Semiporwellismic clan: Difference between revisions

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This is a collection of rank-3 temperaments tempering out the [[semiporwellisma]], 16384/16335 = {{monzo| 14 -3 -1 0 -2 }}.  
{{Technical data page}}
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, 896/891} → [[Sensamagic family #Undecimal sensamagic|Sensamagic family]]
 
* ''[[Kapo]]'', {3025/3024, 5120/5103} → [[Hemifamity family #Kapo|Hemifamity family]]
== Semiporwellic ==
* ''[[Semiporwell]]'', {6144/6125, 9801/9800} → [[Porwell family #Semiporwell|Porwell family]]
[[Subgroup]]: 2.3.5.11


Considered below is the no-7 subgroup temperament, but we can begin by looking at the rank-4 temperament.
[[Comma list]]: 16384/16335


== Semiporwellismic ==
{{Mapping|legend=2| 1 0 0 0 7 | 0 1 1 0 -2 | 0 0 2 0 -1 }}
Subgroup: 2.3.5.7.11
: mapping generators: ~2, ~3, ~128/99


[[Comma list]]: 16384/16335
[[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 }}


[[Mapping]]: [{{val| 1 0 0 0 7 }}, {{val| 0 1 1 0 -2 }}, {{val| 0 0 2 0 -1 }}, {{val| 0 0 0 1 0 }}]
{{Optimal ET sequence|legend=1| 19, 22, 41, 46, 65, 87, 152, 369, 521e, 1194bcee, 1305bcee, 1457bceee, 1609bcceee, 1674bcceee, 1826bcceeee }}


Mapping generators: ~2, ~3, ~128/99, ~7
[[Badness]] (Sintel): 0.761


{{Val list|legend=1| 19, 22, 41, 65d, 68, 84, 87, 111, 130, 152, 239, 282, 328, 369, 521e, 1370bcdeee, 1411bcdeee, 1609bccdeee }}
=== 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]]


[[Badness]]: 0.219 × 10<sup>-6</sup>
Considered below is the add-31 subgroup temperament of semiporwellic.  


== No-7 semiporwellismic ==
== Subgroup extensions ==
Subgroup: 2.3.5.11
=== Semiporwellic (2.3.5.11.31) ===
Subgroup: 2.3.5.11.31


[[Comma list]]: 16384/16335
Comma list: 496/495, 961/960


[[Sval]] [[mapping]]: [{{val| 1 0 0 0 7 }}, {{val| 0 1 1 0 -2 }}, {{val| 0 0 2 0 -1 }}]
Subgroup-val mapping: {{mapping| 1 0 0 0 7 | 0 1 1 0 -2 | 0 0 2 0 -1 }}


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


{{Val list|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:Regular temperament theory]]
[[Category:Temperament clans]]
[[Category:Temperament clans]]
[[Category:Semiporwellismic temperaments| ]] <!-- main article -->
[[Category:Semiporwellismic clan| ]] <!-- main 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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