Tuning systems for qanun: Difference between revisions
Wikispaces>hstraub **Imported revision 248375203 - Original comment: ** |
Wikispaces>hstraub **Imported revision 249050231 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2011-08- | : This revision was by author [[User:hstraub|hstraub]] and made on <tt>2011-08-29 04:24:11 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>249050231</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : 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> | 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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The first rough subdivision of the apotome is always into one [[81_80|syntonic comma (81/80, 21.5 cents)]], one [[25_24|Zarlinian semitone (25/24, 70.7 cents)]] and another syntonic comma. The middle part (25/24, Zarlinian semitone) is then further subdivided into 5 (unequal or equal) parts. The various systems differ mainly in the division of the middle part. | The first rough subdivision of the apotome is always into one [[81_80|syntonic comma (81/80, 21.5 cents)]], one [[25_24|Zarlinian semitone (25/24, 70.7 cents)]] and another syntonic comma. The middle part (25/24, Zarlinian semitone) is then further subdivided into 5 (unequal or equal) parts. The various systems differ mainly in the division of the middle part. | ||
=Notation= | |||
Raising a pitch by an apotome is notated with "#", lowering a pitch by the same amount is notated with "b". | |||
For the steps in between, additional symbols are used - altogether 7 symbols for raising pitches and 7 for lowering pitches. | |||
This gives 15 potential different pitches per base note. Seven base notes (C, D, E, F, G, A, B or Do, Re, Mi, Fa, Sol, La, Si) lead to a notation system of 7*15=105 pitches per octave. | |||
XXX to do: include J.J. Weiss's notation table here. | |||
XXX Does this notation system have a standard name? | |||
=Explanation of the tuning tables= | =Explanation of the tuning tables= | ||
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<h4>Original HTML content:</h4> | <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>tuning systems for qanun</title></head><body><span style="font-size: 150%;"><strong>Tuning systems for the qanun</strong></span><br /> | <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>tuning systems for qanun</title></head><body><span style="font-size: 150%;"><strong>Tuning systems for the qanun</strong></span><br /> | ||
<!-- ws:start:WikiTextTocRule: | <!-- ws:start:WikiTextTocRule:40:&lt;img id=&quot;wikitext@@toc@@normal&quot; class=&quot;WikiMedia WikiMediaToc&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/normal?w=225&amp;h=100&quot;/&gt; --><div id="toc"><h1 class="nopad">Table of Contents</h1><!-- ws:end:WikiTextTocRule:40 --><!-- ws:start:WikiTextTocRule:41: --><div style="margin-left: 1em;"><a href="#Notation">Notation</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:41 --><!-- ws:start:WikiTextTocRule:42: --><div style="margin-left: 1em;"><a href="#Explanation of the tuning tables">Explanation of the tuning tables</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:42 --><!-- ws:start:WikiTextTocRule:43: --><div style="margin-left: 1em;"><a href="#Older systems">Older systems</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:43 --><!-- ws:start:WikiTextTocRule:44: --><div style="margin-left: 2em;"><a href="#Older systems-First System J.J.Weiss">First System J.J.Weiss</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:44 --><!-- ws:start:WikiTextTocRule:45: --><div style="margin-left: 2em;"><a href="#Older systems-Variant with 128/119">Variant with 128/119</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:45 --><!-- ws:start:WikiTextTocRule:46: --><div style="margin-left: 2em;"><a href="#Older systems-Variant with 128/119 ascending/descending">Variant with 128/119 ascending/descending</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:46 --><!-- ws:start:WikiTextTocRule:47: --><div style="margin-left: 2em;"><a href="#Older systems-Variant with 43/40 ascending/descending">Variant with 43/40 ascending/descending</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:47 --><!-- ws:start:WikiTextTocRule:48: --><div style="margin-left: 1em;"><a href="#Newer systems">Newer systems</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:48 --><!-- ws:start:WikiTextTocRule:49: --><div style="margin-left: 2em;"><a href="#Newer systems-System 2, better suited for ottoman maqams">System 2, better suited for ottoman maqams</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:49 --><!-- ws:start:WikiTextTocRule:50: --><div style="margin-left: 2em;"><a href="#Newer systems-Symmetrical and super-symmetrical models">Symmetrical and super-symmetrical models</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:50 --><!-- ws:start:WikiTextTocRule:51: --><div style="margin-left: 3em;"><a href="#Newer systems-Symmetrical and super-symmetrical models-Symmetrical model">Symmetrical model</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:51 --><!-- ws:start:WikiTextTocRule:52: --><div style="margin-left: 3em;"><a href="#Newer systems-Symmetrical and super-symmetrical models-Super-symmetrical model">Super-symmetrical model</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:52 --><!-- ws:start:WikiTextTocRule:53: --><div style="margin-left: 3em;"><a href="#Newer systems-Symmetrical and super-symmetrical models-Unequal division of 65/54">Unequal division of 65/54</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:53 --><!-- ws:start:WikiTextTocRule:54: --><div style="margin-left: 3em;"><a href="#Newer systems-Symmetrical and super-symmetrical models-Equal division of the Zarlinian semitone">Equal division of the Zarlinian semitone</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:54 --><!-- ws:start:WikiTextTocRule:55: --><div style="margin-left: 3em;"><a href="#Newer systems-Symmetrical and super-symmetrical models-Ascending/descending with 54/49">Ascending/descending with 54/49</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:55 --><!-- ws:start:WikiTextTocRule:56: --><div style="margin-left: 3em;"><a href="#Newer systems-Symmetrical and super-symmetrical models-Ascending/descending with 14/13">Ascending/descending with 14/13</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:56 --><!-- ws:start:WikiTextTocRule:57: --><div style="margin-left: 3em;"><a href="#Newer systems-Symmetrical and super-symmetrical models-Ascending/descending with 11/10">Ascending/descending with 11/10</a></div> | ||
<!-- ws:end:WikiTextTocRule:57 --><!-- ws:start:WikiTextTocRule:58: --><div style="margin-left: 3em;"><a href="#Newer systems-Symmetrical and super-symmetrical models-Ascending/descending with 35/32">Ascending/descending with 35/32</a></div> | |||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:58 --><!-- ws:start:WikiTextTocRule:59: --><div style="margin-left: 2em;"><a href="#Newer systems-System Jacques Dudon (2006)">System Jacques Dudon (2006)</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:59 --><!-- ws:start:WikiTextTocRule:60: --><div style="margin-left: 3em;"><a href="#Newer systems-System Jacques Dudon (2006)-Arithmetic system">Arithmetic system</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:60 --><!-- ws:start:WikiTextTocRule:61: --></div> | ||
<!-- ws:end:WikiTextTocRule:61 -->Julien Jalaleddine Weiss, used with permission.<br /> | |||
Reference: Pohlit, Stefan. 2011. Julien Jalâl Ed-Dine Weiss – A New Qānūn System: Its Application in the Performance<br /> | Reference: Pohlit, Stefan. 2011. Julien Jalâl Ed-Dine Weiss – A New Qānūn System: Its Application in the Performance<br /> | ||
Practice of the Ensemble “Al-Kindi” and in Contemporary Western Music. PhD Thesis, MIAM/Istanbul Technical<br /> | Practice of the Ensemble “Al-Kindi” and in Contemporary Western Music. PhD Thesis, MIAM/Istanbul Technical<br /> | ||
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The first rough subdivision of the apotome is always into one <a class="wiki_link" href="/81_80">syntonic comma (81/80, 21.5 cents)</a>, one <a class="wiki_link" href="/25_24">Zarlinian semitone (25/24, 70.7 cents)</a> and another syntonic comma. The middle part (25/24, Zarlinian semitone) is then further subdivided into 5 (unequal or equal) parts. The various systems differ mainly in the division of the middle part.<br /> | The first rough subdivision of the apotome is always into one <a class="wiki_link" href="/81_80">syntonic comma (81/80, 21.5 cents)</a>, one <a class="wiki_link" href="/25_24">Zarlinian semitone (25/24, 70.7 cents)</a> and another syntonic comma. The middle part (25/24, Zarlinian semitone) is then further subdivided into 5 (unequal or equal) parts. The various systems differ mainly in the division of the middle part.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Explanation of the tuning tables"></a><!-- ws:end:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Notation"></a><!-- ws:end:WikiTextHeadingRule:0 -->Notation</h1> | ||
Raising a pitch by an apotome is notated with &quot;#&quot;, lowering a pitch by the same amount is notated with &quot;b&quot;.<br /> | |||
For the steps in between, additional symbols are used - altogether 7 symbols for raising pitches and 7 for lowering pitches.<br /> | |||
This gives 15 potential different pitches per base note. Seven base notes (C, D, E, F, G, A, B or Do, Re, Mi, Fa, Sol, La, Si) lead to a notation system of 7*15=105 pitches per octave.<br /> | |||
XXX to do: include J.J. Weiss's notation table here.<br /> | |||
XXX Does this notation system have a standard name?<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Explanation of the tuning tables"></a><!-- ws:end:WikiTextHeadingRule:2 -->Explanation of the tuning tables</h1> | |||
The whole table covers roughly the range of a fourth (the range where the ajnas - maqam tetrachords - reside). Each row corresponds to one string of the qanun. In the first column stands the basic (relative) tuning of a string while the following columns indicate possible intervals that can be reached via raising/lowering the mandals.<br /> | The whole table covers roughly the range of a fourth (the range where the ajnas - maqam tetrachords - reside). Each row corresponds to one string of the qanun. In the first column stands the basic (relative) tuning of a string while the following columns indicate possible intervals that can be reached via raising/lowering the mandals.<br /> | ||
<br /> | <br /> | ||
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(base for a maqam tetrachord) is represented by a choice of one cell in each row.<br /> | (base for a maqam tetrachord) is represented by a choice of one cell in each row.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Older systems"></a><!-- ws:end:WikiTextHeadingRule:4 -->Older systems</h1> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="Older systems-First System J.J.Weiss"></a><!-- ws:end:WikiTextHeadingRule:6 -->First System J.J.Weiss</h2> | ||
Luthier: Ejder Gulec.<br /> | Luthier: Ejder Gulec.<br /> | ||
Subdivision of 25/24 into 65/64 (26 cents), 144/143 (12 cents) and 55/54 (32 cents).<br /> | Subdivision of 25/24 into 65/64 (26 cents), 144/143 (12 cents) and 55/54 (32 cents).<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="Older systems-Variant with 128/119"></a><!-- ws:end:WikiTextHeadingRule:8 -->Variant with 128/119</h2> | ||
128/119: 126.2 cents<br /> | 128/119: 126.2 cents<br /> | ||
XXX<br /> | XXX<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="Older systems-Variant with 128/119 ascending/descending"></a><!-- ws:end:WikiTextHeadingRule:10 -->Variant with 128/119 ascending/descending</h2> | ||
XXX<br /> | XXX<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="Older systems-Variant with 43/40 ascending/descending"></a><!-- ws:end:WikiTextHeadingRule:12 -->Variant with 43/40 ascending/descending</h2> | ||
43/40: 125.2 cents<br /> | 43/40: 125.2 cents<br /> | ||
XXX<br /> | XXX<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:14:&lt;h1&gt; --><h1 id="toc7"><a name="Newer systems"></a><!-- ws:end:WikiTextHeadingRule:14 -->Newer systems</h1> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:16:&lt;h2&gt; --><h2 id="toc8"><a name="Newer systems-System 2, better suited for ottoman maqams"></a><!-- ws:end:WikiTextHeadingRule:16 -->System 2, better suited for ottoman maqams</h2> | ||
J.J. Weiss, Qanun no. 9. Luthier: Kenan Ozten.<br /> | J.J. Weiss, Qanun no. 9. Luthier: Kenan Ozten.<br /> | ||
<br /> | <br /> | ||
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XXX<br /> | XXX<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:18:&lt;h2&gt; --><h2 id="toc9"><a name="Newer systems-Symmetrical and super-symmetrical models"></a><!-- ws:end:WikiTextHeadingRule:18 -->Symmetrical and super-symmetrical models</h2> | ||
XXX<br /> | XXX<br /> | ||
Characteristics of super-symmetric systems: no difference between ascending and descending ratios.<br /> | Characteristics of super-symmetric systems: no difference between ascending and descending ratios.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:20:&lt;h3&gt; --><h3 id="toc10"><a name="Newer systems-Symmetrical and super-symmetrical models-Symmetrical model"></a><!-- ws:end:WikiTextHeadingRule:20 -->Symmetrical model</h3> | ||
J.J. Weiss<br /> | J.J. Weiss<br /> | ||
Advantage: marked contrast between Segah of Ushaq and Segah of arabic Rast.<br /> | Advantage: marked contrast between Segah of Ushaq and Segah of arabic Rast.<br /> | ||
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XXX<br /> | XXX<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:22:&lt;h3&gt; --><h3 id="toc11"><a name="Newer systems-Symmetrical and super-symmetrical models-Super-symmetrical model"></a><!-- ws:end:WikiTextHeadingRule:22 -->Super-symmetrical model</h3> | ||
J.J. Weiss<br /> | J.J. Weiss<br /> | ||
Equal division of 65/54 (320.98 cents) and its inverse. (XXX Is that formulation correct?)<br /> | Equal division of 65/54 (320.98 cents) and its inverse. (XXX Is that formulation correct?)<br /> | ||
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XXX<br /> | XXX<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:24:&lt;h3&gt; --><h3 id="toc12"><a name="Newer systems-Symmetrical and super-symmetrical models-Unequal division of 65/54"></a><!-- ws:end:WikiTextHeadingRule:24 -->Unequal division of 65/54</h3> | ||
J.J. Weiss<br /> | J.J. Weiss<br /> | ||
<br /> | <br /> | ||
XXX<br /> | XXX<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:26:&lt;h3&gt; --><h3 id="toc13"><a name="Newer systems-Symmetrical and super-symmetrical models-Equal division of the Zarlinian semitone"></a><!-- ws:end:WikiTextHeadingRule:26 -->Equal division of the Zarlinian semitone</h3> | ||
J.J. Weiss<br /> | J.J. Weiss<br /> | ||
This is the simplest variant for luthiers...<br /> | This is the simplest variant for luthiers...<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:28:&lt;h3&gt; --><h3 id="toc14"><a name="Newer systems-Symmetrical and super-symmetrical models-Ascending/descending with 54/49"></a><!-- ws:end:WikiTextHeadingRule:28 -->Ascending/descending with 54/49</h3> | ||
J.J. Weiss<br /> | J.J. Weiss<br /> | ||
<a class="wiki_link" href="/54_49">54/49</a>: 168.2 cents, Zalzal's mujannab (Al Farabi)<br /> | <a class="wiki_link" href="/54_49">54/49</a>: 168.2 cents, Zalzal's mujannab (Al Farabi)<br /> | ||
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Interval table of just intervals XXX<br /> | Interval table of just intervals XXX<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:30:&lt;h3&gt; --><h3 id="toc15"><a name="Newer systems-Symmetrical and super-symmetrical models-Ascending/descending with 14/13"></a><!-- ws:end:WikiTextHeadingRule:30 -->Ascending/descending with 14/13</h3> | ||
J.J. Weiss<br /> | J.J. Weiss<br /> | ||
<span style="color: #00000a; font-family: Tahoma;">14/13: 128.3 cents</span><br /> | <span style="color: #00000a; font-family: Tahoma;">14/13: 128.3 cents</span><br /> | ||
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Interval table XXX<br /> | Interval table XXX<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:32:&lt;h3&gt; --><h3 id="toc16"><a name="Newer systems-Symmetrical and super-symmetrical models-Ascending/descending with 11/10"></a><!-- ws:end:WikiTextHeadingRule:32 -->Ascending/descending with 11/10</h3> | ||
J.J. Weiss<br /> | J.J. Weiss<br /> | ||
11/10: 165 cents<br /> | 11/10: 165 cents<br /> | ||
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Interval table XXX<br /> | Interval table XXX<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:34:&lt;h3&gt; --><h3 id="toc17"><a name="Newer systems-Symmetrical and super-symmetrical models-Ascending/descending with 35/32"></a><!-- ws:end:WikiTextHeadingRule:34 -->Ascending/descending with 35/32</h3> | ||
J.J. Weiss<br /> | J.J. Weiss<br /> | ||
35/32: 155.14 cents<br /> | 35/32: 155.14 cents<br /> | ||
XXX<br /> | XXX<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:36:&lt;h2&gt; --><h2 id="toc18"><a name="Newer systems-System Jacques Dudon (2006)"></a><!-- ws:end:WikiTextHeadingRule:36 -->System Jacques Dudon (2006)</h2> | ||
<br /> | <br /> | ||
Mandal positions (cents): <span style="color: #00000a; font-family: Tahoma;">21,5 | 14,5 | 14,5 | 14,5 | 15 | 12 | 21,5</span><br /> | Mandal positions (cents): <span style="color: #00000a; font-family: Tahoma;">21,5 | 14,5 | 14,5 | 14,5 | 15 | 12 | 21,5</span><br /> | ||
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Interval table of just intervals XXX<br /> | Interval table of just intervals XXX<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:38:&lt;h3&gt; --><h3 id="toc19"><a name="Newer systems-System Jacques Dudon (2006)-Arithmetic system"></a><!-- ws:end:WikiTextHeadingRule:38 -->Arithmetic system</h3> | ||
<br /> | <br /> | ||
Mandal positions (cents): <span style="color: #00000a; font-family: Tahoma;">21,5 | 12 | 15 | 14,5 | 14,5 | 14,5 | 21,5 </span><br /> | Mandal positions (cents): <span style="color: #00000a; font-family: Tahoma;">21,5 | 12 | 15 | 14,5 | 14,5 | 14,5 | 21,5 </span><br /> | ||