User:Inthar/Endoparticular extensions: Difference between revisions
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Suppose the base temp tempers out a comma that is a product of powers of consecutive S-commas with nonzero exponents. An extension is ''endoparticular'' if it additionally tempers out the individual S-commas. | |||
Conjecture: An endoparticular extension of a temperament tempering out one given comma to a given extended subgroup is unique if it exists (since there is at most one S-expression of the comma in a given subgroup). | |||
Stronger conjecture: An endoparticular extension for a given temperament of any rank and a given extended subgroup is unique if it exists (regardless of the choice of comma basis). | |||
== Conjecture: An endoparticular extension of a codimension-1 temperament is unique == | |||
Revision as of 18:52, 4 February 2026
This is a problematic page or section. It lacks sufficient justification, content, or organization, and is subject to future overhaul or deletion.
Suppose the base temp tempers out a comma that is a product of powers of consecutive S-commas with nonzero exponents. An extension is endoparticular if it additionally tempers out the individual S-commas.
Conjecture: An endoparticular extension of a temperament tempering out one given comma to a given extended subgroup is unique if it exists (since there is at most one S-expression of the comma in a given subgroup).
Stronger conjecture: An endoparticular extension for a given temperament of any rank and a given extended subgroup is unique if it exists (regardless of the choice of comma basis).
