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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | {{About|the interval region|the octave as a just ratio|2/1}} |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | {{Wikipedia|Octave}} |
| : This revision was by author [[User:hstraub|hstraub]] and made on <tt>2015-07-29 06:50:43 UTC</tt>.<br>
| | A '''perfect octave''' ('''P8''') or '''octave''' ('''8ve''') is an [[interval]] that is approximately 1200 [[cent]]s in [[interval size measure|size]]. While a rough tuning range for octaves is sharper than 1170 cents according to [[Margo Schulter]]'s theory of interval regions, the term ''octave'' tends to imply a function within music that only works with intervals that corresponding to a [[just]] [[ratio]] of [[2/1]] or a close approximation thereof, usually preferred to be sharp-tempered if tempered. Other intervals are also classified as octaves, sometimes called '''wolf octaves''' or '''imperfect octaves''', if they are reasonably mapped to seven steps of the diatonic scale and twelve steps of the chromatic scale, reflecting the period and equave of both. Enharmonic intervals may be found at multiples of 12 steps along the chain of fifths, such as the diminished ninth (mapped to 8\7) and augmented seventh (6\7). |
| : The original revision id was <tt>555894189</tt>.<br>
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| : The revision comment was: <tt></tt><br>
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| 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"><span style="display: block; text-align: right;">[[オクターブ|日本語]]
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| [[media type="file" key="jid_2_1_pluck_adu_dr220.mp3" width="240" height="20"]] [[file:xenharmonic/jid_2_1_pluck_adu_dr220.mp3|sound sample]] | |
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| The **octave** is one of the most basic [[Gallery of Just Intervals|intervals]] found in musical systems throughout the entire world. It is usually called the "interval of equivalence" because tones separated by an octave are perceived to have the same or similar pitch class to the average human listener. The reason for this phenomenon is probably due to the strong region of attraction of low [[harmonic entropy]], or the strong amplitude of the second [[harmonic]] in most harmonic instruments. | | The aforementioned function is the interval of equivalence, or [[equave]], because tones separated by an octave are perceived to have the same or similar [[pitch class]] to the average human listener. The reason for this phenomenon is probably due to the strong concordance of the octave or the strong amplitude of the second [[harmonic]] in most harmonic instruments. As such, it is common practice to [[octave-reduce]] intervals so that they lie within the octave. |
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| It has a frequency ratio of 2/1 and a size of 1200 [[cent|cents]]. It is used as the standard of (logarithmic) measurement for all intervals, regardless if they are justly tuned or not.
| | Because of that, this page only covers intervals of 1200 cents and flatter, as sharper intervals octave-reduce to [[commas and dieses]]. |
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| Strangely enough, the Pelog and Slendro scales of the Javanese contain near-octaves even though gamelan instruments exhibit inharmonic spectra. It is most likely reminiscent of an older musical system, or derived using the human voice instead of inharmonic instruments.
| | For the sake of simplicity, this page also covers '''interseptimal seventh-octaves''', which are approximately 1150 cents in size and are the complements of [[Comma and diesis|dieses]]. Thus, the interval region considered as "octave" for the purpose of this page is 1140-1200 cents. |
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| ==Links== | | == In just intonation == |
| * [[http://www.kylegann.com/Octave.html|Anatomy of an Octave]] by [[Kyle Gann]]
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| ==see also== | | === By prime limit === |
| * [[Prime Interval]]
| | The only "perfect" octave is the interval [[2/1]], which can be stacked to produce all other 2-limit intervals. It is 1200 cents in size, by definition. However, various "out-of-tune" octaves exist, usually flat or sharp of an octave by a small interval such as a comma. |
| * [[Gallery of Just Intervals]]
| | |
| * [[Toctave]]
| | Several notable ones are: |
| * [[EDO]]
| | |
| * [[Ditave]] - an alternative more neutral name</pre></div>
| | {| class="wikitable sortable center-all right-3" |
| <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>Octave</title></head><body><span style="display: block; text-align: right;"><a class="wiki_link" href="/%E3%82%AA%E3%82%AF%E3%82%BF%E3%83%BC%E3%83%96">日本語</a><br />
| | ! class="unsortable" | Interval |
| </span><br />
| | ! Prime <br>limit |
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| | ! Distance <br>from 2/1 |
| <br />
| | ! Comma |
| The <strong>octave</strong> is one of the most basic <a class="wiki_link" href="/Gallery%20of%20Just%20Intervals">intervals</a> found in musical systems throughout the entire world. It is usually called the &quot;interval of equivalence&quot; because tones separated by an octave are perceived to have the same or similar pitch class to the average human listener. The reason for this phenomenon is probably due to the strong region of attraction of low <a class="wiki_link" href="/harmonic%20entropy">harmonic entropy</a>, or the strong amplitude of the second <a class="wiki_link" href="/harmonic">harmonic</a> in most harmonic instruments.<br />
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| | | [[1048576/531441]] |
| It has a frequency ratio of 2/1 and a size of 1200 <a class="wiki_link" href="/cent">cents</a>. It is used as the standard of (logarithmic) measurement for all intervals, regardless if they are justly tuned or not.<br />
| | | 3 |
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| | | 23.4600 |
| Strangely enough, the Pelog and Slendro scales of the Javanese contain near-octaves even though gamelan instruments exhibit inharmonic spectra. It is most likely reminiscent of an older musical system, or derived using the human voice instead of inharmonic instruments.<br />
| | | [[Pythagorean comma|531441/524288]] |
| <br />
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| <!-- ws:start:WikiTextHeadingRule:1:&lt;h2&gt; --><h2 id="toc0"><a name="x-Links"></a><!-- ws:end:WikiTextHeadingRule:1 -->Links</h2>
| | | [[160/81]] |
| <ul><li><a class="wiki_link_ext" href="http://www.kylegann.com/Octave.html" rel="nofollow">Anatomy of an Octave</a> by <a class="wiki_link" href="/Kyle%20Gann">Kyle Gann</a></li></ul><br />
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| <!-- ws:start:WikiTextHeadingRule:3:&lt;h2&gt; --><h2 id="toc1"><a name="x-see also"></a><!-- ws:end:WikiTextHeadingRule:3 -->see also</h2>
| | | 21.5063 |
| <ul><li><a class="wiki_link" href="/Prime%20Interval">Prime Interval</a></li><li><a class="wiki_link" href="/Gallery%20of%20Just%20Intervals">Gallery of Just Intervals</a></li><li><a class="wiki_link" href="/Toctave">Toctave</a></li><li><a class="wiki_link" href="/EDO">EDO</a></li><li><a class="wiki_link" href="/Ditave">Ditave</a> - an alternative more neutral name</li></ul></body></html></pre></div>
| | | [[81/80]] |
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| | | 41.0589 |
| | | [[128/125]] |
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| | | 27.2641 |
| | | [[64/63]] |
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| | | 7 |
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| | | [[49/48]] |
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| | | 7 |
| | | 48.7704 |
| | | [[36/35]] |
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| | | [[64/33]] |
| | | 11 |
| | | 53.2729 |
| | | [[33/32]] |
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| | | [[33/17]] |
| | | 17 |
| | | 51.6825 |
| | | [[34/33]] |
| | |} |
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| | == In tempered scales == |
| | As the just octave of 2/1 is the interval being equally divided in [[EDO]]s, it is represented perfectly in all of them. It is also represented perfectly in all octave-period MOSes. Note both of these statements assume the octave is untempered. The following table lists other octave-sized intervals (> 1140 cents) that exist in various significant EDOs. |
| | |
| | {| class="wikitable" |
| | |- |
| | ! EDO |
| | ! Suboctaves |
| | |- |
| | | 22 |
| | | 1145{{c}} |
| | |- |
| | | 24 |
| | | 1150{{c}} |
| | |- |
| | | 25 |
| | | 1152{{c}} |
| | |- |
| | | 26 |
| | | 1154{{c}} |
| | |- |
| | | 27 |
| | | 1156{{c}} |
| | |- |
| | | 29 |
| | | 1159{{c}} |
| | |- |
| | | 31 |
| | | 1161{{c}} |
| | |- |
| | | 34 |
| | | 1165{{c}} |
| | |- |
| | | 41 |
| | | 1142{{c}}, 1171{{c}} |
| | |- |
| | | 53 |
| | | 1155{{c}}, 1177{{c}} |
| | |} |
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| | 2/1 is also represented perfectly in most temperaments, or the most common tunings thereof, and is mainly involved in octave-reducing intervals (such as saying that, in meantone, four 3/2s (octave-reduced) stack to 5/4). |
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| | == See also == |
| | * [[Octave]] (disambiguation page) |
| | |
| | {{Navbox intervals}} |