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41edo: Difference between revisions

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→Intervals: added a pic of the 41-edo spiral
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|711.805 (2C7.CE<sub>16</sub>)
|711.805 (2C7.CE<sub>16</sub>)
| | [[11/8|11/8]]
| | [[11/8|11/8]]
| style="text-align:center;" | ^^4
| style="text-align:center;" | ~4
| style="text-align:center;" | ^^G, vAb
| style="text-align:center;" | ^^G, vAb
| | fu
| | fu
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|825.195 (347.32<sub>16</sub>)
|825.195 (347.32<sub>16</sub>)
| | [[16/11|16/11]], [[13/9]]
| | [[16/11|16/11]], [[13/9]]
| style="text-align:center;" | vv5
| style="text-align:center;" | ~5
| style="text-align:center;" | vvA
| style="text-align:center;" | vvA
| | su
| | su
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| style="text-align:center;" | downminor
| style="text-align:center;" | downminor
| style="text-align:center;" | zo
| 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 wa
| style="text-align:center;" | fourthward wa
| style="text-align:center;" | {a, b}, b &lt; -1
| style="text-align:center;" | (a, b) with 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;" | gu
| 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;" | ilo
| style="text-align:center;" | ilo
| 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;" | lu
| 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;" | yo
| 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 wa
| style="text-align:center;" | fifthward wa
| style="text-align:center;" | {a, b}, b &gt; 1
| style="text-align:center;" | (a, b) with 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;" | ru
| 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
|}
|}
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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(vv5) = "D minor double-down five", or possibly Ddim(^^5)
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"
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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. The perfectish categories wouldn't be used much, they are just there for completeness.
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.


[[File:41-edo spiral.png|673x673px]]
[[File:41-edo spiral.png|673x673px]]
Line 1,008: Line 1,008:
''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 22-edo, although there are certain trade-offs.
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.


[[File:The Kite Tuning smaller.jpg|1122x1122px]]
[[File:The Kite Tuning smaller.jpg|1122x1122px]]
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