41edo: Difference between revisions

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Whereas 12edo has a circle of twelve 5ths, 41edo has a <u>spiral</u> of twelve 5ths, since 24\41 is on the 7\12 kite in the scale tree. (See Chapter 5.7 of [https://www.tallkite.com/AlternativeTunings.html Kite's book] for an explanation of kites.) 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|579x579px]]

The same spiral, but with notes not intervals:

[[File:41-edo spiral with notes.png|~~730x730px~~]]

[[File:41-edo spiral with notes.png|549x549px]]

== Regular temperament properties ==

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== Instruments ==

=== Guitars ===

[[File:41-EDD_elektrische_gitaar.jpg|alt=41-EDD elektrische gitaar.jpg|560x745px|41-EDD elektrische gitaar.jpg]]

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''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 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~~.

The [[The Kite Guitar|Kite Guitar]] (see also [https://KiteGuitar.com KiteGuitar.com] and [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.

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

For more photos of Kite guitars, see [[Kite Guitar Photographs]].

=== Keyboards ===

A possible 41edo keyboard design:

[[File:41edo keyboard layout.png|none|thumb|484x484px]]

@@ Line 562: / Line 562: @@
 Whereas 12edo has a circle of twelve 5ths, 41edo has a <u>spiral</u> of twelve 5ths, since 24\41 is on the 7\12 kite in the scale tree. (See Chapter 5.7 of [https://www.tallkite.com/AlternativeTunings.html Kite's book] for an explanation of kites.) 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|579x579px]]
 The same spiral, but with notes not intervals:
-[[File:41-edo spiral with notes.png|730x730px]]
+[[File:41-edo spiral with notes.png|549x549px]]
 == Regular temperament properties ==
@@ Line 1,826: / Line 1,826: @@
 == Instruments ==
+=== Guitars ===
 [[File:41-EDD_elektrische_gitaar.jpg|alt=41-EDD elektrische gitaar.jpg|560x745px|41-EDD elektrische gitaar.jpg]]
@@ Line 1,834: / Line 1,835: @@
 ''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 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.
+The [[The Kite Guitar|Kite Guitar]] (see also [https://KiteGuitar.com KiteGuitar.com] and [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.
 [[File:Caleb's Kite guitar.jpg|480x640px]]
+For more photos of Kite guitars, see [[Kite Guitar Photographs]].
+=== Keyboards ===
 A possible 41edo keyboard design:
 [[File:41edo keyboard layout.png|none|thumb|484x484px]]