Telicity: Difference between revisions

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== Telicity Range and Usable EDO Sizes ==

~~Commas that join prime chains together when tempered out in a manner that satisfies the above equation are called '''telic''' commas, and each~~ telic comma has a numerical range in which it can possibly be telic, that is, a '''telicity range'''. The size of a comma's telicity range is negatively correlated to the size of the comma itself – that is, the smaller the comma in question, the larger the size of that comma's telicity range. The size of a comma's telicity range is evaluated by comparing the size of a given EDO's step with the size of the comma in question – if the comma is more than half the size of the EDO's step, said EDO is outside the comma's telicity range. For example, [[81/80]] has a telicity range of 27, as 27 is the largest EDO with a step size that is more that twice the size of the comma, while [[Mercator's comma]] has a telicity range of 165, as 165 is the largest EDO with a step size that is more that twice the size of that comma. In addition, the concept of telicity can be used to evaluate the usefulness of EDOs relative to the [http://musictheory.zentral.zone/huntsystem2.html#2 JND] of human pitch perception, and, since an interval smaller than 3.5 cents is unlikely to be noticed by even the most trained listeners, it can be said that the JND has a telicity range of 171, meaning that EDOs that are higher than [[171edo|171]] are not all that suitable for use as musical systems outside of pitch bends.

Each telic comma has a numerical range in which it can possibly be telic, that is, a '''telicity range'''. The size of a comma's telicity range is negatively correlated to the size of the comma itself – that is, the smaller the comma in question, the larger the size of that comma's telicity range. The size of a comma's telicity range is evaluated by comparing the size of a given EDO's step with the size of the comma in question – if the comma is more than half the size of the EDO's step, said EDO is outside the comma's telicity range. For example, [[81/80]] has a telicity range of 27, as 27 is the largest EDO with a step size that is more that twice the size of the comma, while [[Mercator's comma]] has a telicity range of 165, as 165 is the largest EDO with a step size that is more that twice the size of that comma. In addition, the concept of telicity can be used to evaluate the usefulness of EDOs relative to the [http://musictheory.zentral.zone/huntsystem2.html#2 JND] of human pitch perception, and, since an interval smaller than 3.5 cents is unlikely to be noticed by even the most trained listeners, it can be said that the JND has a telicity range of 171, meaning that EDOs that are higher than [[171edo|171]] are not all that suitable for use as musical systems outside of pitch bends.

== Telicity Type Designations ==

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 == Telicity Range and Usable EDO Sizes ==
-Commas that join prime chains together when tempered out in a manner that satisfies the above equation are called '''telic''' commas, and each telic comma has a numerical range in which it can possibly be telic, that is, a '''telicity range'''.  The size of a comma's telicity range is negatively correlated to the size of the comma itself – that is, the smaller the comma in question, the larger the size of that comma's telicity range.  The size of a comma's telicity range is evaluated by comparing the size of a given EDO's step with the size of the comma in question – if the comma is more than half the size of the EDO's step, said EDO is outside the comma's telicity range.  For example, [[81/80]] has a telicity range of 27, as 27 is the largest EDO with a step size that is more that twice the size of the comma, while [[Mercator's comma]] has a telicity range of 165, as 165 is the largest EDO with a step size that is more that twice the size of that comma.  In addition, the concept of telicity can be used to evaluate the usefulness of EDOs relative to the [http://musictheory.zentral.zone/huntsystem2.html#2 JND] of human pitch perception, and, since an interval smaller than 3.5 cents is unlikely to be noticed by even the most trained listeners, it can be said that the JND has a telicity range of 171, meaning that EDOs that are higher than [[171edo|171]] are not all that suitable for use as musical systems outside of pitch bends.
+Each telic comma has a numerical range in which it can possibly be telic, that is, a '''telicity range'''.  The size of a comma's telicity range is negatively correlated to the size of the comma itself – that is, the smaller the comma in question, the larger the size of that comma's telicity range.  The size of a comma's telicity range is evaluated by comparing the size of a given EDO's step with the size of the comma in question – if the comma is more than half the size of the EDO's step, said EDO is outside the comma's telicity range.  For example, [[81/80]] has a telicity range of 27, as 27 is the largest EDO with a step size that is more that twice the size of the comma, while [[Mercator's comma]] has a telicity range of 165, as 165 is the largest EDO with a step size that is more that twice the size of that comma.  In addition, the concept of telicity can be used to evaluate the usefulness of EDOs relative to the [http://musictheory.zentral.zone/huntsystem2.html#2 JND] of human pitch perception, and, since an interval smaller than 3.5 cents is unlikely to be noticed by even the most trained listeners, it can be said that the JND has a telicity range of 171, meaning that EDOs that are higher than [[171edo|171]] are not all that suitable for use as musical systems outside of pitch bends.
 == Telicity Type Designations ==