Archytas clan: Difference between revisions
m Text replacement - "Category:Temperament clans" to "Category:Temperament clans Category:Pages with mostly numerical content" |
m →Archy: schism isn't an exo |
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[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[ | * [[WE]]: ~2 = 1196.9552{{c}}, ~3/2 = 707.5215{{c}} | ||
: [[error map]]: {{val| | : [[error map]]: {{val| -3.045 +2.522 +3.952 }} | ||
* [[ | * [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 709.3901{{c}} | ||
: error map: {{val| 0.000 +7. | : error map: {{val| 0.000 +7.435 +12.394 }} | ||
{{Optimal ET sequence|legend=1| 2, 3, 5, 12, 17, 22, 137bdd, 159bddd, 181bbddd }} | {{Optimal ET sequence|legend=1| 2, 3, 5, 12, 17, 22, 137bdd, 159bddd, 181bbddd }} | ||
Line 34: | Line 34: | ||
==== 7-limit extensions ==== | ==== 7-limit extensions ==== | ||
The second comma in the comma list defines which [[7-limit]] family member we are looking at: | The second comma in the comma list defines which [[7-limit]] family member we are looking at: | ||
* [[#Schism|Schism]] adds 360/343, for | * [[#Schism|Schism]] adds 360/343, for a tuning around [[12edo]]; | ||
* Dominant adds [[36/35]], for a tuning | * Dominant adds [[36/35]], for a tuning between [[12edo]] and [[17edo|17c-edo]]; | ||
* [[#Quasisuper|Quasisuper]] adds [[2430/2401]], for a tuning between 17c-edo and [[22edo]]; | * [[#Quasisuper|Quasisuper]] adds [[2430/2401]], for a tuning between 17c-edo and [[22edo]]; | ||
* [[#Superpyth|Superpyth]] adds [[245/243]], for a tuning between 22edo and [[27edo]]; | * [[#Superpyth|Superpyth]] adds [[245/243]], for a tuning between 22edo and [[27edo]]; | ||
Line 57: | Line 57: | ||
* ''[[Brightstone]]'' (+3125/3024) → [[Magic family #Brightstone|Magic family]] | * ''[[Brightstone]]'' (+3125/3024) → [[Magic family #Brightstone|Magic family]] | ||
* ''[[Passion]]'' (+3125/3087) → [[Passion family #Septimal passion|Passion family]] | * ''[[Passion]]'' (+3125/3087) → [[Passion family #Septimal passion|Passion family]] | ||
* | * [[Blackwood]] (+28/27) → [[Limmic temperaments #Blackwood|Limmic temperaments]] | ||
* ''[[Catalan]]'' (+15625/15552) → [[Kleismic family #Catalan|Kleismic family]] | * ''[[Catalan]]'' (+15625/15552) → [[Kleismic family #Catalan|Kleismic family]] | ||
Line 77: | Line 77: | ||
Optimal tunings: | Optimal tunings: | ||
* | * WE: ~2 = 1197.2650{{c}}, ~3/2 = 705.5803{{c}} | ||
* | * CWE: ~2 = 1200.0000{{c}}, ~3/2 = 707.4981{{c}} | ||
{{Optimal ET sequence|legend=0| 5, 12, 17, 39d, 56d }} | {{Optimal ET sequence|legend=0| 5, 12, 17, 39d, 56d }} | ||
Line 98: | Line 98: | ||
Optimal tunings: | Optimal tunings: | ||
* | * WE: ~2 = 1197.1909{{c}}, ~3/2 = 704.4836{{c}} | ||
* | * CWE: ~2 = 1200.0000{{c}}, ~3/2 = 706.4289{{c}} | ||
{{Optimal ET sequence|legend=0| 12f, 17 }} | {{Optimal ET sequence|legend=0| 12f, 17 }} | ||
Line 120: | Line 120: | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[ | * [[WE]]: ~2 = 1197.0549{{c}}, ~3/2 = 708.5478{{c}} | ||
: [[error map]]: {{val| | : [[error map]]: {{val| -2.945 +3.648 -0.548 +2.298 }} | ||
* [[ | * [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 710.1193{{c}} | ||
: error map: {{val| 0.000 +8. | : error map: {{val| 0.000 +8.164 +4.760 +10.935 }} | ||
{{Optimal ET sequence|legend=1| 5, 17, 22, 27, 49, 174bbcddd }} | {{Optimal ET sequence|legend=1| 5, 17, 22, 27, 49, 174bbcddd }} | ||
Line 139: | Line 139: | ||
Optimal tunings: | Optimal tunings: | ||
* | * WE: ~2 = 1197.0673{{c}}, ~3/2 = 708.4391{{c}} | ||
* | * CWE: ~2 = 1200.0000{{c}}, ~3/2 = 710.0129{{c}} | ||
{{Optimal ET sequence|legend=0| 22, 27e, 49 }} | {{Optimal ET sequence|legend=0| 22, 27e, 49 }} | ||
Line 154: | Line 154: | ||
Optimal tunings: | Optimal tunings: | ||
* | * WE: ~2 = 1197.3011{{c}}, ~3/2 = 708.8813{{c}} | ||
* | * CWE: ~2 = 1200.0000{{c}}, ~3/2 = 710.3219{{c}} | ||
{{Optimal ET sequence|legend=0| 22, 27e, 49, 76bcde }} | {{Optimal ET sequence|legend=0| 22, 27e, 49, 76bcde }} | ||
Line 169: | Line 169: | ||
Optimal tunings: | Optimal tunings: | ||
* | * WE: ~2 = 1197.4942{{c}}, ~16/13 = 354.2950{{c}} | ||
* | * CWE: ~2 = 1200.0000{{c}}, ~16/13 = 354.9824{{c}} | ||
{{Optimal ET sequence|legend=0| 27e, 44, 71d, 98bde }} | {{Optimal ET sequence|legend=0| 27e, 44, 71d, 98bde }} | ||
Line 186: | Line 186: | ||
Optimal tunings: | Optimal tunings: | ||
* | * WE: ~2 = 1198.6960{{c}}, ~3/2 = 708.7235{{c}} | ||
* | * CWE: ~2 = 1200.0000{{c}}, ~3/2 = 709.4699{{c}} | ||
{{Optimal ET sequence|legend=0| 5, 17, 22 }} | {{Optimal ET sequence|legend=0| 5, 17, 22 }} | ||
Line 201: | Line 201: | ||
Optimal tunings: | Optimal tunings: | ||
* | * WE: ~2 = 1199.9871{{c}}, ~3/2 = 708.6952{{c}} | ||
* | * CWE: ~2 = 1200.0000{{c}}, ~3/2 = 708.7028{{c}} | ||
{{Optimal ET sequence|legend=0| 5f, 17, 22 }} | {{Optimal ET sequence|legend=0| 5f, 17, 22 }} | ||
Line 218: | Line 218: | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[ | * [[WE]]: ~2 = 1196.9830{{c}}, ~3/2 = 706.4578{{c}} | ||
: [[error map]]: {{val| | : [[error map]]: {{val| -3.017 +1.486 -0.435 +6.190 }} | ||
* [[ | * [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 708.3716{{c}} | ||
: error map: {{val| 0.000 +6. | : error map: {{val| 0.000 +6.417 +4.855 +14.431 }} | ||
{{Optimal ET sequence|legend=1| 17c, 22, 61d }} | {{Optimal ET sequence|legend=1| 17c, 22, 61d }} | ||
Line 237: | Line 237: | ||
Optimal tunings: | Optimal tunings: | ||
* | * WE: ~2 = 1197.5675{{c}}, ~3/2 = 706.7690{{c}} | ||
* | * CWE: ~2 = 1200.0000{{c}}, ~3/2 = 708.3200{{c}} | ||
{{Optimal ET sequence|legend=0| 17c, 22, 39d, 61d }} | {{Optimal ET sequence|legend=0| 17c, 22, 39d, 61d }} | ||
Line 252: | Line 252: | ||
Optimal tunings: | Optimal tunings: | ||
* | * WE: ~2 = 1198.2543{{c}}, ~3/2 = 706.9736{{c}} | ||
* | * CWE: ~2 = 1200.0000{{c}}, ~3/2 = 708.0936{{c}} | ||
{{Optimal ET sequence|legend=0| 17c, 22, 39d }} | {{Optimal ET sequence|legend=0| 17c, 22, 39d }} | ||
Line 267: | Line 267: | ||
Optimal tunings: | Optimal tunings: | ||
* | * WE: ~2 = 1198.8446{{c}}, ~3/2 = 708.3388{{c}} | ||
* | * CWE: ~2 = 1200.0000{{c}}, ~3/2 = 708.0252{{c}} | ||
{{Optimal ET sequence|legend=0| 22 }} | {{Optimal ET sequence|legend=0| 22 }} | ||
Line 286: | Line 286: | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[ | * [[WE]]: ~2 = 1197.2673{{c}}, ~3/2 = 712.0258{{c}} | ||
: [[error map]]: {{val| | : [[error map]]: {{val| -2.733 +7.338 -1.557 -3.808 }} | ||
* [[ | * [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 713.5430{{c}} | ||
: error map: {{val| 0.000 +11. | : error map: {{val| 0.000 +11.588 +3.288 +4.088 }} | ||
{{Optimal ET sequence|legend=1| 5, 27c, 32, 37 }} | {{Optimal ET sequence|legend=1| 5, 27c, 32, 37 }} | ||
Line 303: | Line 303: | ||
Optimal tunings: | Optimal tunings: | ||
* | * WE: ~2 = 1198.0290{{c}}, ~3/2 = 712.2235{{c}} | ||
* | * CWE: ~2 = 1200.0000{{c}}, ~3/2 = 713.3754{{c}} | ||
{{Optimal ET sequence|legend=0| 5, 32, 37 }} | {{Optimal ET sequence|legend=0| 5, 32, 37 }} | ||
Line 318: | Line 318: | ||
Optimal tunings: | Optimal tunings: | ||
* | * WE: ~2 = 1198.1911{{c}}, ~3/2 = 712.4243{{c}} | ||
* | * CWE: ~2 = 1200.0000{{c}}, ~3/2 = 713.4684{{c}} | ||
{{Optimal ET sequence|legend=0| 5, 32, 37 }} | {{Optimal ET sequence|legend=0| 5, 32, 37 }} | ||
Line 333: | Line 333: | ||
Optimal tunings: | Optimal tunings: | ||
* | * WE: ~2 = 1197.2230{{c}}, ~3/2 = 712.1393{{c}} | ||
* | * CWE: ~2 = 1200.0000{{c}}, ~3/2 = 713.6928{{c}} | ||
{{Optimal ET sequence|legend=0| 5e, 32e, 37, 79bce }} | {{Optimal ET sequence|legend=0| 5e, 32e, 37, 79bce }} | ||
Line 348: | Line 348: | ||
Optimal tunings: | Optimal tunings: | ||
* | * WE: ~2 = 1197.2739{{c}}, ~3/2 = 712.1893{{c}} | ||
* | * CWE: ~2 = 1200.0000{{c}}, ~3/2 = 713.7079{{c}} | ||
{{Optimal ET sequence|legend=0| 5e, 32e, 37, 79bcef }} | {{Optimal ET sequence|legend=0| 5e, 32e, 37, 79bcef }} | ||
Line 365: | Line 365: | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[ | * [[WE]]: ~2 = 1196.9257{{c}}, ~3/2 = 709.6211{{c}} | ||
: [[error map]]: {{val| 0.000 +9.883 +0.608 +7.499 }} | : [[error map]]: {{val| 0.000 +9.883 +0.608 +7.499 }} | ||
* [[CWE]]: ~2 = 1200. | * [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 711.5429{{c}} | ||
: error map: {{val| 0.000 +9.588 +5.914 +8.088 }} | : error map: {{val| 0.000 +9.588 +5.914 +8.088 }} | ||
Line 386: | Line 386: | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[ | * [[WE]]: ~2 = 1197.3598{{c}}, ~3/2 = 700.0126{{c}} | ||
: [[error map]]: {{val| | : [[error map]]: {{val| -2.640 -4.583 -4.896 +20.588 }} | ||
* [[ | * [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.7376{{c}} | ||
: error map: {{val| 0.000 -0. | : error map: {{val| 0.000 -0.217 -0.214 +27.699 }} | ||
{{Optimal ET sequence|legend=1| 5c, 7c, 12 }} | {{Optimal ET sequence|legend=1| 5c, 7c, 12 }} | ||
Line 403: | Line 403: | ||
Optimal tunings: | Optimal tunings: | ||
* | * WE: ~2 = 1196.1607{{c}}, ~3/2 = 699.8897{{c}} | ||
* | * CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.4385{{c}} | ||
{{Optimal ET sequence|legend=0| 5c, 7ce, 12, 29de }} | {{Optimal ET sequence|legend=0| 5c, 7ce, 12, 29de }} | ||
Line 424: | Line 424: | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[ | * [[WE]]: ~2 = 1196.6244{{c}}, ~49/40 = 354.9029{{c}} | ||
: [[error map]]: {{val| | : [[error map]]: {{val| -3.376 +4.475 +2.682 -1.940 }} | ||
* [[ | * [[CWE]]: ~2 = 1200.0000{{c}}, ~49/40 = 356.0819{{c}} | ||
: error map: {{val| 0.000 + | : error map: {{val| 0.000 +10.209 +8.949 +6.847 }} | ||
{{Optimal ET sequence|legend=1| 10, 17c, 27, 64b, 91bcd, 118bccd }} | {{Optimal ET sequence|legend=1| 10, 17c, 27, 64b, 91bcd, 118bccd }} | ||
Line 444: | Line 444: | ||
Optimal tunings: | Optimal tunings: | ||
* | * WE: ~2 = 1196.7001{{c}}, ~49/40 = 355.1606{{c}} | ||
* | * CWE: ~2 = 1200.0000{{c}}, ~49/40 = 356.2795{{c}} | ||
{{Optimal ET sequence|legend=0| 10e, 17cee, 27e, 64be, 91bcdee }} | {{Optimal ET sequence|legend=0| 10e, 17cee, 27e, 64be, 91bcdee }} | ||
Line 459: | Line 459: | ||
Optimal tunings: | Optimal tunings: | ||
* | * WE: ~2 = 1197.2504{{c}}, ~16/13 = 355.4132{{c}} | ||
* | * CWE: ~2 = 1200.0000{{c}}, ~16/13 = 356.3273{{c}} | ||
{{Optimal ET sequence|legend=0| 10e, 27e, 37, 64be }} | {{Optimal ET sequence|legend=0| 10e, 27e, 37, 64be }} | ||
Line 474: | Line 474: | ||
Optimal tunings: | Optimal tunings: | ||
* | * WE: ~2 = 1195.4102{{c}}, ~11/9 = 354.0597{{c}} | ||
* | * CWE: ~2 = 1200.0000{{c}}, ~11/9 = 355.5207{{c}} | ||
{{Optimal ET sequence|legend=0| 10, 17c, 27e }} | {{Optimal ET sequence|legend=0| 10, 17c, 27e }} | ||
Line 489: | Line 489: | ||
Optimal tunings: | Optimal tunings: | ||
* | * WE: ~2 = 1195.9943{{c}}, ~11/9 = 354.2695{{c}} | ||
* | * CWE: ~2 = 1200.0000{{c}}, ~11/9 = 355.5398{{c}} | ||
{{Optimal ET sequence|legend=0| 10, 17c, 27e }} | {{Optimal ET sequence|legend=0| 10, 17c, 27e }} | ||
Line 504: | Line 504: | ||
Optimal tunings: | Optimal tunings: | ||
* | * WE: ~2 = 1197.9660{{c}}, ~49/40 = 356.1056{{c}} | ||
* | * CWE: ~2 = 1200.0000{{c}}, ~49/40 = 356.7075{{c}} | ||
{{Optimal ET sequence|legend=0| 10, 27, 37 }} | {{Optimal ET sequence|legend=0| 10, 27, 37 }} | ||
Line 519: | Line 519: | ||
Optimal tunings: | Optimal tunings: | ||
* | * WE: ~2 = 1198.1741{{c}}, ~16/13 = 356.1582{{c}} | ||
* | * CWE: ~2 = 1200.0000{{c}}, ~16/13 = 356.7008{{c}} | ||
{{Optimal ET sequence|legend=0| 10, 27, 37 }} | {{Optimal ET sequence|legend=0| 10, 27, 37 }} | ||
Line 541: | Line 541: | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[ | * [[WE]]: ~2 = 1195.1377{{c}}, ~10/7 = 635.2932{{c}} | ||
: [[error map]]: {{val| | : [[error map]]: {{val| -4.862 +3.925 +12.908 -9.759 }} | ||
* [[ | * [[CWE]]: ~2 = 1200.0000{{c}}, ~10/7 = 638.0791{{c}} | ||
: error map: {{val| 0.000 + | : error map: {{val| 0.000 +12.282 +23.291 +2.700 }} | ||
{{Optimal ET sequence|legend=1| 2, 13, 15, 32c }} | {{Optimal ET sequence|legend=1| 2, 13, 15, 32c }} | ||
Line 558: | Line 558: | ||
Optimal tunings: | Optimal tunings: | ||
* | * WE: ~2 = 1195.4920{{c}}, ~10/7 = 635.5183{{c}} | ||
* | * CWE: ~2 = 1200.0000{{c}}, ~10/7 = 638.0884{{c}} | ||
{{Optimal ET sequence|legend=0| 2, 13, 15, 32c, 47bc }} | {{Optimal ET sequence|legend=0| 2, 13, 15, 32c, 47bc }} | ||
Line 573: | Line 573: | ||
Optimal tunings: | Optimal tunings: | ||
* | * WE: ~2 = 1195.0786{{c}}, ~10/7 = 635.0197{{c}} | ||
* | * CWE: ~2 = 1200.0000{{c}}, ~10/7 = 637.6691{{c}} | ||
{{Optimal ET sequence|legend=0| 15, 17c, 32cf }} | {{Optimal ET sequence|legend=0| 15, 17c, 32cf }} | ||
Line 588: | Line 588: | ||
Optimal tunings: | Optimal tunings: | ||
* | * WE: ~2 = 1196.0245{{c}}, ~10/7 = 634.6516{{c}} | ||
* | * CWE: ~2 = 1200.0000{{c}}, ~10/7 = 636.9528{{c}} | ||
{{Optimal ET sequence|legend=0| 2f, 15f, 17c }} | {{Optimal ET sequence|legend=0| 2f, 15f, 17c }} | ||
Line 609: | Line 609: | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[ | * [[WE]]: ~2 = 1196.2742{{c}}, ~10/7 = 620.2918{{c}} | ||
: [[error map]]: {{val| | : [[error map]]: {{val| -3.726 +3.230 +4.980 -1.550 }} | ||
* [[ | * [[CWE]]: ~2 = 1200.0000{{c}}, ~10/7 = 622.3179{{c}} | ||
: error map: {{val| 0.000 +9. | : error map: {{val| 0.000 +9.634 +12.826 +7.996 }} | ||
{{Optimal ET sequence|legend=1| 2, 25, 27 }} | {{Optimal ET sequence|legend=1| 2, 25, 27 }} | ||
Line 626: | Line 626: | ||
Optimal tunings: | Optimal tunings: | ||
* | * WE: ~2 = 1195.4148{{c}}, ~10/7 = 619.7729{{c}} | ||
* | * CWE: ~2 = 1200.0000{{c}}, ~10/7 = 622.2525{{c}} | ||
{{Optimal ET sequence|legend=0| 2, 25e, 27e }} | {{Optimal ET sequence|legend=0| 2, 25e, 27e }} | ||
Line 641: | Line 641: | ||
Optimal tunings: | Optimal tunings: | ||
* | * WE: ~2 = 1195.6284{{c}}, ~10/7 = 619.6738{{c}} | ||
* | * CWE: ~2 = 1200.0000{{c}}, ~10/7 = 622.0631{{c}} | ||
{{Optimal ET sequence|legend=0| 2f, 27e }} | {{Optimal ET sequence|legend=0| 2f, 27e }} | ||
Line 661: | Line 661: | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[ | * [[WE]]: ~2 = 1198.9028{{c}}, ~6/5 = 337.1334{{c}} | ||
: [[error map]]: {{val| | : [[error map]]: {{val| -1.097 +9.086 -13.503 +2.508 }} | ||
* [[ | * [[CWE]]: ~2 = 1200.0000{{c}}, ~6/5 = 337.4588{{c}} | ||
: error map: {{val| 0.000 +10. | : error map: {{val| 0.000 +10.751 -11.066 +5.762 }} | ||
{{Optimal ET sequence|legend=1| 7, 18d, 25, 32 }} | {{Optimal ET sequence|legend=1| 7, 18d, 25, 32 }} | ||
Line 678: | Line 678: | ||
Optimal tunings: | Optimal tunings: | ||
* | * WE: ~2 = 1198.5480{{c}}, ~6/5 = 337.1557{{c}} | ||
* | * CWE: ~2 = 1200.0000{{c}}, ~6/5 = 337.6000{{c}} | ||
{{Optimal ET sequence|legend=0| 7, 25e, 32 }} | {{Optimal ET sequence|legend=0| 7, 25e, 32 }} | ||
Line 693: | Line 693: | ||
Optimal tunings: | Optimal tunings: | ||
* | * WE: ~2 = 1197.7111{{c}}, ~6/5 = 336.8391{{c}} | ||
* | * CWE: ~2 = 1200.0000{{c}}, ~6/5 = 337.5336{{c}} | ||
{{Optimal ET sequence|legend=0| 7, 25e, 32f }} | {{Optimal ET sequence|legend=0| 7, 25e, 32f }} | ||
Line 708: | Line 708: | ||
Optimal tunings: | Optimal tunings: | ||
* | * WE: ~2 = 1197.7807{{c}}, ~6/5 = 336.8884{{c}} | ||
* | * CWE: ~2 = 1200.0000{{c}}, ~6/5 = 337.5279{{c}} | ||
{{Optimal ET sequence|legend=0| 7, 25e, 32f }} | {{Optimal ET sequence|legend=0| 7, 25e, 32f }} |