Edϕ: Difference between revisions

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Various equal divisions of the octave have close approximations of [[acoustic phi]], or <math>φ</math>, ≈833.090296357¢.

If the <math>m^{th}</math> step of <math>n</math><span>~~ed2~~ is a close approximation of <math>φ</math>, the <math>n^{th}</math> step of <math>m</math><span>ed<math>φ</math> will be a close approximation of 2.

If the <math>m^{th}</math> step of <math>n</math><span>edo is a close approximation of <math>φ</math>, the <math>n^{th}</math> step of <math>m</math><span>ed<math>φ</math> will be a close approximation of 2.

For example, the 7th step of [[10edo]] is 840¢, and the 10th step of 7ed<math>φ</math> is ≈1190.128995¢.

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|+

| rowspan="2" |'''scale step'''

| colspan="4" |'''~~10edo~~'''

| colspan="4" |'''10ed2'''

| colspan="4" |'''7edφ or 10ed(<math>2^{\frac{10log_2{φ}}{7}} ≈ 1.988629015</math>)'''

|-

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|+

| rowspan="2" |'''scale step'''

| colspan="4" |'''~~13edo~~'''

| colspan="4" |'''13ed2'''

| colspan="4" |'''9edφ or 13ed(<math>2^{\frac{13log_2{φ}}{9}} ≈ 2.003876886</math>)'''

|-

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cet33.scl 25 25th root of phi, Walter O´Connell (1993)

cet46.scl 18 18th root of phi, Walter O´Connell (1993)

== Music ==

; [[Bryan Deister]]

* [https://www.youtube.com/shorts/JrGYILddm64 ''12edΦ improv''] (2026)

== See also ==

@@ Line 2: / Line 2: @@
 Various equal divisions of the octave have close approximations of [[acoustic phi]], or <math>φ</math>, ≈833.090296357¢.
-If the <math>m^{th}</math> step of <math>n</math><span>ed2 is a close approximation of <math>φ</math>, the <math>n^{th}</math> step of <math>m</math><span>ed<math>φ</math> will be a close approximation of 2.
+If the <math>m^{th}</math> step of <math>n</math><span>edo is a close approximation of <math>φ</math>, the <math>n^{th}</math> step of <math>m</math><span>ed<math>φ</math> will be a close approximation of 2.
 For example, the 7th step of [[10edo]] is 840¢, and the 10th step of 7ed<math>φ</math> is ≈1190.128995¢.
@@ Line 12: / Line 12: @@
 |+
 | rowspan="2" |'''scale step'''
-| colspan="4" |'''10edo'''
+| colspan="4" |'''10ed2'''
 | colspan="4" |'''7edφ or 10ed(<math>2^{\frac{10log_2{φ}}{7}} ≈ 1.988629015</math>)'''
 |-
@@ Line 128: / Line 128: @@
 |+
 | rowspan="2" |'''scale step'''
-| colspan="4" |'''13edo'''
+| colspan="4" |'''13ed2'''
 | colspan="4" |'''9edφ or 13ed(<math>2^{\frac{13log_2{φ}}{9}} ≈ 2.003876886</math>)'''
 |-
@@ Line 275: / Line 275: @@
   cet33.scl                      25  25th root of phi, Walter O´Connell (1993)
   cet46.scl                      18  18th root of phi, Walter O´Connell (1993)
+== Music ==
+; [[Bryan Deister]]
+* [https://www.youtube.com/shorts/JrGYILddm64 ''12edΦ improv''] (2026)
 == See also ==