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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 = small septendecimal tritone |
| : This revision was by author [[User:spt3125|spt3125]] and made on <tt>2014-06-08 15:52:47 UTC</tt>.<br>
| | | Color name = 17u4, su 4th |
| : The original revision id was <tt>513256572</tt>.<br>
| | | Sound = jid_24_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>
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| <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">**24/17**
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| |3 1 0 0 0 0 -1> | |
| 596.9996 cents
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| [[media type="file" key="jid_24_17_pluck_adu_dr220.mp3"]] [[file:xenharmonic/jid_24_17_pluck_adu_dr220.mp3|sound sample]]
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| In [[17-limit]] [[Just Intonation]], 24/17 is the "first septendecimal tritone," measuring very nearly 597¢. It is the [[mediant]] between [[7_5|7/5]] and [[17_12|17/12]], the "second septendecimal tritone." The two septendecimal tritones are each 3¢ away from the 600¢ half-octave, and so they are well-represented in all even-numbered [[EDO]] systems, including [[12edo]]. Indeed, the latter system, containing good approximations of the 3rd and 17th harmonics, can use the half-octave as 24/17 and 17/12 in close approximations to chords such as 8:12:17 and 16:17:24. [[22edo]] is another good EDO system for using the half-octave in this way. | | In [[17-limit]] [[just intonation]], '''24/17''' is the '''small septendecimal tritone''', measuring very nearly 597¢. It is the [[mediant]] between [[7/5]] and [[17/12]], the "larger septendecimal tritone". The two septendecimal tritones are each 3¢ away from the 600¢ half-octave, and so they are well-represented in all even-numbered [[edo]] systems, including [[12edo]]. Indeed, the latter system, containing good approximations of the 3rd and 17th harmonics, can use the half-octave as 24/17 and 17/12 in close approximations to chords such as 8:12:17 and 16:17:24. [[22edo]] is another good edo system for using the half-octave in this way. |
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| See: [[Gallery of Just Intervals]]</pre></div> | | == Terminology and notation == |
| <h4>Original HTML content:</h4>
| | Conceptualization systems disagree on whether [[17/16]] should be a [[diatonic semitone]] or a [[chromatic semitone]], and as a result the disagreement propagates to all intervals of [[harmonic class|HC17]]. See [[17-limit]] for a detailed discussion. |
| <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>24_17</title></head><body><strong>24/17</strong><br />
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| |3 1 0 0 0 0 -1&gt;<br /> | | For 24/17 specifically: |
| 596.9996 cents<br />
| | * In [[Functional Just System]], it is an augmented fourth, separated by [[4131/4096]] from the [[729/512|Pythagorean augmented fourth (729/512)]]. |
| <!-- ws:start:WikiTextMediaRule:0:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/jid_24_17_pluck_adu_dr220.mp3?h=20&amp;w=240&quot; class=&quot;WikiMedia WikiMediaFile&quot; id=&quot;wikitext@@media@@type=&amp;quot;file&amp;quot; key=&amp;quot;jid_24_17_pluck_adu_dr220.mp3&amp;quot;&quot; title=&quot;Local Media File&quot;height=&quot;20&quot; width=&quot;240&quot;/&gt; --><embed src="/s/mediaplayer.swf" pluginspage="http://www.macromedia.com/go/getflashplayer" type="application/x-shockwave-flash" quality="high" width="240" height="20" wmode="transparent" flashvars="file=http%253A%252F%252Fxenharmonic.wikispaces.com%252Ffile%252Fview%252Fjid_24_17_pluck_adu_dr220.mp3?file_extension=mp3&autostart=false&repeat=false&showdigits=true&showfsbutton=false&width=240&height=20"></embed><!-- ws:end:WikiTextMediaRule:0 --> <a href="http://xenharmonic.wikispaces.com/file/view/jid_24_17_pluck_adu_dr220.mp3/513250112/jid_24_17_pluck_adu_dr220.mp3" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/jid_24_17_pluck_adu_dr220.mp3/513250112/jid_24_17_pluck_adu_dr220.mp3');">sound sample</a><br />
| | * In [[Helmholtz-Ellis notation]], it is a diminished fifth, separated by [[2187/2176]] from the [[1024/729|Pythagorean diminished fifth (1024/729)]]. |
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| In <a class="wiki_link" href="/17-limit">17-limit</a> <a class="wiki_link" href="/Just%20Intonation">Just Intonation</a>, 24/17 is the &quot;first septendecimal tritone,&quot; measuring very nearly 597¢. It is the <a class="wiki_link" href="/mediant">mediant</a> between <a class="wiki_link" href="/7_5">7/5</a> and <a class="wiki_link" href="/17_12">17/12</a>, the &quot;second septendecimal tritone.&quot; The two septendecimal tritones are each 3¢ away from the 600¢ half-octave, and so they are well-represented in all even-numbered <a class="wiki_link" href="/EDO">EDO</a> systems, including <a class="wiki_link" href="/12edo">12edo</a>. Indeed, the latter system, containing good approximations of the 3rd and 17th harmonics, can use the half-octave as 24/17 and 17/12 in close approximations to chords such as 8:12:17 and 16:17:24. <a class="wiki_link" href="/22edo">22edo</a> is another good EDO system for using the half-octave in this way.<br />
| | The term ''small septendecimal tritone'' omits the distinction and only describes its melodic property i.e. the size. It is said in contrast to the large septendecimal tritone of [[17/12]]. |
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| See: <a class="wiki_link" href="/Gallery%20of%20Just%20Intervals">Gallery of Just Intervals</a></body></html></pre></div>
| | == See also == |
| | * [[17/12]] – its [[octave complement]] |
| | * [[17/16]] – its [[fifth complement]] |
| | * [[Gallery of just intervals]] |
| | |
| | [[Category:Tritone]] |
In 17-limit just intonation, 24/17 is the small septendecimal tritone, measuring very nearly 597¢. It is the mediant between 7/5 and 17/12, the "larger septendecimal tritone". The two septendecimal tritones are each 3¢ away from the 600¢ half-octave, and so they are well-represented in all even-numbered edo systems, including 12edo. Indeed, the latter system, containing good approximations of the 3rd and 17th harmonics, can use the half-octave as 24/17 and 17/12 in close approximations to chords such as 8:12:17 and 16:17:24. 22edo is another good edo system for using the half-octave in this way.
Terminology and notation
Conceptualization systems disagree on whether 17/16 should be a diatonic semitone or a chromatic semitone, and as a result the disagreement propagates to all intervals of HC17. See 17-limit for a detailed discussion.
For 24/17 specifically:
The term small septendecimal tritone omits the distinction and only describes its melodic property i.e. the size. It is said in contrast to the large septendecimal tritone of 17/12.
See also