Edϕ: Difference between revisions

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

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

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

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

For example, the 7th step of 10ed2 is 840¢, and the 10th step of 7ed~~~~<math>φ</math~~></span~~> is ≈1190.128995¢.

For example, the 7th step of 10ed2 is 840¢, and the 10th step of 7ed<math>φ</math> is ≈1190.128995¢.

As another example, the 9th step of 13ed2 is ≈830.7692308¢, and the 13th step of 9ed~~~~<math>φ</math~~></span~~> is ≈1203.35265¢.

As another example, the 9th step of 13ed2 is ≈830.7692308¢, and the 13th step of 9ed<math>φ</math> is ≈1203.35265¢.

Such ~~~~<math>m</math>ed~~~~<math>φ</math~~></span~~> are interesting as variants of their respective ~~~~<math>n</math>ed~~~~<math>2</math>, introducing some combination tone powers.

Such <math>m</math>ed<math>φ</math> are interesting as variants of their respective <math>n</math>ed<math>2</math>, introducing some combination tone powers.

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-Various equal divisions of the octave have close approximations of [[acoustic phi]], or <span><math>φ</math></span>, ≈833.090296357¢.
+Various equal divisions of the octave have close approximations of [[acoustic phi]], or <math>φ</math>, ≈833.090296357¢.
-If the <span><math>m^{th}</math></span> step of <span><math>n</math><span>ed2 is a close approximation of <span><math>φ</math></span>, the <span><math>n^{th}</math></span> step of <span><math>m</math><span>ed<span><math>φ</math></span> will be a close approximation of 2.
+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.
-For example, the 7th step of 10ed2 is 840¢, and the 10th step of 7ed<span><math>φ</math></span> is ≈1190.128995¢.
+For example, the 7th step of 10ed2 is 840¢, and the 10th step of 7ed<math>φ</math> is ≈1190.128995¢.
-As another example, the 9th step of 13ed2 is ≈830.7692308¢, and the 13th step of 9ed<span><math>φ</math></span> is ≈1203.35265¢.
+As another example, the 9th step of 13ed2 is ≈830.7692308¢, and the 13th step of 9ed<math>φ</math> is ≈1203.35265¢.
-Such <span><math>m</math><span>ed<span><math>φ</math></span> are interesting as variants of their respective <span><math>n</math><span>ed<span><math>2</math><span>, introducing some combination tone powers.
+Such <math>m</math><span>ed<math>φ</math> are interesting as variants of their respective <math>n</math><span>ed<math>2</math><span>, introducing some combination tone powers.
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