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<span style="display: block; text-align: right;">[[:de:41edo|Deutsch]]</span>
<span style="display: block; text-align: right;">[[:de:41edo|Deutsch]]</span>
__FORCETOC__
__FORCETOC__
-----
-----


=Introduction=
=Introduction=
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]]'' </sup>[[#cite_note-1|[1]]]</sup> , </sup>[[#cite_note-2|[2]]]</sup> , </sup>[[#cite_note-3|[3]]]</sup> the ''[[Magic_family|Magic temperament]]'' </sup>[[#cite_note-4|[4]]]</sup> and the superkleismic (41&amp;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&amp;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. (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).
Line 23: Line 24:
|-
|-
| | odiheim
| | odiheim
| | | -1 2 -4 5 -2 &gt;
| |<nowiki> | -1 2 -4 5 -2 </nowiki>&gt;
| style="text-align:center;" |  
| style="text-align:center;" |  
| | 0.15
| | 0.15
|-
|-
| | harmonisma
| | harmonisma
| | | 3 -2 0 -1 3 -2 &gt;
| |<nowiki> | 3 -2 0 -1 3 -2 </nowiki>&gt;
| style="text-align:center;" | 10648/10647
| style="text-align:center;" | 10648/10647
| | 0.16
| | 0.16
|-
|-
| | tridecimal schisma, Sagittal schismina
| | tridecimal schisma, Sagittal schismina
| | | 12 -2 -1 -1 0 -1/1 &gt;
| |<nowiki> | 12 -2 -1 -1 0 -1/1 </nowiki>&gt;
| style="text-align:center;" | 4096/4095
| style="text-align:center;" | 4096/4095
| | 0.42
| | 0.42
|-
|-
| | Lehmerisma
| | Lehmerisma
| | | -4 -3 2 -1 2 &gt;
| |<nowiki> | -4 -3 2 -1 2 </nowiki>&gt;
| style="text-align:center;" | 3025/3024
| style="text-align:center;" | 3025/3024
| | 0.57
| | 0.57
|-
|-
| | Breedsma
| | Breedsma
| | | -5 -1 -2 4 &gt;
| |<nowiki> | -5 -1 -2 4 </nowiki>&gt;
| style="text-align:center;" | 2401/2400
| style="text-align:center;" | 2401/2400
| | 0.72
| | 0.72
|-
|-
| | Eratosthenes' comma
| | Eratosthenes' comma
| | | 6 -5 -1 0 0 0 0 1 &gt;
| |<nowiki> | 6 -5 -1 0 0 0 0 1 </nowiki>&gt;
| style="text-align:center;" | 1216/1215
| style="text-align:center;" | 1216/1215
| | 1.42
| | 1.42
|-
|-
| | schisma
| | schisma
| | | -15 8 1 &gt;
| |<nowiki> | -15 8 1 </nowiki>&gt;
| style="text-align:center;" | 32805/32768
| style="text-align:center;" | 32805/32768
| | 1.95
| | 1.95
|-
|-
| | squbema
| | squbema
| | | -3 6 0 -1 0 -1 &gt;
| |<nowiki> | -3 6 0 -1 0 -1 </nowiki>&gt;
| style="text-align:center;" | 729/728
| style="text-align:center;" | 729/728
| | 2.38
| | 2.38
|-
|-
| | septendecimal bridge comma
| | septendecimal bridge comma
| | | -1 -1 1 -1 1 1 -1 &gt;
| |<nowiki> | -1 -1 1 -1 1 1 -1 </nowiki>&gt;
| style="text-align:center;" | 715/714
| style="text-align:center;" | 715/714
| | 2.42
| | 2.42
|-
|-
| | Swets' comma, swetisma
| | Swets' comma, swetisma
| | | 2 3 1 -2 -1 &gt;
| |<nowiki> | 2 3 1 -2 -1 </nowiki>&gt;
| style="text-align:center;" | 540/539
| style="text-align:center;" | 540/539
| | 3.21
| | 3.21
|-
|-
| | undevicesimal comma, Boethius' comma
| | undevicesimal comma, Boethius' comma
| | | -9 3 0 0 0 0 0 1 &gt;
| |<nowiki> | -9 3 0 0 0 0 0 1 </nowiki>&gt;
| style="text-align:center;" | 513/512
| style="text-align:center;" | 513/512
| | 3.38
| | 3.38
|-
|-
| | moctdel
| | moctdel
| | | -2 0 3 -3 1 &gt;
| |<nowiki> | -2 0 3 -3 1 </nowiki>&gt;
| style="text-align:center;" | 1375/1372
| style="text-align:center;" | 1375/1372
| | 3.78
| | 3.78
|-
|-
| | Beta 2, septimal schisma, garischisma
| | Beta 2, septimal schisma, garischisma
| | | 25 -14 0 -1 &gt;
| |<nowiki> | 25 -14 0 -1 </nowiki>&gt;
| style="text-align:center;" |  
| style="text-align:center;" |  
| | 3.80
| | 3.80
|-
|-
| | Werckmeister's undecimal septenarian schisma, werckisma
| | Werckmeister's undecimal septenarian schisma, werckisma
| | | -3 2 -1 2 -1 &gt;
| |<nowiki> | -3 2 -1 2 -1 </nowiki>&gt;
| style="text-align:center;" | 441/440
| style="text-align:center;" | 441/440
| | 3.93
| | 3.93
|-
|-
| | cuthbert
| | cuthbert
| | | 0 0 -1 1 2 -2 &gt;
| |<nowiki> | 0 0 -1 1 2 -2 </nowiki>&gt;
| style="text-align:center;" | 847/845
| style="text-align:center;" | 847/845
| | 4.09
| | 4.09
|-
|-
| | undecimal kleisma, keenanisma
| | undecimal kleisma, keenanisma
| | | -7 -1 1 1 1 &gt;
| |<nowiki> | -7 -1 1 1 1 </nowiki>&gt;
| style="text-align:center;" | 385/384
| style="text-align:center;" | 385/384
| | 4.50
| | 4.50
|-
|-
| | gentle comma
| | gentle comma
| | | 2 -1 0 1 -2 1 &gt;
| |<nowiki> | 2 -1 0 1 -2 1 </nowiki>&gt;
| style="text-align:center;" | 364/363
| style="text-align:center;" | 364/363
| | 4.76
| | 4.76
|-
|-
| | minthma
| | minthma
| | | 5 -3 0 0 1 -1 &gt;
| |<nowiki> | 5 -3 0 0 1 -1 </nowiki>&gt;
| style="text-align:center;" | 352/351
| style="text-align:center;" | 352/351
| | 4.93
| | 4.93
|-
|-
| | marveltwin
| | marveltwin
| | | -2 -4 2 0 0 1 &gt;
| |<nowiki> | -2 -4 2 0 0 1 </nowiki>&gt;
| style="text-align:center;" | 325/324
| style="text-align:center;" | 325/324
| | 5.34
| | 5.34
|-
|-
| | Beta 5, Garibaldi comma, hemifamity
| | Beta 5, Garibaldi comma, hemifamity
| | | 10 -6 1 -1 &gt;
| |<nowiki> | 10 -6 1 -1 </nowiki>&gt;
| style="text-align:center;" | 5120/5103
| style="text-align:center;" | 5120/5103
| | 5.76
| | 5.76
|-
|-
| | hemimage
| | hemimage
| | | 5 -7 -1 3 &gt;
| |<nowiki> | 5 -7 -1 3 </nowiki>&gt;
| style="text-align:center;" | 10976/10935
| style="text-align:center;" | 10976/10935
| | 6.48
| | 6.48
|-
|-
| | septendecimal kleisma
| | septendecimal kleisma
| | | 8 -1 -1 0 0 0 -1 &gt;
| |<nowiki> | 8 -1 -1 0 0 0 -1 </nowiki>&gt;
| style="text-align:center;" | 256/255
| style="text-align:center;" | 256/255
| | 6.78
| | 6.78
|-
|-
| | small BP diesis, mirkwai
| | small BP diesis, mirkwai
| | | 0 3 4 -5 &gt;
| |<nowiki> | 0 3 4 -5 </nowiki>&gt;
| style="text-align:center;" | 16875/16807
| style="text-align:center;" | 16875/16807
| | 6.99
| | 6.99
|-
|-
| | neutral third comma, rastma
| | neutral third comma, rastma
| | | -1 5 0 0 -2 &gt;
| |<nowiki> | -1 5 0 0 -2 </nowiki>&gt;
| style="text-align:center;" | 243/242
| style="text-align:center;" | 243/242
| | 7.14
| | 7.14
|-
|-
| | kestrel comma
| | kestrel comma
| | | 2 3 0 -1 1 -2 &gt;
| |<nowiki> | 2 3 0 -1 1 -2 </nowiki>&gt;
| style="text-align:center;" | 1188/1183
| style="text-align:center;" | 1188/1183
| | 7.30
| | 7.30
|-
|-
| | septimal kleisma, marvel comma
| | septimal kleisma, marvel comma
| | | -5 2 2 -1 &gt;
| |<nowiki> | -5 2 2 -1 </nowiki>&gt;
| style="text-align:center;" | 225/224
| style="text-align:center;" | 225/224
| | 7.71
| | 7.71
|-
|-
| | huntma
| | huntma
| | | 7 0 1 -2 0 -1 &gt;
| |<nowiki> | 7 0 1 -2 0 -1 </nowiki>&gt;
| style="text-align:center;" | 640/637
| style="text-align:center;" | 640/637
| | 8.13
| | 8.13
|-
|-
| | spleen comma
| | spleen comma
| | | 1 1 1 1 -1 0 0 -1 &gt;
| |<nowiki> | 1 1 1 1 -1 0 0 -1 </nowiki>&gt;
| style="text-align:center;" | 210/209
| style="text-align:center;" | 210/209
| | 8.26
| | 8.26
|-
|-
| | orgonisma
| | orgonisma
| | | 16 0 0 -2 -3 &gt;
| |<nowiki> | 16 0 0 -2 -3 </nowiki>&gt;
| style="text-align:center;" | 65536/65219
| style="text-align:center;" | 65536/65219
| | 8.39
| | 8.39
|-
|-
| | gamelan residue, gamelisma
| | gamelan residue, gamelisma
| | | -10 1 0 3 &gt;
| |<nowiki> | -10 1 0 3 </nowiki>&gt;
| style="text-align:center;" | 1029/1024
| style="text-align:center;" | 1029/1024
| | 8.43
| | 8.43
|-
|-
| | septendecimal comma
| | septendecimal comma
| | | -7 7 0 0 0 0 -1 &gt;
| |<nowiki> | -7 7 0 0 0 0 -1 </nowiki>&gt;
| style="text-align:center;" | 2187/2176
| style="text-align:center;" | 2187/2176
| | 8.73
| | 8.73
|-
|-
| | mynucuma
| | mynucuma
| | | 2 -1 -1 2 0 -1 &gt;
| |<nowiki> | 2 -1 -1 2 0 -1 </nowiki>&gt;
| style="text-align:center;" | 196/195
| style="text-align:center;" | 196/195
| | 8.86
| | 8.86
|-
|-
| | quince
| | quince
| | | -15 0 -2 7 &gt;
| |<nowiki> | -15 0 -2 7 </nowiki>&gt;
| style="text-align:center;" |  
| style="text-align:center;" |  
| | 9.15
| | 9.15
|-
|-
| | undecimal semicomma, pentacircle (minthma * gentle)
| | undecimal semicomma, pentacircle (minthma * gentle)
| | | 7 -4 0 1 -1 &gt;
| |<nowiki> | 7 -4 0 1 -1 </nowiki>&gt;
| style="text-align:center;" | 896/891
| style="text-align:center;" | 896/891
| | 9.69
| | 9.69
|-
|-
| | 29th-partial chroma
| | 29th-partial chroma
| | | -4 -2 1 0 0 0 0 0 0 1 &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
| | 11.98
| | 11.98
|-
|-
| | grossma
| | grossma
| | | 4 2 0 0 -1 -1 &gt;
| |<nowiki> | 4 2 0 0 -1 -1 </nowiki>&gt;
| style="text-align:center;" | 144/143
| style="text-align:center;" | 144/143
| | 12.06
| | 12.06
|-
|-
| | gassorma
| | gassorma
| | | 0 -1 2 -1 1 -1 &gt;
| |<nowiki> | 0 -1 2 -1 1 -1 </nowiki>&gt;
| style="text-align:center;" | 275/273
| style="text-align:center;" | 275/273
| | 12.64
| | 12.64
|-
|-
| | septimal semicomma, octagar
| | septimal semicomma, octagar
| | | 5 -4 3 -2 &gt;
| |<nowiki> | 5 -4 3 -2 </nowiki>&gt;
| style="text-align:center;" | 4000/3969
| style="text-align:center;" | 4000/3969
| | 13.47
| | 13.47
|-
|-
| | minor BP diesis, sensamagic
| | minor BP diesis, sensamagic
| | | 0 -5 1 2 &gt;
| |<nowiki> | 0 -5 1 2 </nowiki>&gt;
| style="text-align:center;" | 245/243
| style="text-align:center;" | 245/243
| | 14.19
| | 14.19
|-
|-
| | secorian
| | secorian
| | | 12 -7 0 1 0 -1/1 &gt;
| |<nowiki> | 12 -7 0 1 0 -1/1 </nowiki>&gt;
| style="text-align:center;" | 28672/28431
| style="text-align:center;" | 28672/28431
| | 14.61
| | 14.61
|-
|-
| | mirwomo comma
| | mirwomo comma
| | | -15 3 2 2 &gt;
| |<nowiki> | -15 3 2 2 </nowiki>&gt;
| style="text-align:center;" | 33075/32768
| style="text-align:center;" | 33075/32768
| | 16.14
| | 16.14
|-
|-
| | vicesimotertial comma
| | vicesimotertial comma
| | | 5 -6 0 0 0 0 0 0 1 &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
| | 16.54
| | 16.54
|-
|-
| | small tridecimal comma, animist
| | small tridecimal comma, animist
| | | -3 1 1 1 0 -1 &gt;
| |<nowiki> | -3 1 1 1 0 -1 </nowiki>&gt;
| style="text-align:center;" | 105/104
| style="text-align:center;" | 105/104
| | 16.57
| | 16.57
|-
|-
| | hemimin
| | hemimin
| | | 6 1 0 1 -3 &gt;
| |<nowiki> | 6 1 0 1 -3 </nowiki>&gt;
| style="text-align:center;" | 1344/1331
| style="text-align:center;" | 1344/1331
| | 16.83
| | 16.83
|-
|-
| | Ptolemy's comma, ptolemisma
| | Ptolemy's comma, ptolemisma
| | | 2 -2 2 0 -1 &gt;
| |<nowiki> | 2 -2 2 0 -1 </nowiki>&gt;
| style="text-align:center;" | 100/99
| style="text-align:center;" | 100/99
| | 17.40
| | 17.40
|-
|-
| | '41-tone' comma
| | '41-tone' comma
| | | 65 -41 &gt;
| |<nowiki> | 65 -41 </nowiki>&gt;
| style="text-align:center;" |  
| style="text-align:center;" |  
| | 19.84
| | 19.84
|-
|-
| | tolerma
| | tolerma
| | | 10 -11 2 1 &gt;
| |<nowiki> | 10 -11 2 1 </nowiki>&gt;
| style="text-align:center;" |  
| style="text-align:center;" |  
| | 19.95
| | 19.95
|-
|-
| | major BP diesis, gariboh
| | major BP diesis, gariboh
| | | 0 -2 5 -3 &gt;
| |<nowiki> | 0 -2 5 -3 </nowiki>&gt;
| style="text-align:center;" | 3125/3087
| style="text-align:center;" | 3125/3087
| | 21.18
| | 21.18
|-
|-
| | cassacot
| | cassacot
| | | -1 0 1 2 -2 &gt;
| |<nowiki> | -1 0 1 2 -2 </nowiki>&gt;
| style="text-align:center;" | 245/242
| style="text-align:center;" | 245/242
| | 21.33
| | 21.33
|-
|-
| | keema
| | keema
| | | -5 -3 3 1 &gt;
| |<nowiki> | -5 -3 3 1 </nowiki>&gt;
| style="text-align:center;" | 875/864
| style="text-align:center;" | 875/864
| | 21.90
| | 21.90
|-
|-
| | blackjackisma
| | blackjackisma
| | | -10 7 8 -7 &gt;
| |<nowiki> | -10 7 8 -7 </nowiki>&gt;
| style="text-align:center;" |  
| style="text-align:center;" |  
| | 22.41
| | 22.41
|-
|-
| | roda
| | roda
| | | 20 -17 3 &gt;
| |<nowiki> | 20 -17 3 </nowiki>&gt;
| style="text-align:center;" |  
| style="text-align:center;" |  
| | 25.71
| | 25.71
|-
|-
| | minimal diesis, tetracot comma
| | minimal diesis, tetracot comma
| | | 5 -9 4 &gt;
| |<nowiki> | 5 -9 4 </nowiki>&gt;
| style="text-align:center;" | 20000/19683
| style="text-align:center;" | 20000/19683
| | 27.66
| | 27.66
|-
|-
| | small diesis, magic comma
| | small diesis, magic comma
| | | -10 -1 5 &gt;
| |<nowiki> | -10 -1 5 </nowiki>&gt;
| style="text-align:center;" | 3125/3072
| style="text-align:center;" | 3125/3072
| | 29.61
| | 29.61
|-
|-
| | thuja comma
| | thuja comma
| | | 15 0 1 0 -5 &gt;
| |<nowiki> | 15 0 1 0 -5 </nowiki>&gt;
| style="text-align:center;" |  
| style="text-align:center;" |  
| | 29.72
| | 29.72
|-
|-
| | Ampersand's comma
| | Ampersand's comma
| | | -25 7 6 &gt;
| |<nowiki> | -25 7 6 </nowiki>&gt;
| style="text-align:center;" |  
| style="text-align:center;" |  
| | 31.57
| | 31.57
|-
|-
| | great BP diesis
| | great BP diesis
| | | 0 -7 6 -1 &gt;
| |<nowiki> | 0 -7 6 -1 </nowiki>&gt;
| style="text-align:center;" | 15625/15309
| style="text-align:center;" | 15625/15309
| | 35.37
| | 35.37
|-
|-
| | shibboleth
| | shibboleth
| | | -5 -10 9 &gt;
| |<nowiki> | -5 -10 9 </nowiki>&gt;
| style="text-align:center;" |  
| style="text-align:center;" |  
| | 57.27
| | 57.27
Line 765: Line 766:
|-
|-
! | quality
! | quality
! | color
! | [[Kite's color notation|color]]
! | monzo format
! | monzo format
! | examples
! | examples
|-
|-
| style="text-align:center;" | downminor
| style="text-align:center;" | downminor
| style="text-align:center;" | blue
| style="text-align:center;" | zo
| style="text-align:center;" | {a, b, 0, 1}
| style="text-align:center;" | {a, b, 0, 1}
| style="text-align:center;" | 7/6, 7/4
| style="text-align:center;" | 7/6, 7/4
|-
|-
| style="text-align:center;" | minor
| style="text-align:center;" | minor
| style="text-align:center;" | fourthward white
| style="text-align:center;" | fourthward wa
| style="text-align:center;" | {a, b}, b &lt; -1
| style="text-align:center;" | {a, b}, b &lt; -1
| style="text-align:center;" | 32/27, 16/9
| style="text-align:center;" | 32/27, 16/9
|-
|-
| style="text-align:center;" | upminor
| style="text-align:center;" | upminor
| style="text-align:center;" | green
| style="text-align:center;" | gu
| style="text-align:center;" | {a, b, -1}
| style="text-align:center;" | {a, b, -1}
| style="text-align:center;" | 6/5, 9/5
| style="text-align:center;" | 6/5, 9/5
|-
|-
| style="text-align:center;" | mid
| style="text-align:center;" | mid
| style="text-align:center;" | jade
| style="text-align:center;" | lova
| style="text-align:center;" | {a, b, 0, 0, 1}
| style="text-align:center;" | {a, b, 0, 0, 1}
| style="text-align:center;" | 11/9, 11/6
| style="text-align:center;" | 11/9, 11/6
|-
|-
| style="text-align:center;" | "
| style="text-align:center;" | "
| style="text-align:center;" | amber
| style="text-align:center;" | lu
| style="text-align:center;" | {a, b, 0, 0, -1}
| style="text-align:center;" | {a, b, 0, 0, -1}
| style="text-align:center;" | 12/11, 18/11
| style="text-align:center;" | 12/11, 18/11
|-
|-
| style="text-align:center;" | downmajor
| style="text-align:center;" | downmajor
| style="text-align:center;" | yellow
| style="text-align:center;" | yo
| style="text-align:center;" | {a, b, 1}
| style="text-align:center;" | {a, b, 1}
| style="text-align:center;" | 5/4, 5/3
| style="text-align:center;" | 5/4, 5/3
|-
|-
| style="text-align:center;" | major
| style="text-align:center;" | major
| style="text-align:center;" | fifthward white
| style="text-align:center;" | fifthward wa
| style="text-align:center;" | {a, b}, b &gt; 1
| style="text-align:center;" | {a, b}, b &gt; 1
| style="text-align:center;" | 9/8, 27/16
| style="text-align:center;" | 9/8, 27/16
|-
|-
| style="text-align:center;" | upmajor
| style="text-align:center;" | upmajor
| style="text-align:center;" | red
| style="text-align:center;" | ru
| style="text-align:center;" | {a, b, 0, -1}
| style="text-align:center;" | {a, b, 0, -1}
| style="text-align:center;" | 9/7, 12/7
| style="text-align:center;" | 9/7, 12/7
|}
|}
All 41edo chords can be named using ups and downs. Here are the blue, green, jade, yellow and red triads:
All 41edo chords can be named using ups and downs. Here are the zo, gu, lova, yo and ru triads:


{| class="wikitable"
{| class="wikitable"
|-
|-
! | color of the 3rd
! | [[Kite's color notation|color of the 3rd]]
! | JI chord
! | JI chord
! | notes as edosteps
! | notes as edosteps
Line 820: Line 821:
! | spoken name
! | spoken name
|-
|-
| style="text-align:center;" | blue
| style="text-align:center;" | zo
| style="text-align:center;" | 6:7:9
| style="text-align:center;" | 6:7:9
| style="text-align:center;" | 0-9-24
| style="text-align:center;" | 0-9-24
Line 827: Line 828:
| style="text-align:center;" | C downminor
| style="text-align:center;" | C downminor
|-
|-
| style="text-align:center;" | green
| style="text-align:center;" | gu
| style="text-align:center;" | 10:12:15
| style="text-align:center;" | 10:12:15
| style="text-align:center;" | 0-11-24
| style="text-align:center;" | 0-11-24
Line 834: Line 835:
| style="text-align:center;" | C upminor
| style="text-align:center;" | C upminor
|-
|-
| style="text-align:center;" | jade
| style="text-align:center;" | lova
| style="text-align:center;" | 18:22:27
| style="text-align:center;" | 18:22:27
| style="text-align:center;" | 0-12-24
| style="text-align:center;" | 0-12-24
Line 841: Line 842:
| style="text-align:center;" | C mid
| style="text-align:center;" | C mid
|-
|-
| style="text-align:center;" | yellow
| style="text-align:center;" | yo
| style="text-align:center;" | 4:5:6
| style="text-align:center;" | 4:5:6
| style="text-align:center;" | 0-13-24
| style="text-align:center;" | 0-13-24
Line 848: Line 849:
| style="text-align:center;" | C downmajor or C dot down
| style="text-align:center;" | C downmajor or C dot down
|-
|-
| style="text-align:center;" | red
| style="text-align:center;" | ru
| style="text-align:center;" | 14:18:27
| style="text-align:center;" | 14:18:27
| style="text-align:center;" | 0-15-24
| style="text-align:center;" | 0-15-24
Line 969: Line 970:
''41-EDO Classical guitar, by Ron Sword.''
''41-EDO Classical guitar, by Ron Sword.''


A possible system to tune keyboards in 41EDO is discussed in [http://launch.groups.yahoo.com/group/tuning/message/74155 http://launch.groups.yahoo.com/group/tuning/message/74155].
A possible system to tune keyboards in 41EDO is discussed in http://launch.groups.yahoo.com/group/tuning/message/74155.


=Scales and modes=
=Scales and modes=
Line 1,544: Line 1,545:
<ul><li>[http://en.wikipedia.org/wiki/41_equal_temperament Wikipedia article on 41edo]</li><li>[[Magic22_as_srutis#magic22assrutis|Magic22 as srutis]] describes a possible use of 41edo for [[Indian|indian]] music.</li><li>see also [[Magic_family|Magic family]]</li><li>Sword, Ron. [http://www.ronsword.com "Tetracontamonophonic Scales for Guitar"]</li><li>Taylor, Cam. [https://drive.google.com/open?id=0B3wIGTmjY_VZYllwcHI0d3hEc3M Intervals, Scales and Chords in 41EDO], a work in progress using just intonation concepts and simplified Sagittal notation.</li></ul>
<ul><li>[http://en.wikipedia.org/wiki/41_equal_temperament Wikipedia article on 41edo]</li><li>[[Magic22_as_srutis#magic22assrutis|Magic22 as srutis]] describes a possible use of 41edo for [[Indian|indian]] music.</li><li>see also [[Magic_family|Magic family]]</li><li>Sword, Ron. [http://www.ronsword.com "Tetracontamonophonic Scales for Guitar"]</li><li>Taylor, Cam. [https://drive.google.com/open?id=0B3wIGTmjY_VZYllwcHI0d3hEc3M Intervals, Scales and Chords in 41EDO], a work in progress using just intonation concepts and simplified Sagittal notation.</li></ul>
-----
-----
<ol><li>[[#cite_ref-1|^]] [http://x31eq.com/schismic.htm "Schismic Temperaments"] at x31eq.com the website of [[Graham_Breed|Graham Breed]]</li><li>[[#cite_ref-2|^]] [http://x31eq.com/decimal_lattice.htm "Lattices with Decimal Notation"] at x31eq.com</li><li>[[#cite_ref-3|^]] [http://en.wikipedia.org/wiki/Schismatic_temperament Schismatic temperament]</li><li>[[#cite_ref-4|^]] [http://en.wikipedia.org/wiki/Magic_temperament Magic temperament]</li></ol>      [[Category:41edo]]
<ol><li>[[#cite_ref-1|^]] [http://x31eq.com/schismic.htm "Schismic Temperaments"] at x31eq.com the website of [[Graham_Breed|Graham Breed]]</li><li>[[#cite_ref-2|^]] [http://x31eq.com/decimal_lattice.htm "Lattices with Decimal Notation"] at x31eq.com</li><li>[[#cite_ref-3|^]] [http://en.wikipedia.org/wiki/Schismatic_temperament Schismatic temperament]</li><li>[[#cite_ref-4|^]] [http://en.wikipedia.org/wiki/Magic_temperament Magic temperament]</li></ol>       
[[Category:41edo]]
[[Category:edo]]
[[Category:edo]]
[[Category:magic]]
[[Category:magic]]
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