Alphaxenic rank-3 clan: Difference between revisions
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{{Technical data page}} | {{Technical data page}} | ||
The '''alphaxenic rank-3 clan''' of [[temperament]]s [[tempering out|tempers out]] the [[Alpharabian comma]] | The '''alphaxenic rank-3 clan''' of [[temperament]]s [[tempering out|tempers out]] the [[Alpharabian comma]] ({{monzo|legend=1| -17 2 0 0 4 }}, [[ratio]]: 131769/131072). Both no-5 alphaxenic and no-7 alphaxenic can be the head of this clan. | ||
Temperaments discussed elsewhere include: | Temperaments discussed elsewhere include: | ||
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{{Mapping|legend=1| 2 1 0 0 8 | 0 2 0 0 -1 | 0 0 1 0 0 | 0 0 0 1 0 }} | {{Mapping|legend=1| 2 1 0 0 8 | 0 2 0 0 -1 | 0 0 1 0 0 | 0 0 0 1 0 }} | ||
: mapping generators: ~363/256, ~16/11, ~5, ~7 | : mapping generators: ~363/256, ~16/11, ~5, ~7 | ||
[[Optimal tuning]] | [[Optimal tuning]]s: | ||
* [[WE]]: ~363/256 = 600.1590{{c}}, ~16/11 = 650.8508{{c}}, ~5/4 = 385.6773{{c}}, ~7/4 = 968.1894{{c}} | |||
: [[error map]]: {{val| +0.318 -0.094 -0.000 -0.000 -0.897 }} | |||
* [[CWE]]: ~363/256 = 600.0000{{c}}, ~16/11 = 650.7321{{c}}, ~5/4 = 385.7900{{c}}, ~7/4 = 968.1927{{c}} | |||
: error map: {{val| 0.000 -0.491 -0.524 -0.633 -2.050 }} | |||
{{Optimal ET sequence|legend=1| 22, 46, 68, 72, 118, 190, 212, 284, 330e, 402de, 498e, 544e, 616ee, 806dee, 828cee, 946cdeee, 1018cdeee }} | {{Optimal ET sequence|legend=1| 22, 46, 68, 72, 118, 190, 212, 284, 330e, 402de, 498e, 544e, 616ee, 806dee, 828cee, 946cdeee, 1018cdeee }} | ||
[[Badness]]: | [[Badness]] (Sintel): 23.0 | ||
== Rabic == | == Rabic == | ||
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{{Mapping|legend=1| 24 38 0 0 83 | 0 0 1 0 0 | 0 0 0 1 0 }} | {{Mapping|legend=1| 24 38 0 0 83 | 0 0 1 0 0 | 0 0 0 1 0 }} | ||
: mapping generators: ~33/32, ~5, ~7 | : mapping generators: ~33/32, ~5, ~7 | ||
[[Optimal tuning]] | [[Optimal tuning]]s: | ||
* [[WE]]: ~33/32 = 50.0220{{c}}, ~5/4 = 385.0647{{c}}, ~7/4 = 967.3158{{c}} | |||
: [[error map]]: {{val| +0.538 -1.104 -0.002 -0.002 +0.541 }} | |||
* [[CWE]]: ~33/32 = 50.0000{{c}}, ~5/4 = 385.0647{{c}}, ~7/4 = 967.3158{{c}} | |||
: error map: {{val| 0.000 -1.955 -0.937 -1.133 -1.318 }} | |||
{{Optimal ET sequence|legend=1| 24, 48, 72, 264, 336b, 408b, 480bcde }} | {{Optimal ET sequence|legend=1| 24, 48(d), 72, 264, 336b, 408b, 480bcde }} | ||
[[Badness]]: | [[Badness]] (Sintel): 7.30 | ||
[[Category:Temperament clans]] | [[Category:Temperament clans]] | ||
[[Category:Alphaxenic rank-3 clan| ]] <!-- main article --> | [[Category:Alphaxenic rank-3 clan| ]] <!-- main article --> | ||
[[Category:Rank 3]] | [[Category:Rank 3]] | ||
Revision as of 11:00, 15 May 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 alphaxenic rank-3 clan of temperaments tempers out the Alpharabian comma (monzo: [-17 2 0 0 4⟩, ratio: 131769/131072). Both no-5 alphaxenic and no-7 alphaxenic can be the head of this clan.
Temperaments discussed elsewhere include:
- Uniwiz (+385/384) → Keenanismic temperaments
Alphaxenic
Subgroup: 2.3.5.7.11
Comma list: 131769/131072
Mapping: [⟨2 1 0 0 8], ⟨0 2 0 0 -1], ⟨0 0 1 0 0], ⟨0 0 0 1 0]]
- mapping generators: ~363/256, ~16/11, ~5, ~7
- WE: ~363/256 = 600.1590 ¢, ~16/11 = 650.8508 ¢, ~5/4 = 385.6773 ¢, ~7/4 = 968.1894 ¢
- error map: ⟨+0.318 -0.094 -0.000 -0.000 -0.897]
- CWE: ~363/256 = 600.0000 ¢, ~16/11 = 650.7321 ¢, ~5/4 = 385.7900 ¢, ~7/4 = 968.1927 ¢
- error map: ⟨0.000 -0.491 -0.524 -0.633 -2.050]
Optimal ET sequence: 22, 46, 68, 72, 118, 190, 212, 284, 330e, 402de, 498e, 544e, 616ee, 806dee, 828cee, 946cdeee, 1018cdeee
Badness (Sintel): 23.0
Rabic
Whenever the rastma is added to the list of commas tempered out among alphaxenic temperaments, you end up with rabic, which splits the octave into 24 equal parts. This temperament is named as such because tempering out both the Alpharabian comma and the rastma automatically tempers out the Betarabian comma.
Subgroup: 2.3.5.7.11
Comma list: 243/242, 131769/131072
Mapping: [⟨24 38 0 0 83], ⟨0 0 1 0 0], ⟨0 0 0 1 0]]
- mapping generators: ~33/32, ~5, ~7
- WE: ~33/32 = 50.0220 ¢, ~5/4 = 385.0647 ¢, ~7/4 = 967.3158 ¢
- error map: ⟨+0.538 -1.104 -0.002 -0.002 +0.541]
- CWE: ~33/32 = 50.0000 ¢, ~5/4 = 385.0647 ¢, ~7/4 = 967.3158 ¢
- error map: ⟨0.000 -1.955 -0.937 -1.133 -1.318]
Optimal ET sequence: 24, 48(d), 72, 264, 336b, 408b, 480bcde
Badness (Sintel): 7.30