Semiporwellismic clan: Difference between revisions

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{{Technical data page}}
{{Technical data page}}
The '''semiporwellismic clan''' of [[Rank-3 temperament|rank-3]] [[temperament]]s [[Tempering out|tempers out]] the [[semiporwellisma]], 16384/16335 = {{monzo| 14 -3 -1 0 -2 }}.  
The '''semiporwellismic clan''' of [[rank-3 temperament]]s [[tempering out|tempers out]] the [[semiporwellisma]] ({{monzo|legend=1| 14 -3 -1 0 -2 }}, [[ratio]]: 16384/16335).  


Temperaments discussed elsewhere are:
For the rank-4 temperament, see [[Catalog of rank-4 temperaments #Semiporwellismic (16384/16335)]].  
* [[Sensamagic]] (+385/384 or 896/891) → [[Sensamagic family #Undecimal sensamagic|Sensamagic family]]
* ''[[Kapo]]'' (+3025/3024 or 5120/5103) → [[Hemifamity family #Kapo|Hemifamity family]]
* ''[[Semiporwell]]'' (+6144/6125 or 9801/9800) → [[Porwell family #Semiporwell|Porwell family]]
 
Considered below is semiporwellic, the no-7 subgroup temperament. For the rank-4 temperament, see [[Rank-4 temperament #Semiporwellismic (16384/16335)]].  


== Semiporwellic ==
== Semiporwellic ==
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{{Mapping|legend=2| 1 0 0 0 7 | 0 1 1 0 -2 | 0 0 2 0 -1 }}
{{Mapping|legend=2| 1 0 0 0 7 | 0 1 1 0 -2 | 0 0 2 0 -1 }}
: mapping generators: ~2, ~3, ~128/99
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.7329{{c}}, ~3/2 = 702.3657{{c}}, ~128/99 = 442.1589{{c}}
: [[error map]]: {{val| -0.267 +0.144 +0.103 +0.456 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.5107{{c}}, ~128/99 = 442.2243{{c}}
: error map: {{val| 0.000 +0.556 +0.646 +1.436 }}
{{Optimal ET sequence|legend=1| 19, 22, 41, 46, 65, 87, 152, 369, 521e, 1194bcee, 1305bcee, 1457bceee, 1609bcceee, 1674bcceee, 1826bcceeee }}
[[Badness]] (Sintel): 0.761
=== Overview to extensions ===
Temperaments discussed elsewhere are:
* [[Sensamagic]] (+385/384 or 896/891) → [[Sensamagic family #Undecimal sensamagic|Sensamagic family]]
* ''[[Kapo]]'' (+3025/3024 or 5120/5103) → [[Aberschismic family #Kapo|Aberschismic family]]
* ''[[Semiporwell]]'' (+6144/6125 or 9801/9800) → [[Porwell family #Semiporwell|Porwell family]]
Considered below is the add-31 subgroup temperament of semiporwellic.
== Subgroup extensions ==
=== Semiporwellic (2.3.5.11.31) ===
Subgroup: 2.3.5.11.31
Comma list: 496/495, 961/960


: sval mapping generators: ~2, ~3, ~128/99
Subgroup-val mapping: {{mapping| 1 0 0 0 7 | 0 1 1 0 -2 | 0 0 2 0 -1 }}


[[Optimal tuning]] ([[CTE]]) ~2 = 1\1, ~3/2 = 702.4701, ~128/99 = 442.1061
Optimal tunings:
* WE: ~2 = 1199.7927{{c}}, ~3/2 = 702.4205{{c}}, ~31/24 = 442.1885{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.5302{{c}}, ~31/24 = 442.2374{{c}}


{{Optimal ET sequence|legend=1| 19, 22, 41, 46, 65, 87, 152, 369, 521e, 1194bcee, 1305bcee, 1457bceee, 1609bcceee, 1674bcceee, 1826bcceeee }}
{{Optimal ET sequence|legend=0| 19, 22, 41, 46, 65, 87, 152, 369, 521e }}


[[Badness]]: 0.0922 × 10<sup>-3</sup>
Badness (Sintel): 0.201


[[Category:Temperament clans]]
[[Category:Temperament clans]]
[[Category:Semiporwellismic clan| ]] <!-- main article -->
[[Category:Semiporwellismic clan| ]] <!-- main article -->
[[Category:Semiporwellismic| ]] <!-- key article -->
[[Category:Rank 3]]
[[Category:Rank 3]]

Latest revision as of 10:17, 17 June 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 semiporwellismic clan of rank-3 temperaments tempers out the semiporwellisma (monzo: [14 -3 -1 0 -2⟩, ratio: 16384/16335).

For the rank-4 temperament, see Catalog of rank-4 temperaments #Semiporwellismic (16384/16335).

Semiporwellic

Subgroup: 2.3.5.11

Comma list: 16384/16335

Subgroup-val mapping: [⟨1 0 0 0 7], ⟨0 1 1 0 -2], ⟨0 0 2 0 -1]]

mapping generators: ~2, ~3, ~128/99

Optimal tunings:

  • WE: ~2 = 1199.7329 ¢, ~3/2 = 702.3657 ¢, ~128/99 = 442.1589 ¢
error map: ⟨-0.267 +0.144 +0.103 +0.456]
  • CWE: ~2 = 1200.0000 ¢, ~3/2 = 702.5107 ¢, ~128/99 = 442.2243 ¢
error map: ⟨0.000 +0.556 +0.646 +1.436]

Optimal ET sequence: 19, 22, 41, 46, 65, 87, 152, 369, 521e, 1194bcee, 1305bcee, 1457bceee, 1609bcceee, 1674bcceee, 1826bcceeee

Badness (Sintel): 0.761

Overview to extensions

Temperaments discussed elsewhere are:

Considered below is the add-31 subgroup temperament of semiporwellic.

Subgroup extensions

Semiporwellic (2.3.5.11.31)

Subgroup: 2.3.5.11.31

Comma list: 496/495, 961/960

Subgroup-val mapping: [⟨1 0 0 0 7], ⟨0 1 1 0 -2], ⟨0 0 2 0 -1]]

Optimal tunings:

  • WE: ~2 = 1199.7927 ¢, ~3/2 = 702.4205 ¢, ~31/24 = 442.1885 ¢
  • CWE: ~2 = 1200.0000 ¢, ~3/2 = 702.5302 ¢, ~31/24 = 442.2374 ¢

Optimal ET sequence: 19, 22, 41, 46, 65, 87, 152, 369, 521e

Badness (Sintel): 0.201

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