
| P8
| D
| Da
| Do
|}
 
=== Interval quality and chord names in color notation ===
Combining ups and downs notation with [[color notation]], qualities can be loosely associated with colors:
 
{| class="wikitable center-all"
|-
! Quality
! [[Color notation|Color]]
! Monzo format
! Examples
|-
| downminor
| zo
| (a, b, 0, 1)
| 7/6, 7/4
|-
| minor
| fourthward wa
| (a, b) with b < -1
| 32/27, 16/9
|-
| upminor
| gu
| (a, b, -1)
| 6/5, 9/5
|-
| mid
| ilo
| (a, b, 0, 0, 1)
| 11/9, 11/6
|-
| "
| lu
| (a, b, 0, 0, -1)
| 12/11, 18/11
|-
| downmajor
| yo
| (a, b, 1)
| 5/4, 5/3
|-
| major
| fifthward wa
| (a, b) with b > 1
| 9/8, 27/16
|-
| upmajor
| ru
| (a, b, 0, -1)
| 9/7, 12/7
|}
 
All 41edo chords can be named using ups and downs. An up, down or mid immediately after the chord root affects the 3rd, 6th, 7th, and/or the 11th (every other note of a stacked-3rds chord 6-1-3-5-7-9-11-13). Alterations are always enclosed in parentheses, additions never are. Here are the zo, gu, ilo, yo and ru triads:
 
{| class="wikitable center-all"
|-
! [[Color notation|Color of the 3rd]]
! JI chord
! Notes as edosteps
! Notes of C chord
! Written name
! Spoken name
|-
| zo (7-over)
| 6:7:9
| 0-9-24
| C vEb G
| Cvm
| C downminor
|-
|-
| mid
| gu (5-under)
| ilo
| 10:12:15
| (a, b, 0, 0, 1)
| 0-11-24
| 11/9, 11/6
| C ^Eb G
| C^m
| C upminor
|-
|-
| "
| ilo (11-over)
| lu
| 18:22:27
| (a, b, 0, 0, -1)
| 0-12-24
| 12/11, 18/11
| C vvE G
| C~
| C mid
|-
|-
| downmajor
| yo (5-over)
| yo
| 4:5:6
| (a, b, 1)
| 0-13-24
| 5/4, 5/3
| C vE G
| Cv
| C downmajor or C down
|-
|-
| major
| ru (7-under)
| fifthward wa
| 14:18:21
| (a, b) with b > 1
| 0-15-24
| 9/8, 27/16
| C ^E G
|-
| C^
| upmajor
| C upmajor or C up
| ru
| (a, b, 0, -1)
| 9/7, 12/7
|}
|}


All 41edo chords can be named using ups and downs. An up, down or mid immediately after the chord root affects the 3rd, 6th, 7th, and/or the 11th (every other note of a stacked-3rds chord 6-1-3-5-7-9-11-13). Alterations are always enclosed in parentheses, additions never are. Here are the zo, gu, ilo, yo and ru triads:
Other common triads are
* 0-10-20 = D F Ab = Dd = D dim
* 0-10-21 = D F ^Ab = Dd(^5) = D dim up-five
* 0-10-22 = D F vvA = Dm(~5) = D minor mid-five
* 0-10-23 = D F vA = Dm(v5) = D minor down-five
* 0-10-24 = D F A = Dm = D minor
* 0-14-24 = D F# A = D = D or D major
* 0-14-25 = D F# ^A = D(^5) = D up-five
* 0-14-26 = D F# ^^A = D(^^5) = D half-aug
* 0-14-27 = D F# vA# = Da(v5) = D aug down-five or perhaps D(v#5) = D downsharp-five
* 0-14-28 = D F# A# = Da = D aug
 
For a more complete list, see [[41edo chord names]] and [[Ups and downs notation #Chords and chord progressions]].


{| class="wikitable center-all"
== Notations ==
=== Stein–Zimmermann–Gould notation ===
[[Stein–Zimmermann–Gould notation]] uses sharps and flats combined with quartertone accidentals and arrows:
{{Sharpness-sharp4-szg}}
 
The notes within an octave from A are thus:
 
A, B{{sesquiflat2}}, A{{demisharp2}}, B♭, A♯, B{{demiflat2}}, A{{sesquisharp2}}, B, C{{demiflat2}}, B{{demisharp2}}, C, D{{sesquiflat2}}, C{{demisharp2}}, D♭, C♯, D{{demiflat2}}, C{{sesquisharp2}}, D, E{{sesquiflat2}}, D{{demisharp2}}, E♭, D♯, E{{demiflat2}}, D{{sesquisharp2}}, E, F{{demiflat2}}, E{{demisharp2}}, F, G{{sesquiflat2}}, F{{demisharp2}}, G♭, F♯, G{{demiflat2}}, F{{sesquisharp2}}, G, A{{sesquiflat2}}, G{{demisharp2}}, A♭, G♯, A{{demiflat2}}, G{{sesquisharp2}}, A
 
=== Kite's ups and downs notation ===
41edo can also be notated with [[Kite's ups and downs notation|Kite's ups and downs]], spoken as up, dup, downsharp, sharp, upsharp etc. and down, dud, upflat etc. Note that dup is equivalent to dudsharp and dud is equivalent to dupflat.
{{Ups and downs sharpness}}
 
Half-sharps and half-flats can be used to avoid double arrows:
{{Ups and downs sharpness|41|true}}
 
=== Red-Blue notation ===
A red-note/blue-note system, similar to the one proposed for [[36edo]], is another option for notating 41edo. This is a special case of [[Kite's color notation]], treating 41edo as a temperament of the 2.3.7 subgroup. We have the "white key" albitonic notes A–G (7 in total), the "black key" sharps and flats (10 in total), a "red" and "blue" version of each albitonic note (14 in total), a "red" (dark red?) version of each sharp and a "blue" (dark blue?) version of each flat (10 in total), adding up to 41. This would result in quite a colorful keyboard! Note that there are no red flats or blue sharps. Using this nomenclature the notes are:
 
{{colored note|A}}, {{colored note|red|A}}, {{colored note|blue|B♭}}, {{colored note|B♭}}, {{colored note|A♯}}, {{colored note|red|A♯}}, {{colored note|blue|B}}, {{colored note|B}}, {{colored note|red|B}}, {{colored note|blue|C}}, {{colored note|C}}, {{colored note|red|C}}, {{colored note|blue|D♭}}, {{colored note|D♭}}, {{colored note|C♯}}, {{colored note|red|C♯}}, {{colored note|blue|D}}, {{colored note|D}}, {{colored note|red|D}}, {{colored note|blue|E♭}}, {{colored note|E♭}}, {{colored note|D♯}}, {{colored note|red|D♯}}, {{colored note|blue|E}}, {{colored note|E}}, {{colored note|red|E}}, {{colored note|blue|F}}, {{colored note|F}}, {{colored note|red|F}}, {{colored note|blue|G♭}}, {{colored note|G♭}}, {{colored note|F♯}}, {{colored note|red|F♯}}, {{colored note|blue|G}}, {{colored note|G}}, {{colored note|red|G}}, {{colored note|blue|A♭}}, {{colored note|A♭}}, {{colored note|G♯}}, {{colored note|red|G♯}}, {{colored note|blue|A}}, {{colored note|A}}
 
Interval classes could also be named by analogy. The natural, colorless, or gray interval classes are the Pythagorean ones (which show up in the standard diatonic scale), while "red" and "blue" versions are one step higher or lower. Gray thirds, sixths, and sevenths are usually more dissonant than their colorful counterparts, but the reverse is true of fourths and fifths.
 
The step size of 41edo is small enough that the smallest interval (the "red/blue unison", seventh-tone, comma, diesis or whatever you want to call it) is actually fairly consonant with most timbres; it resembles a "noticeably out of tune unison" rather than a minor second, and has its own distinct character and appeal.
 
If "red" is replaced by "up", "blue" by "down", and "neutral" by "mid", and if "gray" is omitted, this notation becomes essentially the same as Kite's ups and downs notation. The only difference is the use of minor tritone and major tritone.
 
=== Sagittal notation ===
41edo can be notated in [[Sagittal notation|Sagittal]] using the [[Sagittal notation #Spartan single-shaft|Spartan set]], with the apotome equal to 4 edosteps and the limma to 3 edosteps. Since the apotome can be split in two and the [[243/242|rastma]] is tempered out, a Stein–Zimmermann half-sharp and a half-flat may be used instead of pakai/pakao. Here is a simplified table:
 
{| class="wikitable" style="text-align: center;"
! colspan="2" |Steps
! '''0'''
! 1
! 2
! 3
! '''4'''
|-
! rowspan="3" |Symbol
! Evo-SZ
| rowspan="3" | <big>{{sagittal| |//| }}</big>
| rowspan="3" | <big>{{sagittal| /| }}</big>
| <big>{{Sagittal| t }}</big>
| rowspan="2" | <big>{{sagittal| \! }}{{sagittal| # }}</big>
| rowspan="2" | <big>{{sagittal| # }}</big>
|-
|-
! [[Color notation|Color of the 3rd]]
! Evo
! JI chord
| rowspan="2" | <big>{{sagittal| /|\ }}</big>
! Notes as edosteps
! Notes of C chord
! Written name
! Spoken name
|-
|-
| zo (7-over)
! Revo
| 6:7:9
| <big>{{sagittal| ||\ }}</big>
| 0-9-24
| <big>{{sagittal| /||\ }}</big>
| C vEb G
|}
| Cvm
The following enharmonics from the Spartan set are present (comma tempered out):
| C downminor
* {{Sagittal| //| }} = {{sagittal| /|) }} = {{sagittal| /|\ }} ([[325/324]], [[352/351]])
|-
* {{Sagittal| /| }} = {{sagittal| |) }} ([[225/224]])
| gu (5-under)
* {{Sagittal| |( }} = {{sagittal| |//| }} ([[5120/5103]])
| 10:12:15
 
| 0-11-24
See [[Sagittal notation #Revo|apotome complements]] for equivalent accidental pairs.
| C ^Eb G
 
| C^m
Featured below is the 41edo gamut notated using the best accidental approximants; in this case, pai/pao and pakai/pakao; the same sagittal sequence as [[34edo #Sagittal notation|34edo]].
| C upminor
 
|-
==== Evo flavor ====
| ilo (11-over)
{{Sagittal chart|Evo}}
| 18:22:27
 
| 0-12-24
==== Evo-SZ flavor ====
| C vvE G
{{Sagittal chart|Evo-SZ}}
| C~
 
| C mid
==== Revo flavor ====
{{Sagittal chart}}
 
We also have a diagram from the appendix to [[The Sagittal Songbook]] by [[Jacob Barton|Jacob A. Barton]], which gives multiple spellings for each pitch, and up to the double-apotome:
 
[[File:41edo Sagittal.png|800px]]
 
== Approximation to JI ==
=== Interval mappings ===
{{Q-odd-limit intervals|41}}
 
== Relationship to 12edo ==
41edo’s [[circle of fifths|circle of 41 fifths]] can be bent into a [[spiral chart|12-spoked "spiral of fifths"]]. This is possible because 24\41 is on the 7\12 kite in the [[scale tree]]. Stated another way, it is possible because the absolute value of 41edo's [[sharpness#dodeca-sharpness|dodeca-sharpness]] (edosteps per [[Pythagorean comma]]) is 1.
 
This "spiral of fifths" can be a useful construct for introducing 41edo to musicians unfamiliar with microtonal music. It may help composers and musicians to make visual sense of the notation, and to understand what size of a jump is likely to land them where compared to 12edo.
 
There are 12 "-ish" categories, where "-ish" means ±1 edostep. The 6 mid intervals are uncategorized, since they are all so far from 12edo.
 
The two innermost and two outermost intervals on the spiral are duplicates, reflecting the fact that it is a repeating circle at heart and the spiral shape is only a helpful illusion.
 
[[File:41-edo spiral.png|579x579px]]
 
The same spiral, but with notes not intervals:
 
[[File:41-edo spiral with notes.png|549x549px]]
 
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
|-
|-
| yo (5-over)
! rowspan="2" | [[Subgroup]]
| 4:5:6
! rowspan="2" | [[Comma list]]
| 0-13-24
! rowspan="2" | [[Mapping]]
| C vE G
! rowspan="2" | Optimal<br>8ve stretch (¢)
| Cv
! colspan="2" | Tuning error
| C downmajor or C down
|-
|-
| ru (7-under)
! [[TE error|Absolute]] (¢)
| 14:18:21
! [[TE simple badness|Relative]] (%)
| 0-15-24
|-
| C ^E G
| 2.3
| C^
| {{Monzo| 65 -41 }}
| C upmajor or C up
| {{Mapping| 41 65 }}
|}
| −0.153
 
| 0.15
Other common triads are
| 0.52
* 0-10-20 = D F Ab = Dd = D dim
|-
* 0-10-21 = D F ^Ab = Dd(^5) = D dim up-five
| 2.3.5
* 0-10-22 = D F vvA = Dm(~5) = D minor mid-five
| 3125/3072, 20000/19683
* 0-10-23 = D F vA = Dm(v5) = D minor down-five
| {{Mapping| 41 65 95 }}
* 0-10-24 = D F A = Dm = D minor
| +0.734
* 0-14-24 = D F# A = D = D or D major
| 1.26
* 0-14-25 = D F# ^A = D(^5) = D up-five
| 4.31
* 0-14-26 = D F# ^^A = D(^^5) = D half-aug
|-
* 0-14-27 = D F# vA# = Da(v5) = D aug down-five or perhaps D(v#5) = D downsharp-five
| 2.3.5.7
* 0-14-28 = D F# A# = Da = D aug
| 225/224, 245/243, 1029/1024
| {{Mapping| 41 65 95 115 }}
| +0.815
| 1.10
| 3.76
|-
| 2.3.5.7.11
| 100/99, 225/224, 243/242, 245/242
| {{Mapping| 41 65 95 115 142 }}
| +0.375
| 1.32
| 4.51
|-
| 2.3.5.7.11.13
| 100/99, 105/104, 144/143, 196/195, 243/242
| {{Mapping| 41 65 95 115 142 152 }}
| −0.060
| 1.55
| 5.29
|-
| 2.3.5.7.11.13.19
| 100/99, 105/104, 133/132, 144/143, 171/169, 196/195
| {{Mapping| 41 65 95 115 142 152 174 }}
| +0.111
| 1.49
| 5.10
|}
* 41et is lower in relative error than any previous equal temperaments in the 3- and 13-limit. The next equal temperament doing better in either subgroup is [[53edo|53]].
* It is even better in the 2.3.5.7.11.19 and 2.3.5.7.11.13.19 subgroups. The next equal temperaments doing better in these subgroups are [[72edo|72]] and 53, respectively.
* It is also notable in the 7-, 11-, 17-, and 19-limit, with lower absolute errors than any previous equal temperaments.


For a more complete list, see [[41edo Chord Names]] and [[Ups and downs notation #Chords and chord progressions]].
=== Commas ===
41et [[tempering out|tempers out]] the following [[comma]]s using its patent [[val]], {{val| 41 65 95 115 142 152 168 174 185 199 203 }}.


== Notations ==
{| class="commatable wikitable center-1 center-2 right-3 center-6"
=== Ups and downs notation ===
|-
41edo can be notated with [[ups and downs]], spoken as up, dup, downsharp, sharp, upsharp etc. and down, dud, upflat etc. Note that dup is equivalent to dudsharp and dud is equivalent to dupflat.
! [[Harmonic limit|Prime<br>limit]]
{{Sharpness-sharp4a}}
! [[Ratio]]<ref>Ratios with more than 8 digits are presented by placeholders with informative hints</ref>
 
! [[Cents]]
41edo can also be notated with quarter-tone accidentals and [[Alternative symbols for ups and downs notation#Sharp-3|ups and downs]]. This can be done by combining sharps and flats with arrows borrowed from extended [[Helmholtz–Ellis notation]]:
! [[Monzo]]
 
! colspan="2" | [[Color name]]
{{Sharpness-sharp4}}
! Name(s)
 
|-
The notes within an octave from A are thus:
| 3
 
| <abbr title="36893488147419103232/36472996377170786403">(40 digits)</abbr>
A, B{{sesquiflat2}}, A{{demisharp2}}, B♭, A♯, B{{demiflat2}}, A{{sesquisharp2}}, B, C{{demiflat2}}, B{{demisharp2}}, C, D{{sesquiflat2}}, C{{demisharp2}}, D♭, C♯, D{{demiflat2}}, C{{sesquisharp2}}, D, E{{sesquiflat2}}, D{{demisharp2}}, E♭, D♯, E{{demiflat2}}, D{{sesquisharp2}}, E, F{{demiflat2}}, E{{demisharp2}}, F, G{{sesquiflat2}}, F{{demisharp2}}, G♭, F♯, G{{demiflat2}}, F{{sesquisharp2}}, G, A{{sesquiflat2}}, G{{demisharp2}}, A♭, G♯, A{{demiflat2}}, G{{sesquisharp2}}, A
| 19.84
 
| {{Monzo| 65 -41 }}
=== Red-Blue notation ===
| Wa-41
A red-note/blue-note system, similar to the one proposed for [[36edo]], is another option for notating 41edo. This is a special case of Kite's [[color notation]], treating 41edo as a temperament of the 2.3.7 subgroup. We have the "white key" albitonic notes A–G (7 in total), the "black key" sharps and flats (10 in total), a "red" and "blue" version of each albitonic note (14 in total), a "red" (dark red?) version of each sharp and a "blue" (dark blue?) version of each flat (10 in total), adding up to 41. This would result in quite a colorful keyboard! Note that there are no red flats or blue sharps. Using this nomenclature the notes are:
| 41-edo
 
| [[41-comma]]
{{colored note|A}}, {{colored note|red|A}}, {{colored note|blue|B♭}}, {{colored note|B♭}}, {{colored note|A♯}}, {{colored note|red|A♯}}, {{colored note|blue|B}}, {{colored note|B}}, {{colored note|red|B}}, {{colored note|blue|C}}, {{colored note|C}}, {{colored note|red|C}}, {{colored note|blue|D♭}}, {{colored note|D♭}}, {{colored note|C♯}}, {{colored note|red|C♯}}, {{colored note|blue|D}}, {{colored note|D}}, {{colored note|red|D}}, {{colored note|blue|E♭}}, {{colored note|E♭}}, {{colored note|D♯}}, {{colored note|red|D♯}}, {{colored note|blue|E}}, {{colored note|E}}, {{colored note|red|E}}, {{colored note|blue|F}}, {{colored note|F}}, {{colored note|red|F}}, {{colored note|blue|G♭}}, {{colored note|G♭}}, {{colored note|F♯}}, {{colored note|red|F♯}}, {{colored note|blue|G}}, {{colored note|G}}, {{colored note|red|G}}, {{colored note|blue|A♭}}, {{colored note|A♭}}, {{colored note|G♯}}, {{colored note|red|G♯}}, {{colored note|blue|A}}, {{colored note|A}}
|-
 
| 5
Interval classes could also be named by analogy. The natural, colorless, or gray interval classes are the Pythagorean ones (which show up in the standard diatonic scale), while "red" and "blue" versions are one step higher or lower. Gray thirds, sixths, and sevenths are usually more dissonant than their colorful counterparts, but the reverse is true of fourths and fifths.
| <abbr title="1953125/1889568">(14 digits)</abbr>
 
| 57.27
The step size of 41edo is small enough that the smallest interval (the "red/blue unison", seventh-tone, comma, diesis or whatever you want to call it) is actually fairly consonant with most timbres; it resembles a "noticeably out of tune unison" rather than a minor second, and has its own distinct character and appeal.
| {{Monzo| -5 -10 9 }}
 
| Tritriyo
If "red" is replaced by "up", "blue" by "down", and "neutral" by "mid", and if "gray" is omitted, this notation becomes essentially the same as [[Ups and downs notation|ups and downs notation]]. The only difference is the use of minor tritone and major tritone.
| y<sup>9</sup>
 
| [[Shibboleth comma]]
=== Sagittal notation ===
|-
This notation uses the same sagittal sequence as [[34edo #Sagittal notation|34edo]].
| 5
 
| [[34171875/33554432|(16 digits)]]
==== Evo flavor ====
| 31.57
<imagemap>
| {{Monzo| -25 7 6 }}
File:41-EDO_Evo_Sagittal.svg
| Lala-tribiyo
desc none
| LLy<sup>3</sup>
rect 80 0 300 50 [[Sagittal_notation]]
| [[Ampersand comma]]
rect 300 0 687 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
|-
rect 20 80 120 106 [[81/80]]
| 5
rect 120 80 240 106 [[33/32]]
| [[3125/3072]]
default [[File:41-EDO_Evo_Sagittal.svg]]
| 29.61
</imagemap>
| {{Monzo| -10 -1 5 }}
 
| Laquinyo
==== Revo flavor ====
| Ly<sup>5</sup>
<imagemap>
| Magic comma
File:41-EDO_Revo_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 300 0 671 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 120 106 [[81/80]]
rect 120 80 240 106 [[33/32]]
default [[File:41-EDO_Revo_Sagittal.svg]]
</imagemap>
 
We also have a diagram from the appendix to [[The Sagittal Songbook]] by [[Jacob Barton|Jacob A. Barton]], which gives multiple spellings for each pitch, and up to the double-apotome:
 
[[File:41edo Sagittal.png|800px]]
 
==== Evo-SZ flavor ====
<imagemap>
File:41-EDO_Evo-SZ_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 300 0 655 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 120 106 [[81/80]]
rect 120 80 240 106 [[33/32]]
default [[File:41-EDO_Evo-SZ_Sagittal.svg]]
</imagemap>
 
== Approximation to JI ==
=== Interval mappings ===
{{Q-odd-limit intervals|41}}
 
== Relationship to 12edo ==
41edo’s [[circle of fifths|circle of 41 fifths]] can be bent into a [[spiral chart|12-spoked "spiral of fifths"]]. This is possible because 24\41 is on the 7\12 kite in the [[scale tree]]. Stated another way, it is possible because the absolute value of 41edo's [[sharpness#dodeca-sharpness|dodeca-sharpness]] (edosteps per [[Pythagorean comma]]) is 1.
 
This "spiral of fifths" can be a useful construct for introducing 41edo to musicians unfamiliar with microtonal music. It may help composers and musicians to make visual sense of the notation, and to understand what size of a jump is likely to land them where compared to 12edo.
 
There are 12 "-ish" categories, where "-ish" means ±1 edostep. The 6 mid intervals are uncategorized, since they are all so far from 12edo.
 
The two innermost and two outermost intervals on the spiral are duplicates, reflecting the fact that it is a repeating circle at heart and the spiral shape is only a helpful illusion.
 
[[File:41-edo spiral.png|579x579px]]
 
The same spiral, but with notes not intervals:
 
[[File:41-edo spiral with notes.png|549x549px]]
 
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
|-
|-
! rowspan="2" | [[Subgroup]]
| 5
! rowspan="2" | [[Comma list]]
| [[20000/19683|(10 digits)]]
! rowspan="2" | [[Mapping]]
| 27.66
! rowspan="2" | Optimal<br>8ve stretch (¢)
| {{Monzo| 5 -9 4 }}
! colspan="2" | Tuning error
| Saquadyo
| sy<sup>4</sup>
| [[Tetracot comma]]
|-
|-
! [[TE error|Absolute]] (¢)
| 5
! [[TE simple badness|Relative]] (%)
| <abbr title="131072000/129140163">(18 digits)</abbr>
| 25.71
| {{Monzo| 20 -17 3 }}
| Sasa-triyo
| ssy<sup>3</sup>
| [[Roda]]
|-
|-
| 2.3
| 5
| {{monzo| 65 -41 }}
| [[32805/32768|(10 digits)]]
| {{mapping| 41 65 }}
| 1.95
| −0.153
| {{Monzo| -15 8 1 }}
| 0.15
| Layo
| 0.52
| Ly
| [[Schisma]]
|-
|-
| 2.3.5
| 7
| 3125/3072, 20000/19683
| [[15625/15309|(10 digits)]]
| {{mapping| 41 65 95 }}
| 35.37
| +0.734
| {{Monzo| 0 -7 6 -1 }}
| 1.26
| Rutribiyo
| 4.31
| ry<sup>6</sup>
| Arcturus comma, great BP diesis
|-
|-
| 2.3.5.7
| 7
| 225/224, 245/243, 1029/1024
| <abbr title="854296875/843308032">(18 digits)</abbr>
| {{mapping| 41 65 95 115 }}
| 22.41
| +0.815
| {{Monzo| -10 7 8 -7 }}
| 1.10
| Lasepru-aquadbiyo
| 3.76
| Lr<sup>7</sup>y<sup>8</sup>
| [[Blackjackisma]]
|-
|-
| 2.3.5.7.11
| 7
| 100/99, 225/224, 243/242, 245/242
| [[875/864]]
| {{mapping| 41 65 95 115 142 }}
| 21.90
| +0.375
| {{Monzo| -5 -3 3 1 }}
| 1.32
| Zotriyo
| 4.51
| zy<sup>3</sup>
| Keema
|-
|-
| 2.3.5.7.11.13
| 7
| 100/99, 105/104, 144/143, 196/195, 243/242
| [[3125/3087]]
| {{mapping| 41 65 95 115 142 152 }}
| 21.18
| −0.060
| {{Monzo| 0 -2 5 -3 }}
| 1.55
| Triru-aquinyo
| 5.29
| r<sup>3</sup>y<sup>5</sup>
| Gariboh comma
|-
|-
| 2.3.5.7.11.13.19
| 7
| 100/99, 105/104, 133/132, 144/143, 171/169, 196/195
| <abbr title="179200/177147">(12 digits)</abbr>
| {{mapping| 41 65 95 115 142 152 174 }}
| 19.95
| +0.111
| {{Monzo| 10 -11 2 1 }}
| 1.49
| Sazoyoyo
| 5.10
| szyy
|}
| [[Tolerma]]
* 41et is lower in relative error than any previous equal temperaments in the 3-, 13- and 19-limit. The next equal temperaments doing better in these subgroups are 53, 53, and 46, respectively. It is even more prominent in the 2.3.5.7.11.19 and 2.3.5.7.11.13.19 subgroup. The next equal temperaments doing better in these subgroups are 72 and 53, respectively.
 
=== Commas ===
41et [[tempering out|tempers out]] the following [[comma]]s using its patent [[val]], {{val| 41 65 95 115 142 152 168 174 185 199 203 }}.
 
{| class="commatable wikitable center-1 center-2 right-3 center-6"
|-
|-
! [[Harmonic limit|Prime<br>limit]]
| 7
! [[Ratio]]<ref>Ratios with more than 8 digits are presented by placeholders with informative hints</ref>
| [[33075/32768|(10 digits)]]
! [[Cents]]
| 16.14
! [[Monzo]]
| {{Monzo| -15 3 2 2 }}
! colspan="2" | [[Color name]]
| Labizoyo
! Name(s)
| Lzzyy
| [[Mirwomo comma]]
|-
|-
| 3
| 7
| <abbr title="36893488147419103232/36472996377170786403">(40 digits)</abbr>
| [[245/243]]
| 19.84
| 14.19
| {{monzo| 65 -41 }}
| {{Monzo| 0 -5 1 2 }}
| Wa-41
| Zozoyo
| 41-edo
| zzy
| [[41-comma]]
| Sensamagic comma
|-
|-
| 5
| 7
| <abbr title="1953125/1889568">(14 digits)</abbr>
| [[4000/3969]]
| 57.27
| 13.47
| {{monzo| -5 -10 9 }}
| {{Monzo| 5 -4 3 -2 }}
| Tritriyo
| Rurutriyo
| y<sup>9</sup>
| rry<sup>3</sup>
| [[Shibboleth comma]]
| Octagar comma
|-
|-
| 5
| 7
| [[34171875/33554432|(16 digits)]]
| <abbr title="823543/819200">(12 digits)</abbr>
| 31.57
| 9.15
| {{monzo| -25 7 6 }}
| {{Monzo| -15 0 -2 7 }}
| Lala-tribiyo
| Lasepzo-agugu
| LLy<sup>3</sup>
| Lz<sup>7</sup>gg
| [[Ampersand comma]]
| [[Quince comma]]
|-
|-
| 5
| 7
| [[3125/3072]]
| [[1029/1024]]
| 29.61
| 8.43
| {{monzo| -10 -1 5 }}
| {{Monzo| -10 1 0 3 }}
| Laquinyo
| Latrizo
| Ly<sup>5</sup>
| Lz<sup>3</sup>
| Magic comma
| Gamelisma
|-
|-
| 5
| 7
| [[20000/19683|(10 digits)]]
| [[225/224]]
| 27.66
| 7.71
| {{monzo| 5 -9 4 }}
| {{Monzo| -5 2 2 -1 }}
| Saquadyo
| Ruyoyo
| sy<sup>4</sup>
| ryy
| [[Tetracot comma]]
| Marvel comma
|-
|-
| 5
| 7
| <abbr title="131072000/129140163">(18 digits)</abbr>
| [[16875/16807|(10 digits)]]
| 25.71
| 6.99
| {{monzo| 20 -17 3 }}
| {{Monzo| 0 3 4 -5 }}
| Sasa-triyo
| Quinru-aquadyo
| ssy<sup>3</sup>
| r<sup>5</sup>y<sup>4</sup>
| [[Roda]]
| [[Mirkwai comma]]
|-
|-
| 5
| 7
| [[32805/32768|(10 digits)]]
| [[10976/10935|(10 digits)]]
| 1.95
| 6.48
| {{monzo| -15 8 1 }}
| {{Monzo| 5 -7 -1 3 }}
| Layo
| Satrizo-agu
| Ly
| sz<sup>3</sup>g
| [[Schisma]]
| [[Hemimage comma]]
|-
|-
| 7
| 7
| [[15625/15309|(10 digits)]]
| [[5120/5103]]
| 35.37
| 5.76
| {{monzo| 0 -7 6 -1 }}
| {{Monzo| 10 -6 1 -1 }}
| Rutribiyo
| Saruyo
| ry<sup>6</sup>
| sry
| Arcturus comma, great BP diesis
| Hemifamity comma
|-
|-
| 7
| 7
| <abbr title="854296875/843308032">(18 digits)</abbr>
| [[33554432/33480783|(16 digits)]]
| 22.41
| 3.80
| {{monzo| -10 7 8 -7 }}
| {{Monzo| 25 -14 0 -1 }}
| Lasepru-aquadbiyo
| Sasaru
| Lr<sup>7</sup>y<sup>8</sup>
| ssr
| [[Blackjackisma]]
| [[Garischisma]]
|-
|-
| 7
| 7
| [[875/864]]
| [[2401/2400]]
| 21.90
| 0.72
| {{monzo| -5 -3 3 1 }}
| {{Monzo| -5 -1 -2 4 }}
| Zotriyo
| Bizozogu
| zy<sup>3</sup>
| z<sup>4</sup>gg
| Keema
| Breedsma
|-
|-
| 7
| 11
| [[3125/3087]]
| <abbr title="163840/161051">(12 digits)</abbr>
| 21.18
| 29.72
| {{monzo| 0 -2 5 -3 }}
| {{Monzo| 15 0 1 0 -5 }}
| Triru-aquinyo
| Saquinlu-ayo
| r<sup>3</sup>y<sup>5</sup>
| s1u<sup>5</sup>y
| Gariboh comma
| [[Thuja comma]]
|-
|-
| 7
| 11
| <abbr title="179200/177147">(12 digits)</abbr>
| [[245/242]]
| 19.95
| 21.33
| {{monzo| 10 -11 2 1 }}
| {{Monzo| -1 0 1 2 -2 }}
| Sazoyoyo
| Luluzozoyo
| szyy
| 1uuzzy
| [[Tolerma]]
| Frostma
|-
|-
| 7
| 11
| [[33075/32768|(10 digits)]]
| [[100/99]]
| 16.14
| 17.40
| {{monzo| -15 3 2 2 }}
| {{Monzo| 2 -2 2 0 -1 }}
| Labizoyo
| Luyoyo
| Lzzyy
| 1uyy
| [[Mirwomo comma]]
| Ptolemisma
|-
|-
| 7
| 11
| [[245/243]]
| [[1344/1331]]
| 14.19
| 16.83
| {{monzo| 0 -5 1 2 }}
| {{Monzo| 6 1 0 1 -3 }}
| Zozoyo
| Trilu-azo
| zzy
| 1u<sup>3</sup>z
| Sensamagic comma
| Hemimin comma
|-
|-
| 7
| 11
| [[4000/3969]]
| [[896/891]]
| 13.47
| 9.69
| {{monzo| 5 -4 3 -2 }}
| {{Monzo| 7 -4 0 1 -1 }}
| Rurutriyo
| Saluzo
| rry<sup>3</sup>
| s1uz
| Octagar comma
| [[Pentacircle comma]]
|-
|-
| 7
| 11
| <abbr title="823543/819200">(12 digits)</abbr>
| [[65536/65219|(10 digits)]]
| 9.15
| 8.39
| {{monzo| -15 0 -2 7 }}
| {{Monzo| 16 0 0 -2 -3 }}
| Lasepzo-agugu
| Satrilu-aruru
| Lz<sup>7</sup>gg
| s1u<sup>3</sup>rr
| [[Quince comma]]
| [[Orgonisma]]
|-
|-
| 7
| 11
| [[1029/1024]]
| [[243/242]]
| 8.43
| 7.14
| {{monzo| -10 1 0 3 }}
| {{Monzo| -1 5 0 0 -2 }}
| Latrizo
| Lulu
| Lz<sup>3</sup>
| 1uu
| Gamelisma
| Rastma
|-
|-
| 7
| 11
| [[225/224]]
| [[385/384]]
| 7.71
| 4.50
| {{monzo| -5 2 2 -1 }}
| {{Monzo| -7 -1 1 1 1 }}
| Ruyoyo
| Lozoyo
| ryy
| 1ozg
| Marvel comma
| Keenanisma
|-
|-
| 7
| 11
| [[16875/16807|(10 digits)]]
| [[441/440]]
| 6.99
| 3.93
| {{monzo| 0 3 4 -5 }}
| {{Monzo| -3 2 -1 2 -1 }}
| Quinru-aquadyo
| Luzozogu
| r<sup>5</sup>y<sup>4</sup>
| 1uzzg
| [[Mirkwai comma]]
| Werckisma
|-
|-
| 7
| 11
| [[10976/10935|(10 digits)]]
| [[1375/1372]]
| 6.48
| 3.78
| {{monzo| 5 -7 -1 3 }}
| {{Monzo| -2 0 3 -3 1 }}
| Satrizo-agu
| Lotriruyo
| sz<sup>3</sup>g
| 1or<sup>3</sup>y
| [[Hemimage comma]]
| Moctdel comma
|-
|-
| 7
| 11
| [[5120/5103]]
| [[540/539]]
| 5.76
| 3.21
| {{monzo| 10 -6 1 -1 }}
| {{Monzo| 2 3 1 -2 -1 }}
| Saruyo
| Lururuyo
| sry
| 1urry
| Hemifamity comma
| Swetisma
|-
|-
| 7
| 11
| [[33554432/33480783|(16 digits)]]
| [[3025/3024]]
| 3.80
| 0.57
| {{monzo| 25 -14 0 -1 }}
| {{Monzo| -4 -3 2 -1 2 }}
| Sasaru
| Loloruyoyo
| ssr
| 1ooryy
| [[Garischisma]]
| Lehmerisma
|-
| 7
| [[2401/2400]]
| 0.72
| {{monzo| -5 -1 -2 4 }}
| Bizozogu
| z<sup>4</sup>gg
| Breedsma
|-
|-
| 11
| 11
| <abbr title="163840/161051">(12 digits)</abbr>
| [[151263/151250|<abbr title="151263/151250">(12 digits)</abbr>]]
| 29.72
| 0.15
| {{monzo| 15 0 1 0 -5 }}
| {{Monzo| -1 2 -4 5 -2 }}
| Saquinlu-ayo
| Luluquinzo-aquadgu
| s1u<sup>5</sup>y
| 1uuz<sup>5</sup>g<sup>4</sup>
| [[Thuja comma]]
| [[Odiheim comma]]
|-
|-
| 11
| 13
| [[245/242]]
| [[343/338]]
| 21.33
| 25.42
| {{monzo| -1 0 1 2 -2 }}
| {{Monzo| -1 0 0 3 0 -2 }}
| Luluzozoyo
| Thuthutrizo
| 1uuzzy
| 3uuz<sup>3</sup>
| Frostma
|  
|-
|-
| 11
| 13
| [[100/99]]
| [[105/104]]
| 17.40
| 16.57
| {{monzo| 2 -2 2 0 -1 }}
| {{Monzo| -3 1 1 1 0 -1 }}
| Luyoyo
| Thuzoyo
| 1uyy
| 3uzy
| Ptolemisma
| Animist comma
|-
|-
| 11
| 13
| [[1344/1331]]
| [[28672/28431|(10 digits)]]
| 16.83
| 14.61
| {{monzo| 6 1 0 1 -3 }}
| {{Monzo| 12 -7 0 1 0 -1 }}
| Trilu-azo
| Sathuzo
| 1u<sup>3</sup>z
| s3uz
| Hemimin comma
| [[Secorian comma]]
|-
|-
| 11
| 13
| [[896/891]]
| [[275/273]]
| 9.69
| 12.64
| {{monzo| 7 -4 0 1 -1 }}
| {{Monzo| 0 -1 2 -1 1 -1 }}
| Saluzo
| Thuloruyoyo
| s1uz
| 3u1oryy
| [[Pentacircle comma]]
| Gassorma
|-
|-
| 11
| 13
| [[65536/65219|(10 digits)]]
| [[144/143]]
| 8.39
| 12.06
| {{monzo| 16 0 0 -2 -3 }}
| {{Monzo| 4 2 0 0 -1 -1 }}
| Satrilu-aruru
| Thulu
| s1u<sup>3</sup>rr
| 3u1u
| [[Orgonisma]]
| Grossma
|-
|-
| 11
| 13
| [[243/242]]
| [[196/195]]
| 7.14
| 8.86
| {{monzo| -1 5 0 0 -2 }}
| {{Monzo| 2 -1 -1 2 0 -1 }}
| Lulu
| Thuzozogu
| 1uu
| 3uzzg
| Rastma
| Mynucuma
|-
|-
| 11
| 13
| [[385/384]]
| [[640/637]]
| 4.50
| 8.13
| {{monzo| -7 -1 1 1 1 }}
| {{Monzo| 7 0 1 -2 0 -1 }}
| Lozoyo
| Thururuyo
| 1ozg
| 3urry
| Keenanisma
| Huntma
|-
|-
| 11
| 13
| [[441/440]]
| [[1188/1183]]
| 3.93
| 7.30
| {{monzo| -3 2 -1 2 -1 }}
| {{Monzo| 2 3 0 -1 1 -2 }}
| Luzozogu
| Thuthuloru
| 1uzzg
| 3uu1or
| Werckisma
| Kestrel comma
|-
|-
| 11
| 13
| [[1375/1372]]
| [[31213/31104]]
| 3.78
| 6.06
| {{monzo| -2 0 3 -3 1 }}
| {{Monzo| -7 -5 0 4 0 1 }}
| Lotriruyo
| Thoquadzo
| 1or<sup>3</sup>y
| 3oz<sup>4</sup>3
| Moctdel comma
| Praveensma
|-
|-
| 11
| 13
| [[540/539]]
| [[325/324]]
| 3.21
| 5.34
| {{monzo| 2 3 1 -2 -1 }}
| {{Monzo| -2 -4 2 0 0 1 }}
| Lururuyo
| Thoyoyo
| 1urry
| 3oyy
| Swetisma
| Marveltwin comma
|-
|-
| 11
| 13
| [[3025/3024]]
| [[352/351]]
| 0.57
| 4.93
| {{monzo| -4 -3 2 -1 2 }}
| {{Monzo| 5 -3 0 0 1 -1 }}
| Loloruyoyo
| Thulo
| 1ooryy
| 3u1o
| Lehmerisma
| Major minthma
|-
| 11
| [[151263/151250|<abbr title="151263/151250">(12 digits)</abbr>]]
| 0.15
| {{monzo| -1 2 -4 5 -2 }}
| Luluquinzo-aquadgu
| 1uuz<sup>5</sup>g<sup>4</sup>
| [[Odiheim comma]]
|-
|-
| 13
| 13
| [[343/338]]
| [[364/363]]
| 25.42
| 4.76
| {{monzo| -1 0 0 3 0 -2 }}
| {{Monzo| 2 -1 0 1 -2 1 }}
| Thuthutrizo
| Tholuluzo
| 3uuz<sup>3</sup>
| 3o1uuz
|  
| Minor minthma
|-
|-
| 13
| 13
| [[105/104]]
| [[847/845]]
| 16.57
| 4.09
| {{monzo| -3 1 1 1 0 -1 }}
| {{Monzo| 0 0 -1 1 2 -2 }}
| Thuzoyo
| Thuthulolozogu
| 3uzy
| 3uu1oozg
| Animist comma
| Cuthbert comma
|-
|-
| 13
| 13
| [[28672/28431|(10 digits)]]
| [[729/728]]
| 14.61
| 2.38
| {{monzo| 12 -7 0 1 0 -1 }}
| {{Monzo| -3 6 0 -1 0 -1 }}
| Sathuzo
| Lathuru
| s3uz
| L3ur
| [[Secorian comma]]
| Squbema
|-
|-
| 13
| 13
| [[275/273]]
| [[2080/2079]]
| 12.64
| 0.83
| {{monzo| 0 -1 2 -1 1 -1 }}
| {{Monzo| 5 -3 1 -1 -1 1 }}
| Thuloruyoyo
| Tholuruyo
| 3u1oryy
| 3o1ury
| Gassorma
| Ibnsinma, sinaisma
|-
|-
| 13
| 13
| [[144/143]]
| [[4096/4095]]
| 12.06
| 0.42
| {{monzo| 4 2 0 0 -1 -1 }}
| {{Monzo| 12 -2 -1 -1 0 -1 }}
| Thulu
| Sathurugu
| 3u1u
| s3urg
| Grossma
| Minisma
|-
|-
| 13
| 13
| [[196/195]]
| [[6656/6655]]
| 8.86
| 0.26
| {{monzo| 2 -1 -1 2 0 -1 }}
| {{Monzo| 9 0 -1 0 -3 1 }}
| Thuzozogu
| Thotrilo-agu
| 3uzzg
| 3u1o<sup>3</sup>g2
| Mynucuma
| Jacobin comma
|-
|-
| 13
| 13
| [[640/637]]
| [[10648/10647|(10 digits)]]
| 8.13
| 0.16
| {{monzo| 7 0 1 -2 0 -1 }}
| {{Monzo| 3 -2 0 -1 3 -2 }}
| Thururuyo
| Thuthutrilo-aru
| 3urry
| 3uu1o<sup>3</sup>r
| Huntma
| [[Harmonisma]]
|-
|-
| 13
| 17
| [[1188/1183]]
| [[2187/2176]]
| 7.30
| 8.73
| {{monzo| 2 3 0 -1 1 -2 }}
| {{Monzo| -7 7 0 0 0 0 -1 }}
| Thuthuloru
| Lasu
| 3uu1or
| L17u
| Kestrel comma
| Septendecimal schisma
|-
|-
| 13
| 17
| [[31213/31104]]
| [[256/255]]
| 6.06
| 6.78
| {{monzo| -7 -5 0 4 0 1 }}
| {{Monzo| 8 -1 -1 0 0 0 -1 }}
| Thoquadzo
| Sugu
| 3oz<sup>4</sup>3
| 17ug
| Praveensma
| Charisma
|-
|-
| 13
| 17
| [[325/324]]
| [[715/714]]
| 5.34
| 2.42
| {{monzo| -2 -4 2 0 0 1 }}
| {{Monzo| -1 -1 1 -1 1 1 -1 }}
| Thoyoyo
| Sutholoruyo
| 3oyy
| 17u3o1ory
| Marveltwin comma
| Septendecimal bridge comma
|-
|-
| 13
| 19
| [[352/351]]
| [[210/209]]
| 4.93
| 8.26
| {{monzo| 5 -3 0 0 1 -1 }}
| {{Monzo| 1 1 1 1 -1 0 0 -1 }}
| Thulo
| Nuluzoyo
| 3u1o
| 19u1uzy
| Major minthma
| Spleen comma
|-
|-
| 13
| 19
| [[364/363]]
| [[361/360]]
| 4.76
| 4.80
| {{monzo| 2 -1 0 1 -2 1 }}
| {{Monzo| -3 -2 -1 0 0 0 0 2 }}
| Tholuluzo
| Nonogu
| 3o1uuz
| 19oog2
| Minor minthma
| Go comma
|-
|-
| 13
| 19
| [[847/845]]
| [[513/512]]
| 4.09
| 3.38
| {{monzo| 0 0 -1 1 2 -2 }}
| {{Monzo| -9 3 0 0 0 0 0 1 }}
| Thuthulolozogu
| Lano
| 3uu1oozg
| L19o
| Cuthbert comma
| Boethius' comma
|-
|-
| 13
| 19
| [[729/728]]
| [[1216/1215]]
| 2.38
| 1.42
| {{monzo| -3 6 0 -1 0 -1 }}
| {{Monzo| 6 -5 -1 0 0 0 0 1 }}
| Lathuru
| Sanogu
| L3ur
| s19og
| Squbema
| Eratosthenes' comma
|-
|-
| 13
| 23
| [[2080/2079]]
| [[736/729]]
| 0.83
| 16.54
| {{monzo| 5 -3 1 -1 -1 1 }}
| {{Monzo| 5 -6 0 0 0 0 0 0 1 }}
| Tholuruyo
| Satwetho
| 3o1ury
| s23o
| Ibnsinma
| Vicesimotertial comma
|-
|-
| 13
| 29
| [[4096/4095]]
| [[145/144]]
| 0.42
| 11.98
| {{monzo| 12 -2 -1 -1 0 -1 }}
| {{Monzo| -4 -2 1 0 0 0 0 0 0 1 }}
| Sathurugu
| Twenoyo
| s3urg
| 29oy
| Schismina
| 29th-partial chroma
|-
|}
| 13
 
| [[6656/6655]]
=== Rank-2 temperaments ===
| 0.26
* [[List of edo-distinct 41et rank two temperaments]]
| {{monzo| 9 0 -1 0 -3 1 }}
* [[Schismic–countercommatic equivalence continuum]]
| Thotrilo-agu
 
| 3u1o<sup>3</sup>g2
{| class="wikitable right-1 right-2"
| Jacobin comma
|+ Table of temperaments by generator
|-
|-
| 13
! Degree
| [[10648/10647|(10 digits)]]
! Cents
| 0.16
! Temperament(s)
| {{monzo| 3 -2 0 -1 3 -2 }}
! [[Pergen]]
| Thuthutrilo-aru
! Mos scales
| 3uu1o<sup>3</sup>r
| [[Harmonisma]]
|-
|-
| 17
| 1
| [[2187/2176]]
| 29.27
| 8.73
| [[Slendi]]
| {{monzo| -7 7 0 0 0 0 -1 }}
| (P8, P4/17)
| Lasu
|  
| L17u
| Septendecimal schisma
|-
|-
| 17
| 2
| [[256/255]]
| 58.54
| 6.78
| [[Hemimiracle]]<br>[[Dodecacot]]
| {{monzo| 8 -1 -1 0 0 0 -1 }}
| (P8, P5/12)
| Sugu
| 21-tone mos
| 17ug
| Charisma
|-
|-
| 17
| 3
| [[715/714]]
| 87.80
| 2.42
| [[Octacot]]
| {{monzo| -1 -1 1 -1 1 1 -1 }}
| (P8, P5/8)
| Sutholoruyo
| 14-tone mos: 3 3 3 3 3 3 3 3 3 3 3 3 3 2
| 17u3o1ory
| Septendecimal bridge comma
|-
|-
| 19
| 4
| [[210/209]]
| 117.07
| 8.26
| [[Miracle]]
| {{monzo| 1 1 1 1 -1 0 0 -1 }}
| (P8, P5/6)
| Nuluzoyo
| 11-tone mos: 4 4 4 4 4 4 4 4 4 4 1
| 19u1uzy
| Spleen comma
|-
|-
| 19
| 5
| [[361/360]]
| 146.34
| 4.80
| [[BPS]] / [[bohpier]]
| {{monzo| -3 -2 -1 0 0 0 0 2 }}
| (P8, P12/13)
| Nonogu
| 20-tone mos
| 19oog2
| Go comma
|-
|-
| 19
| 6
| [[513/512]]
| 175.61
| 3.38
| [[Tetracot]] / [[bunya]] / [[monkey]]<br>[[Sesquiquartififths]] / [[sesquart]]
| {{monzo| -9 3 0 0 0 0 0 1 }}
| (P8, P5/4)
| Lano
| 13-tone mos: 1 5 1 5 1 5 1 5 5 1 5 1 5
| L19o
| Boethius' comma
|-
|-
| 19
| 7
| [[1216/1215]]
| 204.88
| 1.42
| [[Baldy]]<br>[[Quadrimage]]
| {{monzo| 6 -5 -1 0 0 0 0 1 }}
| (P8, c<sup>3</sup>P4/20)
| Sanogu
| 11-tone mos: 6 1 6 6 1 6 1 6 1 6 1
| s19og
|-
| Eratosthenes' comma
| 8
| 234.15
| [[Slendric]] / [[rodan]] / [[guiron]]
| (P8, P5/3)
| 11-tone mos: 7 1 7 1 7 1 7 1 1 7 1
|-
|-
| 23
| 9
| [[736/729]]
| 263.41
| 16.54
| [[Septimin]]
| {{monzo| 5 -6 0 0 0 0 0 0 1 }}
| (P8, ccP4/11)
| Satwetho
| 9-tone mos: 5 4 5 5 4 5 4 5 4
| s23o
| Vicesimotertial comma
|-
|-
| 29
| 10
| [[145/144]]
| 292.68
| 11.98
| [[Quasitemp]]
| {{monzo| -4 -2 1 0 0 0 0 0 0 1 }}
| (P8, c<sup>3</sup>P4/14)
| Twenoyo
| 29-tone mos
| 29oy
| 29th-partial chroma
|}
 
=== Rank-2 temperaments ===
* [[List of edo-distinct 41et rank two temperaments]]
* [[Schismic–countercommatic equivalence continuum]]
 
{| class="wikitable right-1 right-2"
|+ Table of temperaments by generator
|-
|-
! Degree
| 11
! Cents
| 321.95
! Temperament(s)
| [[Superkleismic]]
! [[Pergen]]
| (P8, ccP4/9)
! Mos scales
| 11-tone mos: 5 3 5 3 3 5 3 3 5 3 3
|-
|-
| 1
| 12
| 29.27
| 351.22
| [[Slendi]]
| [[Hemif]] / [[hemififths]] / [[salsa]]<br>[[Karadeniz]]
| (P8, P4/17)
| (P8, P5/2)
|  
| 10-tone mos: 5 2 5 5 2 5 5 5 2 5
|-
|-
| 2
| 13
| 58.54
| 380.49
| [[Hemimiracle]]<br>[[Dodecacot]]
| [[Magic]] / [[witchcraft]]<br>[[Quanharuk]]
| (P8, P5/12)
| (P8, P12/5)
| 21-tone mos
| 10-tone mos: 2 9 2 2 9 2 2 9 2 2
|-
|-
| 3
| 14
| 87.80
| 409.76
| [[Octacot]]
| [[Hocum]]<br>[[Hocus]]
| (P8, P5/8)
| (P8, c<sup>3</sup>P4/10)
| 14-tone mos: 3 3 3 3 3 3 3 3 3 3 3 3 3 2
| 32-tone mos
|-
|-
| 4
| 15
| 117.07
| 439.02
| [[Miracle]]
| [[Superthird]]
| (P8, P5/6)
| (P8, c<sup>6</sup>P5/18)
| 11-tone mos: 4 4 4 4 4 4 4 4 4 4 1
| 11-tone mos: 4 3 4 4 4 3 4 4 3 4 4
|-
|-
| 5
| 16
| 146.34
| 468.29
| [[BPS]] / [[bohpier]]
| [[Barbad]]
| (P8, P12/13)
| (P8, c<sup>7</sup>P4/19)
| 20-tone mos
| 8-tone mos: 7 2 7 7 2 7 7 2
|-
|-
| 6
| 17
| 175.61
| 497.56
| [[Tetracot]] / [[bunya]] / [[monkey]]<br>[[Sesquiquartififths]] / [[sesquart]]
| [[Helmholtz (temperament)|Helmholtz]] / [[garibaldi]] / [[cassandra]] / [[andromeda]]<br>[[Kwai]]
| (P8, P5/4)
| (P8, P5)
| 13-tone mos: 1 5 1 5 1 5 1 5 5 1 5 1 5
| 12-tone mos: 4 3 4 3 3 4 3 4 3 4 3 4 3 3
|-
|-
| 7
| 18
| 204.88
| 526.83
| [[Baldy]]<br>[[Quadrimage]]
| [[Trismegistus]]
| (P8, c<sup>3</sup>P4/20)
| (P8, c<sup>6</sup>P5/15)
| 11-tone mos: 6 1 6 6 1 6 1 6 1 6 1
| 9-tone mos: 5 5 3 5 5 5 5 3 5
|-
|-
| 8
| 19
| 234.15
| 556.10
| [[Slendric]] / [[rodan]] / [[guiron]]
| [[Alphorn]]
| (P8, P5/3)
| (P8, c<sup>7</sup>P4/16)
| 11-tone mos: 7 1 7 1 7 1 7 1 1 7 1
| 9-tone mos: 3 3 3 10 3 3 3 3 10
|-
|-
| 9
| 20
| 263.41
| 585.37
| [[Septimin]]
| [[Pluto]]<br>[[Merman]]
| (P8, ccP4/11)
| (P8, c<sup>3</sup>P4/7)
| 9-tone mos: 5 4 5 5 4 5 4 5 4
|  
|-
|}
| 10
 
| 292.68
== Octave stretch or compression ==
| [[Quasitemp]]
Whether there is intonational improvement from [[stretched and compressed tuning|octave stretch or compression]] depends on which [[subgroup]] of [[JI]] we are focusing on.
| (P8, c<sup>3</sup>P4/14)
 
| 29-tone mos
For the 5-, 7-, and 11-limit, stretch is advised, though in the case of the 11-limit the stretch should be milder. A tuning that does that is [[ZPI|184zpi]].
 
For the 13-limit and in particular the 17-limit, little to no stretch or even compression may be suitable for balancing out the sharp and flat tuning tendencies, as is demonstrated in tunings such as [[65edt]], [[106ed6]], and [[147ed12]].  
 
41edo additionally approximates primes 19, 29, and 31, which all tend flat, so stretching will serve again as we take that into account, especially if we use the temperament in any no-17 or no-13 no-17 settings.
 
== Scales and modes ==
=== Lists of 41edo scales ===
* [[41edo modes]]
* [[List of MOS scales in 41edo]]
* [[The Kite Guitar Scales]]
* [[Kite Giedraitis's Categorizations of 41edo Scales]]
 
=== Harmonic scale ===
41edo is the first edo to do some justice to Mode 8 of the [[harmonic series]], which Dante Rosati calls the "[[overtone scale|Diatonic Harmonic Series Scale]]," consisting of overtones 8 through 16 (sometimes made to repeat at the octave).
 
{| class="wikitable" style="text-align: center;"
|-
|-
! Overtones in "Mode 8":
| 8
| 9
| 10
| 11
| 11
| 321.95
| [[Superkleismic]]
| (P8, ccP4/9)
| 11-tone mos: 5 3 5 3 3 5 3 3 5 3 3
|-
| 12
| 12
| 351.22
| [[Hemif]] / [[hemififths]] / [[salsa]]<br>[[Karadeniz]]
| (P8, P5/2)
| 10-tone mos: 5 2 5 5 2 5 5 5 2 5
|-
| 13
| 13
| 380.49
| [[Magic]] / [[witchcraft]]<br>[[Quanharuk]]
| (P8, P12/5)
| 10-tone mos: 2 9 2 2 9 2 2 9 2 2
|-
| 14
| 14
| 409.76
| [[Hocum]]<br>[[Hocus]]
| (P8, c<sup>3</sup>P4/10)
| 32-tone mos
|-
| 15
| 15
| 439.02
| [[Superthird]]
| (P8, c<sup>6</sup>P5/18)
| 11-tone mos: 4 3 4 4 4 3 4 4 3 4 4
|-
| 16
| 16
| 468.29
| [[Barbad]]
| (P8, c<sup>7</sup>P4/19)
| 8-tone mos: 7 2 7 7 2 7 7 2
|-
|-
| 17
! … as JI Ratio from 1/1:
| 497.56
| 1/1
| [[Helmholtz (temperament)|Helmholtz]] / [[garibaldi]] / [[cassandra]] / [[andromeda]]<br>[[Kwai]]
| 9/8
| (P8, P5)
| 5/4
| 12-tone mos: 4 3 4 3 3 4 3 4 3 4 3 4 3 3
| 11/8
|-
| 3/2
| 18
| 13/8
| 526.83
| 7/4
| [[Trismegistus]]
| 15/8
| (P8, c<sup>6</sup>P5/15)
| 2/1
| 9-tone mos: 5 5 3 5 5 5 5 3 5
|-
! … in cents:
| 0
| 203.9
| 386.3
| 551.3
| 702.0
| 840.5
| 968.8
| 1088.3
| 1200.0
|-
|-
! Nearest degree of 41edo:
| 0
| 7
| 13
| 19
| 19
| 556.10
| 24
| [[Alphorn]]
| 29
| (P8, c<sup>7</sup>P4/16)
| 33
| 9-tone mos: 3 3 3 10 3 3 3 3 10
| 37
|-
| 41
| 20
|-
| 585.37
! … in cents:
| [[Pluto]]<br>[[Merman]]
| 0
| (P8, c<sup>3</sup>P4/7)
| 204.9
|  
| 380.5
| 556.1
| 702.4
| 848.8
| 965.9
| 1082.9
| 1200.0
|}
|}


== Octave stretch or compression ==
While each overtone of Mode 8 is approximated within a reasonable degree of accuracy, the steps between the intervals are not uniquely represented. (41edo is, after all, a temperament.)
Whether there is intonational improvement from [[stretched and compressed tuning|octave stretch or compression]] depends on which [[subgroup]] of [[JI]] we are focusing on.  


For the 5-, 7-, and 11-limit, stretch is advised, though in the case of the 11-limit the stretch should be milder. A tuning that does that is [[ZPI|184zpi]].  
* 7\41 (7 degrees of 41edo) (204.9 cents) stands in for just ratio 9/8 (203.9 cents) – a close match.
* 6\41 (175.6 cents) stands in for both 10/9 (182.4 cents) and 11/10 (165.0 cents).
* 5\41 (146.3 cents) stands in for both 12/11 (150.6 cents) and 13/12 (138.6 cents).
* 4\41 (117.1 cents) stands in for 14/13 (128.3 cents), 15/14 (119.4 cents), and 16/15 (111.7 cents).


For the 13-limit and in particular the 17-limit, little to no stretch or even compression may be suitable for balancing out the sharp and flat tuning tendencies, as is demonstrated in tunings such as [[65edt]], [[106ed6]], and [[147ed12]].  
The scale in 41, as adjacent steps, thus goes: 7 6 6 5 5 4 4 4.


41edo additionally approximates primes 19, 29, and 31, which all tend flat, so stretching will serve again as we take that into account, especially if we use the temperament in any no-17 or no-13 no-17 settings.
=== Nonoctave temperaments ===
Taking every third degree of 41edo produces a scale extremely close to [[88cET]] or 88-cent equal temperament (or the 8th root of 3:2). Likewise, taking every fifth degree produces a scale very close to the equal-tempered <span style="">[[BP|Bohlen–Pierce]]</span>[[BP| Scale]] (or the 13th root of 3). See [[Relationship between Bohlen–Pierce and octave-ful temperaments]], and see this chart:


== Scales and modes ==
{| class="wikitable center-all right-3 right-4 right-5 mw-collapsible mw-collapsed"
=== Lists of 41edo scales ===
* [[41edo modes]]
* [[List of MOS scales in 41edo]]
* [[The Kite Guitar Scales]]
* [[Kite Giedraitis's Categorizations of 41edo Scales]]
 
=== Harmonic scale ===
41edo is the first edo to do some justice to Mode 8 of the [[harmonic series]], which Dante Rosati calls the "[[overtone scale|Diatonic Harmonic Series Scale]]," consisting of overtones 8 through 16 (sometimes made to repeat at the octave).
 
{| class="wikitable" style="text-align: center;"
|-
|-
! Overtones in "Mode 8":
! colspan="3" | 3 degrees of 41edo near 88cET
| 8
! overlap
| 9
! colspan="3" | 5 degrees of 41edo near BP
| 10
| 11
| 12
| 13
| 14
| 15
| 16
|-
|-
! … as JI Ratio from 1/1:
! 41edo
| 1/1
! 88cET
| 9/8
! cents
| 5/4
! cents
| 11/8
! cents
| 3/2
! BP
| 13/8
! 41edo
| 7/4
| 15/8
| 2/1
|-
|-
! … in cents:
| 0
| 0
| 0
| 203.9
|  
| 386.3
| 0
| 551.3
|  
| 702.0
| 840.5
| 968.8
| 1088.3
| 1200.0
|-
! Nearest degree of 41edo:
| 0
| 7
| 13
| 19
| 24
| 29
| 33
| 37
| 41
|-
! … in cents:
| 0
| 204.9
| 380.5
| 556.1
| 702.4
| 848.8
| 965.9
| 1082.9
| 1200.0
|}
 
While each overtone of Mode 8 is approximated within a reasonable degree of accuracy, the steps between the intervals are not uniquely represented. (41edo is, after all, a temperament.)
 
* 7\41 (7 degrees of 41edo) (204.9 cents) stands in for just ratio 9/8 (203.9 cents) – a close match.
* 6\41 (175.6 cents) stands in for both 10/9 (182.4 cents) and 11/10 (165.0 cents).
* 5\41 (146.3 cents) stands in for both 12/11 (150.6 cents) and 13/12 (138.6 cents).
* 4\41 (117.1 cents) stands in for 14/13 (128.3 cents), 15/14 (119.4 cents), and 16/15 (111.7 cents).
 
The scale in 41, as adjacent steps, thus goes: 7 6 6 5 5 4 4 4.
 
=== Nonoctave temperaments ===
Taking every third degree of 41edo produces a scale extremely close to [[88cET]] or 88-cent equal temperament (or the 8th root of 3:2). Likewise, taking every fifth degree produces a scale very close to the equal-tempered <span style="">[[BP|Bohlen–Pierce]]</span>[[BP| Scale]] (or the 13th root of 3). See [[Relationship between Bohlen–Pierce and octave-ful temperaments]], and see this chart:
 
{| class="wikitable center-all right-3 right-4 right-5 mw-collapsible mw-collapsed"
|-
! colspan="3" | 3 degrees of 41edo near 88cET
! overlap
! colspan="3" | 5 degrees of 41edo near BP
|-
! 41edo
! 88cET
! cents
! cents
! cents
! BP
! 41edo
|-
| 0
| 0
|  
| 0
|  
| 0
| 0
| 0
| 0
Line 2,043: Line 2,276:
File:Melleweijters.com 41edo.jpg|[[Melle Weijters]]' 10-string guitar ([https://melleweijters.com Melleweijters.com])
File:Melleweijters.com 41edo.jpg|[[Melle Weijters]]' 10-string guitar ([https://melleweijters.com Melleweijters.com])
File:41-EDD_elektrische_gitaar.jpg|41edo electric guitar, by [[Gregory Sanchez]].
File:41-EDD_elektrische_gitaar.jpg|41edo electric guitar, by [[Gregory Sanchez]].
File:Ron_Sword_with_a_41ET_Guitar.jpg|41edo classical guitar, by [[Ron Sword]].
File:Ron_Sword_with_a_41ET_Guitar.jpg|41edo classical guitar, by [[Ron Sword]].
</gallery>
</gallery>
 
 
The [[Kite Guitar]] is a guitar fretting using every other step of 41edo, i.e. 41ed4 or "20½-edo". However, the interval between two adjacent open strings is always an odd number of 41-edosteps. Thus each string only covers half of 41edo, but the full edo can be found on every pair of adjacent strings. Kite-fretting makes 41edo about as playable as 19edo or 22edo, although there are certain trade-offs.  
The [[Kite Guitar]] is a guitar fretting using every other step of 41edo, i.e. 41ed4 or "20½-edo". However, the interval between two adjacent open strings is always an odd number of 41-edosteps. Thus each string only covers half of 41edo, but the full edo can be found on every pair of adjacent strings. Kite-fretting makes 41edo about as playable as 19edo or 22edo, although there are certain trade-offs.  
 
[[File:Caleb's Kite guitar.jpg|none|thumb|200px|Kite guitar]]
 
There exist Kite-fretted basses, Kite-fretted Chapman sticks, and a Kite-fretted cuatro. For more photos of Kite guitars, see [[Kite Guitar Photographs]].
{{clear}}


[[File:Caleb's Kite guitar.jpg|none|thumb|200px|Kite guitar]]
=== Other string instruments ===
The Turkish [[wikipedia:Lavta|lavta]] is a lute-like instrument with movable frets. The strings are tuned D A D A or D A D G. The frets are mostly placed in clumps of 5, so that there are 5 seconds, 5 thirds, etc. The lavta is arguably fretted to a 27-note subset of 41edo. Each clump would correspond to 41edo's plainminor-upminor-mid-downmajor-plainmajor. The edosteps would be something like 0, 3-7, 10-14, 17, 20-24, 27-31, 34-38 and 41.


For more photos of Kite guitars, see [[Kite Guitar Photographs]].
https://www.facebook.com/groups/497105067092502/permalink/3562297780573200/
{{clear}}


=== Metallophones ===
=== Metallophones ===
Line 2,110: Line 2,348:


== Music ==
== Music ==
=== Modern renderings ===
{{Main|{{ROOTPAGENAME}}/Music}}
; {{W|Johann Sebastian Bach}}
* [https://www.youtube.com/watch?v=vcsqRDDULq4 "Contrapunctus 4" from ''The Art of Fugue'', BWV 1080] (1742–1749) – rendered by Claudi Meneghin (2024)
* [https://www.youtube.com/watch?v=LWd3ZOaAZlY "Contrapunctus 11" from ''The Art of Fugue'', BWV 1080] (1742–1749) – rendered by Claudi Meneghin (2024)
 
; {{W|Nicolaus Bruhns}}
* [https://www.youtube.com/watch?v=8_Rz5kDSDoE ''Prelude in E Minor "The Great"''] – rendered by Claudi Meneghin (2023)
* [https://www.youtube.com/watch?v=DhVrdKowd5Q ''Prelude in E Minor "The Little"''] – rendered by Claudi Meneghin (2024)
 
; {{W|Scott Joplin}}
* [https://www.youtube.com/watch?v=HHn5rrGrVsI ''Maple Leaf Rag''] (1899) – arranged for harpsichord and rendered by Claudi Meneghin (2024)
 
=== 20th century ===
; [[Joseph Monzo]]
* [https://www.youtube.com/watch?v=N0ca5vdBEpI ''Theme from Invisible Haircut''] (1990)
 
=== 21st century ===
; [[Abnormality]]
* [https://www.youtube.com/watch?v=P0vRjzkpOxw FUZZ] (2024)
 
; [[Beheld]]
* [https://www.youtube.com/watch?v=G8hsoaQzRoI ''Subsidence vibe''] (2024)
 
; [[Cameron Bobro]]
* [https://soundcloud.com/cameron-bobro/eveninghorizon-cbobro ''Evening Horizon'']{{dead link}} [https://web.archive.org/web/20201127014810/http://micro.soonlabel.com/gene_ward_smith/Others/Bobro/EveningHorizon_CBobro.mp3 play]
 
; [[Flora Canou]]
* [https://soundcloud.com/floracanou/sets/notes-of-the-generation ''Notes of the Generation''] (2023) – an 8-piece album in 41et
: "Chaotic Witch #1" · "Party Cubes" · "Big Dreamer Pavilion" · "Lost Cyclops" · "Sky Tree" · "Long Night Ahead" · "Fractocraft" · "After the Generation"
 
; [[Bryan Deister]]
* [https://www.youtube.com/shorts/kLMuRP82bZw ''microtonal dance in 41edo ''] (2023)
* [https://www.youtube.com/shorts/m8X-IqH8tok ''Waltz in 41edo''] (2025)
* [https://www.youtube.com/shorts/Ur--SKiRsY0 ''41edo groove''] (2025)
 
; [[Francium]]
* "Tetracotta" from ''XenRhythms'' (2024) – [https://open.spotify.com/track/54Er1Xh83UuePQbuflZzw4 Spotify] | [https://francium223.bandcamp.com/track/tetracotta Bandcamp] | [https://www.youtube.com/watch?v=GN5FTqxhcgc YouTube] – in Tetracot[13], 41edo tuning
* "harmon" from ''TOTMC September to December 2024'' (2024) – [https://open.spotify.com/track/39tYQh4ZQvtyCUIBnLllYB Spotify] | [https://francium223.bandcamp.com/track/harmon Bandcamp] | [https://www.youtube.com/watch?v=IezX2lAjrgw YouTube]
* [https://www.youtube.com/watch?v=4ZLWjUw_O0Q ''We Wish You A Gary Christmas''] (2024) – in gary, 41edo tuning
 
; [[Jake Freivald]]
* [https://soundcloud.com/jdfreivald/little-magical-object ''Little Magical Object''] – in Magic[19], 41edo tuning
 
; [[L4MPLIGHT]]
* ''Caftaphata'' (2024) – [https://www.youtube.com/watch?v=cMnuMjXeHrY YouTube] | [https://soundcloud.com/l4mplight/caftaphata-microtones-conlang SoundCloud] – also partially in just intonation and 12edo
* ''Yxeni'' (2025) - [https://www.youtube.com/watch?v=PrfAz8V4WNc YouTube]
 
; [[Ray Perlner]]
* [https://www.youtube.com/watch?v=UE3FBQBjCPI ''Bohlen–Pierce Fugue for 3 Clarinets in 41EDO BPS9 sLsLsLsLs "Moll II/Pierce"''] (2023)
* [https://www.youtube.com/watch?v=9tMpq2Nvq_Y ''5-Part Bohlen–Pierce Fugue in 41EDO BPS9 sLsLsLssL "Harmonic"''] (2024)
 
; [[Tapeworm Saga]]
* [https://www.youtube.com/watch?v=tzqbmTmNZsU ''Preludium, for microtonal video game ensemble''] (2023)
* [https://www.youtube.com/watch?v=MUFLiMs8IkQ ''Spring's Arrival'', for synth septet] (2024)
 
; [[Tristan Bay]]
* [https://www.youtube.com/watch?v=sD2-2z85YEI ''Chasing Dusk''] (2025)
 
; [[Chris Vaisvil]] ([https://www.chrisvaisvil.com/ site])
* [https://web.archive.org/web/20230610075457/http://micro.soonlabel.com/41edo/20130910_magic%5b19%5dor_41_the_magic_of_belief.mp3 ''The Magic of Belief''] (2013) – in Magic[19], 41edo tuning
 
; [[Xeno Ov Eleas]]
* [https://www.youtube.com/watch?v=oQHOltX4Sos ''A Treasure Lost and Must Be Found''] (2022)
 
=== Kite Guitar recordings ===
; [[Kite Giedraitis]]
* [https://soundcloud.com/tallkite/evening-rondo ''Evening Rondo'']
* [https://soundcloud.com/mbirakite/triadic-etude ''Downminor Etude''] (midi demo)
 
; [[Igliashon Jones]]
* [https://soundcloud.com/sacred-skeleton/modified-kite-guitar-take-1 ''Modified Kite Guitar Take 1 - Clean'']
* [https://soundcloud.com/sacred-skeleton/modified-kite-guitar-take-2 ''Modified Kite Guitar Take 2 - Fuzz'']
 
; [[John Platter]]
* [https://johnplatter.bandcamp.com/album/in-the-know In the Know] - Full album recorded using kite guitar & bass.
 
; [[Pixel Archipelago]]
* [https://pixelarchipelago.bandcamp.com/album/intervallic-prism ''Intervallic Prism''] (2020) – a 7-track album
: "Red" · "Orange" · "Yellow" · "Green" · "Blue" · "Indigo" · "Violet"
 
; [[Aaron Wolf]]
* [https://soundcloud.com/mbirakite/aaron-wolf-12-bar-blues-on-kite-guitar ''12-Bar-Blues on Kite Guitar''] – a simple 12-bar blues
* [https://soundcloud.com/wolftune/fourthward-lang-syne ''Fourthward Lang Syne''] – an arrangement of Auld Lang Syne
 
=== Kite Guitar videos ===
; [[Timmy Barnett]]
* [https://TallKite.com/KiteGuitar/Downminor&#x20;Etude.m4v ''Downminor Etude''] {{dead link}}
 
; [[Wilckerson Ganda]]
* [https://www.youtube.com/watch?v=gQERKtbkMCE ''Vintage Rock'']
 
; [[Travis Johnson]]
* [https://www.youtube.com/watch?v=eAPzZ9oJYyY ''Evening Rondo'']
 
=== Kite Guitar scores ===
; [[Kite Guitar originals]]
; [[Kite Guitar translations]]


== See also ==
== See also ==
Line 2,222: Line 2,364:
[[Category:Magic]]
[[Category:Magic]]
[[Category:Superkleismic]]
[[Category:Superkleismic]]
[[Category:Supermagic]]
[[Category:Keemic]]
[[Category:Tetracot]]
[[Category:Tetracot]]
[[Category:Octacot]]
[[Category:Octacot]]
[[Category:Listen]]
[[Category:Listen]]
Retrieved from "https://en.xen.wiki/w/41edo"