Edϕ: Difference between revisions

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.

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 [[9edϕ|9ed<math>φ</math>]] is ≈1203.35265¢.

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.

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

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

|<math>φ^{\frac{1}{7}}</math> or <math>≈1.988629015^{\frac{1}{10}}</math>

|<math>φ^{\frac{2}{7}}</math> or <math>≈1.988629015^{\frac{2}{10}}</math>

|<math>φ^{\frac{3}{7}}</math> or <math>≈1.988629015^{\frac{3}{10}}</math>

|<math>φ^{\frac{4}{7}}</math> or <math>≈1.988629015^{\frac{4}{10}}</math>

|<math>φ^{\frac{5}{7}}</math> or <math>≈1.988629015^{\frac{5}{10}}</math>

|<math>φ^{\frac{6}{7}}</math> or <math>≈1.988629015^{\frac{6}{10}}</math>

|<math>φ^{\frac{7}{7}}</math> or <math>≈1.988629015^{\frac{7}{10}}</math>

|<math>φ^{\frac{8}{7}}</math> or <math>≈1.988629015^{\frac{8}{10}}</math>

|<math>φ^{\frac{9}{7}}</math> or <math>≈1.988629015^{\frac{9}{10}}</math>

|<math>φ^{\frac{10}{7}}</math> or <math>≈1.988629015^{\frac{10}{10}}</math>