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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 semitone |
| : This revision was by author [[User:spt3125|spt3125]] and made on <tt>2014-06-30 21:03:50 UTC</tt>.<br>
| | | Color name = 17u1, su unison |
| : The original revision id was <tt>515317708</tt>.<br>
| | | Sound = jid_18_17_pluck_adu_dr220.mp3 |
| : The revision comment was: <tt></tt><br>
| | | Comma = yes |
| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
| | }} |
| <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">**18/17**
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| |1 2 0 0 0 0 -1> | |
| 98.9546 cents
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| [[media type="file" key="jid_18_17_pluck_adu_dr220.mp3"]] [[file:xenharmonic/jid_18_17_pluck_adu_dr220.mp3|sound sample]]
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| In [[17-limit]] [[Just Intonation]], 18/17 is the "small septendecimal semitone" of about 99¢. It is very close to [[12edo]]'s "half step" of 100¢, and fairly close to the "large septendecimal semitone" of [[17_16|17/16]] (~105¢). | | In [[17-limit]] [[just intonation]], '''18/17''' is the '''small septendecimal semitone''' of about 99{{cent}}. It is very close to [[12edo]]'s "half step" of 100¢, and fairly close to the "large septendecimal semitone" of [[17/16]] (~105¢). |
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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>18_17</title></head><body><strong>18/17</strong><br />
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| |1 2 0 0 0 0 -1&gt;<br /> | | For 18/17 specifically: |
| 98.9546 cents<br />
| | * In the [[Functional Just System]], it is a chromatic semitone, separated by [[4131/4096]] from the [[2187/2048|Pythagorean augmented unison (2187/2048)]]. |
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| | * In [[Helmholtz-Ellis notation]], it is a diatonic semitone, separated by [[2187/2176]] from the [[256/243|Pythagorean minor second (256/243)]]. |
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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>, 18/17 is the &quot;small septendecimal semitone&quot; of about 99¢. It is very close to <a class="wiki_link" href="/12edo">12edo</a>'s &quot;half step&quot; of 100¢, and fairly close to the &quot;large septendecimal semitone&quot; of <a class="wiki_link" href="/17_16">17/16</a> (~105¢).<br />
| | The term ''small septendecimal semitone'' omits the diatonic/chromatic part and only describes its melodic property i.e. the size. It is said in contrast to the large septendecimal semitone of 17/16. |
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| See: <a class="wiki_link" href="/Gallery%20of%20Just%20Intervals">Gallery of Just Intervals</a></body></html></pre></div> | | == Temperaments == |
| | {{w|Vincenzo Galilei}} (1520-1591) proposed a tuning based on eleven 18/17 semitones and one larger semitone of about 111.5{{cent}} (the [[octave complement]])<ref>Barbour, J. Murray. ''[https://archive.org/details/tuningtemperamen00barb/page/n7/mode/2up Tuning and temperament: a historical survey]'', p. 57.</ref>. This [[well temperament]] provides seven wide perfect fifths of about 705.2{{cent}} and five narrow perfect fifths of about 692.7{{cent}}, whose distribution is [[maximally even]] instead of grouping together the wide and the narrow fifths along the [[circle of fifths]], as is often the case in other well temperaments. |
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| | The following [[linear temperament]]s are [[generate]]d by a [[~]]18/17 in the 2.3.5.17 and 2.3.5.17.19 [[subgroup]]s: |
| | * [[Quintaleap]] |
| | * [[Quindromeda]] |
| | * [[Schismatic_family#Quintilischis_(2.3.5.17)|Quintilischis]]. |
| | {{todo|complete list}} |
| | Note that all of these reach [[4/3]] as a stack of five 18/17 intervals (tempering out the [[quinticular comma]]). |
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| | Some [[12th-octave temperaments]] treat ~18/17 as the period, including [[compton]]'s 17-limit extension. |
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| | == See also == |
| | * [[17/9]] – its [[octave complement]] |
| | * [[17/12]] – its [[fifth complement]] |
| | * [[Gallery of just intervals]] |
| | * [[List of superparticular intervals]] |
| | |
| | == References == |
| | <references/> |
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| | [[Category:Second]] |
| | [[Category:Chroma]] |
| | [[Category:Semitone]] |
| | [[Category:Commas named after their interval size]] |