36ed5: Difference between revisions
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The '''36 equal divisions of the fifth harmonic ([[5/1]])''' is a tuning that divides the pentave into 36 equal steps. It combines [[Carlos Alpha]] scale with [[quarter-comma meantone]]. The step size is 77.3976 cents, thus making the tuning correspond to 15.5044 [[EDO]]. | The '''36 equal divisions of the fifth harmonic ([[5/1]])''' is a tuning that divides the pentave into 36 equal steps. It combines [[Carlos Alpha]] scale with [[quarter-comma meantone]]. The step size is 77.3976 cents, thus making the tuning correspond to 15.5044 [[EDO]]. As a consequence of this, 36ed5 completely misses [[2/1]]. | ||
== Theory == | == Theory == | ||
| Line 12: | Line 12: | ||
|- | |- | ||
| 5 || [[5/4]] || 386.9880 | | 5 || [[5/4]] || 386.9880 | ||
|- | |||
|6 | |||
|[[21/16]] | |||
|464.3856 | |||
|- | |- | ||
| 9 || [[3/2]] || [[Quarter-comma meantone|696.5784]] | | 9 || [[3/2]] || [[Quarter-comma meantone|696.5784]] | ||
| Line 17: | Line 21: | ||
| 19 || [[7/3]] || 1470.554 | | 19 || [[7/3]] || 1470.554 | ||
|- | |- | ||
| 28 || [[7/2]] || 2167. | | 28 || [[7/2]] || 2167.1329 | ||
|- | |- | ||
| 31 || [[4/1]] || 2399.326 | | 31 || [[4/1]] || 2399.326 | ||
| Line 23: | Line 27: | ||
| 36 || '''exact [[5/1]]''' || 2786.314 | | 36 || '''exact [[5/1]]''' || 2786.314 | ||
|} | |} | ||
[[Category:Ed5]] | [[Category:Ed5]] | ||
[[Category:Edonoi]] | [[Category:Edonoi]] | ||
Revision as of 11:42, 28 September 2021
The 36 equal divisions of the fifth harmonic (5/1) is a tuning that divides the pentave into 36 equal steps. It combines Carlos Alpha scale with quarter-comma meantone. The step size is 77.3976 cents, thus making the tuning correspond to 15.5044 EDO. As a consequence of this, 36ed5 completely misses 2/1.
Theory
| Step | Just approximation | Size (cents) |
|---|---|---|
| 1 | 23/22 | 77.3976 |
| 3 | 8/7 | 232.1928 |
| 5 | 5/4 | 386.9880 |
| 6 | 21/16 | 464.3856 |
| 9 | 3/2 | 696.5784 |
| 19 | 7/3 | 1470.554 |
| 28 | 7/2 | 2167.1329 |
| 31 | 4/1 | 2399.326 |
| 36 | exact 5/1 | 2786.314 |