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Kleismic family: Difference between revisions

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The [[5-limit]] parent comma for the '''kleismic family''' is [[15625/15552]], the kleisma. Its monzo is {{monzo| -6 -5 6 }}, and flipping that yields {{multival| 6 5 -6 }} for the [[wedgie]]. This tells us the generator is a minor third, and that to get to the interval class of major thirds will require five of these, and so to get to fifths will require six. In fact, (6/5)<sup>5</sup> = 5/2 × 15625/15552. This 5-limit temperament (virtually a [[microtemperament]]) is commonly called '''Hanson''', and 14\53 is about perfect as a hanson generator, though 9\34 also makes sense, and 5\19 and 4\15 are possible. Other tunings include [[72edo]], [[87edo]] and [[140edo]].
The [[5-limit]] parent comma for the '''kleismic family''' is [[15625/15552]], the kleisma. Its monzo is {{monzo| -6 -5 6 }}, and flipping that yields {{multival| 6 5 -6 }} for the [[wedgie]]. This tells us the generator is a minor third, and that to get to the interval class of major thirds will require five of these, and so to get to fifths will require six. In fact, (6/5)<sup>5</sup> = 5/2 × 15625/15552. This 5-limit temperament (virtually a [[microtemperament]]) is commonly called '''Hanson''', and 14\53 is about perfect as a hanson generator, though 9\34 also makes sense, and 5\19 and 4\15 are possible. Other tunings include [[72edo|72EDO]], [[87edo|87EDO]] and [[140edo|140EDO]].


== Hanson ==
== Hanson ==
Subgroup: 2.3.5
Subgroup: 2.3.5


Line 17: Line 17:


[[Tuning ranges]]:  
[[Tuning ranges]]:  
* [[diamond monotone]] range: [300.000, 327.273] (1\4 to 3\11)
* [[Diamond monotone]] range: [300.000, 327.273] (1\4 to 3\11)
* [[diamond tradeoff]] range: [315.641, 317.263]
* [[Diamond tradeoff]] range: [315.641, 317.263]
* diamond monotone and tradeoff range: [315.641, 317.263]
* Diamond monotone and tradeoff: [315.641, 317.263]


{{Val list|legend=1| 15, 19, 34, 53, 458, 511c, …, 882c }}
{{Val list|legend=1| 15, 19, 34, 53, 458, 511c, …, 882c }}
Line 32: Line 32:
* [http://dkeenan.com/Music/ChainOfMinor3rds.htm 11 note chain-of-minor-thirds scale], by David Keenan</span>
* [http://dkeenan.com/Music/ChainOfMinor3rds.htm 11 note chain-of-minor-thirds scale], by David Keenan</span>


=== Seven limit extensions ===
=== Seven limit extensions ===
The second comma of the [[Normal lists|normal comma list]] defines which [[7-limit]] family member we are looking at. 875/864, the keemic comma, gives keemun, 4375/4374, the ragisma, gives catakleismic, 5120/5103, hemifamity, gives countercata, 6144/6125, the porwell comma, gives hemikleismic, 245/243, sensamagic, gives clyde, 1029/1024, the gamelisma, gives tritikleismic, and 2401/2400, the breedsma, gives quadritikleismic. Keemun, catakleismic and countercata all have octave period and use the minor third as a generator; catakleismic and countercata define the 7/4 more complexly but more accurately than keemun. Hemikleismic splits the 6/5 in half to get a neutral second generator of 35/32, and clyde similarly splits the 5/3 in half to get a 9/7 generator. Finally, tritikleismic has a 1/3 octave period with minor third generator, and quadritikleismic a 1/4 octave period with the minor third generator.
The second comma of the [[Normal lists|normal comma list]] defines which [[7-limit]] family member we are looking at. 875/864, the keemic comma, gives keemun, 4375/4374, the ragisma, gives catakleismic, 5120/5103, hemifamity, gives countercata, 6144/6125, the porwell comma, gives hemikleismic, 245/243, sensamagic, gives clyde, 1029/1024, the gamelisma, gives tritikleismic, and 2401/2400, the breedsma, gives quadritikleismic. Keemun, catakleismic and countercata all have octave period and use the minor third as a generator; catakleismic and countercata define the 7/4 more complexly but more accurately than keemun. Hemikleismic splits the 6/5 in half to get a neutral second generator of 35/32, and clyde similarly splits the 5/3 in half to get a 9/7 generator. Finally, tritikleismic has a 1/3 octave period with minor third generator, and quadritikleismic a 1/4 octave period with the minor third generator.


== Keemun ==
== Keemun ==
{{main|Keemun}}
{{main|Keemun}}


Line 49: Line 49:


[[Tuning ranges]]:  
[[Tuning ranges]]:  
* [[diamond monotone]] range: [300.000, 327.273] (1\4 to 3\11)
* [[Diamond monotone]] range: [300.000, 327.273] (1\4 to 3\11)
* [[diamond tradeoff]] range: [308.744, 322.942]
* [[Diamond tradeoff]] range: [308.744, 322.942]
* diamond monotone and tradeoff range: [308.744, 322.942]
* Diamond monotone and tradeoff: [308.744, 322.942]


{{Val list|legend=1| 15, 19, 53d, 72dd, 91dd }}
{{Val list|legend=1| 15, 19, 53d, 72dd, 91dd }}
Line 57: Line 57:
[[Badness]]: 0.027408
[[Badness]]: 0.027408


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 67: Line 67:


Tuning ranges:  
Tuning ranges:  
* [[diamond monotone]] range: [315.789, 320.000] (5\19 to 4\15)
* Diamond monotone range: [315.789, 320.000] (5\19 to 4\15)
* [[diamond tradeoff]] range: [308.744, 324.341]
* Diamond tradeoff range: [308.744, 324.341]
* diamond monotone and tradeoff range: [315.789, 320.000]
* Diamond monotone and tradeoff: [315.789, 320.000]


Vals: {{Val list| 4, 15, 19, 34 }}
Vals: {{Val list| 4, 15, 19, 34 }}
Line 75: Line 75:
Badness: 0.027410
Badness: 0.027410


==== 13-limit ====
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 85: Line 85:


Tuning ranges:  
Tuning ranges:  
* [[diamond monotone]] range: 315.789 (5\19)
* Diamond monotone range: 315.789 (5\19)
* [[diamond tradeoff]] range: [303.597, 324.341]
* Diamond tradeoff range: [303.597, 324.341]
* diamond monotone and tradeoff range: 315.789
* Diamond monotone and tradeoff: 315.789


Vals: {{Val list| 4, 15f, 19, 53def, 72def }}
Vals: {{Val list| 4, 15f, 19, 53def, 72def }}
Line 93: Line 93:
Badness: 0.029749
Badness: 0.029749


==== Kema ====
==== Kema ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 103: Line 103:


Tuning ranges:  
Tuning ranges:  
* [[diamond monotone]] range: [315.789, 320.000] (5\19 to 4\15)
* Diamond monotone range: [315.789, 320.000] (5\19 to 4\15)
* [[diamond tradeoff]] range: [308.744, 324.341]
* Diamond tradeoff range: [308.744, 324.341]
* diamond monotone and tradeoff range: [315.789, 320.000]
* Diamond monotone and tradeoff: [315.789, 320.000]


Vals: {{Val list| 15, 19, 34, 87ddee }}
Vals: {{Val list| 15, 19, 34, 87ddee }}
Line 111: Line 111:
Badness: 0.022749
Badness: 0.022749


==== Kumbaya ====
==== Kumbaya ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 124: Line 124:
Badness: 0.031633
Badness: 0.031633


=== Qeema ===
=== Qeema ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 137: Line 137:
Badness: 0.040056
Badness: 0.040056


==== 13-limit ====
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 150: Line 150:
Badness: 0.029419
Badness: 0.029419


=== Darjeeling ===
=== Darjeeling ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 163: Line 163:
Badness: 0.027648
Badness: 0.027648


==== 13-limit ====
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 176: Line 176:
Badness: 0.021445
Badness: 0.021445


== Catalan ==
== Catalan ==
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 191: Line 191:
[[Badness]]: 0.094872
[[Badness]]: 0.094872


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 204: Line 204:
Badness: 0.036894
Badness: 0.036894


== Catakleismic ==
== Catakleismic ==
{{main | Catakleismic }}
{{main | Catakleismic }}


Line 218: Line 218:


[[Tuning ranges]]:  
[[Tuning ranges]]:  
* [[diamond monotone]] range: [315.789, 317.647] (5\19 to 9\34)
* [[Diamond monotone]] range: [315.789, 317.647] (5\19 to 9\34)
* [[diamond tradeoff]] range: [315.641, 317.263]
* [[Diamond tradeoff]] range: [315.641, 317.263]
* diamond monotone and tradeoff range: [315.789, 317.263]
* Diamond monotone and tradeoff: [315.789, 317.263]


{{Val list|legend=1| 19, 34d, 53, 72, 197, 269c }}
{{Val list|legend=1| 19, 34d, 53, 72, 197, 269c }}
Line 226: Line 226:
[[Badness]]: 0.021501
[[Badness]]: 0.021501


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 236: Line 236:


Tuning ranges:  
Tuning ranges:  
* [[diamond monotone]] range: [315.789, 316.981] (5\19 to 14\53)
* Diamond monotone range: [315.789, 316.981] (5\19 to 14\53)
* [[diamond tradeoff]] range: [315.641, 317.263]
* Diamond tradeoff range: [315.641, 317.263]
* diamond monotone and tradeoff range: [315.789, 316.981]
* Diamond monotone and tradeoff: [315.789, 316.981]


Vals: {{Val list| 19, 34de, 53, 72, 197e, 269ce, 341ce, 610bccee }}
Vals: {{Val list| 19, 34de, 53, 72, 197e, 269ce, 341ce, 610bccee }}
Line 244: Line 244:
Badness: 0.021849
Badness: 0.021849


==== 13-limit ====
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 254: Line 254:


Tuning ranges:  
Tuning ranges:  
* [[diamond monotone]] range: [315.789, 316.981] (5\19 to 14\53)
* Diamond monotone range: [315.789, 316.981] (5\19 to 14\53)
* [[diamond tradeoff]] range: [315.641, 318.309]
* Diamond tradeoff range: [315.641, 318.309]
* diamond monotone and tradeoff range: [315.789, 316.981]
* Diamond monotone and tradeoff: [315.789, 316.981]


Vals: {{Val list| 19, 34de, 53, 72, 125f, 197ef, 269cef }}
Vals: {{Val list| 19, 34de, 53, 72, 125f, 197ef, 269cef }}
Line 262: Line 262:
Badness: 0.016883
Badness: 0.016883


=== Cataclysmic ===
=== Cataclysmic ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 275: Line 275:
Badness: 0.039954
Badness: 0.039954


==== 13-limit ====
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 288: Line 288:
Badness: 0.022555
Badness: 0.022555


=== Catalytic ===
=== Catalytic ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 301: Line 301:
Badness: 0.030422
Badness: 0.030422


==== 13-limit ====
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 314: Line 314:
Badness: 0.022337
Badness: 0.022337


=== Cataleptic ===
=== Cataleptic ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 327: Line 327:
Badness: 0.044335
Badness: 0.044335


==== 13-limit ====
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 340: Line 340:
Badness: 0.027343
Badness: 0.027343


=== Bikleismic ===
=== Bikleismic ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 353: Line 353:
Badness: 0.029319
Badness: 0.029319


==== 13-limit ====
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 366: Line 366:
Badness: 0.021814
Badness: 0.021814


== Countercata ==
== Countercata ==
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 381: Line 381:
[[Badness]]: 0.052129
[[Badness]]: 0.052129


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 394: Line 394:
Badness: 0.039770
Badness: 0.039770


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 407: Line 407:
Badness: 0.020156
Badness: 0.020156


== Metakleismic ==
== Metakleismic ==
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 422: Line 422:
[[Badness]]: 0.163519
[[Badness]]: 0.163519


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 435: Line 435:
Badness: 0.048570
Badness: 0.048570


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 448: Line 448:
Badness: 0.024371
Badness: 0.024371


== Hemikleismic ==
== Hemikleismic ==
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 463: Line 463:
[[Badness]]: 0.052054
[[Badness]]: 0.052054


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 476: Line 476:
Badness: 0.038023
Badness: 0.038023


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 489: Line 489:
Badness: 0.026005
Badness: 0.026005


== Clyde ==
== Clyde ==
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 503: Line 503:


[[Minimax tuning]]:  
[[Minimax tuning]]:  
* 7- and [[9-odd-limit]]
* 7- and [[9-odd-limit]]: ~9/7 = {{monzo| 12/25 0 0 -1/25 }}
: [{{monzo| 1 0 0 0 }}, {{monzo| 6/25 0 0 12/25 }}, {{monzo| 6/5 0 0 2/5 }}, {{monzo| 0 0 0 1 }}]
: [{{monzo| 1 0 0 0 }}, {{monzo| 6/25 0 0 12/25 }}, {{monzo| 6/5 0 0 2/5 }}, {{monzo| 0 0 0 1 }}]
: [[Eigenmonzo]]s: 2, 7
: [[Eigenmonzo]]s: 2, 7
Line 513: Line 513:
[[Badness]]: 0.047261
[[Badness]]: 0.047261


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 526: Line 526:
Badness: 0.047417
Badness: 0.047417


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 539: Line 539:
Badness: 0.026842
Badness: 0.026842


== Tritikleismic ==
== Tritikleismic ==
{{see also| Gamelismic clan #Tritikleismic }}
{{see also| Gamelismic clan #Tritikleismic }}


Line 555: Line 555:


[[Minimax tuning]]:
[[Minimax tuning]]:
* [[7-odd-limit]]
* [[7-odd-limit]]: ~6/5 = {{monzo| 1/3 0 1/7 -1/7 }}
: [{{monzo| 1 0 0 0 }}, {{monzo| 2 0 6/7 -6/7 }}, {{monzo| 8/3 0 5/7 -5/7 }}, {{monzo| 8/3 0 -2/7 2/7 }}]
: [{{monzo| 1 0 0 0 }}, {{monzo| 2 0 6/7 -6/7 }}, {{monzo| 8/3 0 5/7 -5/7 }}, {{monzo| 8/3 0 -2/7 2/7 }}]
: [[Eigenmonzo]]s: 2, 7/5
: [[Eigenmonzo]]s: 2, 7/5
* [[9-odd-limit]]
* [[9-odd-limit]]: ~6/5 = {{monzo| 5/21 1/7 0 -1/14 }}
: [{{monzo| 1 0 0 0 }}, {{monzo| 10/7 6/7 0 -3/7 }}, {{monzo| 46/21 5/7 0 -5/14 }}, {{monzo| 20/7 -2/7 0 1/7 }}]
: [{{monzo| 1 0 0 0 }}, {{monzo| 10/7 6/7 0 -3/7 }}, {{monzo| 46/21 5/7 0 -5/14 }}, {{monzo| 20/7 -2/7 0 1/7 }}]
: [[Eigenmonzo]]s: 2, 9/7
: [[Eigenmonzo]]s: 2, 9/7
Line 566: Line 566:
[[Badness]]: 0.056337
[[Badness]]: 0.056337


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 578: Line 578:


Minimax tuning:
Minimax tuning:
* 11-odd-limit
* 11-odd-limit: ~6/5 = {{monzo| 5/21 1/7 0 -1/14 }}
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 10/7 6/7 0 -3/7 0 }}, {{monzo| 46/21 5/7 0 -5/14 0 }}, {{monzo| 20/7 -2/7 0 1/7 0 }}, {{monzo| 71/21 3/7 0 -3/14 0 }}]
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 10/7 6/7 0 -3/7 0 }}, {{monzo| 46/21 5/7 0 -5/14 0 }}, {{monzo| 20/7 -2/7 0 1/7 0 }}, {{monzo| 71/21 3/7 0 -3/14 0 }}]
: Eigenmonzos: 2, 9/7
: Eigenmonzos: 2, 9/7
Line 586: Line 586:
Badness: 0.019333
Badness: 0.019333


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 601: Line 601:
Badness: 0.015652
Badness: 0.015652


=== 17-limit ===
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
Subgroup: 2.3.5.7.11.13.17


Line 616: Line 616:
Badness: 0.013551
Badness: 0.013551


== Quadritikleismic ==
== Quadritikleismic ==
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 631: Line 631:
[[Badness]]: 0.039231
[[Badness]]: 0.039231


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 644: Line 644:
Badness: 0.023406
Badness: 0.023406


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 657: Line 657:
Badness: 0.018731
Badness: 0.018731


== Kleiboh ==
== Kleiboh ==
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 672: Line 672:
[[Badness]]: 0.076460
[[Badness]]: 0.076460


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 685: Line 685:
Badness: 0.052805
Badness: 0.052805


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 698: Line 698:
Badness: 0.031074
Badness: 0.031074


== Marfifths ==
== Marfifths ==
The ''marfifths'' temperament (19&amp;140, named by [[User:Xenllium|Xenllium]]) tempers out the [[hemimage comma]], 10976/10935. It splits the interval of major tenth (~10/3) into three marvelous fifth ([[112/75]]) intervals, and uses it for a generator.
The ''marfifths'' temperament (19&amp;140) tempers out the [[hemimage comma]], 10976/10935. It splits the interval of major tenth (~10/3) into three marvelous fifth ([[112/75]]) intervals, and uses it for a generator.


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7
Line 715: Line 715:
[[Badness]]: 0.063448
[[Badness]]: 0.063448


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 728: Line 728:
Badness: 0.058902
Badness: 0.058902


==== 13-limit ====
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 742: Line 742:


=== Diatessic  ===
=== Diatessic  ===
The ''diatessic'' temperament (121&amp;140, named by [[User:Xenllium|Xenllium]]) is closely related to the '''diatess tuning''' (generator: 505.727281 cents).
The ''diatessic'' temperament (121&amp;140) is closely related to the '''diatess tuning''' (generator: 505.727281 cents).


Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11
Line 756: Line 756:
Badness: 0.061172
Badness: 0.061172


==== 13-limit ====
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 769: Line 769:
Badness: 0.028671
Badness: 0.028671


=== Marf ===
=== Marf ===
The ''marf'' temperament (19&amp;121, named by [[User:Xenllium|Xenllium]]) has a POTE generator which strongly approximates the marvelous fifth interval of 112/75.
The ''marf'' temperament (19&amp;121) has a POTE generator which strongly approximates the marvelous fifth interval of 112/75.


Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11
Line 784: Line 784:
Badness: 0.075112
Badness: 0.075112


==== 13-limit ====
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 797: Line 797:
Badness: 0.038317
Badness: 0.038317


== Marthirds ==
== Marthirds ==
The ''marthirds'' temperament (19&amp;193, named by [[User:Xenllium|Xenllium]]) tempers out the sesquiquartisma (laquadru-atruyo comma), 2460375/2458624. It splits the interval of minor tenth (~12/5) into four marvelous major third ([[56/45]]) intervals, and uses it for a generator.
The ''marthirds'' temperament (19&amp;193) tempers out the sesquiquartisma (laquadru-atruyo comma), 2460375/2458624. It splits the interval of minor tenth (~12/5) into four marvelous major third ([[56/45]]) intervals, and uses it for a generator.


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7
Line 814: Line 814:
[[Badness]]: 0.104253
[[Badness]]: 0.104253


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 827: Line 827:
Badness: 0.075624
Badness: 0.075624


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 840: Line 840:
Badness: 0.043728
Badness: 0.043728


== Novemkleismic ==
== Novemkleismic ==
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 855: Line 855:
[[Badness]]: 0.193429
[[Badness]]: 0.193429


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 868: Line 868:
Badness: 0.051730
Badness: 0.051730


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 881: Line 881:
Badness: 0.039072
Badness: 0.039072


== Sqrtphi ==
== Sqrtphi ==
The just value of sqrt (φ) is 416.545 cents.  
The just value of sqrt (φ) is 416.545 cents.  


Line 896: Line 896:
[[Badness]]: 0.070378
[[Badness]]: 0.070378


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 909: Line 909:
Badness: 0.025515
Badness: 0.025515


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 922: Line 922:
Badness: 0.020040
Badness: 0.020040


=== 17-limit ===
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
Subgroup: 2.3.5.7.11.13.17


Line 935: Line 935:
Badness: 0.013028
Badness: 0.013028


=== 19-limit ===
=== 19-limit ===
Subgroup: 2.3.5.7.11.13.17.19
Subgroup: 2.3.5.7.11.13.17.19


Line 948: Line 948:
Badness: 0.014748
Badness: 0.014748


=== Scales   ===
; Scales
* [[Sqrtphi17]]
* [[Sqrtphi17]]
* [[Sqrtphi23]]
* [[Sqrtphi23]]
* [[Sqrtphi49]]
* [[Sqrtphi49]]


=== Music   ===
; Music
* [http://micro.soonlabel.com/sqrt_phi/daily20111123a-sqrt-phi-17.mp3 Prelude for Piano in Square root of Phi Tuning] by [[Chris Vaisvil]]
* [http://micro.soonlabel.com/sqrt_phi/daily20111123a-sqrt-phi-17.mp3 Prelude for Piano in Square root of Phi Tuning] by [[Chris Vaisvil]]
* [http://micro.soonlabel.com/gene_ward_smith/Others/Sicurella/A%20Fight%20For%20Phi.mp3 A Fight for Phi] by [[Vito Sicurella]]
* [http://micro.soonlabel.com/gene_ward_smith/Others/Sicurella/A%20Fight%20For%20Phi.mp3 A Fight for Phi] by [[Vito Sicurella]]
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