Telicity: Difference between revisions

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Because F is not a linear function, it does not satisfy any of the conditions above. So even though rounding sometimes gives us better approximations, it doesn't conserve interval interval arithmetic, and conserving interval arithmetic is why we care about RTT in the first place.

However, people who care about 'both' good approximations 'and' conserving interval arithmetic are seemingly presented with a dilemma- either go with a linear map and risk bad approximations, or go with a non-linear map and risk inconsistent interval arithmetic. This is why telicity is useful- when one is able to work with the section of the EDO's harmonic lattice in which both mapping methods lead to the same result and limit the harmonic lattice to this section, one has the best of both worlds, hence the equation ~~described above~~.

However, people who care about ''both'' good approximations ''and'' conserving interval arithmetic are seemingly presented with a dilemma- either go with a linear map and risk bad approximations, or go with a non-linear map and risk inconsistent interval arithmetic. This is why telicity is useful- when one is able to work with the section of the EDO's harmonic lattice in which both mapping methods lead to the same result and limit the harmonic lattice to this section, one has the best of both worlds, hence the equation val(N)⋅monzo(r) = round(N⋅log2(r)) for telicity.

== Telicity Range and Usable EDO Sizes ==

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 Because F is not a linear function, it does not satisfy any of the conditions above. So even though rounding sometimes gives us better approximations, it doesn't conserve interval interval arithmetic, and conserving interval arithmetic is why we care about RTT in the first place.
-However, people who care about 'both' good approximations 'and' conserving interval arithmetic are seemingly presented with a dilemma- either go with a linear map and risk bad approximations, or go with a non-linear map and risk inconsistent interval arithmetic.  This is why telicity is useful- when one is able to work with the section of the EDO's harmonic lattice in which both mapping methods lead to the same result and limit the harmonic lattice to this section, one has the best of both worlds, hence the equation described above.
+However, people who care about ''both'' good approximations ''and'' conserving interval arithmetic are seemingly presented with a dilemma- either go with a linear map and risk bad approximations, or go with a non-linear map and risk inconsistent interval arithmetic.  This is why telicity is useful- when one is able to work with the section of the EDO's harmonic lattice in which both mapping methods lead to the same result and limit the harmonic lattice to this section, one has the best of both worlds, hence the equation val(N)⋅monzo(r) = round(N⋅log2(r)) for telicity.
 == Telicity Range and Usable EDO Sizes ==