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The 41-tET, 41-EDO, 41-ET, or '''41-Tone Equal Temperament''' is the scale derived by dividing the octave into 41 equally-sized steps. Each step represents a frequency ratio of 29.268 [[cent|cent]]s, an [[interval|interval]] close in size to [[64/63|64/63]], the [[Septimal_comma|septimal comma]]. 41-ET can be seen as a tuning of the ''[[Schismatic_family#Garibaldi|Garibaldi temperament]]'' [[#cite_note-1|[1]]] , [[#cite_note-2|[2]]] , [[#cite_note-3|[3]]] the ''[[Magic_family|Magic temperament]]'' [[#cite_note-4|[4]]] and the superkleismic (41&26) temperament. It is the second smallest equal temperament (after [[29edo|29edo]]) whose perfect fifth is closer to just intonation than that of [[12edo|12-ET]], and is the seventh [[The_Riemann_Zeta_Function_and_Tuning#Zeta EDO lists|zeta integral edo]] after 31; it is not, however, a [[The_Riemann_Zeta_Function_and_Tuning#Zeta EDO lists|zeta gap edo]]. This has to do with the fact that it can deal with the [[11-limit|11-limit]] fairly well, and the [[13-limit|13-limit]] perhaps close enough for government work, though its [[13/10|13/10]] is 14 cents sharp. Various 13-limit [[Magic_extensions|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.
The 41-tET, 41-EDO, 41-ET, or '''41-Tone Equal Temperament''' is the scale derived by dividing the octave into 41 equally-sized steps. Each step represents a frequency ratio of 29.268 [[cent|cent]]s, an [[interval|interval]] close in size to [[64/63|64/63]], the [[Septimal_comma|septimal comma]]. 41-ET can be seen as a tuning of the ''[[Schismatic_family#Garibaldi|Garibaldi temperament]]'' [[#cite_note-1|[1]]] , [[#cite_note-2|[2]]] , [[#cite_note-3|[3]]] the ''[[Magic_family|Magic temperament]]'' [[#cite_note-4|[4]]] and the superkleismic (41&26) temperament. It is the second smallest equal temperament (after [[29edo|29edo]]) whose perfect fifth is closer to just intonation than that of [[12edo|12-ET]], and is the seventh [[The_Riemann_Zeta_Function_and_Tuning#Zeta EDO lists|zeta integral edo]] after 31; it is not, however, a [[The_Riemann_Zeta_Function_and_Tuning#Zeta EDO lists|zeta gap edo]]. This has to do with the fact that it can deal with the [[11-limit|11-limit]] fairly well, and the [[13-limit|13-limit]] perhaps close enough for government work, though its [[13/10|13/10]] is 14 cents sharp. Various 13-limit [[Magic_extensions|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.


41edo is consistent in the 15 odd limit. In fact, ''all'' of its intervals between 100 and 1100 cents in size are 15-odd-limit consonances. (In comparison, [[31edo|31edo]] is only consistent up to the 11-limit, and the intervals 12/31 and 19/31 have no 11-limit approximations).
41edo is consistent in the 15 odd limit. In fact, ''all'' of its intervals between 100 and 1100 cents in size are 15-odd-limit consonances, although 16\41 as 13/10 is debatable. (In comparison, [[31edo|31edo]] is only consistent up to the 11-limit, and the intervals 12/31 and 19/31 have no 11-limit approximations).


41-ET forms the foundation of the [http://www.h-pi.com/theory/huntsystem1.html H-System], which uses the scale degrees of 41-ET as the basic [[13-limit|13-limit]] intervals requiring fine tuning +/- 1 [http://www.h-pi.com/theory/huntsystem2.html average JND] from the 41-ET circle in [[205edo|205edo]].
41-ET forms the foundation of the [http://www.h-pi.com/theory/huntsystem1.html H-System], which uses the scale degrees of 41-ET as the basic [[13-limit|13-limit]] intervals requiring fine tuning +/- 1 [http://www.h-pi.com/theory/huntsystem2.html average JND] from the 41-ET circle in [[205edo|205edo]].
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|-
|-
! | Name
! | Name
! colspan="2" |[[Color notation/Temperament Names|color name]]
! | Monzo
! | Monzo
! | Ratio
! | Ratio
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|-
|-
| | odiheim
| | odiheim
|Luluquinzo-aquadgu
|1uuz<sup>5</sup>g<sup>4</sup>
| |<nowiki> | -1 2 -4 5 -2 </nowiki>&gt;
| |<nowiki> | -1 2 -4 5 -2 </nowiki>&gt;
| style="text-align:center;" |  
| style="text-align:center;" |  
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|-
|-
| | harmonisma
| | harmonisma
|Thuthutrilo-aru
|3uu1o<sup>3</sup>r
| |<nowiki> | 3 -2 0 -1 3 -2 </nowiki>&gt;
| |<nowiki> | 3 -2 0 -1 3 -2 </nowiki>&gt;
| style="text-align:center;" | 10648/10647
| style="text-align:center;" | 10648/10647
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|-
|-
| | tridecimal schisma, Sagittal schismina
| | tridecimal schisma, Sagittal schismina
| |<nowiki> | 12 -2 -1 -1 0 -1/1 </nowiki>&gt;
|Sathurugu
|s3urg
| |<nowiki> | 12 -2 -1 -1 0 -1 </nowiki>&gt;
| style="text-align:center;" | 4096/4095
| style="text-align:center;" | 4096/4095
| | 0.42
| | 0.42
|-
|-
| | Lehmerisma
| | Lehmerisma
|Loloruyoyo
|1ooryy
| |<nowiki> | -4 -3 2 -1 2 </nowiki>&gt;
| |<nowiki> | -4 -3 2 -1 2 </nowiki>&gt;
| style="text-align:center;" | 3025/3024
| style="text-align:center;" | 3025/3024
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|-
|-
| | Breedsma
| | Breedsma
|Bizozogu
|z<sup>4</sup>gg
| |<nowiki> | -5 -1 -2 4 </nowiki>&gt;
| |<nowiki> | -5 -1 -2 4 </nowiki>&gt;
| style="text-align:center;" | 2401/2400
| style="text-align:center;" | 2401/2400
Line 49: Line 60:
|-
|-
| | Eratosthenes' comma
| | Eratosthenes' comma
|Sanogu
|s19og
| |<nowiki> | 6 -5 -1 0 0 0 0 1 </nowiki>&gt;
| |<nowiki> | 6 -5 -1 0 0 0 0 1 </nowiki>&gt;
| style="text-align:center;" | 1216/1215
| style="text-align:center;" | 1216/1215
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|-
|-
| | schisma
| | schisma
|Layo
|Ly
| |<nowiki> | -15 8 1 </nowiki>&gt;
| |<nowiki> | -15 8 1 </nowiki>&gt;
| style="text-align:center;" | 32805/32768
| style="text-align:center;" | 32805/32768
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|-
|-
| | squbema
| | squbema
|Lathuru
|L3ur
| |<nowiki> | -3 6 0 -1 0 -1 </nowiki>&gt;
| |<nowiki> | -3 6 0 -1 0 -1 </nowiki>&gt;
| style="text-align:center;" | 729/728
| style="text-align:center;" | 729/728
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|-
|-
| | septendecimal bridge comma
| | septendecimal bridge comma
|Sutholoruyo
|17u3o1ory
| |<nowiki> | -1 -1 1 -1 1 1 -1 </nowiki>&gt;
| |<nowiki> | -1 -1 1 -1 1 1 -1 </nowiki>&gt;
| style="text-align:center;" | 715/714
| style="text-align:center;" | 715/714
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|-
|-
| | Swets' comma, swetisma
| | Swets' comma, swetisma
|Lururuyo
|1urry
| |<nowiki> | 2 3 1 -2 -1 </nowiki>&gt;
| |<nowiki> | 2 3 1 -2 -1 </nowiki>&gt;
| style="text-align:center;" | 540/539
| style="text-align:center;" | 540/539
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|-
|-
| | undevicesimal comma, Boethius' comma
| | undevicesimal comma, Boethius' comma
|Lano
|L19o
| |<nowiki> | -9 3 0 0 0 0 0 1 </nowiki>&gt;
| |<nowiki> | -9 3 0 0 0 0 0 1 </nowiki>&gt;
| style="text-align:center;" | 513/512
| style="text-align:center;" | 513/512
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|-
|-
| | moctdel
| | moctdel
|Lotriruyo
|1or<sup>3</sup>y
| |<nowiki> | -2 0 3 -3 1 </nowiki>&gt;
| |<nowiki> | -2 0 3 -3 1 </nowiki>&gt;
| style="text-align:center;" | 1375/1372
| style="text-align:center;" | 1375/1372
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|-
|-
| | Beta 2, septimal schisma, garischisma
| | Beta 2, septimal schisma, garischisma
|Sasaru
|ssr
| |<nowiki> | 25 -14 0 -1 </nowiki>&gt;
| |<nowiki> | 25 -14 0 -1 </nowiki>&gt;
| style="text-align:center;" |  
| style="text-align:center;" |  
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|-
|-
| | Werckmeister's undecimal septenarian schisma, werckisma
| | Werckmeister's undecimal septenarian schisma, werckisma
|Luzozogu
|1uzzg
| |<nowiki> | -3 2 -1 2 -1 </nowiki>&gt;
| |<nowiki> | -3 2 -1 2 -1 </nowiki>&gt;
| style="text-align:center;" | 441/440
| style="text-align:center;" | 441/440
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|-
|-
| | cuthbert
| | cuthbert
|Thuthulolozogu
|3uu1oozg
| |<nowiki> | 0 0 -1 1 2 -2 </nowiki>&gt;
| |<nowiki> | 0 0 -1 1 2 -2 </nowiki>&gt;
| style="text-align:center;" | 847/845
| style="text-align:center;" | 847/845
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|-
|-
| | undecimal kleisma, keenanisma
| | undecimal kleisma, keenanisma
|Lozoyo
|1ozg
| |<nowiki> | -7 -1 1 1 1 </nowiki>&gt;
| |<nowiki> | -7 -1 1 1 1 </nowiki>&gt;
| style="text-align:center;" | 385/384
| style="text-align:center;" | 385/384
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|-
|-
| | gentle comma
| | gentle comma
|Tholuluzo
|3o1uuz
| |<nowiki> | 2 -1 0 1 -2 1 </nowiki>&gt;
| |<nowiki> | 2 -1 0 1 -2 1 </nowiki>&gt;
| style="text-align:center;" | 364/363
| style="text-align:center;" | 364/363
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|-
|-
| | minthma
| | minthma
|Thulo
|3u1o
| |<nowiki> | 5 -3 0 0 1 -1 </nowiki>&gt;
| |<nowiki> | 5 -3 0 0 1 -1 </nowiki>&gt;
| style="text-align:center;" | 352/351
| style="text-align:center;" | 352/351
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|-
|-
| | marveltwin
| | marveltwin
|Thoyoyo
|3oyy
| |<nowiki> | -2 -4 2 0 0 1 </nowiki>&gt;
| |<nowiki> | -2 -4 2 0 0 1 </nowiki>&gt;
| style="text-align:center;" | 325/324
| style="text-align:center;" | 325/324
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|-
|-
| | Beta 5, Garibaldi comma, hemifamity
| | Beta 5, Garibaldi comma, hemifamity
|Saruyo
|sry
| |<nowiki> | 10 -6 1 -1 </nowiki>&gt;
| |<nowiki> | 10 -6 1 -1 </nowiki>&gt;
| style="text-align:center;" | 5120/5103
| style="text-align:center;" | 5120/5103
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|-
|-
| | hemimage
| | hemimage
|Satrizo-agu
|sz<sup>3</sup>g
| |<nowiki> | 5 -7 -1 3 </nowiki>&gt;
| |<nowiki> | 5 -7 -1 3 </nowiki>&gt;
| style="text-align:center;" | 10976/10935
| style="text-align:center;" | 10976/10935
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|-
|-
| | septendecimal kleisma
| | septendecimal kleisma
|Sugu
|17ug
| |<nowiki> | 8 -1 -1 0 0 0 -1 </nowiki>&gt;
| |<nowiki> | 8 -1 -1 0 0 0 -1 </nowiki>&gt;
| style="text-align:center;" | 256/255
| style="text-align:center;" | 256/255
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|-
|-
| | small BP diesis, mirkwai
| | small BP diesis, mirkwai
|Quinru-aquadyo
|r<sup>5</sup>y<sup>4</sup>
| |<nowiki> | 0 3 4 -5 </nowiki>&gt;
| |<nowiki> | 0 3 4 -5 </nowiki>&gt;
| style="text-align:center;" | 16875/16807
| style="text-align:center;" | 16875/16807
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|-
|-
| | neutral third comma, rastma
| | neutral third comma, rastma
|Lulu
|1uu
| |<nowiki> | -1 5 0 0 -2 </nowiki>&gt;
| |<nowiki> | -1 5 0 0 -2 </nowiki>&gt;
| style="text-align:center;" | 243/242
| style="text-align:center;" | 243/242
Line 144: Line 193:
|-
|-
| | kestrel comma
| | kestrel comma
|Thuthuloru
|3uu1or
| |<nowiki> | 2 3 0 -1 1 -2 </nowiki>&gt;
| |<nowiki> | 2 3 0 -1 1 -2 </nowiki>&gt;
| style="text-align:center;" | 1188/1183
| style="text-align:center;" | 1188/1183
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|-
|-
| | septimal kleisma, marvel comma
| | septimal kleisma, marvel comma
|Ruyoyo
|ryy
| |<nowiki> | -5 2 2 -1 </nowiki>&gt;
| |<nowiki> | -5 2 2 -1 </nowiki>&gt;
| style="text-align:center;" | 225/224
| style="text-align:center;" | 225/224
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|-
|-
| | huntma
| | huntma
|Thururuyo
|3urry
| |<nowiki> | 7 0 1 -2 0 -1 </nowiki>&gt;
| |<nowiki> | 7 0 1 -2 0 -1 </nowiki>&gt;
| style="text-align:center;" | 640/637
| style="text-align:center;" | 640/637
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|-
|-
| | spleen comma
| | spleen comma
|Nuluzoyo
|19u1uzy
| |<nowiki> | 1 1 1 1 -1 0 0 -1 </nowiki>&gt;
| |<nowiki> | 1 1 1 1 -1 0 0 -1 </nowiki>&gt;
| style="text-align:center;" | 210/209
| style="text-align:center;" | 210/209
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|-
|-
| | orgonisma
| | orgonisma
|Satrilu-aruru
|s1u<sup>3</sup>rr
| |<nowiki> | 16 0 0 -2 -3 </nowiki>&gt;
| |<nowiki> | 16 0 0 -2 -3 </nowiki>&gt;
| style="text-align:center;" | 65536/65219
| style="text-align:center;" | 65536/65219
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|-
|-
| | gamelan residue, gamelisma
| | gamelan residue, gamelisma
|Latrizo
|Lz<sup>3</sup>
| |<nowiki> | -10 1 0 3 </nowiki>&gt;
| |<nowiki> | -10 1 0 3 </nowiki>&gt;
| style="text-align:center;" | 1029/1024
| style="text-align:center;" | 1029/1024
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|-
|-
| | septendecimal comma
| | septendecimal comma
|Lasu
|L17u
| |<nowiki> | -7 7 0 0 0 0 -1 </nowiki>&gt;
| |<nowiki> | -7 7 0 0 0 0 -1 </nowiki>&gt;
| style="text-align:center;" | 2187/2176
| style="text-align:center;" | 2187/2176
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|-
|-
| | mynucuma
| | mynucuma
|Thuzozogu
|3uzzg
| |<nowiki> | 2 -1 -1 2 0 -1 </nowiki>&gt;
| |<nowiki> | 2 -1 -1 2 0 -1 </nowiki>&gt;
| style="text-align:center;" | 196/195
| style="text-align:center;" | 196/195
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|-
|-
| | quince
| | quince
|Lasepzo-agugu
|Lz<sup>7</sup>gg
| |<nowiki> | -15 0 -2 7 </nowiki>&gt;
| |<nowiki> | -15 0 -2 7 </nowiki>&gt;
| style="text-align:center;" |  
| style="text-align:center;" |  
Line 189: Line 256:
|-
|-
| | undecimal semicomma, pentacircle (minthma * gentle)
| | undecimal semicomma, pentacircle (minthma * gentle)
|Saluzo
|s1uz
| |<nowiki> | 7 -4 0 1 -1 </nowiki>&gt;
| |<nowiki> | 7 -4 0 1 -1 </nowiki>&gt;
| style="text-align:center;" | 896/891
| style="text-align:center;" | 896/891
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|-
|-
| | 29th-partial chroma
| | 29th-partial chroma
|Twenty-noyo
|29oy
| |<nowiki> | -4 -2 1 0 0 0 0 0 0 1 </nowiki>&gt;
| |<nowiki> | -4 -2 1 0 0 0 0 0 0 1 </nowiki>&gt;
| style="text-align:center;" | 145/144
| style="text-align:center;" | 145/144
Line 199: Line 270:
|-
|-
| | grossma
| | grossma
|Thulu
|3u1u
| |<nowiki> | 4 2 0 0 -1 -1 </nowiki>&gt;
| |<nowiki> | 4 2 0 0 -1 -1 </nowiki>&gt;
| style="text-align:center;" | 144/143
| style="text-align:center;" | 144/143
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|-
|-
| | gassorma
| | gassorma
|Thuloruyoyo
|3u1oryy
| |<nowiki> | 0 -1 2 -1 1 -1 </nowiki>&gt;
| |<nowiki> | 0 -1 2 -1 1 -1 </nowiki>&gt;
| style="text-align:center;" | 275/273
| style="text-align:center;" | 275/273
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|-
|-
| | septimal semicomma, octagar
| | septimal semicomma, octagar
|Rurutriyo
|rry<sup>3</sup>
| |<nowiki> | 5 -4 3 -2 </nowiki>&gt;
| |<nowiki> | 5 -4 3 -2 </nowiki>&gt;
| style="text-align:center;" | 4000/3969
| style="text-align:center;" | 4000/3969
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|-
|-
| | minor BP diesis, sensamagic
| | minor BP diesis, sensamagic
|Zozoyo
|zzy
| |<nowiki> | 0 -5 1 2 </nowiki>&gt;
| |<nowiki> | 0 -5 1 2 </nowiki>&gt;
| style="text-align:center;" | 245/243
| style="text-align:center;" | 245/243
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|-
|-
| | secorian
| | secorian
| |<nowiki> | 12 -7 0 1 0 -1/1 </nowiki>&gt;
|Sathuzo
|s3uz
| |<nowiki> | 12 -7 0 1 0 -1 </nowiki>&gt;
| style="text-align:center;" | 28672/28431
| style="text-align:center;" | 28672/28431
| | 14.61
| | 14.61
|-
|-
| | mirwomo comma
| | mirwomo comma
|Labizoyo
|Lzzyy
| |<nowiki> | -15 3 2 2 </nowiki>&gt;
| |<nowiki> | -15 3 2 2 </nowiki>&gt;
| style="text-align:center;" | 33075/32768
| style="text-align:center;" | 33075/32768
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|-
|-
| | vicesimotertial comma
| | vicesimotertial comma
|Sa-twenty-tho
|s23o
| |<nowiki> | 5 -6 0 0 0 0 0 0 1 </nowiki>&gt;
| |<nowiki> | 5 -6 0 0 0 0 0 0 1 </nowiki>&gt;
| style="text-align:center;" | 736/729
| style="text-align:center;" | 736/729
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|-
|-
| | small tridecimal comma, animist
| | small tridecimal comma, animist
|Thuzoyo
|3uzy
| |<nowiki> | -3 1 1 1 0 -1 </nowiki>&gt;
| |<nowiki> | -3 1 1 1 0 -1 </nowiki>&gt;
| style="text-align:center;" | 105/104
| style="text-align:center;" | 105/104
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|-
|-
| | hemimin
| | hemimin
|Trilu-azo
|1u<sup>3</sup>z
| |<nowiki> | 6 1 0 1 -3 </nowiki>&gt;
| |<nowiki> | 6 1 0 1 -3 </nowiki>&gt;
| style="text-align:center;" | 1344/1331
| style="text-align:center;" | 1344/1331
Line 244: Line 333:
|-
|-
| | Ptolemy's comma, ptolemisma
| | Ptolemy's comma, ptolemisma
|Luyoyo
|1uyy
| |<nowiki> | 2 -2 2 0 -1 </nowiki>&gt;
| |<nowiki> | 2 -2 2 0 -1 </nowiki>&gt;
| style="text-align:center;" | 100/99
| style="text-align:center;" | 100/99
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|-
|-
| | '41-tone' comma
| | '41-tone' comma
|Wa-41
|41-edo
| |<nowiki> | 65 -41 </nowiki>&gt;
| |<nowiki> | 65 -41 </nowiki>&gt;
| style="text-align:center;" |  
| style="text-align:center;" |  
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|-
|-
| | tolerma
| | tolerma
|Sazoyoyo
|szyy
| |<nowiki> | 10 -11 2 1 </nowiki>&gt;
| |<nowiki> | 10 -11 2 1 </nowiki>&gt;
| style="text-align:center;" |  
| style="text-align:center;" |  
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|-
|-
| | major BP diesis, gariboh
| | major BP diesis, gariboh
|Triru-aquinyo
|r<sup>3</sup>y<sup>5</sup>
| |<nowiki> | 0 -2 5 -3 </nowiki>&gt;
| |<nowiki> | 0 -2 5 -3 </nowiki>&gt;
| style="text-align:center;" | 3125/3087
| style="text-align:center;" | 3125/3087
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|-
|-
| | cassacot
| | cassacot
|Luluzozoyo
|1uuzzy
| |<nowiki> | -1 0 1 2 -2 </nowiki>&gt;
| |<nowiki> | -1 0 1 2 -2 </nowiki>&gt;
| style="text-align:center;" | 245/242
| style="text-align:center;" | 245/242
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|-
|-
| | keema
| | keema
|Zotriyo
|zy<sup>3</sup>
| |<nowiki> | -5 -3 3 1 </nowiki>&gt;
| |<nowiki> | -5 -3 3 1 </nowiki>&gt;
| style="text-align:center;" | 875/864
| style="text-align:center;" | 875/864
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|-
|-
| | blackjackisma
| | blackjackisma
|Lasepru-aquadbiyo
|Lr<sup>7</sup>y<sup>8</sup>
| |<nowiki> | -10 7 8 -7 </nowiki>&gt;
| |<nowiki> | -10 7 8 -7 </nowiki>&gt;
| style="text-align:center;" |  
| style="text-align:center;" |  
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|-
|-
| | roda
| | roda
|Sasa-triyo
|ssy<sup>3</sup>
| |<nowiki> | 20 -17 3 </nowiki>&gt;
| |<nowiki> | 20 -17 3 </nowiki>&gt;
| style="text-align:center;" |  
| style="text-align:center;" |  
Line 284: Line 389:
|-
|-
| | minimal diesis, tetracot comma
| | minimal diesis, tetracot comma
|Saquadyo
|sy<sup>4</sup>
| |<nowiki> | 5 -9 4 </nowiki>&gt;
| |<nowiki> | 5 -9 4 </nowiki>&gt;
| style="text-align:center;" | 20000/19683
| style="text-align:center;" | 20000/19683
Line 289: Line 396:
|-
|-
| | small diesis, magic comma
| | small diesis, magic comma
|Laquinyo
|Ly<sup>5</sup>
| |<nowiki> | -10 -1 5 </nowiki>&gt;
| |<nowiki> | -10 -1 5 </nowiki>&gt;
| style="text-align:center;" | 3125/3072
| style="text-align:center;" | 3125/3072
Line 294: Line 403:
|-
|-
| | thuja comma
| | thuja comma
|Saquinlu-ayo
|s1u<sup>5</sup>y
| |<nowiki> | 15 0 1 0 -5 </nowiki>&gt;
| |<nowiki> | 15 0 1 0 -5 </nowiki>&gt;
| style="text-align:center;" |  
| style="text-align:center;" |  
Line 299: Line 410:
|-
|-
| | Ampersand's comma
| | Ampersand's comma
|Lala-tribiyo
|LLy<sup>3</sup>
| |<nowiki> | -25 7 6 </nowiki>&gt;
| |<nowiki> | -25 7 6 </nowiki>&gt;
| style="text-align:center;" |  
| style="text-align:center;" |  
Line 304: Line 417:
|-
|-
| | great BP diesis
| | great BP diesis
|Rutribiyo
|ry<sup>6</sup>
| |<nowiki> | 0 -7 6 -1 </nowiki>&gt;
| |<nowiki> | 0 -7 6 -1 </nowiki>&gt;
| style="text-align:center;" | 15625/15309
| style="text-align:center;" | 15625/15309
Line 309: Line 424:
|-
|-
| | shibboleth
| | shibboleth
|Tritriyo
|y<sup>9</sup>
| |<nowiki> | -5 -10 9 </nowiki>&gt;
| |<nowiki> | -5 -10 9 </nowiki>&gt;
| style="text-align:center;" |  
| style="text-align:center;" |  
Line 446: Line 563:
|310.24
|310.24
|374.63 (176.A2<sub>16</sub>)
|374.63 (176.A2<sub>16</sub>)
| | [[32/27|32/27]]
| | [[32/27|32/27]], [[13/11]]
| style="text-align:center;" | m3
| style="text-align:center;" | m3
| style="text-align:center;" | F
| style="text-align:center;" | F
Line 512: Line 629:
|496.39
|496.39
|599.415 (257.6A<sub>16</sub>)
|599.415 (257.6A<sub>16</sub>)
| | [[21/16|21/16]]
| | [[21/16|21/16]], [[13/10]]
| style="text-align:center;" | v4
| style="text-align:center;" | v4
| style="text-align:center;" | vG
| style="text-align:center;" | vG
Line 611: Line 728:
|775.61
|775.61
|936.585 (3A8.96<sub>16</sub>)
|936.585 (3A8.96<sub>16</sub>)
| | [[32/21|32/21]]
| | [[32/21|32/21]], [[20/13]]
| style="text-align:center;" | ^5
| style="text-align:center;" | ^5
| style="text-align:center;" | ^A
| style="text-align:center;" | ^A
Line 890: Line 1,007:
| style="text-align:center;" | C upmajor or C up
| style="text-align:center;" | C upmajor or C up
|}
|}
0-10-20 = D F Ab = Ddim = "D dim"
0-10-20 = D F Ab = Ddim = D dim


0-10-21 = D F ^Ab = Ddim(^5) = "D dim up-five"
0-10-21 = D F ^Ab = Ddim(^5) = D dim up-five


0-10-22 = D F vvA = Dm(~5) = "D minor mid-five"
0-10-22 = D F vvA = Dm(~5) = D minor mid-five


0-10-23 = D F vA = Dm(v5) = "D minor down-five"
0-10-23 = D F vA = Dm(v5) = D minor down-five


0-10-24 = D F A = Dm = "D minor"
0-10-24 = D F A = Dm = D minor


0-14-24 = D F# A = D = "D" or "D major"
0-14-24 = D F# A = D = D or D major


0-14-25 = D F# ^A = D(^5) = "D up-five"
0-14-25 = D F# ^A = D(^5) = D up-five


0-14-26 = D F# ^^A = D(^^5) = "D double-up-five", or possibly Daug(vv5)
0-14-26 = D F# ^^A = D(^^5) = D double-up-five, or possibly Daug(vv5)


0-14-27 = D F# vA# = Daug(v5) = "D aug down-five"
0-14-27 = D F# vA# = Daug(v5) = D aug down-five


0-14-28 = D F# A# is Daug = "D aug"
0-14-28 = D F# A# is Daug = D aug


etc.
etc.
Line 914: Line 1,031:
For a more complete list, see [[Ups_and_Downs_Notation#Chord names in other EDOs|Ups and Downs Notation - Chord names in other EDOs]].
For a more complete list, see [[Ups_and_Downs_Notation#Chord names in other EDOs|Ups and Downs Notation - Chord names in other EDOs]].


This chart shows 41-edo in a 12-edo-friendly format. Excellent for introducing 41-edo to musicians unfamiliar with xen. There are 12 "-ish" categories. The 6 mid intervals are uncategorized, since they are all so far from 12edo.
This chart shows 41-edo in a 12-edo-friendly format. Excellent for introducing 41-edo to musicians unfamiliar with xen. There are 12 "-ish" categories, where "-ish" means ±1 edostep. The 6 mid intervals are uncategorized, since they are all so far from 12edo. The two innermost and two outermost intervals on the spiral are duplicates.


[[File:41-edo spiral.png|673x673px]]
[[File:41-edo spiral.png|673x673px]]
Line 926: Line 1,043:
| | '''Error (abs., in [[cent|cents]])'''
| | '''Error (abs., in [[cent|cents]])'''
|-
|-
| style="text-align:center;" | [[4/3|4/3]], [[3/2|3/2]]
| style="text-align:center;" | '''[[4/3|4/3]], [[3/2|3/2]]'''
| style="text-align:center;" | 0.484
| style="text-align:center;" | '''0.484'''
|-
|-
| style="text-align:center;" | [[9/8|9/8]], [[16/9|16/9]]
| style="text-align:center;" | [[9/8|9/8]], [[16/9|16/9]]
Line 938: Line 1,055:
| style="text-align:center;" | 2.854
| style="text-align:center;" | 2.854
|-
|-
| style="text-align:center;" | [[8/7|8/7]], [[7/4|7/4]]
| style="text-align:center;" | '''[[8/7|8/7]], [[7/4|7/4]]'''
| style="text-align:center;" | 2.972
| style="text-align:center;" | '''2.972'''
|-
|-
| style="text-align:center;" | [[7/6|7/6]], [[12/7|12/7]]
| style="text-align:center;" | [[7/6|7/6]], [[12/7|12/7]]
Line 956: Line 1,073:
| style="text-align:center;" | 4.296
| style="text-align:center;" | 4.296
|-
|-
| style="text-align:center;" | [[11/8|11/8]], [[16/11|16/11]]
| style="text-align:center;" | '''[[11/8|11/8]], [[16/11|16/11]]'''
| style="text-align:center;" | 4.780
| style="text-align:center;" | '''4.780'''
|-
|-
| style="text-align:center;" | [[16/15|16/15]], [[15/8|15/8]]
| style="text-align:center;" | [[16/15|16/15]], [[15/8|15/8]]
| style="text-align:center;" | 5.342
| style="text-align:center;" | 5.342
|-
|-
| style="text-align:center;" | [[5/4|5/4]], [[8/5|8/5]]
| style="text-align:center;" | '''[[5/4|5/4]], [[8/5|8/5]]'''
| style="text-align:center;" | 5.826
| style="text-align:center;" | '''5.826'''
|-
|-
| style="text-align:center;" | [[6/5|6/5]], [[5/3|5/3]]
| style="text-align:center;" | [[6/5|6/5]], [[5/3|5/3]]
Line 980: Line 1,097:
| style="text-align:center;" | 7.769
| style="text-align:center;" | 7.769
|-
|-
| style="text-align:center;" | [[16/13|16/13]], [[13/8|13/8]]
| style="text-align:center;" | '''[[16/13|16/13]], [[13/8|13/8]]'''
| style="text-align:center;" | 8.253
| style="text-align:center;" | '''8.253'''
|-
|-
| style="text-align:center;" | [[15/11|15/11]], [[22/15|22/15]]
| style="text-align:center;" | [[15/11|15/11]], [[22/15|22/15]]
Line 1,008: Line 1,125:
''41-EDO Classical guitar, by Ron Sword.''
''41-EDO Classical guitar, by Ron Sword.''


The [http://tallkite.com/misc_files/The%20Kite%20Tuning.pdf Kite Tuning] is a guitar fretting using every other step of 41-edo, i.e. 41-ED4 or "20½-edo". However, the interval between two adjacent open strings is always an odd number of 41-edosteps. Thus each string only covers half of 41-edo, but the full edo can be found on every pair of adjacent strings.The Kite Tuning makes 41-edo about as playable as 19-edo or 22-edo, although there are certain trade-offs.
The [[The Kite Guitar|Kite Guitar]] (see also [http://tallkite.com/misc_files/The%20Kite%20Tuning.pdf Kite Tuning]) is a guitar fretting using every other step of 41-edo, i.e. 41-ED4 or "20½-edo". However, the interval between two adjacent open strings is always an odd number of 41-edosteps. Thus each string only covers half of 41-edo, but the full edo can be found on every pair of adjacent strings.The Kite Tuning makes 41-edo about as playable as 19-edo or 22-edo, although there are certain trade-offs.


[[File:The Kite Tuning smaller.jpg|1122x1122px]]
[[File:The Kite Tuning smaller.jpg|1122x1122px]]
Retrieved from "https://en.xen.wiki/w/41edo"