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Septiennealimmal clan: Difference between revisions

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Switch to Sintel's badness, WE & CWE tunings (4/)
Switch to Sintel's badness, WE & CWE tunings (5/5)
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Optimal tunings:  
Optimal tunings:  
* CTE: ~3072/3025 = 26.6667{{c}}, ~55/32 = 937.6658{{c}} (~385/384 = 4.3325{{c}})
* WE: ~3072/3025 = 26.6668{{c}}, ~55/32 = 937.6664{{c}} (~385/384 = 4.3288{{c}})
* CWE: ~3072/3025 = 26.6667{{c}}, ~55/32 = 937.6630{{c}} (~385/384 = 4.3397{{c}})
* CWE: ~3072/3025 = 26.6667{{c}}, ~55/32 = 937.6630{{c}} (~385/384 = 4.3297{{c}})


{{Optimal ET sequence|legend=0| 45, 225c, 270, 1125, 1395, 1665, 5265d }}
{{Optimal ET sequence|legend=0| 45, 225c, 270, 1125, 1395, 1665, 5265d }}


Badness (Smith): 0.0381
Badness (Sintel): 1.26


==== 13-limit ====
==== 13-limit ====
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Optimal tunings:  
Optimal tunings:  
* CTE: ~66/65 = 26.6667{{c}}, ~55/32 = 937.6569{{c}} (~385/384 = 4.3236{{c}})
* WE: ~66/65 = 26.6670{{c}}, ~55/32 = 937.6633{{c}} (~385/384 = 4.3172{{c}})
* CWE: ~66/65 = 26.6667{{c}}, ~55/32 = 937.6515{{c}} (~385/384 = 4.3182{{c}})
* CWE: ~66/65 = 26.6667{{c}}, ~55/32 = 937.6515{{c}} (~385/384 = 4.3182{{c}})


{{Optimal ET sequence|legend=0| 45, 270, 855, 1125, 1395, 1665, 3060d, 4725df }}
{{Optimal ET sequence|legend=0| 45, 270, 855, 1125, 1395, 1665, 3060d, 4725df }}


Badness (Smith): 0.0226
Badness (Sintel): 0.936


== Undecentic ==
== Undecentic ==
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{{Mapping|legend=1| 99 157 230 278 0 | 0 0 0 0 1 }}
{{Mapping|legend=1| 99 157 230 278 0 | 0 0 0 0 1 }}
: mapping generators: ~126/125, ~11


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[POTE]]: ~126/125 = 12.121{{c}}, ~11/8 = 552.756{{c}}
* [[WE]]: ~126/125 = 12.1170{{c}}, ~11/8 = 552.5647{{c}}
* [[CWE]]: ~126/125 = 12.1212{{c}}, ~11/8 = 552.4684{{c}}


{{Optimal ET sequence|legend=1| 99e, 198, 297e, 495ce }}
{{Optimal ET sequence|legend=1| 99e, 198, 297e, 495ce }}


[[Badness]] (Smith): 0.058801
[[Badness]] (Sintel): 1.94


=== 13-limit ===
=== 13-limit ===
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Optimal tunings:  
Optimal tunings:  
* POTE: ~144/143 = 12.121{{c}}, ~11/8 = 552.024{{c}}
* WE: ~144/143 = 12.1170{{c}}, ~11/8 = 551.8308{{c}}
* CWE: ~144/143 = 12.1212{{c}}, ~11/8 = 551.7241{{c}}


{{Optimal ET sequence|legend=0| 99ef, 198 }}
{{Optimal ET sequence|legend=0| 99ef, 198, 693bcdefff }}


Badness (Smith): 0.042547
Badness (Sintel): 1.76


== Schisennealimmal ==
== Schisennealimmal ==
Schisennealimmal ({{nowrap| 171 & 342 }}) has a period of 1/171 octave. [[171edo]] and its multiples are members of both [[schismatic family|schismic]] and ennealimmal, and from this it derives its name.
Schisennealimmal ({{nowrap| 171 & 342 }}) has a period of 1/171 octave. [[171edo]] and its multiples are members of both [[schismic]] and ennealimmal, and from this it derives its name.


[[Subgroup]]: 2.3.5.7.11
[[Subgroup]]: 2.3.5.7.11
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{{Mapping|legend=1| 171 271 397 480 0 | 0 0 0 0 1 }}
{{Mapping|legend=1| 171 271 397 480 0 | 0 0 0 0 1 }}
: mapping generators: ~225/224, ~11


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[POTE]]: ~225/224 = 7.018{{c}}, ~11/8 = 550.954{{c}}
* [[WE]]: ~225/224 = 7.0182{{c}}, ~11/8 = 551.0022{{c}}
* [[CWE]]: ~225/224 = 7.0175{{c}}, ~11/8 = 551.0267{{c}}


{{Optimal ET sequence|legend=1| 171, 342 }}
{{Optimal ET sequence|legend=1| 171, 342 }}


[[Badness]] (Smith): 0.031739
[[Badness]] (Sintel): 1.05


=== 13-limit ===
=== 13-limit ===
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Optimal tunings:  
Optimal tunings:  
* POTE: ~225/224 = 7.018{{c}}, ~11/8 = 551.322{{c}}
* WE: ~225/224 = 7.0175{{c}}, ~11/8 = 551.3212{{c}}
* CWE: ~225/224 = 7.0175{{c}}, ~11/8 = 551.3210{{c}}


{{Optimal ET sequence|legend=0| 171, 342, 855ff, 1197fff }}
{{Optimal ET sequence|legend=0| 171, 342 }}


Badness (Smith): 0.054029
Badness (Sintel): 2.23


==== 17-limit ====
==== 17-limit ====
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Optimal tunings:  
Optimal tunings:  
* POTE: ~225/224 = 7.018{{c}}, ~11/8 = 551.365{{c}}
* WE: ~225/224 = 7.0175{{c}}, ~11/8 = 551.3583{{c}}
* CWE: ~225/224 = 7.0175{{c}}, ~11/8 = 551.3578{{c}}


{{Optimal ET sequence|legend=0| 171, 342, 855ff, 1197fff }}
{{Optimal ET sequence|legend=0| 171, 342, 855ff, 1197fff }}


Badness (Smith): 0.031323
Badness (Sintel): 1.60


=== Schisennealimmic ===
=== Schisennealimmic ===
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Optimal tunings:  
Optimal tunings:  
* POTE: ~225/224 = 7.018{{c}}, ~11/8 = 551.625{{c}}
* WE: ~225/224 = 7.0182{{c}}, ~11/8 = 551.6748{{c}}
* CWE: ~225/224 = 7.0175{{c}}, ~11/8 = 551.7024{{c}}


{{Optimal ET sequence|legend=1| 171, 342f, 513, 855f }}
{{Optimal ET sequence|legend=1| 171, 342f, 513 }}


Badness (Smith): 0.046843
Badness (Sintel): 1.94


==== 17-limit ====
==== 17-limit ====
Line 742: Line 750:


Optimal tunings:  
Optimal tunings:  
* POTE: ~225/224 = 7.018{{c}}, ~11/8 = 551.756{{c}}
* WE: ~225/224 = 7.0180{{c}}, ~11/8 = 551.7893{{c}}
* CWE: ~225/224 = 7.0175{{c}}, ~11/8 = 551.7990{{c}}


{{Optimal ET sequence|legend=0| 171, 342f, 513, 855f }}
{{Optimal ET sequence|legend=0| 171, 342f, 513 }}


Badness (Smith): 0.030622
Badness (Sintel): 1.56


== Lunennealimmal ==
== Lunennealimmal ==
Lunennealimmal ({{nowrap| 441 & 882 }}) has has a period of 1/441 octave. [[441edo]] and its multiples are members of both [[luna family|luna]] and ennealimmal, and from this it derives its name.
Lunennealimmal ({{nowrap| 441 & 882 }}) has has a period of 1/441 octave. [[441edo]] and its multiples are members of both [[luna]] and ennealimmal, and from this it derives its name.


[[Subgroup]]: 2.3.5.7.11
[[Subgroup]]: 2.3.5.7.11
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{{Mapping|legend=1| 441 699 1024 1238 1526 | 0 0 0 0 -1 }}
{{Mapping|legend=1| 441 699 1024 1238 1526 | 0 0 0 0 -1 }}
: mapping generators: ~32805/32768, ~11


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[POTE]]: ~32805/32768 = 2.7211{{c}}, ~11/8 = 551.3584{{c}}
* [[WE]]: ~32805/32768 = 2.7211{{c}}, ~11/8 = 551.3530{{c}}
* [[CWE]]: ~32805/32768 = 2.7211{{c}}, ~11/8 = 551.3503{{c}}


{{Optimal ET sequence|legend=1| 441, 882, 1323, 2205, 3528 }}
{{Optimal ET sequence|legend=1| 441, 882, 1323, 2205, 3528 }}


[[Badness]] (Smith): 0.091939
[[Badness]] (Sintel): 3.04


=== 13-limit ===
=== 13-limit ===
Line 772: Line 783:


Optimal tunings:  
Optimal tunings:  
* POTE: ~729/728 = 2.7211{{c}}, ~11/8 = 551.4043{{c}}
* WE: ~729/728 = 2.7210{{c}}, ~11/8 = 551.3928{{c}}
* CWE: ~729/728 = 2.7211{{c}}, ~11/8 = 551.3899{{c}}


{{Optimal ET sequence|legend=0| 441, 882, 1323, 3528f, 4851ff, 6174dff }}
{{Optimal ET sequence|legend=0| 441, 882, 1323 }}


Badness (Smith): 0.042975
Badness (Sintel): 1.78


=== 17-limit ===
=== 17-limit ===
Line 786: Line 798:


Optimal tunings:  
Optimal tunings:  
* POTE: ~729/728 = 2.7211{{c}}, ~11/8 = 551.3688{{c}}
* WE: ~729/728 = 2.7210{{c}}, ~11/8 = 551.3572{{c}}
* CWE: ~729/728 = 2.7211{{c}}, ~11/8 = 551.3532{{c}}


{{Optimal ET sequence|legend=0| 441, 882, 1323, 2205f, 3528f }}
{{Optimal ET sequence|legend=0| 441, 882, 1323, 2205f }}


Badness (Smith): 0.029334
Badness (Sintel): 1.49


[[Category:Septiennealimmal clan| ]] <!-- main article -->
[[Category:Septiennealimmal clan| ]] <!-- main article -->
[[Category:Temperament clans]]
[[Category:Temperament clans]]
Retrieved from "https://en.xen.wiki/w/Septiennealimmal_clan"