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

Scales

Music