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| Fifth = 24\41 (702¢)
| Fifth = 24\41 (702¢)
| Major 2nd = 7\41 (205¢)
| Major 2nd = 7\41 (205¢)
| Minor 2nd = 3\41 (88¢)
| Semitones = 4:3 (117¢ : 88¢)
| Augmented 1sn = 4\41 (117¢)
| Consistency = 15
| Monotonicity = 21
}}
}}
{{Wikipedia| 41 equal temperament }}
{{Wikipedia| 41 equal temperament }}
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<nowiki>*</nowiki> Based on treating 41-edo as a 2.3.5.7.11.13.19 subgroup temperament; other approaches are possible.  
<nowiki>*</nowiki> Based on treating 41edo as a 2.3.5.7.11.13.19 subgroup temperament; other approaches are possible.  


Combining ups and downs notation with [[color notation]], qualities can be loosely associated with colors:
Combining ups and downs notation with [[color notation]], qualities can be loosely associated with colors:
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== Relationship to 12-edo ==
== Relationship to 12-edo ==


Whereas 12-edo has a circle of twelve 5ths, 41-edo has a spiral of twelve 5ths (since 24\41 is on the 7\12 kite in the scale tree). This spiral of 5th shows 41-edo in a 12-edo-friendly format. Excellent for introducing 41-edo to musicians unfamiliar with microtonal music. 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.
Whereas 12edo has a circle of twelve 5ths, 41edo has a spiral of twelve 5ths (since 24\41 is on the 7\12 kite in the scale tree). This spiral of 5th shows 41edo in a 12edo-friendly format. Excellent for introducing 41edo to musicians unfamiliar with microtonal music. 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]]
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41et is lower in relative error than any previous equal temperaments in the 3-, 13- and 19-limit. The next ETs 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 ETs better in these subgroups are 72 and 53, respectively.  
41et is lower in relative error than any previous equal temperaments in the 3-, 13- and 19-limit. The next ETs 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 ETs doing better in these subgroups are 72 and 53, respectively.  


=== Commas ===
=== Commas ===
41 EDO [[tempers out]] the following [[comma]]s using its patent [[val]], {{val| 41 65 95 115 142 152 168 174 185 199 203 }}.
41edo [[tempers out]] the following [[comma]]s using its patent [[val]], {{val| 41 65 95 115 142 152 168 174 185 199 203 }}.


{| class="commatable wikitable center-1 center-2 right-3 center-6"
{| class="commatable wikitable center-1 center-2 right-3 center-6"
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[[File:41-EDD_elektrische_gitaar.jpg|alt=41-EDD elektrische gitaar.jpg|560x745px|41-EDD elektrische gitaar.jpg]]
[[File:41-EDD_elektrische_gitaar.jpg|alt=41-EDD elektrische gitaar.jpg|560x745px|41-EDD elektrische gitaar.jpg]]


''41-EDO Electric guitar, by Gregory Sanchez.''
''41edo Electric guitar, by Gregory Sanchez.''


[[File:Ron_Sword_with_a_41ET_Guitar.jpg|alt=Ron_Sword_with_a_41ET_Guitar.jpg|Ron_Sword_with_a_41ET_Guitar.jpg]]
[[File:Ron_Sword_with_a_41ET_Guitar.jpg|alt=Ron_Sword_with_a_41ET_Guitar.jpg|Ron_Sword_with_a_41ET_Guitar.jpg]]


''41-EDO Classical guitar, by Ron Sword.''
''41edo Classical guitar, by Ron Sword.''


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. Kite-fretting makes 41-edo about as playable as 19-edo or 22-edo, although there are certain trade-offs. If the interval between strings is 13\41, 25 of the 41 intervals are in easy reach: vm2, ^m2, vM2, M2, ^M2, vm3, ^m3, vM3, ^M3, P4, ~4, d5, A4, ~5, P5, vm6, ^m6, vM6, ^M6, vm7, m7, ^m7, vM7, ^M7, P8.
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 41edo, i.e. 41ed4 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 41edo, but the full edo can be found on every pair of adjacent strings. Kite-fretting makes 41edo about as playable as 19edo or 22edo, although there are certain trade-offs. If the interval between strings is 13\41, 25 of the 41 intervals are in easy reach: vm2, ^m2, vM2, M2, ^M2, vm3, ^m3, vM3, ^M3, P4, ~4, d5, A4, ~5, P5, vm6, ^m6, vM6, ^M6, vm7, m7, ^m7, vM7, ^M7, P8.


[[File:Caleb's Kite guitar.jpg|480x640px]]
[[File:Caleb's Kite guitar.jpg|480x640px]]


A possible 41-edo keyboard design:
A possible 41edo keyboard design:
[[File:41edo keyboard layout.png|none|thumb|484x484px]]
[[File:41edo keyboard layout.png|none|thumb|484x484px]]


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