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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | {{interwiki |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | | de = Naturterz |
| : This revision was by author [[User:spt3125|spt3125]] and made on <tt>2014-06-07 16:31:13 UTC</tt>.<br>
| | | en = 5/4 |
| : The original revision id was <tt>513196954</tt>.<br>
| | | es = |
| : The revision comment was: <tt></tt><br>
| | | ja = |
| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
| | | ro = 5/4 (ro) |
| <h4>Original Wikitext content:</h4>
| | }} |
| <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">**5/4**
| | {{Infobox Interval |
| |-2 0 1>
| | | Name = just major third, classic(al) major third, ptolemaic major third |
| 386.31371 cents
| | | Color name = y3, yo 3rd |
| [[media type="file" key="jid_5_4_pluck_adu_dr220.mp3" width="240" height="20"]] [[file:xenharmonic/jid_5_4_pluck_adu_dr220.mp3|sound sample]]
| | | Sound = jid_5_4_pluck_adu_dr220.mp3 |
| | }} |
| | {{Wikipedia|Major third}} |
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| In [[Just Intonation]], **5/4** is the frequency ratio between the 5th and 4th harmonics. Measuring about 386.3[[Cent|¢]], it is about 13.7¢ away from [[12edo]]'s major third of 400¢. It has a distinctive "sweet" sound, and has been described as more "laid back" than its 12edo counterpart. Providing a novel consonance after 3, it is the basis for [[5-limit]] harmony. It is distinguished from the [[Pythagorean]] major third of [[81_64|81/64]] by the syntonic comma of [[81_80|81/80]], which measures about 21.5¢. 81/64 and 5/4 are both just intonation "major thirds," 81/64 having a more active and discordant quality, 5/4 sounding more "restful". | | In [[5-limit]] [[just intonation]], '''5/4''' is the [[frequency ratio]] between the 5th and 4th [[harmonic]]s. It has been called the '''just major third''', '''classic(al) major third''', or '''ptolemaic major third'''<ref>For reference, see [[5-limit]].</ref> to distinguish it from other intervals in that neighborhood. Measuring about 386.3 [[cent|¢]], it is about 13.7{{c}} away from [[12edo]]'s major third of 400{{c}}. It has a distinctive "sweet" sound, and has been described as more "laid back" than its 12edo counterpart. Providing a novel consonance after 3, it is the basis for [[5-limit]] harmony. It is distinguished from the [[Pythagorean]] major third of [[81/64]] by the syntonic comma of [[81/80]], which measures about 21.5{{c}}, and from the Pythagorean diminished fourth of [[8192/6561]] by the [[schisma]], which measures about 1.95{{c}}. 81/64 and 5/4 are both just intonation "major thirds", 81/64 having a more active and discordant quality, 5/4 sounding more "restful". |
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| In the context of the harmonic series, 5/4 can be heard between the 4th and 5th member of the series, demonstrated here melodically in singing into a resonant [[@udderbot/home|udderbot]] (from the fundamental up to 5 and then noodling between 5 and 4). | | In the context of the harmonic series, 5/4 can be heard between the 4th and 5th member of the series, demonstrated in [[:File: 5-4.mp3]] melodically in singing into a resonant [[udderbot]] (from the fundamental up to 5 and then noodling between 5 and 4). |
| [[media type="file" key="5-4.mp3" width="240" height="20"]]
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| [[file:5-4.mp3]]
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| 5/4 converted to cents (¢): 1200 * log (5/4) / log (2) = 386.314...
| | == Approximations by edos == |
| | Following [[edo]]s (up to 200, and also 643) contain good approximations<ref>error magnitude below 7, both, absolute (in ¢) and relative (in r¢)</ref> of the interval 5/4. Errors are given by magnitude, the arrows in the table show if the edo representation is sharp (↑) or flat (↓). |
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| 5/4 the interval, like all //intervals//, refers to a //relation// between two pitches. It has been called the //just major third// to distinguish it from the other intervals in that neighborhood. | | {| class="wikitable sortable right-1 center-2 right-3 right-4 center-5" |
| | |- |
| | ! [[Edo]] |
| | ! class="unsortable" | deg\edo |
| | ! Absolute <br> error ([[Cent|¢]]) |
| | ! Relative <br> error ([[Relative cent|r¢]]) |
| | ! ↕ |
| | ! class="unsortable" | Equally acceptable multiples <ref>Super-edos up to 200 within the same error tolerance</ref> |
| | |- |
| | | [[25edo|25]] || 8\25 || 2.3137 || 4.8202 || ↓ || |
| | |- |
| | | [[28edo|28]] || 9\28 || 0.5994 || 1.3987 || ↓ || [[56edo|18\56]], [[84edo|27\84]], [[112edo|36\112]], [[140edo|45\140]] |
| | |- |
| | | [[31edo|31]] || 10\31 || 0.7831 || 2.0229 || ↑ || [[62edo|20\62]], [[93edo|30\93]] |
| | |- |
| | | [[34edo|34]] || 11\34 || 1.9216 || 5.4445 || ↑ || |
| | |- |
| | | [[53edo|53]] || 17\53 || 1.4081 || 6.2189 || ↓ || |
| | |- |
| | | [[59edo|59]] || 19\59 || 0.1270 || 0.6242 || ↑ || [[118edo|38\118]], [[177edo|57\177]] |
| | |- |
| | | [[87edo|87]] || 28\87 || 0.1068 || 0.7744 || ↓ || [[174edo|56\174]] |
| | |- |
| | | [[90edo|90]] || 29\90 || 0.3530 || 2.6471 || ↑ || [[180edo|58\180]] |
| | |- |
| | | [[115edo|115]] || 37\115 || 0.2268 || 2.1731 || ↓ || |
| | |- |
| | | [[121edo|121]] || 39\121 || 0.4631 || 4.6701 || ↑ || |
| | |- |
| | | [[143edo|143]] || 46\143 || 0.2997 || 3.5718 || ↓ || |
| | |- |
| | | [[146edo|146]] || 47\146 || 0.0123 || 0.1502 || ↓ || |
| | |- |
| | | [[149edo|149]] || 48\149 || 0.2635 || 3.2714 || ↑ || |
| | |- |
| | | [[152edo|152]] || 49\152 || 0.5284 || 6.6930 || ↑ || |
| | |- |
| | | [[171edo|171]] || 55\171 || 0.3488 || 4.9704 || ↓ || |
| | |- |
| | | [[199edo|199]] || 64\199 || 0.3841 || 6.3691 || ↓ || |
| | |- |
| | | [[643edo|643]] || 207\643 || 0.0004 || 0.0235 || ↑ || |
| | |} |
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| ==5/4 quotes== | | == See also == |
| got any?
| | * [[8/5]] – its [[octave complement]] |
| | * [[6/5]] – its [[fifth complement]] |
| | * [[16/15]] – its [[fourth complement]] |
| | * [[5/2]] – the interval up one [[octave]] which sounds even more [[consonant]] |
| | * [[Ed5/4]] |
| | * [[Gallery of just intervals]] |
| | * [[List of superparticular intervals]] |
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| See: [[Gallery of Just Intervals]]</pre></div>
| | == Notes == |
| <h4>Original HTML content:</h4>
| | <references/> |
| <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>5_4</title></head><body><strong>5/4</strong><br />
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| |-2 0 1&gt;<br />
| | [[Category:Third]] |
| 386.31371 cents<br />
| | [[Category:Major third]] |
| <!-- ws:start:WikiTextMediaRule:0:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/jid_5_4_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_5_4_pluck_adu_dr220.mp3&amp;quot; width=&amp;quot;240&amp;quot; height=&amp;quot;20&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_5_4_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_5_4_pluck_adu_dr220.mp3/513182478/jid_5_4_pluck_adu_dr220.mp3" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/jid_5_4_pluck_adu_dr220.mp3/513182478/jid_5_4_pluck_adu_dr220.mp3');">sound sample</a><br />
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| <br />
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| In <a class="wiki_link" href="/Just%20Intonation">Just Intonation</a>, <strong>5/4</strong> is the frequency ratio between the 5th and 4th harmonics. Measuring about 386.3<a class="wiki_link" href="/Cent">¢</a>, it is about 13.7¢ away from <a class="wiki_link" href="/12edo">12edo</a>'s major third of 400¢. It has a distinctive &quot;sweet&quot; sound, and has been described as more &quot;laid back&quot; than its 12edo counterpart. Providing a novel consonance after 3, it is the basis for <a class="wiki_link" href="/5-limit">5-limit</a> harmony. It is distinguished from the <a class="wiki_link" href="/Pythagorean">Pythagorean</a> major third of <a class="wiki_link" href="/81_64">81/64</a> by the syntonic comma of <a class="wiki_link" href="/81_80">81/80</a>, which measures about 21.5¢. 81/64 and 5/4 are both just intonation &quot;major thirds,&quot; 81/64 having a more active and discordant quality, 5/4 sounding more &quot;restful&quot;.<br />
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| <br />
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| In the context of the harmonic series, 5/4 can be heard between the 4th and 5th member of the series, demonstrated here melodically in singing into a resonant <a class="wiki_link" href="http://udderbot.wikispaces.com/home" target="_blank">udderbot</a> (from the fundamental up to 5 and then noodling between 5 and 4).<br />
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| <!-- ws:start:WikiTextMediaRule:1:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/5-4.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;5-4.mp3&amp;quot; width=&amp;quot;240&amp;quot; height=&amp;quot;20&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%252F5-4.mp3?file_extension=mp3&autostart=false&repeat=false&showdigits=true&showfsbutton=false&width=240&height=20"></embed><!-- ws:end:WikiTextMediaRule:1 --><br />
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| <!-- ws:start:WikiTextFileRule:5:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file/5-4.mp3?h=52&amp;w=320&quot; class=&quot;WikiFile&quot; id=&quot;wikitext@@file@@5-4.mp3&quot; title=&quot;File: 5-4.mp3&quot; width=&quot;320&quot; height=&quot;52&quot; /&gt; --><div class="objectEmbed"><a href="/file/view/5-4.mp3/30382423/5-4.mp3" onclick="ws.common.trackFileLink('/file/view/5-4.mp3/30382423/5-4.mp3');"><img src="http://www.wikispaces.com/i/mime/32/audio/mpeg.png" height="32" width="32" alt="5-4.mp3" /></a><div><a href="/file/view/5-4.mp3/30382423/5-4.mp3" onclick="ws.common.trackFileLink('/file/view/5-4.mp3/30382423/5-4.mp3');" class="filename" title="5-4.mp3">5-4.mp3</a><br /><ul><li><a href="/file/detail/5-4.mp3">Details</a></li><li><a href="/file/view/5-4.mp3/30382423/5-4.mp3">Download</a></li><li style="color: #666">402 KB</li></ul></div></div><!-- ws:end:WikiTextFileRule:5 --><br />
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| <br />
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| 5/4 converted to cents (¢): 1200 * log (5/4) / log (2) = 386.314...<br />
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| <br />
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| 5/4 the interval, like all <em>intervals</em>, refers to a <em>relation</em> between two pitches. It has been called the <em>just major third</em> to distinguish it from the other intervals in that neighborhood.<br />
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| <!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc0"><a name="x-5/4 quotes"></a><!-- ws:end:WikiTextHeadingRule:2 -->5/4 quotes</h2>
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| got any?<br />
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| <br />
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| See: <a class="wiki_link" href="/Gallery%20of%20Just%20Intervals">Gallery of Just Intervals</a></body></html></pre></div>
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