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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.
Line 30: Line 30:


=== 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 contains [[41ed4]]. Although not technically subsets, 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''.
Line 37: Line 37:


== Intervals ==
== Intervals ==
{| class="wikitable center-1 right-2"
|-
! #
! Cents
! Approximate ratios*
! [[Kite's ups and downs notation|Ups and downs notation]]
|-
| 0
| 0.0
| [[1/1]]
| {{UDnote|step=0}}
|-
| 1
| 29.3
| [[49/48]], [[50/49]], [[64/63]], [[81/80]]
| {{UDnote|step=1}}
|-
| 2
| 58.5
| [[25/24]], [[28/27]], [[33/32]], [[36/35]]
| {{UDnote|step=2}}
|-
| 3
| 87.8
| [[19/18]], [[20/19]], [[21/20]], [[22/21]]
| {{UDnote|step=3}}
|-
| 4
| 117.1
| [[14/13]], [[15/14]], [[16/15]]
| {{UDnote|step=4}}
|-
| 5
| 146.3
| [[12/11]], [[13/12]]
| {{UDnote|step=5}}
|-
| 6
| 175.6
| [[10/9]], [[11/10]], [[21/19]]
| {{UDnote|step=6}}
|-
| 7
| 204.9
| [[9/8]]
| {{UDnote|step=7}}
|-
| 8
| 234.1
| [[8/7]], [[15/13]]
| {{UDnote|step=8}}
|-
| 9
| 263.4
| [[7/6]], [[22/19]]
| {{UDnote|step=9}}
|-
| 10
| 292.7
| [[13/11]], [[19/16]], [[32/27]]
| {{UDnote|step=10}}
|-
| 11
| 322.0
| [[6/5]]
| {{UDnote|step=11}}
|-
| 12
| 351.2
| [[11/9]], [[16/13]]
| {{UDnote|step=12}}
|-
| 13
| 380.5
| [[5/4]], [[26/21]]
| {{UDnote|step=13}}
|-
| 14
| 409.8
| [[14/11]], [[19/15]], [[24/19]]
| {{UDnote|step=14}}
|-
| 15
| 439.0
| [[9/7]], [[32/25]]
| {{UDnote|step=15}}
|-
| 16
| 468.3
| [[21/16]], [[13/10]]
| {{UDnote|step=16}}
|-
| 17
| 497.6
| [[4/3]]
| {{UDnote|step=17}}
|-
| 18
| 526.8
| [[15/11]], [[19/14]], [[27/20]]
| {{UDnote|step=18}}
|-
| 19
| 556.1
| [[11/8]], [[18/13]], [[26/19]]
| {{UDnote|step=19}}
|-
| 20
| 585.4
| [[7/5]], [[45/32]]
| {{UDnote|step=20}}
|-
| 21
| 614.6
| [[10/7]], [[64/45]]
| {{UDnote|step=21}}
|-
| 22
| 643.9
| [[13/9]], [[16/11]], [[19/13]]
| {{UDnote|step=22}}
|-
| 23
| 673.2
| [[22/15]], [[28/19]], [[40/27]]
| {{UDnote|step=23}}
|-
| 24
| 702.4
| [[3/2]]
| {{UDnote|step=24}}
|-
| 25
| 731.7
| [[20/13]], [[32/21]]
| {{UDnote|step=25}}
|-
| 26
| 761.0
| [[14/9]], [[25/16]]
| {{UDnote|step=26}}
|-
| 27
| 790.2
| [[11/7]], [[19/12]], [[30/19]]
| {{UDnote|step=27}}
|-
| 28
| 819.5
| [[8/5]], [[21/13]]
| {{UDnote|step=28}}
|-
| 29
| 848.8
| [[13/8]], [[18/11]]
| {{UDnote|step=29}}
|-
| 30
| 878.0
| [[5/3]]
| {{UDnote|step=30}}
|-
| 31
| 907.3
| [[22/13]], [[27/16]], [[32/19]]
| {{UDnote|step=31}}
|-
| 32
| 936.6
| [[12/7]], [[19/11]]
| {{UDnote|step=32}}
|-
| 33
| 965.9
| [[7/4]], [[26/15]]
| {{UDnote|step=33}}
|-
| 34
| 995.1
| [[16/9]]
| {{UDnote|step=34}}
|-
| 35
| 1024.4
| [[9/5]], [[20/11]], [[38/21]]
| {{UDnote|step=35}}
|-
| 36
| 1053.7
| [[11/6]], [[24/13]]
| {{UDnote|step=36}}
|-
| 37
| 1082.9
| [[13/7]], [[15/8]], [[28/15]]
| {{UDnote|step=37}}
|-
| 38
| 1112.2
| [[19/10]], [[21/11]], [[36/19]], [[40/21]]
| {{UDnote|step=38}}
|-
| 39
| 1141.5
| [[27/14]], [[35/18]], [[48/25]], [[64/33]]
| {{UDnote|step=39}}
|-
| 40
| 1170.7
| [[49/25]], [[63/32]], [[96/49]], [[160/81]]
| {{UDnote|step=40}}
|-
| 41
| 1200.0
| [[2/1]]
| {{UDnote|step=41}}
|}
<nowiki>*</nowiki> Based on treating 41edo as a 2.3.5.7.11.13.19-subgroup temperament; other approaches are possible.
=== Proposed interval names and solfèges ===
{{See also| 41edo solfege }}
{{See also| 41edo solfege }}


{| class="wikitable center-1 right-2 center-5 center-6 center-8 center-9"
{| 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
|-
|-
! #
! #
! Cents
! Cents
! Approximate ratios*
! 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)
! colspan="3" | [[Ups and downs notation]]<br>([[Enharmonic unisons in ups and downs notation|EUs]]: v<sup>4</sup>A1 and ^d2)
! colspan="3" | [[SKULO interval names|SKULO notation]]<br>(K or S = 1, U = 2)
! colspan="3" | [[SKULO interval names|SKULO notation]] (K or S = 1, U = 2)
! Kite's<br>solfège
! [[41edo solfege|Kite's<br>solfege]]
! Andrew's<br>solfège
! [[41edo solfege|Andrew's<br>solfege]]
|-
|-
| 0
| 0
| 0.0
| 0.0
| [[1/1]]
| perfect unison
| perfect unison
| P1
| P1
Line 63: Line 282:
| 1
| 1
| 29.3
| 29.3
| [[49/48]], [[50/49]], [[64/63]], [[81/80]]
| up-unison
| up-unison
| ^1
| ^1
Line 75: Line 293:
| 2
| 2
| 58.5
| 58.5
| [[25/24]], [[28/27]], [[33/32]], [[36/35]]
| dup-unison, downminor 2nd
| dup-unison, downminor 2nd
| ^^1, vm2
| ^^1, vm2
Line 87: Line 304:
| 3
| 3
| 87.8
| 87.8
| [[19/18]], [[20/19]], [[21/20]], [[22/21]]
| down-aug 1sn, minor 2nd
| down-aug 1sn, minor 2nd
| vA1, m2
| vA1, m2
Line 99: Line 315:
| 4
| 4
| 117.1
| 117.1
| [[14/13]], [[15/14]], [[16/15]]
| augmented 1sn, upminor 2nd
| augmented 1sn, upminor 2nd
| A1, ^m2
| A1, ^m2
Line 111: Line 326:
| 5
| 5
| 146.3
| 146.3
| [[12/11]], [[13/12]]
| mid 2nd
| mid 2nd
| ~2
| ~2
Line 123: Line 337:
| 6
| 6
| 175.6
| 175.6
| [[10/9]], [[11/10]], [[21/19]]
| downmajor 2nd
| downmajor 2nd
| vM2
| vM2
Line 135: Line 348:
| 7
| 7
| 204.9
| 204.9
| [[9/8]]
| major 2nd
| major 2nd
| M2
| M2
Line 147: Line 359:
| 8
| 8
| 234.1
| 234.1
| [[8/7]], [[15/13]]
| upmajor 2nd
| upmajor 2nd
| ^M2
| ^M2
Line 159: Line 370:
| 9
| 9
| 263.4
| 263.4
| [[7/6]], [[22/19]]
| downminor 3rd
| downminor 3rd
| vm3
| vm3
Line 171: Line 381:
| 10
| 10
| 292.7
| 292.7
| [[13/11]], [[19/16]], [[32/27]]
| minor 3rd
| minor 3rd
| m3
| m3
Line 183: Line 392:
| 11
| 11
| 322.0
| 322.0
| [[6/5]]
| upminor 3rd
| upminor 3rd
| ^m3
| ^m3
Line 195: Line 403:
| 12
| 12
| 351.2
| 351.2
| [[11/9]], [[16/13]]
| mid 3rd
| mid 3rd
| ~3
| ~3
Line 207: Line 414:
| 13
| 13
| 380.5
| 380.5
| [[5/4]], [[26/21]]
| downmajor 3rd
| downmajor 3rd
| vM3
| vM3
Line 219: Line 425:
| 14
| 14
| 409.8
| 409.8
| [[14/11]], [[19/15]], [[24/19]]
| major 3rd
| major 3rd
| M3
| M3
Line 231: Line 436:
| 15
| 15
| 439.0
| 439.0
| [[9/7]], [[32/25]]
| upmajor 3rd
| upmajor 3rd
| ^M3
| ^M3
Line 243: Line 447:
| 16
| 16
| 468.3
| 468.3
| [[21/16]], [[13/10]]
| down-4th
| down-4th
| v4
| v4
Line 255: Line 458:
| 17
| 17
| 497.6
| 497.6
| [[4/3]]
| perfect 4th
| perfect 4th
| P4
| P4
Line 267: Line 469:
| 18
| 18
| 526.8
| 526.8
| [[15/11]], [[19/14]], [[27/20]]
| up-4th
| up-4th
| ^4
| ^4
Line 279: Line 480:
| 19
| 19
| 556.1
| 556.1
| [[11/8]], [[18/13]], [[26/19]]
| mid-4th, downdim 5th
| mid-4th, downdim 5th
| ~4, vd5
| ~4, vd5
Line 291: Line 491:
| 20
| 20
| 585.4
| 585.4
| [[7/5]], [[45/32]]
| downaug 4th, dim 5th
| downaug 4th, dim 5th
| vA4, d5
| vA4, d5
Line 303: Line 502:
| 21
| 21
| 614.6
| 614.6
| [[10/7]], [[64/45]]
| aug 4th, updim 5th
| aug 4th, updim 5th
| A4, ^d5
| A4, ^d5
Line 315: Line 513:
| 22
| 22
| 643.9
| 643.9
| [[13/9]], [[16/11]], [[19/13]]
| mid-5th, upaug 4th
| mid-5th, upaug 4th
| ~5, ^A4
| ~5, ^A4
Line 327: Line 524:
| 23
| 23
| 673.2
| 673.2
| [[22/15]], [[28/19]], [[40/27]]
| down-5th
| down-5th
| v5
| v5
Line 339: Line 535:
| 24
| 24
| 702.4
| 702.4
| [[3/2]]
| perfect 5th
| perfect 5th
| P5
| P5
Line 351: Line 546:
| 25
| 25
| 731.7
| 731.7
| [[20/13]], [[32/21]]
| up-5th
| up-5th
| ^5
| ^5
Line 363: Line 557:
| 26
| 26
| 761.0
| 761.0
| [[14/9]], [[25/16]]
| downminor 6th
| downminor 6th
| vm6
| vm6
Line 375: Line 568:
| 27
| 27
| 790.2
| 790.2
| [[11/7]], [[19/12]], [[30/19]]
| minor 6th
| minor 6th
| m6
| m6
Line 387: Line 579:
| 28
| 28
| 819.5
| 819.5
| [[8/5]], [[21/13]]
| upminor 6th
| upminor 6th
| ^m6
| ^m6
Line 399: Line 590:
| 29
| 29
| 848.8
| 848.8
| [[13/8]], [[18/11]]
| mid 6th
| mid 6th
| ~6
| ~6
Line 411: Line 601:
| 30
| 30
| 878.0
| 878.0
| [[5/3]]
| downmajor 6th
| downmajor 6th
| vM6
| vM6
Line 423: Line 612:
| 31
| 31
| 907.3
| 907.3
| [[22/13]], [[27/16]], [[32/19]]
| major 6th
| major 6th
| M6
| M6
Line 435: Line 623:
| 32
| 32
| 936.6
| 936.6
| [[12/7]], [[19/11]]
| upmajor 6th
| upmajor 6th
| ^M6
| ^M6
Line 447: Line 634:
| 33
| 33
| 965.9
| 965.9
| [[7/4]], [[26/15]]
| downminor 7th
| downminor 7th
| vm7
| vm7
Line 459: Line 645:
| 34
| 34
| 995.1
| 995.1
| [[16/9]]
| minor 7th
| minor 7th
| m7
| m7
Line 471: Line 656:
| 35
| 35
| 1024.4
| 1024.4
| [[9/5]], [[20/11]], [[38/21]]
| upminor 7th
| upminor 7th
| ^m7
| ^m7
Line 483: Line 667:
| 36
| 36
| 1053.7
| 1053.7
| [[11/6]], [[24/13]]
| mid 7th
| mid 7th
| ~7
| ~7
Line 495: Line 678:
| 37
| 37
| 1082.9
| 1082.9
| [[13/7]], [[15/8]], [[28/15]]
| downmajor 7th
| downmajor 7th
| vM7
| vM7
Line 507: Line 689:
| 38
| 38
| 1112.2
| 1112.2
| [[19/10]], [[21/11]], [[36/19]], [[40/21]]
| major 7th
| major 7th
| M7
| M7
Line 519: Line 700:
| 39
| 39
| 1141.5
| 1141.5
| [[27/14]], [[35/18]], [[48/25]], [[64/33]]
| upmajor 7th
| upmajor 7th
| ^M7
| ^M7
Line 531: Line 711:
| 40
| 40
| 1170.7
| 1170.7
| [[49/25]], [[63/32]], [[96/49]], [[160/81]]
| dim 8ve
| dim 8ve
| v8
| v8
Line 543: Line 722:
| 41
| 41
| 1200.0
| 1200.0
| [[2/1]]
| perfect 8ve
| perfect 8ve
| P8
| P8
Line 553: Line 731:
| Do
| Do
|}
|}
<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 ===
=== Interval quality and chord names in color notation ===
Line 665: Line 842:
* 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 869:
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 ====
<imagemap>
{{Sagittal chart|Evo}}
File:41-EDO_Evo_Sagittal.svg
 
desc none
==== Evo-SZ flavor ====
rect 80 0 300 50 [[Sagittal_notation]]
{{Sagittal chart|Evo-SZ}}
rect 300 0 687 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_Sagittal.svg]]
</imagemap>


==== Revo flavor ====
==== Revo flavor ====
<imagemap>
{{Sagittal chart}}
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:
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]]
[[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 ==
== Approximation to JI ==
Line 766: Line 951:
|-
|-
| 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 774: Line 959:
| 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 781: Line 966:
| 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 788: Line 973:
| 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 795: Line 980:
| 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 802: Line 987:
| 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 824: Line 1,011:
| <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 832: Line 1,019:
| <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 840: Line 1,027:
| [[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 848: Line 1,035:
| [[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 856: Line 1,043:
| [[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 864: Line 1,051:
| <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 872: Line 1,059:
| [[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 880: Line 1,067:
| [[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 888: Line 1,075:
| <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 896: Line 1,083:
| [[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 904: Line 1,091:
| [[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 912: Line 1,099:
| <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 920: Line 1,107:
| [[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 928: Line 1,115:
| [[245/243]]
| [[245/243]]
| 14.19
| 14.19
| {{monzo| 0 -5 1 2 }}
| {{Monzo| 0 -5 1 2 }}
| Zozoyo
| Zozoyo
| zzy
| zzy
Line 936: Line 1,123:
| [[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 944: Line 1,131:
| <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 952: Line 1,139:
| [[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 960: Line 1,147:
| [[225/224]]
| [[225/224]]
| 7.71
| 7.71
| {{monzo| -5 2 2 -1 }}
| {{Monzo| -5 2 2 -1 }}
| Ruyoyo
| Ruyoyo
| ryy
| ryy
Line 968: Line 1,155:
| [[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 976: Line 1,163:
| [[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 984: Line 1,171:
| [[5120/5103]]
| [[5120/5103]]
| 5.76
| 5.76
| {{monzo| 10 -6 1 -1 }}
| {{Monzo| 10 -6 1 -1 }}
| Saruyo
| Saruyo
| sry
| sry
Line 992: Line 1,179:
| [[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 1,000: Line 1,187:
| [[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 1,008: Line 1,195:
| <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 1,016: Line 1,203:
| [[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 1,024: Line 1,211:
| [[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 1,032: Line 1,219:
| [[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 1,040: Line 1,227:
| [[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 1,048: Line 1,235:
| [[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 1,056: Line 1,243:
| [[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 1,064: Line 1,251:
| [[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 1,072: Line 1,259:
| [[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 1,080: Line 1,267:
| [[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 1,088: Line 1,275:
| [[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 1,096: Line 1,283:
| [[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 1,104: Line 1,291:
| [[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 1,112: Line 1,299:
| [[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 1,120: Line 1,307:
| [[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 1,128: Line 1,315:
| [[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 1,136: Line 1,323:
| [[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 1,144: Line 1,331:
| [[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 1,152: Line 1,339:
| [[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 1,160: Line 1,347:
| [[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 1,168: Line 1,355:
| [[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 1,176: Line 1,363:
| [[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 1,184: Line 1,371:
| [[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 1,192: Line 1,379:
| [[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 1,200: Line 1,387:
| [[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 1,208: Line 1,395:
| [[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 1,216: Line 1,403:
| [[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 1,224: Line 1,411:
| [[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 1,248: Line 1,435:
| [[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 1,256: Line 1,443:
| [[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 1,264: Line 1,451:
| [[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 1,272: Line 1,459:
| [[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 1,280: Line 1,467:
| [[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 1,288: Line 1,475:
| [[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 1,296: Line 1,483:
| [[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 1,304: Line 1,491:
| [[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 1,312: Line 1,499:
| [[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 1,320: Line 1,507:
| [[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
Retrieved from "https://en.xen.wiki/w/41edo"