Tuning systems for qanun: Difference between revisions
Wikispaces>hstraub **Imported revision 258777168 - Original comment: ** |
Wikispaces>hstraub **Imported revision 259752452 - 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>2011-09- | : This revision was by author [[User:hstraub|hstraub]] and made on <tt>2011-09-29 16:19:57 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>259752452</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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Online version of Stefan Pohlit's dissertation: see [[http://stefanpohlit.com/dissertation.engl..htm]] | Online version of Stefan Pohlit's dissertation: see [[http://stefanpohlit.com/dissertation.engl..htm]] | ||
The tuning tables on this page are specifically designed for the tuning system of the [[qanun]] (see the link for details on the system of tuning and playing a qanun with mandals/orabs). | The tuning tables on this page are specifically designed for the tuning system of the [[qanun]] (see the link for details on the system of tuning and playing a qanun with mandals/orabs). The logic behind the systems is as follows: | ||
The possible pitches of a string obtained via raising/lowering the mandals lie within | The empty strings of the qanun are tuned to a pythagorean diatonic scale, with a major third of [[81_80|81/80]], a major sixth of [[27_16|27/16]] and a major seventh of [[243_128|243/128]]. | ||
The possible pitches of a string obtained via raising/lowering the mandals lie within two [[2187_2048|apotomes (2187/2048, 113.7 cents)]]. The base note is assumed in the middle and can be raised and lowered by maximally one apotome. | |||
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. | One apotome is divided into 7 parts, which requires 14 mandals per string (one apotome up and down). 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 tuning systems are all described by a series of cent values, which describe the subdivision of one apotome. The first and the last value are always one syntomic comma (22 cents or 21.5 cents). This subdivision pattern occurs twice on each string (one apotome up and one down), alltogether 14 times per octave. | |||
An notable property (of all systems) is that the second-highest mandal position of, say, the C string is 114-22=92 cents, while the lowest mandal position on the following string (D in the example) is 214 (one wholetone above C) - 114 = 90 cents - we have two notes differing by one [[32805_32768|schisma (2 cents)]]. | |||
The interval of the schisma is present and can be played on a qanun in any of the tuning systems described here. | |||
=Notation= | =Notation= | ||
Raising a pitch by an apotome is notated with "#", lowering a pitch by the same amount is notated with "b". | 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. | 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. See the following document. | 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. See the following document, which also gives all the pitches in one octave (in ratios and cents) that can be played by system 1 and 2 (described below). | ||
[[file:Tableaux JJW VIII-2011.pdf]] | [[file:Tableaux JJW VIII-2011.pdf]] | ||
(used with permission J. J. Weiss/S. Pohlit) | (used with permission J. J. Weiss/S. Pohlit) | ||
Sharps are higher than flats: C# is one apotome (114 cents) above C, while Db is 9/8 (214 cents) minus one apotome = 90 cents. Sharps being higher than flats is a property of pythagorean systems (unlike [[meantone]] systems). | |||
=Older systems= | =Older systems= | ||
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Online version of Stefan Pohlit's dissertation: see <a class="wiki_link_ext" href="http://stefanpohlit.com/dissertation.engl..htm" rel="nofollow">http://stefanpohlit.com/dissertation.engl..htm</a><br /> | Online version of Stefan Pohlit's dissertation: see <a class="wiki_link_ext" href="http://stefanpohlit.com/dissertation.engl..htm" rel="nofollow">http://stefanpohlit.com/dissertation.engl..htm</a><br /> | ||
<br /> | <br /> | ||
The tuning tables on this page are specifically designed for the tuning system of the <a class="wiki_link" href="/qanun">qanun</a> (see the link for details on the system of tuning and playing a qanun with mandals/orabs).<br /> | The tuning tables on this page are specifically designed for the tuning system of the <a class="wiki_link" href="/qanun">qanun</a> (see the link for details on the system of tuning and playing a qanun with mandals/orabs). The logic behind the systems is as follows:<br /> | ||
<br /> | |||
The empty strings of the qanun are tuned to a pythagorean diatonic scale, with a major third of <a class="wiki_link" href="/81_80">81/80</a>, a major sixth of <a class="wiki_link" href="/27_16">27/16</a> and a major seventh of <a class="wiki_link" href="/243_128">243/128</a>. <br /> | |||
The possible pitches of a string obtained via raising/lowering the mandals lie within two <a class="wiki_link" href="/2187_2048">apotomes (2187/2048, 113.7 cents)</a>. The base note is assumed in the middle and can be raised and lowered by maximally one apotome.<br /> | |||
<br /> | <br /> | ||
The | One apotome is divided into 7 parts, which requires 14 mandals per string (one apotome up and down). 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 /> | ||
The | The tuning systems are all described by a series of cent values, which describe the subdivision of one apotome. The first and the last value are always one syntomic comma (22 cents or 21.5 cents). This subdivision pattern occurs twice on each string (one apotome up and one down), alltogether 14 times per octave.<br /> | ||
<br /> | |||
An notable property (of all systems) is that the second-highest mandal position of, say, the C string is 114-22=92 cents, while the lowest mandal position on the following string (D in the example) is 214 (one wholetone above C) - 114 = 90 cents - we have two notes differing by one <a class="wiki_link" href="/32805_32768">schisma (2 cents)</a>.<br /> | |||
The interval of the schisma is present and can be played on a qanun in any of the tuning systems described here.<br /> | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Notation"></a><!-- ws:end:WikiTextHeadingRule:0 -->Notation</h1> | <!-- 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 /> | 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 /> | 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. See the following document.<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. See the following document, which also gives all the pitches in one octave (in ratios and cents) that can be played by system 1 and 2 (described below).<br /> | ||
<!-- ws:start:WikiTextFileRule:62:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file/Tableaux%20JJW%20VIII-2011.pdf?h=52&amp;w=320&quot; class=&quot;WikiFile&quot; id=&quot;wikitext@@file@@Tableaux JJW VIII-2011.pdf&quot; title=&quot;File: Tableaux JJW VIII-2011.pdf&quot; width=&quot;320&quot; height=&quot;52&quot; /&gt; --><div class="objectEmbed"><a href="/file/view/Tableaux%20JJW%20VIII-2011.pdf/253043932/Tableaux%20JJW%20VIII-2011.pdf" onclick="ws.common.trackFileLink('/file/view/Tableaux%20JJW%20VIII-2011.pdf/253043932/Tableaux%20JJW%20VIII-2011.pdf');"><img src="http://www.wikispaces.com/i/mime/32/application/pdf.png" height="32" width="32" alt="Tableaux JJW VIII-2011.pdf" /></a><div><a href="/file/view/Tableaux%20JJW%20VIII-2011.pdf/253043932/Tableaux%20JJW%20VIII-2011.pdf" onclick="ws.common.trackFileLink('/file/view/Tableaux%20JJW%20VIII-2011.pdf/253043932/Tableaux%20JJW%20VIII-2011.pdf');" class="filename" title="Tableaux JJW VIII-2011.pdf">Tableaux JJW VIII-2011.pdf</a><br /><ul><li><a href="/file/detail/Tableaux%20JJW%20VIII-2011.pdf">Details</a></li><li><a href="/file/view/Tableaux%20JJW%20VIII-2011.pdf/253043932/Tableaux%20JJW%20VIII-2011.pdf">Download</a></li><li style="color: #666">130 KB</li></ul></div></div><!-- ws:end:WikiTextFileRule:62 --><br /> | <!-- ws:start:WikiTextFileRule:62:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file/Tableaux%20JJW%20VIII-2011.pdf?h=52&amp;w=320&quot; class=&quot;WikiFile&quot; id=&quot;wikitext@@file@@Tableaux JJW VIII-2011.pdf&quot; title=&quot;File: Tableaux JJW VIII-2011.pdf&quot; width=&quot;320&quot; height=&quot;52&quot; /&gt; --><div class="objectEmbed"><a href="/file/view/Tableaux%20JJW%20VIII-2011.pdf/253043932/Tableaux%20JJW%20VIII-2011.pdf" onclick="ws.common.trackFileLink('/file/view/Tableaux%20JJW%20VIII-2011.pdf/253043932/Tableaux%20JJW%20VIII-2011.pdf');"><img src="http://www.wikispaces.com/i/mime/32/application/pdf.png" height="32" width="32" alt="Tableaux JJW VIII-2011.pdf" /></a><div><a href="/file/view/Tableaux%20JJW%20VIII-2011.pdf/253043932/Tableaux%20JJW%20VIII-2011.pdf" onclick="ws.common.trackFileLink('/file/view/Tableaux%20JJW%20VIII-2011.pdf/253043932/Tableaux%20JJW%20VIII-2011.pdf');" class="filename" title="Tableaux JJW VIII-2011.pdf">Tableaux JJW VIII-2011.pdf</a><br /><ul><li><a href="/file/detail/Tableaux%20JJW%20VIII-2011.pdf">Details</a></li><li><a href="/file/view/Tableaux%20JJW%20VIII-2011.pdf/253043932/Tableaux%20JJW%20VIII-2011.pdf">Download</a></li><li style="color: #666">130 KB</li></ul></div></div><!-- ws:end:WikiTextFileRule:62 --><br /> | ||
<br /> | <br /> | ||
(used with permission J. J. Weiss/S. Pohlit)<br /> | (used with permission J. J. Weiss/S. Pohlit)<br /> | ||
<br /> | <br /> | ||
Sharps are higher than flats: C# is one apotome (114 cents) above C, while Db is 9/8 (214 cents) minus one apotome = 90 cents. Sharps being higher than flats is a property of pythagorean systems (unlike <a class="wiki_link" href="/meantone">meantone</a> systems).<br /> | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Older systems"></a><!-- ws:end:WikiTextHeadingRule:2 -->Older systems</h1> | <!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Older systems"></a><!-- ws:end:WikiTextHeadingRule:2 -->Older systems</h1> | ||