|
|
| (34 intermediate revisions by 15 users not shown) |
| Line 1: |
Line 1: |
| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | {{interwiki |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | | de = 7/5 |
| : This revision was by author [[User:k9assassin|k9assassin]] and made on <tt>2015-03-24 20:44:47 UTC</tt>.<br>
| | | en = 7/5 |
| : The original revision id was <tt>545214878</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>
| | }} |
| <h4>Original Wikitext content:</h4>
| | {{Infobox Interval |
| <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">[[image:ji glyph 7 5.png width="147" height="116" caption="JI glyph for 7/5
| | | Name = narrow tritone, lesser septimal tritone, Huygens' tritone |
| "]]
| | | Color name = zg5, zogu 5th |
| | | Sound = jid_7_5_pluck_adu_dr220.mp3 |
| | }} |
| | {{Wikipedia|Septimal tritone}} |
|
| |
|
| **7/5**
| | In [[7-limit]] [[just intonation]], '''7/5''' is a '''narrow [[tritone]]''' (or '''Huygens' tritone''') measuring about 582.5¢. It is a noticeable 17.5¢ away from the 600¢ half-octave (square root of 2) tritone of [[12edo]] and every even-numbered [[edo]]. It represents the difference between [[7/4]] and [[5/4]]. |
| |0 0 -1 1>
| |
| 582.51219 cents | |
| [[media type="file" key="jid_7_5_pluck_adu_dr220.mp3" width="240" height="20"]] [[file:xenharmonic/jid_7_5_pluck_adu_dr220.mp3|sound sample]] | |
|
| |
|
| In [[7-limit]] [[Just Intonation]], 7/5 is a narrow [[@http://en.wikipedia.org/wiki/Tritone|tritone]] measuring about 582.5¢. It is a noticeable 17.5¢ away from the 600¢ half-octave (square root of 2) tritone of [[12edo]] and every even-numbered [[EDO]]. It represents the difference between [[7_4|7/4]] and [[5_4|5/4]].
| | While in the context of the [[harmonic seventh chord]], it is rightly recognized as a type of diminished fifth, it can also be argued on the basis of the fact that 7/5 interval is smaller than 600 cents that it acts more as a type of augmented fourth than a diminished fifth – an analysis that is required in cases where this interval occurs in a [[5L 2s|diatonic scale]] that demonstrates [[Rothenberg propriety]]. This is one of the reasons why 7/4 can be argued to be a type of "sinth" – a cross between a sixth and a seventh – as opposed to merely a subminor seventh. |
|
| |
|
| 7/5 is notable for its low [[harmonic entropy]], and is often reported to sound more consonant than the half-octave tritone; indeed it appears in the 4:5:6:7 tetrad that forms the basis of consonance in 7-limit JI. Its inversion is [[10_7|10/7]], which measures about 617.5¢, and these two septimal tritones differ by the [[superparticular]] interval [[50_49|50/49]], about 35.0¢. Systems which temper out 50/49 will equate 7/5 and 10/7, usually to the 600¢ half-octave. | | 7/5 is notable for its low [[harmonic entropy]], and is often reported to sound more consonant than the half-octave tritone; indeed it appears in the harmonic seventh chord that forms the basis of consonance in 7-limit JI. Its inversion is [[10/7]], which measures about 617.5¢, and these two septimal tritones differ by the [[superparticular]] interval [[50/49]], about 35.0¢. Systems which temper out 50/49 will equate 7/5 and [[10/7]], usually to the 600¢ half-octave. |
|
| |
|
| Another just tritone is the [[3-limit]] 729/512, 611.7¢, and this is literally a tri-tone, since it is (9/8)<span style="vertical-align: super;">3</span>, or three "whole tones". Yet another is [[45_32|45/32]], about 590.2¢, which appears in the [[5-limit]]. See also [[13_9|13/9]], [[18_13|18/13]], [[17_12|17/12]] and [[24_17|24/17]]. | | Another just tritone is [[729/512]] (611.7¢), and this is literally a tri-tone, since it is (9/8)<sup>3</sup>, or three "whole tones". Yet another is [[45/32]], about 590.2¢, which appears in the [[5-limit]] (inversion is [[64/45]]). See also [[13/9]], [[18/13]], [[17/12]], [[24/17]], [[25/18]] and [[36/25]]. |
| | == Approximation == |
| | {{Interval edo approximation|7/5}} |
| | == See also == |
|
| |
|
| See: [[Gallery of Just Intervals]]</pre></div>
| | * [[10/7]] – its [[octave complement]] |
| <h4>Original HTML content:</h4>
| | * [[15/14]] – its [[fifth complement]] |
| <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>7_5</title></head><body><!-- ws:start:WikiTextLocalImageRule:1:&lt;img src=&quot;/file/view/ji%20glyph%207%205.png/545214466/147x116/ji%20glyph%207%205.png&quot; alt=&quot;JI glyph for 7/5&quot; title=&quot;JI glyph for 7/5&quot; style=&quot;height: 116px; width: 147px;&quot; /&gt; --><table class="captionBox"><tr><td class="captionedImage"><img src="/file/view/ji%20glyph%207%205.png/545214466/147x116/ji%20glyph%207%205.png" alt="ji glyph 7 5.png" title="ji glyph 7 5.png" style="height: 116px; width: 147px;" /></td></tr><tr><td class="imageCaption">JI glyph for 7/5</td></tr></table><!-- ws:end:WikiTextLocalImageRule:1 --><br />
| | * [[Gallery of just intervals]] |
| <br />
| | |
| <strong>7/5</strong><br />
| | [[Category:Tritone]] |
| |0 0 -1 1&gt;<br />
| | [[Category:Over-5 intervals]] |
| 582.51219 cents<br />
| | [[Category:Taxicab-2 intervals]] |
| <!-- ws:start:WikiTextMediaRule:0:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/jid_7_5_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_7_5_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_7_5_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_7_5_pluck_adu_dr220.mp3/513183034/jid_7_5_pluck_adu_dr220.mp3" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/jid_7_5_pluck_adu_dr220.mp3/513183034/jid_7_5_pluck_adu_dr220.mp3');">sound sample</a><br />
| |
| <br />
| |
| In <a class="wiki_link" href="/7-limit">7-limit</a> <a class="wiki_link" href="/Just%20Intonation">Just Intonation</a>, 7/5 is a narrow <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Tritone" rel="nofollow" target="_blank">tritone</a> measuring about 582.5¢. It is a noticeable 17.5¢ away from the 600¢ half-octave (square root of 2) tritone of <a class="wiki_link" href="/12edo">12edo</a> and every even-numbered <a class="wiki_link" href="/EDO">EDO</a>. It represents the difference between <a class="wiki_link" href="/7_4">7/4</a> and <a class="wiki_link" href="/5_4">5/4</a>.<br />
| |
| <br />
| |
| 7/5 is notable for its low <a class="wiki_link" href="/harmonic%20entropy">harmonic entropy</a>, and is often reported to sound more consonant than the half-octave tritone; indeed it appears in the 4:5:6:7 tetrad that forms the basis of consonance in 7-limit JI. Its inversion is <a class="wiki_link" href="/10_7">10/7</a>, which measures about 617.5¢, and these two septimal tritones differ by the <a class="wiki_link" href="/superparticular">superparticular</a> interval <a class="wiki_link" href="/50_49">50/49</a>, about 35.0¢. Systems which temper out 50/49 will equate 7/5 and 10/7, usually to the 600¢ half-octave.<br />
| |
| <br />
| |
| Another just tritone is the <a class="wiki_link" href="/3-limit">3-limit</a> 729/512, 611.7¢, and this is literally a tri-tone, since it is (9/8)<span style="vertical-align: super;">3</span>, or three &quot;whole tones&quot;. Yet another is <a class="wiki_link" href="/45_32">45/32</a>, about 590.2¢, which appears in the <a class="wiki_link" href="/5-limit">5-limit</a>. See also <a class="wiki_link" href="/13_9">13/9</a>, <a class="wiki_link" href="/18_13">18/13</a>, <a class="wiki_link" href="/17_12">17/12</a> and <a class="wiki_link" href="/24_17">24/17</a>.<br />
| |
| <br />
| |
| See: <a class="wiki_link" href="/Gallery%20of%20Just%20Intervals">Gallery of Just Intervals</a></body></html></pre></div>
| |
In 7-limit just intonation, 7/5 is a narrow tritone (or Huygens' tritone) measuring about 582.5¢. It is a noticeable 17.5¢ away from the 600¢ half-octave (square root of 2) tritone of 12edo and every even-numbered edo. It represents the difference between 7/4 and 5/4.
While in the context of the harmonic seventh chord, it is rightly recognized as a type of diminished fifth, it can also be argued on the basis of the fact that 7/5 interval is smaller than 600 cents that it acts more as a type of augmented fourth than a diminished fifth – an analysis that is required in cases where this interval occurs in a diatonic scale that demonstrates Rothenberg propriety. This is one of the reasons why 7/4 can be argued to be a type of "sinth" – a cross between a sixth and a seventh – as opposed to merely a subminor seventh.
7/5 is notable for its low harmonic entropy, and is often reported to sound more consonant than the half-octave tritone; indeed it appears in the harmonic seventh chord that forms the basis of consonance in 7-limit JI. Its inversion is 10/7, which measures about 617.5¢, and these two septimal tritones differ by the superparticular interval 50/49, about 35.0¢. Systems which temper out 50/49 will equate 7/5 and 10/7, usually to the 600¢ half-octave.
Another just tritone is 729/512 (611.7¢), and this is literally a tri-tone, since it is (9/8)3, or three "whole tones". Yet another is 45/32, about 590.2¢, which appears in the 5-limit (inversion is 64/45). See also 13/9, 18/13, 17/12, 24/17, 25/18 and 36/25.
Approximation
Edo approximations for 7/5 (582.51 ¢)
≤ 80edo, relative error ≤ 10%
| Edo |
Step size |
Cents (¢) |
Absolute error (¢) |
Relative error (%)
|
| 2 |
1\2 |
600.00 |
+17.49 |
+2.91
|
| 4 |
2\4 |
600.00 |
+17.49 |
+5.83
|
| 6 |
3\6 |
600.00 |
+17.49 |
+8.74
|
| 29 |
14\29 |
579.31 |
-3.20 |
-7.74
|
| 31 |
15\31 |
580.65 |
-1.87 |
-4.82
|
| 33 |
16\33 |
581.82 |
-0.69 |
-1.91
|
| 35 |
17\35 |
582.86 |
+0.34 |
+1.01
|
| 37 |
18\37 |
583.78 |
+1.27 |
+3.92
|
| 39 |
19\39 |
584.62 |
+2.10 |
+6.84
|
| 41 |
20\41 |
585.37 |
+2.85 |
+9.75
|
| 62 |
30\62 |
580.65 |
-1.87 |
-9.65
|
| 64 |
31\64 |
581.25 |
-1.26 |
-6.73
|
| 66 |
32\66 |
581.82 |
-0.69 |
-3.82
|
| 68 |
33\68 |
582.35 |
-0.16 |
-0.90
|
| 70 |
34\70 |
582.86 |
+0.34 |
+2.01
|
| 72 |
35\72 |
583.33 |
+0.82 |
+4.93
|
| 74 |
36\74 |
583.78 |
+1.27 |
+7.84
|
See also
