41edo: Difference between revisions

Line 7:

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, although 16\41 as 13/10 is debatable. (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).

41-ET forms the foundation of the [http://www.h-pi.com/theory/huntsystem1.html H-System], which uses the scale degrees of 41-ET as the basic [[13-limit|13-limit]] intervals requiring fine tuning +/- 1 [http://www.h-pi.com/theory/huntsystem2.html average JND] from the 41-ET circle in [[205edo|205edo]].

41-ET forms the foundation of the [http://www.h-pi.com/theory/huntsystem1.html H-System], which uses the scale degrees of 41-ET as the basic [[13-limit|13-limit]] intervals requiring fine tuning +/- 1 [http://www.h-pi.com/theory/huntsystem2.html average JND] from the 41-ET circle in [[205edo|205edo]]. 41-ET is also used by the [[The Kite Guitar|Kite Guitar]], see below in "Instruments".

41edo is the 13th [[prime_numbers|prime]] edo, following [[37edo|37edo]] and coming before [[43edo|43edo]].

Line 1,741:

''41-EDO 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.The Kite Tuning makes 41-edo about as playable as 19-edo or 22-edo, although there are certain trade-offs.

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.The Kite Tuning 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.

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

@@ Line 7: / Line 7: @@
 edo 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, although 16\41 as 13/10 is debatable. (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).
--ET forms the foundation of the [http://www.h-pi.com/theory/huntsystem1.html H-System], which uses the scale degrees of 41-ET as the basic [[13-limit|13-limit]] intervals requiring fine tuning +/- 1 [http://www.h-pi.com/theory/huntsystem2.html average JND] from the 41-ET circle in [[205edo|205edo]].
+-ET forms the foundation of the [http://www.h-pi.com/theory/huntsystem1.html H-System], which uses the scale degrees of 41-ET as the basic [[13-limit|13-limit]] intervals requiring fine tuning +/- 1 [http://www.h-pi.com/theory/huntsystem2.html average JND] from the 41-ET circle in [[205edo|205edo]]. 41-ET is also used by the [[The Kite Guitar|Kite Guitar]], see below in "Instruments".
 edo is the 13th [[prime_numbers|prime]] edo, following [[37edo|37edo]] and coming before [[43edo|43edo]].
@@ Line 1,741: / Line 1,741: @@
 ''41-EDO 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.The Kite Tuning makes 41-edo about as playable as 19-edo or 22-edo, although there are certain trade-offs.
+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.The Kite Tuning 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.
 [[File:Caleb's Kite guitar.jpg|480x640px]]