User:Eufalesio/Telicity: Difference between revisions

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* The equal division of m is a denominator appearing in the continued fraction of logm(n).

* The comma that arises from stacking m^{numerator}/n^{denominator} of the convergent is smaller than half an ed-m-step.

* The comma that arises from stacking m<sup>numerator</sup>/n<sup>denominator</sup> of the convergent is smaller than half an ed-m-step.

Mathematically, this is satisfied with the following:

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=== Multitelicity ===

If said produced comma is also smaller than k halves of an ed-m-step, then the edm is k-strong m-n telic, which means that the comma is smaller than not only half of an ed-m-step, but also half/2 (a quarter), or half/3 (a sixth)... etc. Essentially not only the {denominator}ed-m is convergent, but also its multiples. This makes it '''multitelic'''.

If said produced comma is also smaller than k halves of an ed-m-step, then the edm is k-strong m-n telic, which means that the comma is smaller than not only half of an ed-m-step, but also half/2 (a quarter), or half/3 (a sixth)... etc. Essentially not only the (denominator)ed-m is convergent, but also its multiples. This makes it '''multitelic'''.

Mathematically, this is expressed as the following:

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Of those, 41edo is not telic because its comma, the countercomp comma, is larger than half an edostep. (19.845*2 > 29.268). The next non-telic convergent is [[111202edo]].

Of those, 12, 53, 665 are multitelic, because they have a k-~~strong~~ value greater than one; being 2, 3, and 11 respectively, which means that [[24edo|24]], [[106edo|106]], [[159edo|159]], [[1330edo|1330]], [[1995edo|1995]], [[2660edo|2660]], [[3325edo|3325]], [[3990edo|3990]], [[4655edo|4655]], [[5320edo|5320]], [[5985edo|5985]], [[6650edo|6650]], [[7315edo|7315]]. are also 3-2 telic.

Of those, 12, 53, 665 are multitelic, because they have a k-strength value greater than one; being 2, 3, and 11 respectively, which means that [[24edo|24]], [[106edo|106]], [[159edo|159]], [[1330edo|1330]], [[1995edo|1995]], [[2660edo|2660]], [[3325edo|3325]], [[3990edo|3990]], [[4655edo|4655]], [[5320edo|5320]], [[5985edo|5985]], [[6650edo|6650]], and [[7315edo|7315]] are also 3-2 telic.

== Applications ==

@@ Line 19: / Line 19: @@
 * The equal division of m is a denominator appearing in the continued fraction of logm(n).
-* The comma that arises from stacking m^{numerator}/n^{denominator} of the convergent is smaller than half an ed-m-step.
+* The comma that arises from stacking m<sup>numerator</sup>/n<sup>denominator</sup> of the convergent is smaller than half an ed-m-step.
 Mathematically, this is satisfied with the following:
@@ Line 28: / Line 28: @@
 === Multitelicity ===
-If said produced comma is also smaller than k halves of an ed-m-step, then the edm is k-strong m-n telic, which means that the comma is smaller than not only half of an ed-m-step, but also half/2 (a quarter), or half/3 (a sixth)... etc. Essentially not only the {denominator}ed-m is convergent, but also its multiples. This makes it '''multitelic'''.
+If said produced comma is also smaller than k halves of an ed-m-step, then the edm is k-strong m-n telic, which means that the comma is smaller than not only half of an ed-m-step, but also half/2 (a quarter), or half/3 (a sixth)... etc. Essentially not only the (denominator)ed-m is convergent, but also its multiples. This makes it '''multitelic'''.
 Mathematically, this is expressed as the following:
@@ Line 54: / Line 54: @@
 Of those, 41edo is not telic because its comma, the countercomp comma, is larger than half an edostep. (19.845*2 > 29.268). The next non-telic convergent is [[111202edo]].
-Of those, 12, 53, 665 are multitelic, because they have a k-strong value greater than one; being 2, 3, and 11 respectively, which means that [[24edo|24]], [[106edo|106]], [[159edo|159]], [[1330edo|1330]], [[1995edo|1995]], [[2660edo|2660]], [[3325edo|3325]], [[3990edo|3990]], [[4655edo|4655]], [[5320edo|5320]], [[5985edo|5985]], [[6650edo|6650]], [[7315edo|7315]]. are also 3-2 telic.
+Of those, 12, 53, 665 are multitelic, because they have a k-strength value greater than one; being 2, 3, and 11 respectively, which means that [[24edo|24]], [[106edo|106]], [[159edo|159]], [[1330edo|1330]], [[1995edo|1995]], [[2660edo|2660]], [[3325edo|3325]], [[3990edo|3990]], [[4655edo|4655]], [[5320edo|5320]], [[5985edo|5985]], [[6650edo|6650]], and [[7315edo|7315]] are also 3-2 telic.
 == Applications ==