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Moctdelismic clan: Difference between revisions

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Created page with "{{Technical data page}} The '''moctdelismic clan''' of rank-3 temperaments tempers out the moctdel comma, 1375/1372, the amount by which a stack of three 7/5s falls short of 11/4, one octave above 11/8. The second comma in the comma list determines how we extend the no-3 subgroup temperament to include the harmonic 3. Indra adds 540/539 as well as 3025/3024, prodigy adds 225/224 as well as 441/4..."
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{{Technical data page}}
{{Technical data page}}
The '''moctdelismic clan''' of [[Rank-3 temperament|rank-3]] [[temperament]]s [[Tempering out|tempers out]] the moctdel comma, [[1375/1372]], the amount by which a stack of three [[7/5]]s falls short of [[11/4]], one octave above [[11/8]].  
The '''moctdelismic clan''' of [[rank-3 temperament|rank-3]] [[regular temperament|temperament]]s [[tempering out|tempers out]] the moctdelisma, [[1375/1372]], the amount by which a stack of three [[7/5]]'s falls short of [[11/4]], one octave above [[11/8]].  


== Moctdelic ==
[[Subgroup]]: 2.5.7.11
[[Comma list]]: 1375/1372
{{Mapping|legend=2| 1 0 0 2 | 0 1 0 -3 | 0 0 1 3 }}
: Mapping generators: ~2, ~5, ~7
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.0558{{c}}, ~5/4 = 385.7504{{c}}, ~7/4 = 969.3743{{c}}
: [[error map]]: {{val| +0.056 -0.452 +0.660 -0.334 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~5/4 = 385.7894{{c}}, ~7/4 = 969.4163{{c}}
: error map: {{val| 0.000 -0.524 +0.590 -0.437 }}
{{Optimal ET sequence|legend=1| 25, 29, 31, 37, 72, 103, 109, 255, 364, 734, 843, 952 }}
[[Badness]] (Sintel): 0.110
=== Overview to extensions ===
The second comma in the comma list determines how we extend the no-3 subgroup temperament to include the harmonic 3. Indra adds [[540/539]] as well as [[3025/3024]], prodigy adds [[225/224]] as well as [[441/440]], and agni adds [[385/384]] as well as [[2401/2400]]. Dimcomp adds [[6250/6237]] as well as [[9801/9800]], splitting the octave in four.
The second comma in the comma list determines how we extend the no-3 subgroup temperament to include the harmonic 3. Indra adds [[540/539]] as well as [[3025/3024]], prodigy adds [[225/224]] as well as [[441/440]], and agni adds [[385/384]] as well as [[2401/2400]]. Dimcomp adds [[6250/6237]] as well as [[9801/9800]], splitting the octave in four.


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* ''[[Prodigy]]'' (+225/224 or 441/440) → [[Marvel family #Prodigy|Marvel family]]
* ''[[Prodigy]]'' (+225/224 or 441/440) → [[Marvel family #Prodigy|Marvel family]]
* ''[[Agni]]'' (+385/384 or 2401/2400) → [[Breed family #Agni|Breed family]]
* ''[[Agni]]'' (+385/384 or 2401/2400) → [[Breed family #Agni|Breed family]]
* ''[[Indra]]'' (+540/539 or 441/440) → [[Mirkwai family #Prodigy|Mirkwai family]]
* ''[[Indra]]'' (+540/539) → [[Swetismic temperaments #Indra|Swetismic temperaments]]
* ''[[Moctpine]]'' (+4000/3993) → [[Wizardharry clan #Moctpine|Wizardharry clan]]
* ''[[Dimcomp]]'' (+6250/6237 or 9801/9800) → [[Dimcomp family #Undecimal dimcomp|Dimcomp family]]
* ''[[Dimcomp]]'' (+6250/6237 or 9801/9800) → [[Dimcomp family #Undecimal dimcomp|Dimcomp family]]


Considered below are mendel (12 & 31 & 152) and moctpine (29 & 72 & 80), besides the no-3 subgroup temperament.  
Considered below are mendel and compass, besides the no-3 subgroup temperament.  
 
== Mendel ==
: ''For the 7-limit version of this temperament, see [[Miscellaneous 7-limit temperaments #Metric]].''


== Moctdelic ==
Named by [[Xenllium]] in 2026, mendel tempers out the vishdel comma, [[5632/5625]], as well as [[meter]] (703125/702464). It can be extended to the 13-limit by adding [[352/351]] or [[625/624]] to the comma basis.
[[Subgroup]]: 2.5.7.11


[[Comma list]]: 1375/1372
[[Subgroup]]: 2.3.5.7.11


{{Mapping|legend=2| 1 0 0 2 | 0 1 0 -3 | 0 0 1 3 }}
[[Comma list]]: 1375/1372, 5632/5625


: Sval mapping generators: ~2, ~5, ~7
{{Mapping|legend=1| 1 0 -1 -6 -13 | 0 1 1 3 6 | 0 0 3 7 12 }}
: Mapping generators: ~2, ~3, ~112/75


[[Optimal tuning]]s:
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.056¢, ~5 = 2785.862¢, ~7 = 3369.486¢
* [[WE]]: ~2 = 1199.8401{{c}}, ~3 = 702.2508{{c}}, ~112/75 = 694.6555{{c}}
* [[CWE]]: ~2 = 1200.000¢, ~5 = 2785.789¢, ~7 = 3369.416¢
: [[error map]]: {{val| -0.160 +0.136 -0.097 +0.994 -0.828 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3 = 702.2809{{c}}, ~112/75 = 694.7567{{c}}
: error map: {{val| 0.000 +0.326 +0.237 +1.314 -0.552 }}
 
{{Optimal ET sequence|legend=1| 12, 19e, 31, 90e, 109, 121, 140, 152, 292, 323, 444d, 475d, 627d }}


{{Optimal ET sequence|legend=1| 25, 29, 31, 37 }}
[[Badness]] (Sintel): 1.20


[[Badness]] (Sintel): 0.110
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


== Mendel ==
Comma list: 352/351, 625/624, 1375/1372
[[Subgroup]]: 2.3.5.7.11


[[Comma list]]: 1375/1372, 5632/5625
Mapping: {{mapping| 1 0 -1 -6 -13 -8 | 0 1 1 3 6 3 | 0 0 3 7 12 12 }}


{{Mapping|legend=1| 1 0 2 1 -1 | 0 1 1 3 6 | 0 0 -3 -7 -12 }}
Optimal tunings:
* WE: ~2 = 1199.7481{{c}}, ~3 = 702.7304{{c}}, ~112/75 = 694.3426{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3 = 702.8125{{c}}, ~112/75 = 694.4843{{c}}


: Mapping generators: ~2, ~3, ~75/56
{{Optimal ET sequence|legend=0| 12f, 19e, 31, 78f, 90e, 109, 121, 140, 152f, 261, 292 }}


[[Optimal tuning]]s:
Badness (Sintel): 1.34
* [[WE]]: ~2 = 1199.840¢, ~3 = 1902.091¢, ~75/56 = 505.185¢
* [[CWE]]: ~2 = 1200.000¢, ~3 = 1902.281¢, ~75/56 = 505.243¢


{{Optimal ET sequence|legend=1| 12, 19e, 31, 90e, 109, 121, 140, 152, 292 }}
== Compass ==
: ''For the 7-limit version of this temperament, see [[Miscellaneous 7-limit temperaments #Compass]].''


[[Badness]] (Sintel): 1.202
Named by [[Xenllium]] in 2021, compass tempers out [[4375/4356]].  


== Moctpine ==
[[Subgroup]]: 2.3.5.7.11
[[Subgroup]]: 2.3.5.7.11


[[Comma list]]: 1375/1372, 4000/3993
[[Comma list]]: 1375/1372, 4375/4356
 
{{Mapping|legend=1| 1 2 0 -2 -4 | 0 -5 0 2 6 | 0 0 1 2 3 }}
: Mapping generators: ~2, ~35/33, ~5
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.1322{{c}}, ~35/33 = 99.6163{{c}}, ~5/4 = 384.7310{{c}}
: [[error map]]: {{val| +0.132 +0.228 -1.318 +0.133 +0.838 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~35/33 = 99.5842{{c}}, ~5/4 = 384.8078{{c}}
: error map: {{val| 0.000 +0.124 -1.506 -0.042 +0.611 }}
 
{{Optimal ET sequence|legend=1| 12, …, 37, 49, 60e, 72, 181, 193, 265, 446c, 518c }}
 
[[Badness]] (Sintel): 1.68
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


{{Mapping|legend=1| 1 2 1 1 2 | 0 -3 -1 -1 0 | 0 0 3 4 3 }}
Comma list: 364/363, 625/624, 1375/1372


: Mapping generators: ~2, ~11/10, ~7/5
Mapping: {{mapping| 1 2 0 -2 -4 -6 | 0 -5 0 2 6 5 | 0 0 1 2 3 4 }}


[[Optimal tuning]]s:
Optimal tunings:
* [[WE]]: ~2 = 1199.975¢, ~11/10 = 165.985¢, ~7/5 = 583.872¢
* WE: ~2 = 1199.9110{{c}}, ~35/33 = 99.5193{{c}}, ~5/4 = 385.3897{{c}}
* [[CWE]]: ~2 = 1200.000¢, ~11/10 = 165.994¢, ~7/5 = 583.877¢
* CWE: ~2 = 1200.0000{{c}}, ~35/33 = 99.5397{{c}}, ~5/4 = 385.3536{{c}}


{{Optimal ET sequence|legend=1| 29, 37, 43, 72, 152, 224 }}
{{Optimal ET sequence|legend=0| 12f, …, 37, 49f, 72, 121, 193 }}


[[Badness]] (Sintel): 1.275
Badness (Sintel): 1.36


[[Category:Temperament clans]]
[[Category:Temperament clans]]
[[Category:Moctdelismic clan| ]] <!-- main article -->
[[Category:Moctdelismic clan| ]] <!-- main article -->
[[Category:Moctdelismic| ]] <!-- key article -->
[[Category:Rank 3]]
[[Category:Rank 3]]
Retrieved from "https://en.xen.wiki/w/Moctdelismic_clan"