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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 = septimal narrow major third, marvel-ptolemaic major third, hemifamity diminished fourth |
| : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2014-06-28 12:55:32 UTC</tt>.<br>
| | | Color name = zg4, zogu 4th |
| : The original revision id was <tt>515167234</tt>.<br>
| | | Sound = jid_56_45_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>
| | '''56/45''', the '''septimal narrow major third''', or '''marvel-ptolemaic major third''', is the interval between various [[9-odd-limit]] consonances – [[5/4]] and [[14/9]], [[9/7]] and [[8/5]], [[9/8]] and [[7/5]], and [[10/7]] and [[16/9]] – with it also being [[6/5]] away from the marvelous fifth, [[112/75]]. It is flat of the [[81/64|Pythagorean major third]] by [[3645/3584]], namely a [[81/80|syntonic comma]] plus a [[225/224|marvel comma]]. [[Marvel]] tempering makes all of these intervals into classical major thirds, and turns chords like 1–5/4–8/5 or 1–5/4–14/9 into [[essentially tempered dyadic chord]]s. It is a third of a cent flatter than the 6\19 major third of [[19edo]]; however, it functionally doubles as a type of diminished fourth, flat of the [[8192/6561|Pythagorean diminished fourth]] by [[5120/5103]]. This gives rise to the name '''hemifamity diminished fourth'''. |
| <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">**56/45**
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| |3 -2 -1 1> | |
| 378.6022 cents
| |
| [[media type="file" key="jid_56_45_pluck_adu_dr220.mp3"]] [[file:xenharmonic/jid_56_45_pluck_adu_dr220.mp3|sound sample]] | |
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| According to [[Ozan Yarman]], the perde segah of Turkish maqam music should range from **56/45**, which is flatter than [[5_4|5/4]] by the [[septimal kleisma]] of [[225_224|225/224]], to 5/4. 56/45 is the interval between various 9-limit consonances: 5/4 and 14/9, 9/7 and 8/5, 9/8 and 7/5, and 10/7 and 16/9. [[Marvel]] tempering makes all of these intervals into major thirds like any other, and turns chords like 1-5/4-8/5 or 1-5/4-14/9 into [[Dyadic chord|essentially tempered dyadic chords]]. The 56/45 third is [[6_5|6/5]] away from the marvelous fifth, [[112_75|112/75]], and may also be called the marvelous major third. It is a third of a cent flatter than the 6\19 major third of 19et.</pre></div> | | According to [[Ozan Yarman]], the perde segah of [[Arabic, Turkish, Persian music|Turkish maqam music]] should range from 56/45 to 5/4. |
| <h4>Original HTML 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;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>56_45</title></head><body><strong>56/45</strong><br />
| | == Approximation == |
| |3 -2 -1 1&gt;<br />
| | {{Interval edo approximation|56/45}} |
| 378.6022 cents<br />
| | |
| <!-- ws:start:WikiTextMediaRule:0:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/jid_56_45_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_56_45_pluck_adu_dr220.mp3&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_56_45_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_56_45_pluck_adu_dr220.mp3/513250356/jid_56_45_pluck_adu_dr220.mp3" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/jid_56_45_pluck_adu_dr220.mp3/513250356/jid_56_45_pluck_adu_dr220.mp3');">sound sample</a><br />
| | == See also == |
| <br />
| | * [[45/28]] – its [[octave complement]] |
| According to <a class="wiki_link" href="/Ozan%20Yarman">Ozan Yarman</a>, the perde segah of Turkish maqam music should range from <strong>56/45</strong>, which is flatter than <a class="wiki_link" href="/5_4">5/4</a> by the <a class="wiki_link" href="/septimal%20kleisma">septimal kleisma</a> of <a class="wiki_link" href="/225_224">225/224</a>, to 5/4. 56/45 is the interval between various 9-limit consonances: 5/4 and 14/9, 9/7 and 8/5, 9/8 and 7/5, and 10/7 and 16/9. <a class="wiki_link" href="/Marvel">Marvel</a> tempering makes all of these intervals into major thirds like any other, and turns chords like 1-5/4-8/5 or 1-5/4-14/9 into <a class="wiki_link" href="/Dyadic%20chord">essentially tempered dyadic chords</a>. The 56/45 third is <a class="wiki_link" href="/6_5">6/5</a> away from the marvelous fifth, <a class="wiki_link" href="/112_75">112/75</a>, and may also be called the marvelous major third. It is a third of a cent flatter than the 6\19 major third of 19et.</body></html></pre></div>
| | * [[135/112]] – its [[fifth complement]] |
| | * [[Gallery of just intervals]] |
| | |
| | [[Category:Third]] |
| | [[Category:Major third]] |
| | [[Category:Fourth]] |
| | [[Category:Diminished fourth]] |
| | [[Category:Aberschismic]] |
56/45, the septimal narrow major third, or marvel-ptolemaic major third, is the interval between various 9-odd-limit consonances – 5/4 and 14/9, 9/7 and 8/5, 9/8 and 7/5, and 10/7 and 16/9 – with it also being 6/5 away from the marvelous fifth, 112/75. It is flat of the Pythagorean major third by 3645/3584, namely a syntonic comma plus a marvel comma. Marvel tempering makes all of these intervals into classical major thirds, and turns chords like 1–5/4–8/5 or 1–5/4–14/9 into essentially tempered dyadic chords. It is a third of a cent flatter than the 6\19 major third of 19edo; however, it functionally doubles as a type of diminished fourth, flat of the Pythagorean diminished fourth by 5120/5103. This gives rise to the name hemifamity diminished fourth.
According to Ozan Yarman, the perde segah of Turkish maqam music should range from 56/45 to 5/4.
Approximation
Edo approximations for 56/45 (378.60 ¢)
≤ 80edo, relative error ≤ 10%
| Edo |
Step size |
Cents (¢) |
Absolute error (¢) |
Relative error (%)
|
| 3 |
1\3 |
400.00 |
+21.40 |
+5.35
|
| 16 |
5\16 |
375.00 |
-3.60 |
-4.80
|
| 19 |
6\19 |
378.95 |
+0.35 |
+0.55
|
| 22 |
7\22 |
381.82 |
+3.22 |
+5.90
|
| 32 |
10\32 |
375.00 |
-3.60 |
-9.61
|
| 35 |
11\35 |
377.14 |
-1.46 |
-4.26
|
| 38 |
12\38 |
378.95 |
+0.35 |
+1.09
|
| 41 |
13\41 |
380.49 |
+1.89 |
+6.44
|
| 51 |
16\51 |
376.47 |
-2.13 |
-9.06
|
| 54 |
17\54 |
377.78 |
-0.82 |
-3.71
|
| 57 |
18\57 |
378.95 |
+0.35 |
+1.64
|
| 60 |
19\60 |
380.00 |
+1.40 |
+6.99
|
| 70 |
22\70 |
377.14 |
-1.46 |
-8.51
|
| 73 |
23\73 |
378.08 |
-0.52 |
-3.16
|
| 76 |
24\76 |
378.95 |
+0.35 |
+2.19
|
| 79 |
25\79 |
379.75 |
+1.14 |
+7.54
|
See also