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! Approximate Ratios*
! Approximate Ratios*
! colspan="3" | [[Ups and Downs Notation]]
! colspan="3" | [[Ups and Downs Notation]]
! colspan="3" |[[SKULO interval names|SKULO notation]] (K or S = 1, U = 2)
! colspan="3" | [[SKULO interval names | SKULO notation]] (K or S = 1, U = 2)
! [[41edo solfege|Kite's<br>Solfege]]
! [[41edo solfege | Kite's<br>Solfege]]
! [[41edo solfege|Andrew's<br>Solfege]]
! [[41edo solfege | Andrew's<br>Solfege]]
|-
|-
| 0
| 0
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| P1
| P1
| D
| D
|perfect unison
| perfect unison
|P1
| P1
|D
| D
| Da
| Da
| Do
| Do
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| ^1
| ^1
| ^D
| ^D
|comma-wide unison, super unison
| comma-wide unison, super unison
|K1/S1
| K1/S1
|KD, SD
| KD, SD
| Du
| Du
| Di
| Di
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| ^^1, vm2
| ^^1, vm2
| ^^D, vEb
| ^^D, vEb
|subminor 2nd, classic aug unison, uber unison
| subminor 2nd, classic aug unison, uber unison
|sm2, kkA1, U1
| sm2, kkA1, U1
|sEb, kkD#, UD
| sEb, kkD#, UD
| Fro
| Fro
| Ro
| Ro
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| vA1, m2
| vA1, m2
| vD#, Eb
| vD#, Eb
|minor 2nd, comma-narrow augmented unison
| minor 2nd, comma-narrow augmented unison
|m2, kA1
| m2, kA1
|Eb, kD#
| Eb, kD#
| Fra
| Fra
| Rih
| Rih
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| A1, ^m2
| A1, ^m2
| D#, ^Eb
| D#, ^Eb
|classic minor 2nd, augmented unison
| classic minor 2nd, augmented unison
|Km2, A1
| Km2, A1
|KEb, D#
| KEb, D#
| Fru
| Fru
| Ra
| Ra
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| ~2
| ~2
| ^D#, vvE
| ^D#, vvE
|neutral second, super augmented unison
| neutral second, super augmented unison
|N2, sA1
| N2, sA1
|UEb/uE, sD#
| UEb/uE, sD#
| Ri
| Ri
| Ru
| Ru
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| vM2
| vM2
| vE
| vE
|classic/comma-wide major 2nd
| classic/comma-wide major 2nd
|kM2
| kM2
|kE
| kE
| Ro
| Ro
| Reh
| Reh
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| M2
| M2
| E
| E
|major 2nd
| major 2nd
|M2
| M2
|E
| E
| Ra
| Ra
| Re
| Re
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| ^M2
| ^M2
| ^E
| ^E
|supermajor 2nd
| supermajor 2nd
|SM2
| SM2
|SE
| SE
| Ru
| Ru
| Ri
| Ri
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| vm3
| vm3
| vF
| vF
|subminor 3rd
| subminor 3rd
|sm3
| sm3
|sF
| sF
| No
| No
| Ma
| Ma
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| m3
| m3
| F
| F
|minor 3rd
| minor 3rd
|m3
| m3
|F
| F
| Na
| Na
| Meh
| Meh
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| ^m3
| ^m3
| ^F
| ^F
|classicminor 3rd
| classicminor 3rd
|Km3
| Km3
|KF
| KF
| Nu
| Nu
| Me
| Me
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| ~3
| ~3
| ^^F, vGb
| ^^F, vGb
|neutral 3rd, sub diminished 4th
| neutral 3rd, sub diminished 4th
|N3, sd4
| N3, sd4
|UF/uF#, sGb
| UF/uF#, sGb
| Mi
| Mi
| Mu
| Mu
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| vM3
| vM3
| vF#, Gb
| vF#, Gb
|classic major 3rd, diminished 4th
| classic major 3rd, diminished 4th
|kM3, d4
| kM3, d4
|kF#, Gb
| kF#, Gb
| Mo
| Mo
| Mi
| Mi
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| M3
| M3
| F#, ^Gb
| F#, ^Gb
|major 3rd, comma-wide diminished 4th
| major 3rd, comma-wide diminished 4th
|M3, Kd4
| M3, Kd4
|F#, KGb
| F#, KGb
| Ma
| Ma
| Maa
| Maa
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| ^M3
| ^M3
| ^F#, vvG
| ^F#, vvG
|supermajor 3rd, classic diminished 4th
| supermajor 3rd, classic diminished 4th
|SM3, KKd4
| SM3, KKd4
|SF#, KKGb
| SF#, KKGb
| Mu
| Mu
| Mo
| Mo
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| v4
| v4
| vG
| vG
|sub 4th
| sub 4th
|s4
| s4
|sG
| sG
| Fo
| Fo
| Fe
| Fe
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| P4
| P4
| G
| G
|perfect 4th
| perfect 4th
|P4
| P4
|G
| G
| Fa
| Fa
| Fa
| Fa
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| ^4
| ^4
| ^G
| ^G
|comma-wide 4th
| comma-wide 4th
|K4
| K4
|KG
| KG
| Fu
| Fu
| Fih
| Fih
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| ~4, vd5
| ~4, vd5
| ^^G, vAb
| ^^G, vAb
|uber/neutral 4th, classic augmented 4th
| uber/neutral 4th, classic augmented 4th
|U4/N4, kkA4
| U4/N4, kkA4
|UG, kkG#
| UG, kkG#
| Fi/Sho
| Fi/Sho
| Fu
| Fu
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| vA4, d5
| vA4, d5
| vG#, Ab
| vG#, Ab
|comma-narrow augmented 4th, diminished 5th
| comma-narrow augmented 4th, diminished 5th
|kA4/d5
| kA4/d5
|kG#, Ab
| kG#, Ab
| Po/Sha
| Po/Sha
| Fi
| Fi
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| A4, ^d5
| A4, ^d5
| G#, ^Ab
| G#, ^Ab
|augmented 4th, comma-wide diminished 5th
| augmented 4th, comma-wide diminished 5th
|A4/Kd5
| A4/Kd5
|G#, KAb
| G#, KAb
|Pa/Shu
| Pa/Shu
| Se
| Se
|-
|-
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| ~5, ^A4
| ~5, ^A4
| ^G#, vvA
| ^G#, vvA
|unter/neutral 5th, classic diminished 5th
| unter/neutral 5th, classic diminished 5th
|u5/N5, KKd5
| u5/N5, KKd5
|uA, KKAb
| uA, KKAb
| Pu/Si
| Pu/Si
| Su
| Su
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| v5
| v5
| vA
| vA
|comma-narrow 5th
| comma-narrow 5th
|k5
| k5
|kA
| kA
| So
| So
| Sih
| Sih
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| P5
| P5
| A
| A
|perfect 5th
| perfect 5th
|P5
| P5
|A
| A
| Sa
| Sa
| Sol
| Sol
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| ^5
| ^5
| ^A
| ^A
|super 5th
| super 5th
|S5
| S5
|SA
| SA
| Su
| Su
| Si
| Si
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| vm6
| vm6
| ^^A, vBb
| ^^A, vBb
|subminor 6th, classic augmented 5th
| subminor 6th, classic augmented 5th
|sm6
| sm6
|sBb, kkA#
| sBb, kkA#
| Flo
| Flo
| Lo
| Lo
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| m6
| m6
| vA#, Bb
| vA#, Bb
|minor 6th, comma-narrow augmented 5th
| minor 6th, comma-narrow augmented 5th
|m6
| m6
|Bb, kA#
| Bb, kA#
| Fla
| Fla
| Leh
| Leh
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| ^m6
| ^m6
| A#, ^Bb
| A#, ^Bb
|classic minor 6th, augmented 5th
| classic minor 6th, augmented 5th
|Km6, A5
| Km6, A5
|KBb, A#
| KBb, A#
| Flu
| Flu
| Le
| Le
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| ~6
| ~6
| ^A#, vvB
| ^A#, vvB
|neutral 6th, super augmented 5th
| neutral 6th, super augmented 5th
|N6
| N6
|UBb/uB, sA#
| UBb/uB, sA#
| Li
| Li
| Lu
| Lu
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| vM6
| vM6
| vB
| vB
|classic major 6th
| classic major 6th
|kM6
| kM6
|kB
| kB
| Lo
| Lo
| La
| La
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| M6
| M6
| B
| B
|major 6th
| major 6th
|M6
| M6
|B
| B
| La
| La
| Laa
| Laa
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| ^M6
| ^M6
| ^B
| ^B
|supermajor 6th
| supermajor 6th
|SM6
| SM6
|SB
| SB
| Lu
| Lu
| Li
| Li
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| vm7
| vm7
| vC
| vC
|subminor 7th
| subminor 7th
|sm7
| sm7
|sC
| sC
| Tho
| Tho
| Ta
| Ta
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| m7
| m7
| C
| C
|minor 7th
| minor 7th
|m7
| m7
|C
| C
| Tha
| Tha
| Teh
| Teh
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| ^m7
| ^m7
| ^C
| ^C
|classic/comma-wide minor seventh
| classic/comma-wide minor seventh
|Km7
| Km7
|KC
| KC
| Thu
| Thu
| Te
| Te
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| ~7
| ~7
| ^^C, vDb
| ^^C, vDb
|neutral 7th, sub diminished 8ve
| neutral 7th, sub diminished 8ve
|N7
| N7
|UC/uC#, sDb
| UC/uC#, sDb
| Ti
| Ti
| Tu
| Tu
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| vM7
| vM7
| vC#, Db
| vC#, Db
|classic major 7th, diminished 8ve
| classic major 7th, diminished 8ve
|kM7, d8
| kM7, d8
|kC#, Db
| kC#, Db
| To
| To
| Ti
| Ti
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| M7
| M7
| C#, ^Db
| C#, ^Db
|major 7th, comma-wide diminished 8ve
| major 7th, comma-wide diminished 8ve
|M7, Kd8
| M7, Kd8
|C#, KDb
| C#, KDb
| Ta
| Ta
| Taa
| Taa
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| ^M7
| ^M7
| C#^, vvD
| C#^, vvD
|supermajor 7th, classic dim 8ve, unter 8ve
| supermajor 7th, classic dim 8ve, unter 8ve
|SM7, KKd8, U8
| SM7, KKd8, U8
|SC#, KKDb, u8
| SC#, KKDb, u8
| Tu
| Tu
| To
| To
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| v8
| v8
| vD
| vD
|comma-narrow 8ve, sub 8ve
| comma-narrow 8ve, sub 8ve
|k8/s8
| k8/s8
|kD, sD
| kD, sD
| Do
| Do
| Da
| Da
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| P8
| P8
| D
| D
|perfect 8ve
| perfect 8ve
|P8
| P8
|D
| D
| Da
| Da
| Do
| Do
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A red-note/blue-note system, similar to the one proposed for [[36edo]], is one 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 one 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}}


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.
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.
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=== Ups and downs notation ===
=== Ups and downs notation ===
41edo can also be notated with [[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]] with quarter tone accidentals:
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]]:


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


== Approximation to JI ==
== Approximation to JI ==
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