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| de = 41-EDO
| de = 41-EDO
| en = 41edo
| en = 41edo
| es =  
| es = 41edo
| ja =  
| ja =  
}}
}}
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41edo can be seen as a tuning of the [[magic]] temperament, as well as [[superkleismic]], [[garibaldi]], [[miracle]], 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
| Eb, kD#
| Fra
| Rih
|-
| 4
| 117.1
| 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
| No
| Ma
|-
| 10
| 292.7
| [[13/11]], [[19/16]], [[32/27]]
| [[13/11]], [[19/16]], [[32/27]]
| minor 3rd
|m3
| m3
| {{UDnote|step=10}}
| 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
| Mu
| Mo
|-
| 16
| 468.3
| [[21/16]], [[13/10]]
| [[21/16]], [[13/10]]
| down-4th
|v4
| v4
| {{UDnote|step=16}}
| 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
| Pa/Shu
| Se
|-
| 22
| 643.9
| [[13/9]], [[16/11]], [[19/13]]
| [[13/9]], [[16/11]], [[19/13]]
| mid-5th, upaug 4th
|~5, ^A4
| ~5, ^A4
| {{UDnote|step=22}}
| ^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#
| Fla
| Leh
|-
| 28
| 819.5
| [[8/5]], [[21/13]]
| [[8/5]], [[21/13]]
| upminor 6th
|^m6
| ^m6
| {{UDnote|step=28}}
| 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
| Tho
| Ta
|-
| 34
| 995.1
| [[16/9]]
| [[16/9]]
| minor 7th
|m7
| m7
| {{UDnote|step=34}}
| 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
| Tu
| To
|-
| 40
| 1170.7
| [[49/25]], [[63/32]], [[96/49]], [[160/81]]
| [[49/25]], [[63/32]], [[96/49]], [[160/81]]
| dim 8ve
|v8
| v8
| {{UDnote|step=40}}
| 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
| mid
|-
| ilo
| 2
| (a, b, 0, 0, 1)
| 58.5
| 11/9, 11/6
| dup-unison, downminor 2nd
|-
| ^^1, vm2
| "
| ^^D, vEb
| lu
| subminor 2nd, classic aug unison, uber unison
| (a, b, 0, 0, -1)
| sm2, kkA1, U1
| 12/11, 18/11
| sEb, kkD#, UD
|-
| Fro
| downmajor
| Ro
| yo
|-
| (a, b, 1)
| 3
| 5/4, 5/3
| 87.8
|-
| down-aug 1sn, minor 2nd
| major
| vA1, m2
| fifthward wa
| vD#, Eb
| (a, b) with b > 1
| minor 2nd, comma-narrow augmented unison
| 9/8, 27/16
| m2, kA1
|-
| Eb, kD#
| upmajor
| Fra
| ru
| Rih
| (a, b, 0, -1)
|-
| 9/7, 12/7
| 4
|}
| 117.1
 
| augmented 1sn, upminor 2nd
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:
| A1, ^m2
 
| D#, ^Eb
{| class="wikitable center-all"
| classic minor 2nd, augmented unison
|-
| Km2, A1
! [[Color notation|Color of the 3rd]]
| KEb, D#
! JI chord
| Fru
! Notes as edosteps
| Ra
! Notes of C chord
|-
! Written name
| 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
! Spoken name
|-
|-
Line 665: Line 885:
* 0-14-28 = D F# A# = Da = D aug
* 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]].
For a more complete list, see [[41edo chord names]] and [[Ups and downs notation #Chords and chord progressions]].


== Notations ==
== Notations ==
=== Ups and downs notation ===
=== Stein–Zimmermann–Gould 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.
[[Stein–Zimmermann–Gould notation]] uses sharps and flats combined with quartertone accidentals and arrows:
{{Ups and downs sharpness}}
{{Sharpness-sharp4-szg}}


41edo can also be notated with quarter-tone accidentals and [[Alternative symbols for ups and downs notation#Sharp-3|ups and downs]].
The notes within an octave from A are thus:
{{Ups and downs sharpness|41|true}}


Arrows borrowed from extended [[Helmholtz–Ellis notation]] can also be used:
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


{{Sharpness-sharp4}}
=== 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}}


The notes within an octave from A are thus:
Half-sharps and half-flats can be used to avoid double arrows:  
 
{{Ups and downs sharpness|41|true}}
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


=== Red-Blue notation ===
=== 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:
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}}
{{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}}
Line 692: Line 912:
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.
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 [[Ups and downs notation|ups and downs notation]]. The only difference is the use of minor tritone and major tritone.
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 ===
=== Sagittal notation ===
This notation uses the same sagittal sequence as [[34edo #Sagittal notation|34edo]].
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>
|-
! Evo
| rowspan="2" | <big>{{sagittal| /|\ }}</big>
|-
! Revo
| <big>{{sagittal| ||\ }}</big>
| <big>{{sagittal| /||\ }}</big>
|}
The following enharmonics from the Spartan set are present (comma tempered out):
* {{Sagittal| //| }} = {{sagittal| /|) }} = {{sagittal| /|\ }} ([[325/324]], [[352/351]])
* {{Sagittal| /| }} = {{sagittal| |) }} ([[225/224]])
* {{Sagittal| |( }} = {{sagittal| |//| }} ([[5120/5103]])
 
See [[Sagittal notation #Revo|apotome complements]] for equivalent accidental pairs.
 
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]].


==== Evo flavor ====
==== Evo flavor ====
Line 742: Line 994:
|-
|-
| 2.3
| 2.3
| {{monzo| 65 -41 }}
| {{Monzo| 65 -41 }}
| {{mapping| 41 65 }}
| {{Mapping| 41 65 }}
| −0.153
| −0.153
| 0.15
| 0.15
Line 750: Line 1,002:
| 2.3.5
| 2.3.5
| 3125/3072, 20000/19683
| 3125/3072, 20000/19683
| {{mapping| 41 65 95 }}
| {{Mapping| 41 65 95 }}
| +0.734
| +0.734
| 1.26
| 1.26
Line 757: Line 1,009:
| 2.3.5.7
| 2.3.5.7
| 225/224, 245/243, 1029/1024
| 225/224, 245/243, 1029/1024
| {{mapping| 41 65 95 115 }}
| {{Mapping| 41 65 95 115 }}
| +0.815
| +0.815
| 1.10
| 1.10
Line 764: Line 1,016:
| 2.3.5.7.11
| 2.3.5.7.11
| 100/99, 225/224, 243/242, 245/242
| 100/99, 225/224, 243/242, 245/242
| {{mapping| 41 65 95 115 142 }}
| {{Mapping| 41 65 95 115 142 }}
| +0.375
| +0.375
| 1.32
| 1.32
Line 771: Line 1,023:
| 2.3.5.7.11.13
| 2.3.5.7.11.13
| 100/99, 105/104, 144/143, 196/195, 243/242
| 100/99, 105/104, 144/143, 196/195, 243/242
| {{mapping| 41 65 95 115 142 152 }}
| {{Mapping| 41 65 95 115 142 152 }}
| −0.060
| −0.060
| 1.55
| 1.55
Line 778: Line 1,030:
| 2.3.5.7.11.13.19
| 2.3.5.7.11.13.19
| 100/99, 105/104, 133/132, 144/143, 171/169, 196/195
| 100/99, 105/104, 133/132, 144/143, 171/169, 196/195
| {{mapping| 41 65 95 115 142 152 174 }}
| {{Mapping| 41 65 95 115 142 152 174 }}
| +0.111
| +0.111
| 1.49
| 1.49
| 5.10
| 5.10
|}
|}
* 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.  
* 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.  


=== Commas ===
=== Commas ===
Line 800: Line 1,054:
| <abbr title="36893488147419103232/36472996377170786403">(40 digits)</abbr>
| <abbr title="36893488147419103232/36472996377170786403">(40 digits)</abbr>
| 19.84
| 19.84
| {{monzo| 65 -41 }}
| {{Monzo| 65 -41 }}
| Wa-41
| Wa-41
| 41-edo
| 41-edo
Line 808: Line 1,062:
| <abbr title="1953125/1889568">(14 digits)</abbr>
| <abbr title="1953125/1889568">(14 digits)</abbr>
| 57.27
| 57.27
| {{monzo| -5 -10 9 }}
| {{Monzo| -5 -10 9 }}
| Tritriyo
| Tritriyo
| y<sup>9</sup>
| y<sup>9</sup>
Line 816: Line 1,070:
| [[34171875/33554432|(16 digits)]]
| [[34171875/33554432|(16 digits)]]
| 31.57
| 31.57
| {{monzo| -25 7 6 }}
| {{Monzo| -25 7 6 }}
| Lala-tribiyo
| Lala-tribiyo
| LLy<sup>3</sup>
| LLy<sup>3</sup>
Line 824: Line 1,078:
| [[3125/3072]]
| [[3125/3072]]
| 29.61
| 29.61
| {{monzo| -10 -1 5 }}
| {{Monzo| -10 -1 5 }}
| Laquinyo
| Laquinyo
| Ly<sup>5</sup>
| Ly<sup>5</sup>
Line 832: Line 1,086:
| [[20000/19683|(10 digits)]]
| [[20000/19683|(10 digits)]]
| 27.66
| 27.66
| {{monzo| 5 -9 4 }}
| {{Monzo| 5 -9 4 }}
| Saquadyo
| Saquadyo
| sy<sup>4</sup>
| sy<sup>4</sup>
Line 840: Line 1,094:
| <abbr title="131072000/129140163">(18 digits)</abbr>
| <abbr title="131072000/129140163">(18 digits)</abbr>
| 25.71
| 25.71
| {{monzo| 20 -17 3 }}
| {{Monzo| 20 -17 3 }}
| Sasa-triyo
| Sasa-triyo
| ssy<sup>3</sup>
| ssy<sup>3</sup>
Line 848: Line 1,102:
| [[32805/32768|(10 digits)]]
| [[32805/32768|(10 digits)]]
| 1.95
| 1.95
| {{monzo| -15 8 1 }}
| {{Monzo| -15 8 1 }}
| Layo
| Layo
| Ly
| Ly
Line 856: Line 1,110:
| [[15625/15309|(10 digits)]]
| [[15625/15309|(10 digits)]]
| 35.37
| 35.37
| {{monzo| 0 -7 6 -1 }}
| {{Monzo| 0 -7 6 -1 }}
| Rutribiyo
| Rutribiyo
| ry<sup>6</sup>
| ry<sup>6</sup>
Line 864: Line 1,118:
| <abbr title="854296875/843308032">(18 digits)</abbr>
| <abbr title="854296875/843308032">(18 digits)</abbr>
| 22.41
| 22.41
| {{monzo| -10 7 8 -7 }}
| {{Monzo| -10 7 8 -7 }}
| Lasepru-aquadbiyo
| Lasepru-aquadbiyo
| Lr<sup>7</sup>y<sup>8</sup>
| Lr<sup>7</sup>y<sup>8</sup>
Line 872: Line 1,126:
| [[875/864]]
| [[875/864]]
| 21.90
| 21.90
| {{monzo| -5 -3 3 1 }}
| {{Monzo| -5 -3 3 1 }}
| Zotriyo
| Zotriyo
| zy<sup>3</sup>
| zy<sup>3</sup>
Line 880: Line 1,134:
| [[3125/3087]]
| [[3125/3087]]
| 21.18
| 21.18
| {{monzo| 0 -2 5 -3 }}
| {{Monzo| 0 -2 5 -3 }}
| Triru-aquinyo
| Triru-aquinyo
| r<sup>3</sup>y<sup>5</sup>
| r<sup>3</sup>y<sup>5</sup>
Line 888: Line 1,142:
| <abbr title="179200/177147">(12 digits)</abbr>
| <abbr title="179200/177147">(12 digits)</abbr>
| 19.95
| 19.95
| {{monzo| 10 -11 2 1 }}
| {{Monzo| 10 -11 2 1 }}
| Sazoyoyo
| Sazoyoyo
| szyy
| szyy
Line 896: Line 1,150:
| [[33075/32768|(10 digits)]]
| [[33075/32768|(10 digits)]]
| 16.14
| 16.14
| {{monzo| -15 3 2 2 }}
| {{Monzo| -15 3 2 2 }}
| Labizoyo
| Labizoyo
| Lzzyy
| Lzzyy
Line 904: Line 1,158:
| [[245/243]]
| [[245/243]]
| 14.19
| 14.19
| {{monzo| 0 -5 1 2 }}
| {{Monzo| 0 -5 1 2 }}
| Zozoyo
| Zozoyo
| zzy
| zzy
Line 912: Line 1,166:
| [[4000/3969]]
| [[4000/3969]]
| 13.47
| 13.47
| {{monzo| 5 -4 3 -2 }}
| {{Monzo| 5 -4 3 -2 }}
| Rurutriyo
| Rurutriyo
| rry<sup>3</sup>
| rry<sup>3</sup>
Line 920: Line 1,174:
| <abbr title="823543/819200">(12 digits)</abbr>
| <abbr title="823543/819200">(12 digits)</abbr>
| 9.15
| 9.15
| {{monzo| -15 0 -2 7 }}
| {{Monzo| -15 0 -2 7 }}
| Lasepzo-agugu
| Lasepzo-agugu
| Lz<sup>7</sup>gg
| Lz<sup>7</sup>gg
Line 928: Line 1,182:
| [[1029/1024]]
| [[1029/1024]]
| 8.43
| 8.43
| {{monzo| -10 1 0 3 }}
| {{Monzo| -10 1 0 3 }}
| Latrizo
| Latrizo
| Lz<sup>3</sup>
| Lz<sup>3</sup>
Line 936: Line 1,190:
| [[225/224]]
| [[225/224]]
| 7.71
| 7.71
| {{monzo| -5 2 2 -1 }}
| {{Monzo| -5 2 2 -1 }}
| Ruyoyo
| Ruyoyo
| ryy
| ryy
Line 944: Line 1,198:
| [[16875/16807|(10 digits)]]
| [[16875/16807|(10 digits)]]
| 6.99
| 6.99
| {{monzo| 0 3 4 -5 }}
| {{Monzo| 0 3 4 -5 }}
| Quinru-aquadyo
| Quinru-aquadyo
| r<sup>5</sup>y<sup>4</sup>
| r<sup>5</sup>y<sup>4</sup>
Line 952: Line 1,206:
| [[10976/10935|(10 digits)]]
| [[10976/10935|(10 digits)]]
| 6.48
| 6.48
| {{monzo| 5 -7 -1 3 }}
| {{Monzo| 5 -7 -1 3 }}
| Satrizo-agu
| Satrizo-agu
| sz<sup>3</sup>g
| sz<sup>3</sup>g
Line 960: Line 1,214:
| [[5120/5103]]
| [[5120/5103]]
| 5.76
| 5.76
| {{monzo| 10 -6 1 -1 }}
| {{Monzo| 10 -6 1 -1 }}
| Saruyo
| Saruyo
| sry
| sry
Line 968: Line 1,222:
| [[33554432/33480783|(16 digits)]]
| [[33554432/33480783|(16 digits)]]
| 3.80
| 3.80
| {{monzo| 25 -14 0 -1 }}
| {{Monzo| 25 -14 0 -1 }}
| Sasaru
| Sasaru
| ssr
| ssr
Line 976: Line 1,230:
| [[2401/2400]]
| [[2401/2400]]
| 0.72
| 0.72
| {{monzo| -5 -1 -2 4 }}
| {{Monzo| -5 -1 -2 4 }}
| Bizozogu
| Bizozogu
| z<sup>4</sup>gg
| z<sup>4</sup>gg
Line 984: Line 1,238:
| <abbr title="163840/161051">(12 digits)</abbr>
| <abbr title="163840/161051">(12 digits)</abbr>
| 29.72
| 29.72
| {{monzo| 15 0 1 0 -5 }}
| {{Monzo| 15 0 1 0 -5 }}
| Saquinlu-ayo
| Saquinlu-ayo
| s1u<sup>5</sup>y
| s1u<sup>5</sup>y
Line 992: Line 1,246:
| [[245/242]]
| [[245/242]]
| 21.33
| 21.33
| {{monzo| -1 0 1 2 -2 }}
| {{Monzo| -1 0 1 2 -2 }}
| Luluzozoyo
| Luluzozoyo
| 1uuzzy
| 1uuzzy
Line 1,000: Line 1,254:
| [[100/99]]
| [[100/99]]
| 17.40
| 17.40
| {{monzo| 2 -2 2 0 -1 }}
| {{Monzo| 2 -2 2 0 -1 }}
| Luyoyo
| Luyoyo
| 1uyy
| 1uyy
Line 1,008: Line 1,262:
| [[1344/1331]]
| [[1344/1331]]
| 16.83
| 16.83
| {{monzo| 6 1 0 1 -3 }}
| {{Monzo| 6 1 0 1 -3 }}
| Trilu-azo
| Trilu-azo
| 1u<sup>3</sup>z
| 1u<sup>3</sup>z
Line 1,016: Line 1,270:
| [[896/891]]
| [[896/891]]
| 9.69
| 9.69
| {{monzo| 7 -4 0 1 -1 }}
| {{Monzo| 7 -4 0 1 -1 }}
| Saluzo
| Saluzo
| s1uz
| s1uz
Line 1,024: Line 1,278:
| [[65536/65219|(10 digits)]]
| [[65536/65219|(10 digits)]]
| 8.39
| 8.39
| {{monzo| 16 0 0 -2 -3 }}
| {{Monzo| 16 0 0 -2 -3 }}
| Satrilu-aruru
| Satrilu-aruru
| s1u<sup>3</sup>rr
| s1u<sup>3</sup>rr
Line 1,032: Line 1,286:
| [[243/242]]
| [[243/242]]
| 7.14
| 7.14
| {{monzo| -1 5 0 0 -2 }}
| {{Monzo| -1 5 0 0 -2 }}
| Lulu
| Lulu
| 1uu
| 1uu
Line 1,040: Line 1,294:
| [[385/384]]
| [[385/384]]
| 4.50
| 4.50
| {{monzo| -7 -1 1 1 1 }}
| {{Monzo| -7 -1 1 1 1 }}
| Lozoyo
| Lozoyo
| 1ozg
| 1ozg
Line 1,048: Line 1,302:
| [[441/440]]
| [[441/440]]
| 3.93
| 3.93
| {{monzo| -3 2 -1 2 -1 }}
| {{Monzo| -3 2 -1 2 -1 }}
| Luzozogu
| Luzozogu
| 1uzzg
| 1uzzg
Line 1,056: Line 1,310:
| [[1375/1372]]
| [[1375/1372]]
| 3.78
| 3.78
| {{monzo| -2 0 3 -3 1 }}
| {{Monzo| -2 0 3 -3 1 }}
| Lotriruyo
| Lotriruyo
| 1or<sup>3</sup>y
| 1or<sup>3</sup>y
Line 1,064: Line 1,318:
| [[540/539]]
| [[540/539]]
| 3.21
| 3.21
| {{monzo| 2 3 1 -2 -1 }}
| {{Monzo| 2 3 1 -2 -1 }}
| Lururuyo
| Lururuyo
| 1urry
| 1urry
Line 1,072: Line 1,326:
| [[3025/3024]]
| [[3025/3024]]
| 0.57
| 0.57
| {{monzo| -4 -3 2 -1 2 }}
| {{Monzo| -4 -3 2 -1 2 }}
| Loloruyoyo
| Loloruyoyo
| 1ooryy
| 1ooryy
Line 1,080: Line 1,334:
| [[151263/151250|<abbr title="151263/151250">(12 digits)</abbr>]]
| [[151263/151250|<abbr title="151263/151250">(12 digits)</abbr>]]
| 0.15
| 0.15
| {{monzo| -1 2 -4 5 -2 }}
| {{Monzo| -1 2 -4 5 -2 }}
| Luluquinzo-aquadgu
| Luluquinzo-aquadgu
| 1uuz<sup>5</sup>g<sup>4</sup>
| 1uuz<sup>5</sup>g<sup>4</sup>
Line 1,088: Line 1,342:
| [[343/338]]
| [[343/338]]
| 25.42
| 25.42
| {{monzo| -1 0 0 3 0 -2 }}
| {{Monzo| -1 0 0 3 0 -2 }}
| Thuthutrizo
| Thuthutrizo
| 3uuz<sup>3</sup>
| 3uuz<sup>3</sup>
Line 1,096: Line 1,350:
| [[105/104]]
| [[105/104]]
| 16.57
| 16.57
| {{monzo| -3 1 1 1 0 -1 }}
| {{Monzo| -3 1 1 1 0 -1 }}
| Thuzoyo
| Thuzoyo
| 3uzy
| 3uzy
Line 1,104: Line 1,358:
| [[28672/28431|(10 digits)]]
| [[28672/28431|(10 digits)]]
| 14.61
| 14.61
| {{monzo| 12 -7 0 1 0 -1 }}
| {{Monzo| 12 -7 0 1 0 -1 }}
| Sathuzo
| Sathuzo
| s3uz
| s3uz
Line 1,112: Line 1,366:
| [[275/273]]
| [[275/273]]
| 12.64
| 12.64
| {{monzo| 0 -1 2 -1 1 -1 }}
| {{Monzo| 0 -1 2 -1 1 -1 }}
| Thuloruyoyo
| Thuloruyoyo
| 3u1oryy
| 3u1oryy
Line 1,120: Line 1,374:
| [[144/143]]
| [[144/143]]
| 12.06
| 12.06
| {{monzo| 4 2 0 0 -1 -1 }}
| {{Monzo| 4 2 0 0 -1 -1 }}
| Thulu
| Thulu
| 3u1u
| 3u1u
Line 1,128: Line 1,382:
| [[196/195]]
| [[196/195]]
| 8.86
| 8.86
| {{monzo| 2 -1 -1 2 0 -1 }}
| {{Monzo| 2 -1 -1 2 0 -1 }}
| Thuzozogu
| Thuzozogu
| 3uzzg
| 3uzzg
Line 1,136: Line 1,390:
| [[640/637]]
| [[640/637]]
| 8.13
| 8.13
| {{monzo| 7 0 1 -2 0 -1 }}
| {{Monzo| 7 0 1 -2 0 -1 }}
| Thururuyo
| Thururuyo
| 3urry
| 3urry
Line 1,144: Line 1,398:
| [[1188/1183]]
| [[1188/1183]]
| 7.30
| 7.30
| {{monzo| 2 3 0 -1 1 -2 }}
| {{Monzo| 2 3 0 -1 1 -2 }}
| Thuthuloru
| Thuthuloru
| 3uu1or
| 3uu1or
Line 1,152: Line 1,406:
| [[31213/31104]]
| [[31213/31104]]
| 6.06
| 6.06
| {{monzo| -7 -5 0 4 0 1 }}
| {{Monzo| -7 -5 0 4 0 1 }}
| Thoquadzo
| Thoquadzo
| 3oz<sup>4</sup>3
| 3oz<sup>4</sup>3
Line 1,160: Line 1,414:
| [[325/324]]
| [[325/324]]
| 5.34
| 5.34
| {{monzo| -2 -4 2 0 0 1 }}
| {{Monzo| -2 -4 2 0 0 1 }}
| Thoyoyo
| Thoyoyo
| 3oyy
| 3oyy
Line 1,168: Line 1,422:
| [[352/351]]
| [[352/351]]
| 4.93
| 4.93
| {{monzo| 5 -3 0 0 1 -1 }}
| {{Monzo| 5 -3 0 0 1 -1 }}
| Thulo
| Thulo
| 3u1o
| 3u1o
Line 1,176: Line 1,430:
| [[364/363]]
| [[364/363]]
| 4.76
| 4.76
| {{monzo| 2 -1 0 1 -2 1 }}
| {{Monzo| 2 -1 0 1 -2 1 }}
| Tholuluzo
| Tholuluzo
| 3o1uuz
| 3o1uuz
Line 1,184: Line 1,438:
| [[847/845]]
| [[847/845]]
| 4.09
| 4.09
| {{monzo| 0 0 -1 1 2 -2 }}
| {{Monzo| 0 0 -1 1 2 -2 }}
| Thuthulolozogu
| Thuthulolozogu
| 3uu1oozg
| 3uu1oozg
Line 1,192: Line 1,446:
| [[729/728]]
| [[729/728]]
| 2.38
| 2.38
| {{monzo| -3 6 0 -1 0 -1 }}
| {{Monzo| -3 6 0 -1 0 -1 }}
| Lathuru
| Lathuru
| L3ur
| L3ur
Line 1,200: Line 1,454:
| [[2080/2079]]
| [[2080/2079]]
| 0.83
| 0.83
| {{monzo| 5 -3 1 -1 -1 1 }}
| {{Monzo| 5 -3 1 -1 -1 1 }}
| Tholuruyo
| Tholuruyo
| 3o1ury
| 3o1ury
| Ibnsinma
| Ibnsinma, sinaisma
|-
|-
| 13
| 13
| [[4096/4095]]
| [[4096/4095]]
| 0.42
| 0.42
| {{monzo| 12 -2 -1 -1 0 -1 }}
| {{Monzo| 12 -2 -1 -1 0 -1 }}
| Sathurugu
| Sathurugu
| s3urg
| s3urg
| Schismina
| Minisma
|-
|-
| 13
| 13
| [[6656/6655]]
| [[6656/6655]]
| 0.26
| 0.26
| {{monzo| 9 0 -1 0 -3 1 }}
| {{Monzo| 9 0 -1 0 -3 1 }}
| Thotrilo-agu
| Thotrilo-agu
| 3u1o<sup>3</sup>g2
| 3u1o<sup>3</sup>g2
Line 1,224: Line 1,478:
| [[10648/10647|(10 digits)]]
| [[10648/10647|(10 digits)]]
| 0.16
| 0.16
| {{monzo| 3 -2 0 -1 3 -2 }}
| {{Monzo| 3 -2 0 -1 3 -2 }}
| Thuthutrilo-aru
| Thuthutrilo-aru
| 3uu1o<sup>3</sup>r
| 3uu1o<sup>3</sup>r
Line 1,232: Line 1,486:
| [[2187/2176]]
| [[2187/2176]]
| 8.73
| 8.73
| {{monzo| -7 7 0 0 0 0 -1 }}
| {{Monzo| -7 7 0 0 0 0 -1 }}
| Lasu
| Lasu
| L17u
| L17u
Line 1,240: Line 1,494:
| [[256/255]]
| [[256/255]]
| 6.78
| 6.78
| {{monzo| 8 -1 -1 0 0 0 -1 }}
| {{Monzo| 8 -1 -1 0 0 0 -1 }}
| Sugu
| Sugu
| 17ug
| 17ug
Line 1,248: Line 1,502:
| [[715/714]]
| [[715/714]]
| 2.42
| 2.42
| {{monzo| -1 -1 1 -1 1 1 -1 }}
| {{Monzo| -1 -1 1 -1 1 1 -1 }}
| Sutholoruyo
| Sutholoruyo
| 17u3o1ory
| 17u3o1ory
Line 1,256: Line 1,510:
| [[210/209]]
| [[210/209]]
| 8.26
| 8.26
| {{monzo| 1 1 1 1 -1 0 0 -1 }}
| {{Monzo| 1 1 1 1 -1 0 0 -1 }}
| Nuluzoyo
| Nuluzoyo
| 19u1uzy
| 19u1uzy
Line 1,264: Line 1,518:
| [[361/360]]
| [[361/360]]
| 4.80
| 4.80
| {{monzo| -3 -2 -1 0 0 0 0 2 }}
| {{Monzo| -3 -2 -1 0 0 0 0 2 }}
| Nonogu
| Nonogu
| 19oog2
| 19oog2
Line 1,272: Line 1,526:
| [[513/512]]
| [[513/512]]
| 3.38
| 3.38
| {{monzo| -9 3 0 0 0 0 0 1 }}
| {{Monzo| -9 3 0 0 0 0 0 1 }}
| Lano
| Lano
| L19o
| L19o
Line 1,280: Line 1,534:
| [[1216/1215]]
| [[1216/1215]]
| 1.42
| 1.42
| {{monzo| 6 -5 -1 0 0 0 0 1 }}
| {{Monzo| 6 -5 -1 0 0 0 0 1 }}
| Sanogu
| Sanogu
| s19og
| s19og
Line 1,288: Line 1,542:
| [[736/729]]
| [[736/729]]
| 16.54
| 16.54
| {{monzo| 5 -6 0 0 0 0 0 0 1 }}
| {{Monzo| 5 -6 0 0 0 0 0 0 1 }}
| Satwetho
| Satwetho
| s23o
| s23o
Line 1,296: Line 1,550:
| [[145/144]]
| [[145/144]]
| 11.98
| 11.98
| {{monzo| -4 -2 1 0 0 0 0 0 0 1 }}
| {{Monzo| -4 -2 1 0 0 0 0 0 0 1 }}
| Twenoyo
| Twenoyo
| 29oy
| 29oy
Line 2,029: Line 2,283:
[[File:Caleb's Kite guitar.jpg|none|thumb|200px|Kite guitar]]
[[File:Caleb's Kite guitar.jpg|none|thumb|200px|Kite guitar]]


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


=== Metallophones ===
=== Metallophones ===
Retrieved from "https://en.xen.wiki/w/41edo"