Sqrtphi
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The sqrtphi is a temperament for the 7, 11, 13, 17, and 19 prime limits. It is a member of kleismic family, mirkwai clan and wizmic temperaments. The name "sqrtphi" stands for "square root of phi", which means the positive square root of the golden ratio [math](\sqrt{\varphi} = \sqrt{\frac{1+\sqrt{5}}{2}})[/math] as a frequency ratio.
See Kleismic family for more technical data.
Tuning spectrum
Gencom: [2 14/11; 325/324 364/363 375/374 400/399 442/441 595/594]
Gencom mapping: [⟨1 12 11 16 17 28 27 -2], ⟨0 -30 -25 -38 -39 -70 -66 18]]
| eigenmonzo (unchanged-interval) |
undecimal major third (¢) |
comments |
|---|---|---|
| 26/21 | 415.12662 | |
| 17/13 | 416.10694 | |
| 18/13 | 416.33823 | |
| 15/11 | 416.44058 | |
| 13/11 | 416.47711 | |
| 18/17 | 416.49243 | |
| 15/14 | 416.50336 | |
| 14/13 | 416.50932 | |
| 15/13 | 416.51607 | |
| 19/16 | 416.52850 | |
| 22/17 | 416.53195 | |
| 13/12 | 416.53568 | |
| 20/19 | 416.53952 | |
| 11/9 | 416.54324 | |
| (φ) | 416.54515 | square root of phi |
| 5/4 | 416.54745 | |
| 26/19 | 416.55665 | |
| 16/13 | 416.56389 | |
| 19/15 | 416.56499 | |
| 17/14 | 416.56680 | |
| 22/21 | 416.57024 | |
| 13/10 | 416.57302 | 13, 15, 17, 19 and 21-odd-limit minimax |
| 24/19 | 416.57413 | |
| 16/15 | 416.57693 | |
| 19/17 | 416.57807 | |
| 24/17 | 416.58332 | |
| 19/14 | 416.58370 | |
| 19/18 | 416.58465 | |
| 9/7 | 416.58709 | |
| 21/19 | 416.58991 | |
| 17/16 | 416.59158 | |
| 22/19 | 416.59991 | |
| 4/3 | 416.60150 | 5-odd-limit minimax |
| 21/16 | 416.60616 | |
| 8/7 | 416.60984 | 7 and 9-odd-limit minimax |
| 20/17 | 416.61850 | |
| 11/8 | 416.63287 | 11-odd-limit minimax |
| 10/9 | 416.64011 | |
| 21/20 | 416.64030 | |
| 7/6 | 416.64114 | |
| 17/15 | 416.66485 | |
| 7/5 | 416.72983 | |
| 12/11 | 416.73745 | |
| 11/10 | 416.78541 | |
| 6/5 | 416.87174 | |
| 21/17 | 417.08725 | |
| 14/11 | 417.50796 |