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[[2460edo]] has potential for a 41edo analog to [[Cent|cents]]. It divides the 41edo step into 60 equal parts, and 60 is a highly composite (a.k.a. antiprime) number, so it contains many other multiples of 41edo, including 205edo, and also contains [[12edo]] among other equal tunings. It also accurately represents [[14afdo|mode 14 of the harmonic series]], as it is consistent all the way up to the 27-odd-limit. This allows for precise detunings in a 41-tone framework to approximate pure just intonation more closely, especially for some higher harmonics. Its step of 1\2460 is called a ''mina''.
[[2460edo]] has potential for a 41edo analog to [[Cent|cents]]. It divides the 41edo step into 60 equal parts, and 60 is a highly composite (a.k.a. antiprime) number, so it contains many other multiples of 41edo, including 205edo, and also contains [[12edo]] among other equal tunings. It also accurately represents [[14afdo|mode 14 of the harmonic series]], as it is consistent all the way up to the 27-odd-limit. This allows for precise detunings in a 41-tone framework to approximate pure just intonation more closely, especially for some higher harmonics. Its step of 1\2460 is called a ''mina''.
See also [[countercomp family]] and [[41st-octave temperaments]] for temperaments that augment 41edo.


== Intervals ==
== Intervals ==
Line 42: Line 44:
! Cents
! Cents
! Approximate ratios*
! Approximate ratios*
! [[Kite's ups and downs notation|Ups and downs notation]]
! colspan="2" |[[Kite's ups and downs notation|Ups and downs notation]]
([[Enharmonic unisons in ups and downs notation|EUs]]: v<sup>4</sup>A1 and ^d2)
|-
|-
| 0
| 0
| 0.0
| 0.0
| [[1/1]]
| [[1/1]]
|P1
| {{UDnote|step=0}}
| {{UDnote|step=0}}
|-
|-
Line 52: Line 56:
| 29.3
| 29.3
| [[49/48]], [[50/49]], [[64/63]], [[81/80]]
| [[49/48]], [[50/49]], [[64/63]], [[81/80]]
|^1
| {{UDnote|step=1}}
| {{UDnote|step=1}}
|-
|-
Line 57: Line 62:
| 58.5
| 58.5
| [[25/24]], [[28/27]], [[33/32]], [[36/35]]
| [[25/24]], [[28/27]], [[33/32]], [[36/35]]
|^^1, vm2
| {{UDnote|step=2}}
| {{UDnote|step=2}}
|-
|-
Line 62: Line 68:
| 87.8
| 87.8
| [[19/18]], [[20/19]], [[21/20]], [[22/21]]
| [[19/18]], [[20/19]], [[21/20]], [[22/21]]
|vA1, m2
| {{UDnote|step=3}}
| {{UDnote|step=3}}
|-
|-
Line 67: Line 74:
| 117.1
| 117.1
| [[14/13]], [[15/14]], [[16/15]]
| [[14/13]], [[15/14]], [[16/15]]
|A1, ^m2
| {{UDnote|step=4}}
| {{UDnote|step=4}}
|-
|-
Line 72: Line 80:
| 146.3
| 146.3
| [[12/11]], [[13/12]]
| [[12/11]], [[13/12]]
|~2
| {{UDnote|step=5}}
| {{UDnote|step=5}}
|-
|-
Line 77: Line 86:
| 175.6
| 175.6
| [[10/9]], [[11/10]], [[21/19]]
| [[10/9]], [[11/10]], [[21/19]]
|vM2
| {{UDnote|step=6}}
| {{UDnote|step=6}}
|-
|-
Line 82: Line 92:
| 204.9
| 204.9
| [[9/8]]
| [[9/8]]
|M2
| {{UDnote|step=7}}
| {{UDnote|step=7}}
|-
|-
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| 234.1
| 234.1
| [[8/7]], [[15/13]]
| [[8/7]], [[15/13]]
|^M2
| {{UDnote|step=8}}
| {{UDnote|step=8}}
|-
|-
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| 263.4
| 263.4
| [[7/6]], [[22/19]]
| [[7/6]], [[22/19]]
|vm3
| {{UDnote|step=9}}
| {{UDnote|step=9}}
|-
|-
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| 292.7
| 292.7
| [[13/11]], [[19/16]], [[32/27]]
| [[13/11]], [[19/16]], [[32/27]]
|m3
| {{UDnote|step=10}}
| {{UDnote|step=10}}
|-
|-
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| 322.0
| 322.0
| [[6/5]]
| [[6/5]]
|^m3
| {{UDnote|step=11}}
| {{UDnote|step=11}}
|-
|-
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| 351.2
| 351.2
| [[11/9]], [[16/13]]
| [[11/9]], [[16/13]]
|~3
| {{UDnote|step=12}}
| {{UDnote|step=12}}
|-
|-
Line 112: Line 128:
| 380.5
| 380.5
| [[5/4]], [[26/21]]
| [[5/4]], [[26/21]]
|vM3
| {{UDnote|step=13}}
| {{UDnote|step=13}}
|-
|-
Line 117: Line 134:
| 409.8
| 409.8
| [[14/11]], [[19/15]], [[24/19]]
| [[14/11]], [[19/15]], [[24/19]]
|M3
| {{UDnote|step=14}}
| {{UDnote|step=14}}
|-
|-
Line 122: Line 140:
| 439.0
| 439.0
| [[9/7]], [[32/25]]
| [[9/7]], [[32/25]]
|^M3
| {{UDnote|step=15}}
| {{UDnote|step=15}}
|-
|-
Line 127: Line 146:
| 468.3
| 468.3
| [[21/16]], [[13/10]]
| [[21/16]], [[13/10]]
|v4
| {{UDnote|step=16}}
| {{UDnote|step=16}}
|-
|-
Line 132: Line 152:
| 497.6
| 497.6
| [[4/3]]
| [[4/3]]
|P4
| {{UDnote|step=17}}
| {{UDnote|step=17}}
|-
|-
Line 137: Line 158:
| 526.8
| 526.8
| [[15/11]], [[19/14]], [[27/20]]
| [[15/11]], [[19/14]], [[27/20]]
|^4
| {{UDnote|step=18}}
| {{UDnote|step=18}}
|-
|-
Line 142: Line 164:
| 556.1
| 556.1
| [[11/8]], [[18/13]], [[26/19]]
| [[11/8]], [[18/13]], [[26/19]]
|~4, vd5
| {{UDnote|step=19}}
| {{UDnote|step=19}}
|-
|-
Line 147: Line 170:
| 585.4
| 585.4
| [[7/5]], [[45/32]]
| [[7/5]], [[45/32]]
|vA4, d5
| {{UDnote|step=20}}
| {{UDnote|step=20}}
|-
|-
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| 614.6
| 614.6
| [[10/7]], [[64/45]]
| [[10/7]], [[64/45]]
|A4, ^d5
| {{UDnote|step=21}}
| {{UDnote|step=21}}
|-
|-
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| 643.9
| 643.9
| [[13/9]], [[16/11]], [[19/13]]
| [[13/9]], [[16/11]], [[19/13]]
|~5, ^A4
| {{UDnote|step=22}}
| {{UDnote|step=22}}
|-
|-
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| 673.2
| 673.2
| [[22/15]], [[28/19]], [[40/27]]
| [[22/15]], [[28/19]], [[40/27]]
|v5
| {{UDnote|step=23}}
| {{UDnote|step=23}}
|-
|-
Line 167: Line 194:
| 702.4
| 702.4
| [[3/2]]
| [[3/2]]
|P5
| {{UDnote|step=24}}
| {{UDnote|step=24}}
|-
|-
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| 731.7
| 731.7
| [[20/13]], [[32/21]]
| [[20/13]], [[32/21]]
|^5
| {{UDnote|step=25}}
| {{UDnote|step=25}}
|-
|-
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| 761.0
| 761.0
| [[14/9]], [[25/16]]
| [[14/9]], [[25/16]]
|vm6
| {{UDnote|step=26}}
| {{UDnote|step=26}}
|-
|-
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| 790.2
| 790.2
| [[11/7]], [[19/12]], [[30/19]]
| [[11/7]], [[19/12]], [[30/19]]
|m6
| {{UDnote|step=27}}
| {{UDnote|step=27}}
|-
|-
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| 819.5
| 819.5
| [[8/5]], [[21/13]]
| [[8/5]], [[21/13]]
|^m6
| {{UDnote|step=28}}
| {{UDnote|step=28}}
|-
|-
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| 848.8
| 848.8
| [[13/8]], [[18/11]]
| [[13/8]], [[18/11]]
|~6
| {{UDnote|step=29}}
| {{UDnote|step=29}}
|-
|-
Line 197: Line 230:
| 878.0
| 878.0
| [[5/3]]
| [[5/3]]
|vM6
| {{UDnote|step=30}}
| {{UDnote|step=30}}
|-
|-
Line 202: Line 236:
| 907.3
| 907.3
| [[22/13]], [[27/16]], [[32/19]]
| [[22/13]], [[27/16]], [[32/19]]
|M6
| {{UDnote|step=31}}
| {{UDnote|step=31}}
|-
|-
Line 207: Line 242:
| 936.6
| 936.6
| [[12/7]], [[19/11]]
| [[12/7]], [[19/11]]
|^M6
| {{UDnote|step=32}}
| {{UDnote|step=32}}
|-
|-
Line 212: Line 248:
| 965.9
| 965.9
| [[7/4]], [[26/15]]
| [[7/4]], [[26/15]]
|vm7
| {{UDnote|step=33}}
| {{UDnote|step=33}}
|-
|-
Line 217: Line 254:
| 995.1
| 995.1
| [[16/9]]
| [[16/9]]
|m7
| {{UDnote|step=34}}
| {{UDnote|step=34}}
|-
|-
Line 222: Line 260:
| 1024.4
| 1024.4
| [[9/5]], [[20/11]], [[38/21]]
| [[9/5]], [[20/11]], [[38/21]]
|^m7
| {{UDnote|step=35}}
| {{UDnote|step=35}}
|-
|-
Line 227: Line 266:
| 1053.7
| 1053.7
| [[11/6]], [[24/13]]
| [[11/6]], [[24/13]]
|~7
| {{UDnote|step=36}}
| {{UDnote|step=36}}
|-
|-
Line 232: Line 272:
| 1082.9
| 1082.9
| [[13/7]], [[15/8]], [[28/15]]
| [[13/7]], [[15/8]], [[28/15]]
|vM7
| {{UDnote|step=37}}
| {{UDnote|step=37}}
|-
|-
Line 237: Line 278:
| 1112.2
| 1112.2
| [[19/10]], [[21/11]], [[36/19]], [[40/21]]
| [[19/10]], [[21/11]], [[36/19]], [[40/21]]
|M7
| {{UDnote|step=38}}
| {{UDnote|step=38}}
|-
|-
Line 242: Line 284:
| 1141.5
| 1141.5
| [[27/14]], [[35/18]], [[48/25]], [[64/33]]
| [[27/14]], [[35/18]], [[48/25]], [[64/33]]
|^M7
| {{UDnote|step=39}}
| {{UDnote|step=39}}
|-
|-
Line 247: Line 290:
| 1170.7
| 1170.7
| [[49/25]], [[63/32]], [[96/49]], [[160/81]]
| [[49/25]], [[63/32]], [[96/49]], [[160/81]]
|v8
| {{UDnote|step=40}}
| {{UDnote|step=40}}
|-
|-
Line 252: Line 296:
| 1200.0
| 1200.0
| [[2/1]]
| [[2/1]]
|P8
| {{UDnote|step=41}}
| {{UDnote|step=41}}
|}
|}
Line 2,240: Line 2,285:
[[File:Caleb's Kite guitar.jpg|none|thumb|200px|Kite guitar]]
[[File:Caleb's Kite guitar.jpg|none|thumb|200px|Kite guitar]]


For more photos of Kite guitars, see [[Kite Guitar Photographs]].
There exist Kite-fretted basses, Kite-fretted Chapman sticks, and a Kite-fretted cuatro. For more photos of Kite guitars, see [[Kite Guitar Photographs]].
{{clear}}
{{clear}}
=== Other string instruments ===
The Turkish [[wikipedia:Lavta|lavta]] is a lute-like instrument with movable frets. The strings are tuned D A D A or D A D G. The frets are mostly placed in clumps of 5, so that there are 5 seconds, 5 thirds, etc. The lavta is arguably fretted to a 27-note subset of 41edo. Each clump would correspond to 41edo's plainminor-upminor-mid-downmajor-plainmajor. The edosteps would be something like 0, 3-7, 10-14, 17, 20-24, 27-31, 34-38 and 41.
https://www.facebook.com/groups/497105067092502/permalink/3562297780573200/


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