Moctdelismic clan: Difference between revisions

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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 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 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.
 
Discussed elsewhere are:
* ''[[Prodigy]]'' (+225/224 or 441/440) → [[Marvel family #Prodigy|Marvel family]]
* ''[[Agni]]'' (+385/384 or 2401/2400) → [[Breed family #Agni|Breed family]]
* ''[[Indra]]'' (+540/539 or 441/440) → [[Mirkwai family #Prodigy|Mirkwai family]]
* ''[[Dimcomp]]'' (+6250/6237 or 9801/9800) → [[Dimcomp family #Undecimal dimcomp|Dimcomp family]]
 
Considered below are mendel, moctpine, and compass, besides the no-3 subgroup temperament.  


== Moctdelic ==
== Moctdelic ==
Line 18: Line 8:


{{Mapping|legend=2| 1 0 0 2 | 0 1 0 -3 | 0 0 1 3 }}
{{Mapping|legend=2| 1 0 0 2 | 0 1 0 -3 | 0 0 1 3 }}
 
: Mapping generators: ~2, ~5, ~7
: Sval mapping generators: ~2, ~5, ~7


[[Optimal tuning]]s:
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.056¢, ~5 = 2785.862¢, ~7 = 3369.486¢
* [[WE]]: ~2 = 1200.0558{{c}}, ~5/4 = 385.7504{{c}}, ~7/4 = 969.3743{{c}}
* [[CWE]]: ~2 = 1200.000¢, ~5 = 2785.789¢, ~7 = 3369.416¢
: [[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 }}
{{Optimal ET sequence|legend=1| 25, 29, 31, 37, 72, 103, 109, 255, 364, 734, 843, 952 }}


[[Badness]] (Sintel): 0.110
[[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.
Discussed elsewhere are:
* ''[[Prodigy]]'' (+225/224 or 441/440) → [[Marvel family #Prodigy|Marvel family]]
* ''[[Agni]]'' (+385/384 or 2401/2400) → [[Breed family #Agni|Breed family]]
* ''[[Indra]]'' (+540/539) → [[Mirkwai family #Prodigy|Mirkwai family]]
* ''[[Dimcomp]]'' (+6250/6237 or 9801/9800) → [[Dimcomp family #Undecimal dimcomp|Dimcomp family]]
Considered below are mendel, moctpine, and compass, besides the no-3 subgroup temperament.


== Mendel ==
== Mendel ==
Line 38: Line 40:
[[Comma list]]: 1375/1372, 5632/5625
[[Comma list]]: 1375/1372, 5632/5625


{{Mapping|legend=1| 1 0 2 1 -1 | 0 1 1 3 6 | 0 0 -3 -7 -12 }}
{{Mapping|legend=1| 1 0 -1 -6 -13 | 0 1 1 3 6 | 0 0 3 7 12 }}
 
: Mapping generators: ~2, ~3, ~112/75
: Mapping generators: ~2, ~3, ~75/56


[[Optimal tuning]]s:
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.840¢, ~3 = 1902.091¢, ~75/56 = 505.185¢
* [[WE]]: ~2 = 1199.8401{{c}}, ~3 = 702.2508{{c}}, ~112/75 = 694.6555{{c}}
* [[CWE]]: ~2 = 1200.000¢, ~3 = 1902.281¢, ~75/56 = 505.243¢
: [[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 }}
{{Optimal ET sequence|legend=1| 12, 19e, 31, 90e, 109, 121, 140, 152, 292, 323, 444d, 475d, 627d }}


[[Badness]] (Sintel): 1.202
[[Badness]] (Sintel): 1.20


=== 13-limit ===
=== 13-limit ===
[[Subgroup]]: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


[[Comma list]]: 352/351, 625/624, 1375/1372
Comma list: 352/351, 625/624, 1375/1372


{{Mapping|legend=1| 1 0 2 1 -1 4 | 0 1 1 3 6 3 | 0 0 -3 -7 -12 -12 }}
Mapping: {{mapping| 1 0 -1 -6 -13 -8 | 0 1 1 3 6 3 | 0 0 3 7 12 12 }}


[[Optimal tuning]]s:
Optimal tunings:
* [[WE]]: ~2 = 1199.748¢, ~3 = 1902.479¢, ~75/56 = 505.405¢
* WE: ~2 = 1199.7481{{c}}, ~3 = 702.7304{{c}}, ~112/75 = 694.3426{{c}}
* [[CWE]]: ~2 = 1200.000¢, ~3 = 1902.813¢, ~75/56 = 505.516¢
* CWE: ~2 = 1200.0000{{c}}, ~3 = 702.8125{{c}}, ~112/75 = 694.4843{{c}}


{{Optimal ET sequence|legend=1| 12f, 19e, 31, 90e, 109, 121, 140, 152f, 261, 292 }}
{{Optimal ET sequence|legend=0| 12f, 19e, 31, 78f, 90e, 109, 121, 140, 152f, 261, 292 }}


[[Badness]] (Sintel): 1.339
Badness (Sintel): 1.34


== Moctpine ==
== Moctpine ==
Line 71: Line 74:


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


[[Optimal tuning]]s:
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.975¢, ~11/10 = 165.985¢, ~7/5 = 583.872¢
* [[WE]]: ~2 = 1199.9745{{c}}, ~11/10 = 165.9846{{c}}, ~7/5 = 583.8721{{c}}
* [[CWE]]: ~2 = 1200.000¢, ~11/10 = 165.994¢, ~7/5 = 583.877¢
: [[error map]]: {{val| -0.025 +0.040 -0.707 +0.652 +0.247 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~11/10 = 165.9939{{c}}, ~7/5 = 583.8766{{c}}
: error map: {{val| 0.000 +0.063 -0.678 +0.686 +0.312 }}


{{Optimal ET sequence|legend=1| 29, 37, 43, 72, 152, 224 }}
{{Optimal ET sequence|legend=1| 29, 37, 43, 72, 152, 224, 629, 781, 853c }}


[[Badness]] (Sintel): 1.275
[[Badness]] (Sintel): 1.28


== Compass ==
== Compass ==
Line 90: Line 94:


{{Mapping|legend=1| 1 2 0 -2 -4 | 0 -5 0 2 6 | 0 0 1 2 3 }}
{{Mapping|legend=1| 1 2 0 -2 -4 | 0 -5 0 2 6 | 0 0 1 2 3 }}
: Mapping generators: ~2, ~35/33, ~5
: Mapping generators: ~2, ~35/33, ~5


[[Optimal tuning]]s:
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.132¢, ~35/33 = 99.616¢, ~5 = 2784.996¢
* [[WE]]: ~2 = 1200.1322{{c}}, ~35/33 = 99.6163{{c}}, ~5/4 = 384.7310{{c}}
* [[CWE]]: ~2 = 1200.000¢, ~35/33 = 99.584¢, ~5 = 2784.808¢
: [[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 }}
{{Optimal ET sequence|legend=1| 12, …, 37, 49, 60e, 72, 181, 193, 265, 446c, 518c }}


[[Badness]] (Sintel): 1.679
[[Badness]] (Sintel): 1.68


=== 13-limit ===
=== 13-limit ===
[[Subgroup]]: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13
 
[[Comma list]]: 364/363, 625/624, 1375/1372


{{Mapping|legend=1| 1 2 0 -2 -4 -6 | 0 -5 0 2 6 5 | 0 0 1 2 3 4 }}
Comma list: 364/363, 625/624, 1375/1372


: Mapping generators: ~2, ~35/33, ~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 = 1199.911¢, ~35/33 = 99.519¢, ~5 = 2785.212¢
* WE: ~2 = 1199.9110{{c}}, ~35/33 = 99.5193{{c}}, ~5/4 = 385.3897{{c}}
* [[CWE]]: ~2 = 1200.000¢, ~35/33 = 99.540¢, ~5 = 2785.354¢
* CWE: ~2 = 1200.0000{{c}}, ~35/33 = 99.5397{{c}}, ~5/4 = 385.3536{{c}}


{{Optimal ET sequence|legend=1| 12f, 25f, 37, 49f, 72, 121, 193 }}
{{Optimal ET sequence|legend=0| 12f, …, 37, 49f, 72, 121, 193 }}


[[Badness]] (Sintel): 1.362
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]]

Revision as of 16:48, 17 January 2026

This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.

The moctdelismic clan of rank-3 temperaments 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.

Moctdelic

Subgroup: 2.5.7.11

Comma list: 1375/1372

Subgroup-val mapping: [⟨1 0 0 2], ⟨0 1 0 -3], ⟨0 0 1 3]]

Mapping generators: ~2, ~5, ~7

Optimal tunings:

  • WE: ~2 = 1200.0558 ¢, ~5/4 = 385.7504 ¢, ~7/4 = 969.3743 ¢
error map: ⟨+0.056 -0.452 +0.660 -0.334]
  • CWE: ~2 = 1200.0000 ¢, ~5/4 = 385.7894 ¢, ~7/4 = 969.4163 ¢
error map: ⟨0.000 -0.524 +0.590 -0.437]

Optimal ET sequence: 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.

Discussed elsewhere are:

Considered below are mendel, moctpine, and compass, besides the no-3 subgroup temperament.

Mendel

For the 7-limit version of this temperament, see Miscellaneous 7-limit temperaments #Metric.

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: 2.3.5.7.11

Comma list: 1375/1372, 5632/5625

Mapping: [⟨1 0 -1 -6 -13], ⟨0 1 1 3 6], ⟨0 0 3 7 12]]

Mapping generators: ~2, ~3, ~112/75

Optimal tunings:

  • WE: ~2 = 1199.8401 ¢, ~3 = 702.2508 ¢, ~112/75 = 694.6555 ¢
error map: ⟨-0.160 +0.136 -0.097 +0.994 -0.828]
  • CWE: ~2 = 1200.0000 ¢, ~3 = 702.2809 ¢, ~112/75 = 694.7567 ¢
error map: ⟨0.000 +0.326 +0.237 +1.314 -0.552]

Optimal ET sequence: 12, 19e, 31, 90e, 109, 121, 140, 152, 292, 323, 444d, 475d, 627d

Badness (Sintel): 1.20

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 352/351, 625/624, 1375/1372

Mapping: [⟨1 0 -1 -6 -13 -8], ⟨0 1 1 3 6 3], ⟨0 0 3 7 12 12]]

Optimal tunings:

  • WE: ~2 = 1199.7481 ¢, ~3 = 702.7304 ¢, ~112/75 = 694.3426 ¢
  • CWE: ~2 = 1200.0000 ¢, ~3 = 702.8125 ¢, ~112/75 = 694.4843 ¢

Optimal ET sequence: 12f, 19e, 31, 78f, 90e, 109, 121, 140, 152f, 261, 292

Badness (Sintel): 1.34

Moctpine

Subgroup: 2.3.5.7.11

Comma list: 1375/1372, 4000/3993

Mapping: [⟨1 2 1 1 2], ⟨0 -3 -1 -1 0], ⟨0 0 3 4 3]]

Mapping generators: ~2, ~11/10, ~7/5

Optimal tunings:

  • WE: ~2 = 1199.9745 ¢, ~11/10 = 165.9846 ¢, ~7/5 = 583.8721 ¢
error map: ⟨-0.025 +0.040 -0.707 +0.652 +0.247]
  • CWE: ~2 = 1200.0000 ¢, ~11/10 = 165.9939 ¢, ~7/5 = 583.8766 ¢
error map: ⟨0.000 +0.063 -0.678 +0.686 +0.312]

Optimal ET sequence: 29, 37, 43, 72, 152, 224, 629, 781, 853c

Badness (Sintel): 1.28

Compass

For the 7-limit version of this temperament, see Miscellaneous 7-limit temperaments #Compass.

Subgroup: 2.3.5.7.11

Comma list: 1375/1372, 4375/4356

Mapping: [⟨1 2 0 -2 -4], ⟨0 -5 0 2 6], ⟨0 0 1 2 3]]

Mapping generators: ~2, ~35/33, ~5

Optimal tunings:

  • WE: ~2 = 1200.1322 ¢, ~35/33 = 99.6163 ¢, ~5/4 = 384.7310 ¢
error map: ⟨+0.132 +0.228 -1.318 +0.133 +0.838]
  • CWE: ~2 = 1200.0000 ¢, ~35/33 = 99.5842 ¢, ~5/4 = 384.8078 ¢
error map: ⟨0.000 +0.124 -1.506 -0.042 +0.611]

Optimal ET sequence: 12, …, 37, 49, 60e, 72, 181, 193, 265, 446c, 518c

Badness (Sintel): 1.68

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 364/363, 625/624, 1375/1372

Mapping: [⟨1 2 0 -2 -4 -6], ⟨0 -5 0 2 6 5], ⟨0 0 1 2 3 4]]

Optimal tunings:

  • WE: ~2 = 1199.9110 ¢, ~35/33 = 99.5193 ¢, ~5/4 = 385.3897 ¢
  • CWE: ~2 = 1200.0000 ¢, ~35/33 = 99.5397 ¢, ~5/4 = 385.3536 ¢

Optimal ET sequence: 12f, …, 37, 49f, 72, 121, 193

Badness (Sintel): 1.36

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