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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
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| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | | de = Naturterz |
| : This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2011-12-08 03:14:52 UTC</tt>.<br>
| | | en = 5/4 |
| : The original revision id was <tt>283594398</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">In [[Just Intonation]], 5/4 is the frequency ratio between the 5th and 4th harmonics. Measuring about 386.3¢, 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".
| | {{Infobox Interval |
| | | Name = just major third, classic(al) major third, ptolemaic major third |
| | | Color name = y3, yo 3rd |
| | | Sound = jid_5_4_pluck_adu_dr220.mp3 |
| | }} |
| | {{Wikipedia|Major third}} |
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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 (from the fundamental up to 5 and then noodling between 5 and 4). [[file:5-4.mp3]] Hear it? | | 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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| 5/4 converted to cents (¢): 1200 * log (5/4) / log (2) = 386.314... | | 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). |
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| When two notes sound a 5/4 together,
| | == Approximations by edos == |
| | Following [[edo]]s (up to 200) contain good approximations<ref>error magnitude below 7, both, absolute (in ¢) and relative (in r¢)</ref> of the interval 5/4. |
| | {{Interval edo approximation|interval = 5/4| max_edo=200}} |
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| 5/4 the interval, like all //intervals//, refers to a //relation// between two pitches. We speak of this relation (one pitch beating 5/4 times as fast as the other) after we are able to distinguish it from other relations. | | == See also == |
| | * [[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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| In relation to 12 tone equal, 5/4 is about 13.7¢ flatter than the 4th degree (400¢). 5/4 the interval has been called the //perfect major third// to distinguish it from the other intervals in that neighborhood.
| | == Notes == |
| | <references/> |
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| ==5/4 quotes==
| | [[Category:Third]] |
| got any?
| | [[Category:Major third]] |
| | |
| See: [[Gallery of Just Intervals|Galley of Just Intervals]]</pre></div>
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| <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>5_4</title></head><body>In <a class="wiki_link" href="/Just%20Intonation">Just Intonation</a>, 5/4 is the frequency ratio between the 5th and 4th harmonics. Measuring about 386.3¢, 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 5-limit harmony. It is distinguished from the Pythagorean 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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| 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 (from the fundamental up to 5 and then noodling between 5 and 4). <!-- ws:start:WikiTextFileRule:2:&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:2 --> Hear it?<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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| When two notes sound a 5/4 together,<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. We speak of this relation (one pitch beating 5/4 times as fast as the other) after we are able to distinguish it from other relations.<br />
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| <br />
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| In relation to 12 tone equal, 5/4 is about 13.7¢ flatter than the 4th degree (400¢). 5/4 the interval has been called the <em>perfect major third</em> to distinguish it from the other intervals in that neighborhood.<br />
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| <br />
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| <!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-5/4 quotes"></a><!-- ws:end:WikiTextHeadingRule:0 -->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">Galley of Just Intervals</a></body></html></pre></div>
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In 5-limit just intonation, 5/4 is the frequency ratio between the 5th and 4th harmonics. It has been called the just major third, classic(al) major third, or ptolemaic major third[1] to distinguish it from other intervals in that neighborhood. Measuring about 386.3 ¢, 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 by the syntonic comma of 81/80, which measures about 21.5 ¢, and from the Pythagorean diminished fourth of 8192/6561 by the schisma, which measures about 1.95 ¢. 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 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).
Approximations by edos
Following edos (up to 200) contain good approximations[2] of the interval 5/4.
Edo approximations for 5/4 (386.31 ¢)
≤ 200edo, relative error ≤ 10%
| Edo |
Step size |
Cents (¢) |
Absolute error (¢) |
Relative error (%)
|
| 3 |
1\3 |
400.00 |
+13.69 |
+3.42
|
| 6 |
2\6 |
400.00 |
+13.69 |
+6.84
|
| 22 |
7\22 |
381.82 |
-4.50 |
-8.24
|
| 25 |
8\25 |
384.00 |
-2.31 |
-4.82
|
| 28 |
9\28 |
385.71 |
-0.60 |
-1.40
|
| 31 |
10\31 |
387.10 |
+0.78 |
+2.02
|
| 34 |
11\34 |
388.24 |
+1.92 |
+5.44
|
| 37 |
12\37 |
389.19 |
+2.88 |
+8.87
|
| 50 |
16\50 |
384.00 |
-2.31 |
-9.64
|
| 53 |
17\53 |
384.91 |
-1.41 |
-6.22
|
| 56 |
18\56 |
385.71 |
-0.60 |
-2.80
|
| 59 |
19\59 |
386.44 |
+0.13 |
+0.62
|
| 62 |
20\62 |
387.10 |
+0.78 |
+4.05
|
| 65 |
21\65 |
387.69 |
+1.38 |
+7.47
|
| 81 |
26\81 |
385.19 |
-1.13 |
-7.62
|
| 84 |
27\84 |
385.71 |
-0.60 |
-4.20
|
| 87 |
28\87 |
386.21 |
-0.11 |
-0.77
|
| 90 |
29\90 |
386.67 |
+0.35 |
+2.65
|
| 93 |
30\93 |
387.10 |
+0.78 |
+6.07
|
| 96 |
31\96 |
387.50 |
+1.19 |
+9.49
|
| 109 |
35\109 |
385.32 |
-0.99 |
-9.02
|
| 112 |
36\112 |
385.71 |
-0.60 |
-5.59
|
| 115 |
37\115 |
386.09 |
-0.23 |
-2.17
|
| 118 |
38\118 |
386.44 |
+0.13 |
+1.25
|
| 121 |
39\121 |
386.78 |
+0.46 |
+4.67
|
| 124 |
40\124 |
387.10 |
+0.78 |
+8.09
|
| 140 |
45\140 |
385.71 |
-0.60 |
-6.99
|
| 143 |
46\143 |
386.01 |
-0.30 |
-3.57
|
| 146 |
47\146 |
386.30 |
-0.01 |
-0.15
|
| 149 |
48\149 |
386.58 |
+0.26 |
+3.27
|
| 152 |
49\152 |
386.84 |
+0.53 |
+6.69
|
| 168 |
54\168 |
385.71 |
-0.60 |
-8.39
|
| 171 |
55\171 |
385.96 |
-0.35 |
-4.97
|
| 174 |
56\174 |
386.21 |
-0.11 |
-1.55
|
| 177 |
57\177 |
386.44 |
+0.13 |
+1.87
|
| 180 |
58\180 |
386.67 |
+0.35 |
+5.29
|
| 183 |
59\183 |
386.89 |
+0.57 |
+8.72
|
| 196 |
63\196 |
385.71 |
-0.60 |
-9.79
|
| 199 |
64\199 |
385.93 |
-0.38 |
-6.37
|
See also
Notes
- ↑ For reference, see 5-limit.
- ↑ error magnitude below 7, both, absolute (in ¢) and relative (in r¢)
