Bixby: Difference between revisions

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Bixby is the temperament that tempers out 4/3, setting the perfect fifth equal to the octave. It can be represented by only [[1edo]] in its patent [[val]] (and in fact is represented specifically by 1edo in terms of edos), and is equivalent to using a no-threes harmonic system.
{{Infobox Regtemp
 
| Subgroups = 2.3.5
| Comma basis = 4/3
| Mapping = 1 0; 0 1
| Generator = 5/4 |
| Generator tuning = 386.3137
| Optimization method = CTE
}}
'''Bixby''' is the temperament that tempers out 4/3, setting the perfect fifth equal to the octave. It can be represented by only [[1edo]] in its patent [[val]] (and in fact is represented specifically by 1edo in terms of edos), and is equivalent to using a no-threes harmonic system.


It is the first [[comptonesque]] temperament; equivalently, it is the first [[circular temperament]] of 3. It is also the first temperament of a square particular comma.
It is the first [[comptonesque]] temperament; equivalently, it is the first [[circular temperament]] of 3. It is also the first temperament of a square particular comma.


{{Infobox Regtemp|Comma basis=4/3|Generator tuning=386.3137|Mapping=1 0; 0 1|Subgroups=2.3.5|Generator=5/4|Optimization method=CTE}}
[[Category:Bixby| ]] <!-- main article -->
 
[[Category:Circular temperaments]]
[[Category:Rank-2 temperaments]]
[[Category:Rank-2 temperaments]]
[[Category:Exotemperaments]]
[[Category:Exotemperaments]]

Revision as of 13:50, 28 April 2025

Bixby
Subgroups 2.3.5
Comma basis 4/3
Reduced mapping ⟨1 0; 0 1]
Edo join [[edo|]] & [[edo|]]
Generator (CTE) ~5/4 = 386.3137 ¢
Ploidacot aploid monocot
Minimax error (-odd limit)  ¢
Target scale size (-odd limit) notes

Bixby is the temperament that tempers out 4/3, setting the perfect fifth equal to the octave. It can be represented by only 1edo in its patent val (and in fact is represented specifically by 1edo in terms of edos), and is equivalent to using a no-threes harmonic system.

It is the first comptonesque temperament; equivalently, it is the first circular temperament of 3. It is also the first temperament of a square particular comma.