10edo: Difference between revisions

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10EDO can be thought of as two circles of [[5edo|5EDO]] separated by 120 cents (or 5 circles of [[2edo|2EDO]]). It adds to 5EDO a small neutral second (or large minor 2nd) and its inversion a large neutral seventh (or small major 7th); an excellent approximation of [[13/8]] and its inversion [[16/13]]; and the happy 600-cent tritone that appears in every even-numbered EDO. Taking the the 360 cent large neutral third as a generator produces a heptatonic [[MOS scales|moment of symmetry scale]] of the form 1 2 1 2 1 2 1 ([[3L 4s|3L 4s - mosh]]). While not an integral or gap ~~edo~~, it is a [[The Riemann Zeta Function and Tuning #Zeta EDO lists|zeta peak EDO]]. One way to interpret it in terms of a temperament of just intonation is as a 2.7.13.15 subgroup, such that 105/104, 225/224, and 16807/16384 are tempered out. It can also be treated as a full 13-limit temperament, but it is a closer match to the aforementioned subgroup.

10EDO can be thought of as two circles of [[5edo|5EDO]] separated by 120 cents (or 5 circles of [[2edo|2EDO]]). It adds to 5EDO a small neutral second (or large minor 2nd) and its inversion a large neutral seventh (or small major 7th); an excellent approximation of [[13/8]] and its inversion [[16/13]]; and the happy 600-cent tritone that appears in every even-numbered EDO. Taking the the 360 cent large neutral third as a generator produces a heptatonic [[MOS scales|moment of symmetry scale]] of the form 1 2 1 2 1 2 1 ([[3L 4s|3L 4s - mosh]]). While not an integral or gap EDO, it is a [[The Riemann Zeta Function and Tuning #Zeta EDO lists|zeta peak EDO]]. One way to interpret it in terms of a temperament of just intonation is as a 2.7.13.15 subgroup, such that 105/104, 225/224, and 16807/16384 are tempered out. It can also be treated as a full 13-limit temperament, but it is a closer match to the aforementioned subgroup.

== Intervals ==

Line 439:

| Thozogu

| Superleap

|-

| 13

| [[196/195]]

| {{Monzo| 2 -1 -1 2 0 -1 }}

| 8.86

| Thuzozogu

| Mynucuma

|-

| 13

@@ Line 19: / Line 19: @@
 {{Odd harmonics in edo|edo=10}}
-EDO can be thought of as two circles of [[5edo|5EDO]] separated by 120 cents (or 5 circles of [[2edo|2EDO]]). It adds to 5EDO a small neutral second (or large minor 2nd) and its inversion a large neutral seventh (or small major 7th); an excellent approximation of [[13/8]] and its inversion [[16/13]]; and the happy 600-cent tritone that appears in every even-numbered EDO. Taking the the 360 cent large neutral third as a generator produces a heptatonic [[MOS scales|moment of symmetry scale]] of the form 1 2 1 2 1 2 1 ([[3L 4s|3L 4s - mosh]]). While not an integral or gap edo, it is a [[The Riemann Zeta Function and Tuning #Zeta EDO lists|zeta peak EDO]]. One way to interpret it in terms of a temperament of just intonation is as a 2.7.13.15 subgroup, such that 105/104, 225/224, and 16807/16384 are tempered out. It can also be treated as a full 13-limit temperament, but it is a closer match to the aforementioned subgroup.
+EDO can be thought of as two circles of [[5edo|5EDO]] separated by 120 cents (or 5 circles of [[2edo|2EDO]]). It adds to 5EDO a small neutral second (or large minor 2nd) and its inversion a large neutral seventh (or small major 7th); an excellent approximation of [[13/8]] and its inversion [[16/13]]; and the happy 600-cent tritone that appears in every even-numbered EDO. Taking the the 360 cent large neutral third as a generator produces a heptatonic [[MOS scales|moment of symmetry scale]] of the form 1 2 1 2 1 2 1 ([[3L 4s|3L 4s - mosh]]). While not an integral or gap EDO, it is a [[The Riemann Zeta Function and Tuning #Zeta EDO lists|zeta peak EDO]]. One way to interpret it in terms of a temperament of just intonation is as a 2.7.13.15 subgroup, such that 105/104, 225/224, and 16807/16384 are tempered out. It can also be treated as a full 13-limit temperament, but it is a closer match to the aforementioned subgroup.
 == Intervals ==
@@ Line 439: / Line 439: @@
 | Thozogu
 | Superleap
+|-
+| 13
+| [[196/195]]
+| {{Monzo| 2 -1 -1 2 0 -1 }}
+| 8.86
+| Thuzozogu
+| Mynucuma
 |-
 | 13