32edt: Difference between revisions

Line 2:

'''32EDT''' is the [[Edt|equal division of the third harmonic]] into 32 parts of 59.4361 [[cent|cents]] each, corresponding to 20.1898 [[edo]]. It has a distinct sharp tendency, in the sense that if 3 is pure, 5, 7, 11, 13, 17, and 19 are all sharp. It tempers out 3125/3087 and 885735/823543 in the 7-limit; 891/875, 1331/1323, and 2475/2401 in the 11-limit; 275/273, 351/343, 729/715, and 847/845 in the 13-limit; 121/119, 189/187, 225/221, 459/455, and 845/833 in the 17-limit; 135/133, 171/169, 247/245, 325/323, and 363/361 in the 19-limit (no-twos subgroup). It is the eighth [[The_Riemann_Zeta_Function_and_Tuning#Removing primes|zeta peak tritave division]].

==Harmonics==

{{Harmonics in equal

| steps = 19

| num = 3

| denom = 1

| intervals = prime

}}

{{Harmonics in equal

| steps = 19

| num = 3

| denom = 1

| start = 12

| collapsed = 1

| intervals = prime

}}

== Intervals ==

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 '''32EDT''' is the [[Edt|equal division of the third harmonic]] into 32 parts of 59.4361 [[cent|cents]] each, corresponding to 20.1898 [[edo]]. It has a distinct sharp tendency, in the sense that if 3 is pure, 5, 7, 11, 13, 17, and 19 are all sharp. It tempers out 3125/3087 and 885735/823543 in the 7-limit; 891/875, 1331/1323, and 2475/2401 in the 11-limit; 275/273, 351/343, 729/715, and 847/845 in the 13-limit; 121/119, 189/187, 225/221, 459/455, and 845/833 in the 17-limit; 135/133, 171/169, 247/245, 325/323, and 363/361 in the 19-limit (no-twos subgroup). It is the eighth [[The_Riemann_Zeta_Function_and_Tuning#Removing primes|zeta peak tritave division]].
-{{Harmonics in equal|32|3|1|intervals=prime}}
+==Harmonics==
+{{Harmonics in equal
+| steps = 19
+| num = 3
+| denom = 1
+| intervals = prime
+}}
+{{Harmonics in equal
+| steps = 19
+| num = 3
+| denom = 1
+| start = 12
+| collapsed = 1
+| intervals = prime
+}}
 == Intervals ==