17/9: Difference between revisions
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In [[17-limit]] [[just intonation]], '''17/9''' is the '''septendecimal diminished octave''' or the '''septendecimal major seventh''', depending on how one views it. It measures about 1101¢. It is the [[mediant]] between [[15/8]] and [[2/1]]. Its inversion is [[18/17]], the "small septendecimal semitone". | In [[17-limit]] [[just intonation]], '''17/9''' is the '''septendecimal diminished octave''' or the '''septendecimal major seventh''', depending on how one views it. It measures about 1101¢. It is the [[mediant]] between [[15/8]] and [[2/1]]. Its inversion is [[18/17]], the "small septendecimal semitone". | ||
== Terminology == | == Terminology and notation == | ||
There exists a disagreement in different conceptualization systems on whether 17/9 should be a major seventh or a diminished octave. The diminished octave view corresponds to [[Functional Just System]], with the formal comma [[4131/4096]] separating it from [[4096/2187]], the Pythagorean diminished octave. The major seventh view corresponds to [[Helmholtz-Ellis notation]], with the formal comma [[2187/2176]] separating it from [[243/128]], the Pythagorean major seventh. | There exists a disagreement in different conceptualization systems on whether 17/9 should be a major seventh or a diminished octave. The diminished octave view corresponds to [[Functional Just System]], with the formal comma [[4131/4096]] separating it from [[4096/2187]], the Pythagorean diminished octave. The major seventh view corresponds to [[Helmholtz-Ellis notation]], with the formal comma [[2187/2176]] separating it from [[243/128]], the Pythagorean major seventh. | ||
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 == | == See also == | ||
Latest revision as of 09:38, 12 January 2023
| Interval information |
[sound info]
In 17-limit just intonation, 17/9 is the septendecimal diminished octave or the septendecimal major seventh, depending on how one views it. It measures about 1101¢. It is the mediant between 15/8 and 2/1. Its inversion is 18/17, the "small septendecimal semitone".
Terminology and notation
There exists a disagreement in different conceptualization systems on whether 17/9 should be a major seventh or a diminished octave. The diminished octave view corresponds to Functional Just System, with the formal comma 4131/4096 separating it from 4096/2187, the Pythagorean diminished octave. The major seventh view corresponds to Helmholtz-Ellis notation, with the formal comma 2187/2176 separating it from 243/128, the Pythagorean major seventh.
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.