Sqrtphi

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]\displaystyle{ (\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

• Sqrtphi17
• Sqrtphi23
• Sqrtphi49

Music

Vito Sicurella

• A Fight for Phi

Chris Vaisvil

• Prelude for Piano in Square root of Phi Tuning