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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | {{Infobox Interval |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | | Name = septendecimal major seventh, septendecimal diminished octave |
| : This revision was by author [[User:spt3125|spt3125]] and made on <tt>2014-06-08 21:25:01 UTC</tt>.<br>
| | | Color name = 17u7, su 7th |
| : The original revision id was <tt>513278398</tt>.<br>
| | | Sound = jid_32_17_pluck_adu_dr220.mp3 |
| : The revision comment was: <tt></tt><br>
| | }} |
| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
| | 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]]. |
| <h4>Original Wikitext content:</h4>
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| <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">**32/17**
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| |5 0 0 0 0 0 -1>
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| 1095.0446 cents | |
| [[media type="file" key="jid_32_17_pluck_adu_dr220.mp3"]] [[file:xenharmonic/jid_32_17_pluck_adu_dr220.mp3|sound sample]] | |
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| In [[17-limit]] [[Just Intonation]], 32/17 is the "small septendecimal major seventh," as well as the 17th [[subharmonic]] octave-reduced. Measuring about 1095¢, it is the [[mediant]] between [[15_8|15/8]] and [[17_9|17/9]], the "large septendecimal major seventh". Its inversion is [[17_16|17/16]], the "large septendecimal semitone".
| | == 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. |
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| See: [[Gallery of Just Intervals]]</pre></div>
| | 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. |
| <h4>Original HTML content:</h4>
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| <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>32_17</title></head><body><strong>32/17</strong><br />
| | == See also == |
| |5 0 0 0 0 0 -1&gt;<br />
| | * [[17/16]] – its [[octave complement]] |
| 1095.0446 cents<br />
| | * [[Gallery of just intervals]] |
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| | [[Category:Seventh]] |
| In <a class="wiki_link" href="/17-limit">17-limit</a> <a class="wiki_link" href="/Just%20Intonation">Just Intonation</a>, 32/17 is the &quot;small septendecimal major seventh,&quot; as well as the 17th <a class="wiki_link" href="/subharmonic">subharmonic</a> octave-reduced. Measuring about 1095¢, it is the <a class="wiki_link" href="/mediant">mediant</a> between <a class="wiki_link" href="/15_8">15/8</a> and <a class="wiki_link" href="/17_9">17/9</a>, the &quot;large septendecimal major seventh&quot;. Its inversion is <a class="wiki_link" href="/17_16">17/16</a>, the &quot;large septendecimal semitone&quot;.<br />
| | [[Category:Major seventh]] |
| <br />
| | [[Category:Octave]] |
| See: <a class="wiki_link" href="/Gallery%20of%20Just%20Intervals">Gallery of Just Intervals</a></body></html></pre></div>
| | [[Category:Diminished octave]] |
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.
See also