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{{Infobox Interval | {{Infobox Interval | ||
| Name = | | Name = septendecimal major seventh, septendecimal diminished octave | ||
| Color name = 17u7, su 7th | | Color name = 17u7, su 7th | ||
| Sound = jid_32_17_pluck_adu_dr220.mp3 | | Sound = jid_32_17_pluck_adu_dr220.mp3 | ||
}} | }} | ||
In [[17-limit]] [[just intonation]], '''32/17''' is the ''' | In [[17-limit]] [[just intonation]], '''32/17''' is the '''septendecimal major seventh''' or the '''septendecimal diminished octave''', depending on how one views it. It is also the octave-reduced 17th [[subharmonic]]. Its inversion is [[17/16]], the octave-reduced 17th harmonic. Measuring about 1095{{cent}}, it is the [[mediant]] between [[15/8]] and [[17/9]]. | ||
There exists a disagreement in different | == Terminology and notation == | ||
There exists a disagreement in different conceptualization systems on whether 32/17 should be a major seventh or a diminished octave. The major seventh view corresponds to [[Functional Just System]], with the formal comma [[4131/4096]] separating it from [[243/128]], the Pythagorean major seventh. The diminished octave view corresponds to [[Helmholtz-Ellis notation]], with the formal comma [[2187/2176]] separating it from [[4096/2187]], the Pythagorean diminished octave. | |||
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 == | ||
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[[Category:Seventh]] | [[Category:Seventh]] | ||
[[Category:Major seventh]] | [[Category:Major seventh]] | ||
[[Category:Octave]] | |||
[[Category:Diminished octave]] | |||
Latest revision as of 09:37, 12 January 2023
| Interval information |
septendecimal diminished octave
reduced subharmonic
[sound info]
In 17-limit just intonation, 32/17 is the septendecimal major seventh or the septendecimal diminished octave, depending on how one views it. It is also the octave-reduced 17th subharmonic. Its inversion is 17/16, the octave-reduced 17th harmonic. Measuring about 1095 ¢, it is the mediant between 15/8 and 17/9.
Terminology and notation
There exists a disagreement in different conceptualization systems on whether 32/17 should be a major seventh or a diminished octave. The major seventh view corresponds to Functional Just System, with the formal comma 4131/4096 separating it from 243/128, the Pythagorean major seventh. The diminished octave view corresponds to Helmholtz-Ellis notation, with the formal comma 2187/2176 separating it from 4096/2187, the Pythagorean diminished octave.
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.