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See [[Kleismic_family#Sqrtphi|Kleismic family]].
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 microtemperaments|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 #Sqrtphi|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: [2 14/11; 325/324 364/363 375/374 400/399 442/441 595/594]


Gencom map: [&lt;1 12 11 16 17 28 27 -2|, &lt;0 -30 -25 -38 -39 -70 -66 18|]
Gencom mapping: [{{val|1 12 11 16 17 28 27 -2}}, {{val|0 -30 -25 -38 -39 -70 -66 18}}]


=Spectrum of Sqrtphi Tunings by Eigenmonzos=
{| class="wikitable center-all"
 
{| class="wikitable"
|-
|-
! | Eigenmonzo
! | [[eigenmonzo|eigenmonzo<br>(unchanged-interval]])
! | Undecimal Major Third
! | undecimal<br>major third (¢)
! | comments
|-
|-
| | 26/21
| | 26/21
| | 415.12662
| | 415.12662
| |
|-
|-
| | 17/13
| | 17/13
| | 416.10694
| | 416.10694
| |
|-
|-
| | 18/13
| | 18/13
| | 416.33823
| | 416.33823
| |
|-
|-
| | 15/11
| | 15/11
| | 416.44058
| | 416.44058
| |
|-
|-
| | 13/11
| | 13/11
| | 416.47711
| | 416.47711
| |
|-
|-
| | 18/17
| | 18/17
| | 416.49243
| | 416.49243
| |
|-
|-
| | [[15/14|15/14]]
| | 15/14
| | 416.50336
| | 416.50336
| |
|-
|-
| | [[14/13|14/13]]
| | 14/13
| | 416.50932
| | 416.50932
| |
|-
|-
| | [[15/13|15/13]]
| | 15/13
| | 416.51607
| | 416.51607
| |
|-
|-
| | [[19/16|19/16]]
| | 19/16
| | 416.52850
| | 416.52850
| |
|-
|-
| | 22/17
| | 22/17
| | 416.53195
| | 416.53195
| |
|-
|-
| | 13/12
| | 13/12
| | 416.53568
| | 416.53568
| |
|-
|-
| | 20/19
| | 20/19
| | 416.53952
| | 416.53952
| |
|-
|-
| | [[11/9|11/9]]
| | 11/9
| | 416.54324
| | 416.54324
| |
|-
|-
| | φ
| | (φ)
| | 416.54515
| | 416.54515
| | square root of phi
|-
|-
| | [[5/4|5/4]]
| | 5/4
| | 416.54745
| | 416.54745
| |
|-
|-
| | 26/19
| | 26/19
| | 416.55665
| | 416.55665
| |
|-
|-
| | 16/13
| | 16/13
| | 416.56389
| | 416.56389
| |
|-
|-
| | 19/15
| | 19/15
| | 416.56499
| | 416.56499
| |
|-
|-
| | 17/14
| | 17/14
| | 416.56680
| | 416.56680
| |
|-
|-
| | 22/21
| | 22/21
| | 416.57024
| | 416.57024
| |
|-
|-
| | 13/10
| | 13/10
| | 416.57302 (13, 15, 17, 19 and 21 limit minimax)
| | 416.57302
| | 13, 15, 17, 19 and 21-odd-limit minimax
|-
|-
| | 24/19
| | 24/19
| | 416.57413
| | 416.57413
| |
|-
|-
| | 16/15
| | 16/15
| | 416.57693
| | 416.57693
| |
|-
|-
| | 19/17
| | 19/17
| | 416.57807
| | 416.57807
| |
|-
|-
| | 24/17
| | 24/17
| | 416.58332
| | 416.58332
| |
|-
|-
| | 19/14
| | 19/14
| | 416.58370
| | 416.58370
| |
|-
|-
| | 19/18
| | 19/18
| | 416.58465
| | 416.58465
| |
|-
|-
| | [[9/7|9/7]]
| | 9/7
| | 416.58709
| | 416.58709
| |
|-
|-
| | 21/19
| | 21/19
| | 416.58991
| | 416.58991
| |
|-
|-
| | 17/16
| | 17/16
| | 416.59158
| | 416.59158
| |
|-
|-
| | 22/19
| | 22/19
| | 416.59991
| | 416.59991
| |
|-
|-
| | [[4/3|4/3]]
| | 4/3
| | 416.60150 (5 limit minimax)
| | 416.60150
| | 5-odd-limit minimax
|-
|-
| | 21/16
| | 21/16
| | 416.60616
| | 416.60616
| |
|-
|-
| | [[8/7|8/7]]
| | 8/7
| | 416.60984 (7 and 9 limit minimax)
| | 416.60984
| | 7 and 9-odd-limit minimax
|-
|-
| | 20/17
| | 20/17
| | 416.61850
| | 416.61850
| |
|-
|-
| | [[11/8|11/8]]
| | 11/8
| | 416.63287 (11 limit minimax)
| | 416.63287
| | 11-odd-limit minimax
|-
|-
| | [[10/9|10/9]]
| | 10/9
| | 416.64011
| | 416.64011
| |
|-
|-
| | 21/20
| | 21/20
| | 416.64030
| | 416.64030
| |
|-
|-
| | [[7/6|7/6]]
| | 7/6
| | 416.64114
| | 416.64114
| |
|-
|-
| | 17/15
| | 17/15
| | 416.66485
| | 416.66485
| |
|-
|-
| | [[7/5|7/5]]
| | 7/5
| | 416.72983
| | 416.72983
| |
|-
|-
| | 12/11
| | 12/11
| | 416.73745
| | 416.73745
| |
|-
|-
| | 11/10
| | 11/10
| | 416.78541
| | 416.78541
| |
|-
|-
| | [[6/5|6/5]]
| | 6/5
| | 416.87174
| | 416.87174
| |
|-
|-
| | 21/17
| | 21/17
| | 417.08725
| | 417.08725
| |
|-
|-
| | 14/11
| | 14/11
| | 417.50796
| | 417.50796
| |
|}
|}
[[Category:todo:add_definition]]
 
[[Category:todo:intro]]
== Scales ==
* [[Sqrtphi17]]
* [[Sqrtphi23]]
* [[Sqrtphi49]]
 
== Music ==
'''[[Vito Sicurella]]'''
* [http://micro.soonlabel.com/gene_ward_smith/Others/Sicurella/A%20Fight%20For%20Phi.mp3 A Fight for Phi]
'''[[Chris Vaisvil]]'''
* [http://micro.soonlabel.com/sqrt_phi/daily20111123a-sqrt-phi-17.mp3 Prelude for Piano in Square root of Phi Tuning]
 
[[Category:Sqrtphi| ]] <!-- main article -->
[[Category:Rank-2 temperaments]]
[[Category:Kleismic family]]
[[Category:Golden ratio]]
Retrieved from "https://en.xen.wiki/w/Sqrtphi"