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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 = large septendecimal semitone <br>minor diatonic semitone |
| : This revision was by author [[User:spt3125|spt3125]] and made on <tt>2014-06-30 21:37:24 UTC</tt>.<br>
| | | Color name = 17o2, iso 2nd |
| : The original revision id was <tt>515319714</tt>.<br>
| | | Sound = jid_17_16_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>
| | {{Wikipedia|Minor diatonic semitone}} |
| <h4>Original Wikitext content:</h4>
| | In [[17-limit]] [[just intonation]], '''17/16''' is the 17th [[harmonic]], [[octave reduced]], and may be called the '''large septendecimal semitone'''. Measuring about 105{{cent}}, it is close to the [[12edo]] semitone of 100{{cent}}, and thus 12edo can be said to approximate it closely, although an even better approximation is available in [[23edo]]. In a chord, it can function similarly to a jazz "minor ninth"—for instance, 8:10:12:14:17 (although here the interval is [[17/8]], which is a little less harsh sounding than 17/16). In 17-limit JI, [[17/1]] is treated as the next basic consonance after [[13/1|13]] and [[15/1|15]]. |
| <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">**17/16**
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| |-4 0 0 0 0 0 1>
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| 104.9554 cents
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| [[media type="file" key="jid_17_16_pluck_adu_dr220.mp3"]] [[file:xenharmonic/jid_17_16_pluck_adu_dr220.mp3|sound sample]] | |
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| In [[17-limit]] [[Just Intonation]], 17/16 is the 17th overtone, octave reduced, and may be called the "large septendecimal semitone". Measuring about 105¢, it is close to the [[12edo]] semitone of 100¢, and thus 12edo can be said to approximate it closely. In a chord, it can function similarly to a jazz "minor ninth" -- for instance, 8:10:12:14:17 (although here the interval is 17/8, which is a little less harsh sounding than 17/16). In 17-limit JI, it is treated as the next basic consonance after 13 and 15.
| | 17/16 is one of two [[superparticular]] semitones in the 17-limit; the other is [[18/17]], the small septendecimal semitone, which measures about 99{{c}}. The difference between them is [[289/288]], about 6{{c}}. If 12edo is treated as a harmonic system approximating 9 and 17, then 289/288 is tempered out. |
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| 17/16 is one of two [[superparticular]] semitones in the 17-limit; the other is [[18_17|18/17]], which measures about 99¢. The difference between them is 289/288, about 6¢. If 12edo is treated as a harmonic system approximating 9 and 17, then 289/288 is tempered out. | | 17/16 is almost exactly 1/3 of the [[6/5]] minor third. The difference between 6/5 and three 17/16 semitones is [[24576/24565]], an interval of approximately 0.8{{c}}. 17/16 is also almost exactly 1/8 of [[13/8]], with the difference between 13/8 and (17/16)<sup>8</sup> being approximately 0.9{{c}}. The difference between ten 17/16's and [[11/6]] is approximately 0.2{{c}}, while the difference between thirteen 17/16's and [[11/5]] is approximately 0.6{{c}}. |
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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>17_16</title></head><body><strong>17/16</strong><br />
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| |-4 0 0 0 0 0 1&gt;<br /> | | For 17/16 specifically: |
| 104.9554 cents<br />
| | * In [[Functional Just System]], it is a diatonic semitone, separated by [[4131/4096]] from the [[256/243|Pythagorean minor second (256/243)]]. It is also called the '''minor diatonic semitone''', which contrasts the [[5-limit]] major diatonic semitone of [[16/15]] by [[256/255]], about 6.8{{c}}. |
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| | * In [[Helmholtz–Ellis notation]], it is a chromatic semitone, separated by [[2187/2176]] from the [[2187/2048|Pythagorean augmented unison (2187/2048)]]. |
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| | It could also be reasonable to treat 17/16 as the formal comma for prime 17 in its own right, as it is roughly the same size as the 3-limit accidental 2187/2048. |
| In <a class="wiki_link" href="/17-limit">17-limit</a> <a class="wiki_link" href="/Just%20Intonation">Just Intonation</a>, 17/16 is the 17th overtone, octave reduced, and may be called the &quot;large septendecimal semitone&quot;. Measuring about 105¢, it is close to the <a class="wiki_link" href="/12edo">12edo</a> semitone of 100¢, and thus 12edo can be said to approximate it closely. In a chord, it can function similarly to a jazz &quot;minor ninth&quot; -- for instance, 8:10:12:14:17 (although here the interval is 17/8, which is a little less harsh sounding than 17/16). In 17-limit JI, it is treated as the next basic consonance after 13 and 15.<br />
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| | The term ''large septendecimal semitone'' omits the diatonic/chromatic part and only describes its melodic property i.e. the size. It is said in contrast to the small septendecimal semitone of 18/17. |
| 17/16 is one of two <a class="wiki_link" href="/superparticular">superparticular</a> semitones in the 17-limit; the other is <a class="wiki_link" href="/18_17">18/17</a>, which measures about 99¢. The difference between them is 289/288, about 6¢. If 12edo is treated as a harmonic system approximating 9 and 17, then 289/288 is tempered out.<br />
| | == Approximation == |
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| | {{Interval edo approximation|17/16}} |
| See: <a class="wiki_link" href="/Gallery%20of%20Just%20Intervals">Gallery of Just Intervals</a></body></html></pre></div>
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| | == Temperaments == |
| | The 17/16 interval generates [[srutal archagall]] with a half-octave period, where it also represents [[16/15]] and [[18/17]]. With a full-octave period it generates [[septendesemi]], the 80 & 103 temperament. It is also a good generator for [[lithium]] with a 1/3-octave period, as well as the less accurate [[august]]. |
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| | It is very close to 7 steps of [[80edo]], and is tempered as such in many [[80th-octave temperaments]]. |
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| | == See also == |
| | * [[32/17]] – its [[octave complement]] |
| | * [[24/17]] – its [[fifth complement]] |
| | * [[17/8]] – same interval, one octave higher |
| | * [[Gallery of just intervals]] |
| | * [[List of superparticular intervals]] |
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| | [[Category:Second]] |
| | [[Category:Semitone]] |
| | [[Category:Chroma]] |