17/12: Difference between revisions

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In [[17-limit]] [[just intonation]], '''17/12''' is the '''larger septendecimal tritone''', measuring very nearly 603¢. Its inversion is the smaller septendecimal tritone, [[24/17]], and the interval that separates them is the small [[comma]] [[289/288]], about 6¢. This difference is usually negligible, and tempering out this comma allows the 600¢ half-octave to function as both septendecimal tritones. Thus, every even-numbered [[~~EDO~~]] system contains a close approximation to these intervals.

In [[17-limit]] [[just intonation]], '''17/12''' is the '''larger septendecimal tritone''', measuring very nearly 603¢. Its inversion is the smaller septendecimal tritone, [[24/17]], and the interval that separates them is the small [[comma]] [[289/288]], about 6¢. This difference is usually negligible, and tempering out this comma allows the 600¢ half-octave to function as both septendecimal tritones. Thus, every even-numbered [[edo]] system contains a close approximation to these intervals.

17/12 is the [[mediant]] between the two septimal tritones [[7/5]] and [[10/7]].

== Terminology and notation ==

There exists a disagreement in different conceptualization systems on whether 17/12 should be an augmented fourth or a diminished fifth. In [[Functional Just System]], it is a diminished fifth, separated by [[4131/4096]] from [[1024/729]], the Pythagorean diminished fifth In [[Helmholtz-Ellis notation]], it is an augmented fourth, separated by [[2187/2176]] from [[729/512]], the Pythagorean augmented fourth. The term "large septendecimal tritone" omits the distinction and only describes its melodic property i.e. the size.

In practice, the interval category may, arguably, vary by context. One solution for the JI user who uses expanded [[circle-of-fifths notation]] is to prepare a [[Pythagorean comma]] accidental so that the interval can be notated in either category.

== See also ==

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-In [[17-limit]] [[just intonation]], '''17/12''' is the '''larger septendecimal tritone''', measuring very nearly 603¢. Its inversion is the smaller septendecimal tritone, [[24/17]], and the interval that separates them is the small [[comma]] [[289/288]], about 6¢. This difference is usually negligible, and tempering out this comma allows the 600¢ half-octave to function as both septendecimal tritones. Thus, every even-numbered [[EDO]] system contains a close approximation to these intervals.
+In [[17-limit]] [[just intonation]], '''17/12''' is the '''larger septendecimal tritone''', measuring very nearly 603¢. Its inversion is the smaller septendecimal tritone, [[24/17]], and the interval that separates them is the small [[comma]] [[289/288]], about 6¢. This difference is usually negligible, and tempering out this comma allows the 600¢ half-octave to function as both septendecimal tritones. Thus, every even-numbered [[edo]] system contains a close approximation to these intervals.
 /12 is the [[mediant]] between the two septimal tritones [[7/5]] and [[10/7]].
+== Terminology and notation ==
+There exists a disagreement in different conceptualization systems on whether 17/12 should be an augmented fourth or a diminished fifth. In [[Functional Just System]], it is a diminished fifth, separated by [[4131/4096]] from [[1024/729]], the Pythagorean diminished fifth In [[Helmholtz-Ellis notation]], it is an augmented fourth, separated by [[2187/2176]] from [[729/512]], the Pythagorean augmented fourth. The term "large septendecimal tritone" omits the distinction and only describes its melodic property i.e. the size.
+In practice, the interval category may, arguably, vary by context. One solution for the JI user who uses expanded [[circle-of-fifths notation]] is to prepare a [[Pythagorean comma]] accidental so that the interval can be notated in either category.
 == See also ==