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. | 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: There is at most one S-expression for a comma in a given extended subgroup. | Conjecture: There is at most one S-expression for a comma in a given extended subgroup. As a corollary, an endoparticular extension of a temperament tempering out one given comma to a given extended subgroup is unique if it exists. | ||
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). | 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 one-comma temperament is unique == | == Conjecture: An endoparticular extension of a one-comma temperament is unique == | ||
Revision as of 18:54, 4 February 2026
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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: There is at most one S-expression for a comma in a given extended subgroup. As a corollary, an endoparticular extension of a temperament tempering out one given comma to a given extended subgroup is unique if it exists.
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).
