Tuning systems for qanun - Revision history

ArrowHead294 at 18:26, 11 February 2025

2025-02-11T18:26:18Z

← Older revision		Revision as of 18:26, 11 February 2025
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	32/27 (294), 6/5 (316), 63/52 (332), 72/59 (345), 59/48 (357), 26/21 (370), 5/4 (386), 81/64 (408)</li></ul>		32/27 (294), 6/5 (316), 63/52 (332), 72/59 (345), 59/48 (357), 26/21 (370), 5/4 (386), 81/64 (408)</li></ul>

			{{Navbox notation}}
	{{~~Notation navbox~~}}

	{{Todo\| cleanup }}		{{Todo\| cleanup }}

BudjarnLambeth: {{Notation navbox}}

2024-12-02T23:50:36Z

← Older revision		Revision as of 23:50, 2 December 2024
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	32/27 (294), 6/5 (316), 63/52 (332), 72/59 (345), 59/48 (357), 26/21 (370), 5/4 (386), 81/64 (408)</li></ul>		32/27 (294), 6/5 (316), 63/52 (332), 72/59 (345), 59/48 (357), 26/21 (370), 5/4 (386), 81/64 (408)</li></ul>


			{{Notation navbox}}

	{{Todo\| cleanup }}		{{Todo\| cleanup }}

	[[Category:Arabic music]]		[[Category:Arabic music]]
	[[Category:Persian music]]		[[Category:Persian music]]
	[[Category:Turkish music]]		[[Category:Turkish music]]
	[[Category:Qanun]]		[[Category:Qanun]]

FloraC: Recategorize

2023-08-29T08:49:24Z

Recategorize

← Older revision		Revision as of 08:49, 29 August 2023
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	256/243 (90), 16/15/112), 14/13 (128), 64/59 (141), 59/54 /153), 209/189 (166), 10(9 (182), 9/8 (204)</li><li>On the E string (from Eb to E):		256/243 (90), 16/15/112), 14/13 (128), 64/59 (141), 59/54 /153), 209/189 (166), 10(9 (182), 9/8 (204)</li><li>On the E string (from Eb to E):

	32/27 (294), 6/5 (316), 63/52 (332), 72/59 (345), 59/48 (357), 26/21 (370), 5/4 (386), 81/64 (408)</li></ul> ~~[[Category:arabic]]~~		32/27 (294), 6/5 (316), 63/52 (332), 72/59 (345), 59/48 (357), 26/21 (370), 5/4 (386), 81/64 (408)</li></ul>
	~~[[Category:kanoun]]~~
	[[Category:~~kanun~~]]		{{Todo\| cleanup }}
	[[Category:~~persian~~]]
	[[Category:~~qanun~~]]		[[Category:Arabic music]]
	[[Category:~~turkish~~]]		[[Category:Persian music]]
			[[Category:Turkish music]]
			[[Category:Qanun]]

Wikispaces>FREEZE at 00:00, 17 July 2018

2018-07-17T00:00:00Z

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Wikispaces>xenwolf: Imported revision 597692908 - Original comment: removed tel links

2016-11-01T18:34:52Z

**Imported revision 597692908 - Original comment: removed tel links**

Wikispaces>hstraub: Imported revision 567029271 - Original comment:

2015-11-19T04:26:04Z

**Imported revision 567029271 - Original comment: **

← Older revision		Revision as of 04:26, 19 November 2015
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	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>2015-09-~~01 03~~:13:08 UTC</tt>.<br>		: This revision was by author [[User:hstraub\|hstraub]] and made on <tt>2015-11-19 04:26:04 UTC</tt>.<br>
	: The original revision id was <tt>~~557870945~~</tt>.<br>		: The original revision id was <tt>567029271</tt>.<br>
	: The revision comment was: <tt></tt><br>		: The revision comment was: <tt></tt><br>
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	\|\|~ String \|\|~ b \|\|~ \|\|~ \|\|~ \|\|~ \|\|~ \|\|~ \|\|~ Base note \|\|~ \|\|~ \|\|~ \|\|~ \|\|~ \|\|~ \|\|~ # \|\|		\|\|~ String \|\|~ b \|\|~ \|\|~ \|\|~ \|\|~ \|\|~ \|\|~ \|\|~ Base note \|\|~ \|\|~ \|\|~ \|\|~ \|\|~ \|\|~ \|\|~ # \|\|
	\|\|~ C \|\| \|\| \|\| \|\| \|\| \|\| \|\| \|\|= 0 \|\| 22 \|\| 36 \|\| 48 \|\| 66 \|\| 78 \|\| 92 \|\| 114 \|\|		\|\|~ C \|\| \|\| \|\| \|\| \|\| \|\| \|\| \|\|= 0 \|\| 22 \|\| 36 \|\| 48 \|\| 66 \|\| 78 \|\| 92 \|\| 114 \|\|
	\|\|~ D \|\| 90 \|\| 112 \|\| 126 \|\| 138 \|\| 156 \|\| 168 \|\| 182 \|\|= 204 \|\| 226 \|\| 240 \|\| 252 \|\| ~~170~~ \|\| ~~182~~ \|\| ~~196~~ \|\| 318 \|\|		\|\|~ D \|\| 90 \|\| 112 \|\| 126 \|\| 138 \|\| 156 \|\| 168 \|\| 182 \|\|= 204 \|\| 226 \|\| 240 \|\| 252 \|\| 270 \|\| 282 \|\| 296 \|\| 318 \|\|
	\|\|~ E \|\| 294 \|\| 316 \|\| 330 \|\| 342 \|\| 360 \|\| 372 \|\| 386 \|\|= 408 \|\| 430 \|\| 444 \|\| 456 \|\| ~~374~~ \|\| ~~386~~ \|\| ~~400~~ \|\| ~~422~~ \|\|		\|\|~ E \|\| 294 \|\| 316 \|\| 330 \|\| 342 \|\| 360 \|\| 372 \|\| 386 \|\|= 408 \|\| 430 \|\| 444 \|\| 456 \|\| 474 \|\| 486 \|\| 500 \|\| 522 \|\|
	\|\|~ F \|\| 384 \|\| 406 \|\| 420 \|\| 433 \|\| 450 \|\| 462 \|\| 476 \|\|= 498 \|\| 520 \|\| 534 \|\| 546 \|\| 464 \|\| 476 \|\| 590 \|\| 612 \|\|		\|\|~ F \|\| 384 \|\| 406 \|\| 420 \|\| 433 \|\| 450 \|\| 462 \|\| 476 \|\|= 498 \|\| 520 \|\| 534 \|\| 546 \|\| 464 \|\| 476 \|\| 590 \|\| 612 \|\|

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	<td>252<br />		<td>252<br />
	</td>		</td>
	<td>~~170~~<br />		<td>270<br />
	</td>		</td>
	<td>~~182~~<br />		<td>282<br />
	</td>		</td>
	<td>~~196~~<br />		<td>296<br />
	</td>		</td>
	<td>318<br />		<td>318<br />
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	<td>456<br />		<td>456<br />
	</td>		</td>
	<td>~~374~~<br />		<td>474<br />
	</td>		</td>
	<td>~~386~~<br />		<td>486<br />
	</td>		</td>
	<td>~~400~~<br />		<td>500<br />
	</td>		</td>
	<td>~~422~~<br />		<td>522<br />
	</td>		</td>
	</tr>		</tr>

Wikispaces>hstraub: Imported revision 557870945 - Original comment:

2015-09-01T03:13:08Z

**Imported revision 557870945 - Original comment: **

← Older revision		Revision as of 03:13, 1 September 2015
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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:~~JosephRuhf~~\|~~JosephRuhf~~]] and made on <tt>~~2012~~-06-01 14:02:47 UTC</tt>.<br>		: This revision was by author [[User:hstraub\|hstraub]] and made on <tt>2015-09-01 03:13:08 UTC</tt>.<br>
	: The original revision id was <tt>~~341825802~~</tt>.<br>		: The original revision id was <tt>557870945</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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	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, ~~correpsonding~~ to the mandals. Seven base notes (C, D, E, F, G, A, B or Do, Re, Mi, Fa, Sol, La, Si), corresponding to the strings, lead to a notation system of 7*15=105 pitches, in accordance with the real playing capabilities of the qanun. 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.		This gives 15 potential different pitches per base note, corresponding to the mandals. Seven base notes (C, D, E, F, G, A, B or Do, Re, Mi, Fa, Sol, La, Si), corresponding to the strings, lead to a notation system of 7*15=105 pitches, in accordance with the real playing capabilities of the qanun. 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.
	[[file:Tableaux JJW VIII-2011.pdf]]		[[file:Tableaux JJW VIII-2011.pdf]]

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	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 />
	<br />		<br />
	This gives 15 potential different pitches per base note, ~~correpsonding~~ to the mandals. Seven base notes (C, D, E, F, G, A, B or Do, Re, Mi, Fa, Sol, La, Si), corresponding to the strings, lead to a notation system of 7*15=105 pitches, in accordance with the real playing capabilities of the qanun. 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.<br />		This gives 15 potential different pitches per base note, corresponding to the mandals. Seven base notes (C, D, E, F, G, A, B or Do, Re, Mi, Fa, Sol, La, Si), corresponding to the strings, lead to a notation system of 7*15=105 pitches, in accordance with the real playing capabilities of the qanun. 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.<br />
	<!-- ws:start:WikiTextFileRule:610:&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:610 --><br />		<!-- ws:start:WikiTextFileRule:610:&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:610 --><br />
	<br />		<br />

Wikispaces>JosephRuhf: Imported revision 341825802 - Original comment:

2012-06-01T14:02:47Z

**Imported revision 341825802 - Original comment: **

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 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2012-06-01 13:55:47 UTC</tt>.<br>
+: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2012-06-01 14:02:47 UTC</tt>.<br>
-: The original revision id was <tt>341822682</tt>.<br>
+: The original revision id was <tt>341825802</tt>.<br>
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 ||~ E || 294 || 316 || 330 || 342 || 360 || 372 || 386 ||= 408 || 430 || 444 || 456 || 374 || 386 || 400 || 422 ||
 ||~ F || 384 || 406 || 420 || 433 || 450 || 462 || 476 ||= 498 || 520 || 534 || 546 || 464 || 476 || 590 || 612 ||
 Interval ratios, ascending from C:
@@ Line 212: / Line 211: @@
 &lt;br /&gt;
 This gives 15 potential different pitches per base note, correpsonding to the mandals. Seven base notes (C, D, E, F, G, A, B or Do, Re, Mi, Fa, Sol, La, Si), corresponding to the strings, lead to a notation system of 7*15=105 pitches, in accordance with the real playing capabilities of the qanun. 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.&lt;br /&gt;
-&lt;!-- ws:start:WikiTextFileRule:644:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file/Tableaux%20JJW%20VIII-2011.pdf?h=52&amp;amp;w=320&amp;quot; class=&amp;quot;WikiFile&amp;quot; id=&amp;quot;wikitext@@file@@Tableaux JJW VIII-2011.pdf&amp;quot; title=&amp;quot;File: Tableaux JJW VIII-2011.pdf&amp;quot; width=&amp;quot;320&amp;quot; height=&amp;quot;52&amp;quot; /&amp;gt; --&gt;&lt;div class="objectEmbed"&gt;&lt;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');"&gt;&lt;img src="http://www.wikispaces.com/i/mime/32/application/pdf.png" height="32" width="32" alt="Tableaux JJW VIII-2011.pdf" /&gt;&lt;/a&gt;&lt;div&gt;&lt;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"&gt;Tableaux JJW VIII-2011.pdf&lt;/a&gt;&lt;br /&gt;&lt;ul&gt;&lt;li&gt;&lt;a href="/file/detail/Tableaux%20JJW%20VIII-2011.pdf"&gt;Details&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a href="/file/view/Tableaux%20JJW%20VIII-2011.pdf/253043932/Tableaux%20JJW%20VIII-2011.pdf"&gt;Download&lt;/a&gt;&lt;/li&gt;&lt;li style="color: #666"&gt;130 KB&lt;/li&gt;&lt;/ul&gt;&lt;/div&gt;&lt;/div&gt;&lt;!-- ws:end:WikiTextFileRule:644 --&gt;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextFileRule:610:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file/Tableaux%20JJW%20VIII-2011.pdf?h=52&amp;amp;w=320&amp;quot; class=&amp;quot;WikiFile&amp;quot; id=&amp;quot;wikitext@@file@@Tableaux JJW VIII-2011.pdf&amp;quot; title=&amp;quot;File: Tableaux JJW VIII-2011.pdf&amp;quot; width=&amp;quot;320&amp;quot; height=&amp;quot;52&amp;quot; /&amp;gt; --&gt;&lt;div class="objectEmbed"&gt;&lt;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');"&gt;&lt;img src="http://www.wikispaces.com/i/mime/32/application/pdf.png" height="32" width="32" alt="Tableaux JJW VIII-2011.pdf" /&gt;&lt;/a&gt;&lt;div&gt;&lt;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"&gt;Tableaux JJW VIII-2011.pdf&lt;/a&gt;&lt;br /&gt;&lt;ul&gt;&lt;li&gt;&lt;a href="/file/detail/Tableaux%20JJW%20VIII-2011.pdf"&gt;Details&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a href="/file/view/Tableaux%20JJW%20VIII-2011.pdf/253043932/Tableaux%20JJW%20VIII-2011.pdf"&gt;Download&lt;/a&gt;&lt;/li&gt;&lt;li style="color: #666"&gt;130 KB&lt;/li&gt;&lt;/ul&gt;&lt;/div&gt;&lt;/div&gt;&lt;!-- ws:end:WikiTextFileRule:610 --&gt;&lt;br /&gt;
 &lt;br /&gt;
 (used with permission J. J. Weiss/S. Pohlit)&lt;br /&gt;
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          &lt;td&gt;612&lt;br /&gt;
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Wikispaces>JosephRuhf: Imported revision 341822682 - Original comment:

2012-06-01T13:55:47Z

**Imported revision 341822682 - Original comment: **

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Wikispaces>hstraub: Imported revision 318985762 - Original comment:

2012-04-10T03:35:24Z

**Imported revision 318985762 - Original comment: **

← Older revision		Revision as of 03:35, 10 April 2012
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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:~~xenjacob~~\|~~xenjacob~~]] and made on <tt>~~2011~~-11-~~08 16~~:21:54 UTC</tt>.<br>		: This revision was by author [[User:hstraub\|hstraub]] and made on <tt>2012-04-10 03:35:24 UTC</tt>.<br>
	: The original revision id was <tt>~~273301084~~</tt>.<br>		: The original revision id was <tt>318985762</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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	Each apotome is divided into 7 unequal parts, which requires 14 mandals per string. 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.		Each apotome is divided into 7 unequal parts, which requires 14 mandals per string. 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. According to the system sketched above, the first and the last value are always 22 cents (or 21.5 cents). This subdivision pattern occurs twice on each string, altogether 14 times per octave. This is followed by listings of some important rational intervals that are possible in this tuning, mainly in the range of a fourth (the range where the ajnas - maqam tetrachords - reside),		The tuning systems are all described by a series of cent values, which describe the subdivision of one apotome. According to the system sketched above, the first and the last value are always 22 cents (or 21.5 cents). This subdivision pattern occurs twice on each string, altogether 14 times per octave. This is followed by listings of some important rational intervals that are possible in this tuning, mainly in the range of a fourth (the range where the ajnas - maqam [[tetrachord\|tetrachords]] - reside),

	An notable property (of all systems) is that the second-highest mandal position of, say, the C string is 114-22=92 cents (the [[135_128\|major limma]]), while the lowest mandal position on the following string (D in the example) is 214 (one wholetone above C) - 114 = 90 cents (the [[256_243\|pythagorean limma]], the same interval as between E and F) - we have two notes differing by one [[32805_32768\|schisma (2 cents)]]. So the interval of the schisma is present and can be played on a qanun in any of the tuning systems described here.		An notable property (of all systems) is that the second-highest mandal position of, say, the C string is 114-22=92 cents (the [[135_128\|major limma]]), while the lowest mandal position on the following string (D in the example) is 214 (one wholetone above C) - 114 = 90 cents (the [[256_243\|pythagorean limma]], the same interval as between E and F) - we have two notes differing by one [[32805_32768\|schisma (2 cents)]]. So the interval of the schisma is present and can be played on a qanun in any of the tuning systems described here.
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	Each apotome is divided into 7 unequal parts, which requires 14 mandals per string. 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 />		Each apotome is divided into 7 unequal parts, which requires 14 mandals per string. 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 tuning systems are all described by a series of cent values, which describe the subdivision of one apotome. According to the system sketched above, the first and the last value are always 22 cents (or 21.5 cents). This subdivision pattern occurs twice on each string, altogether 14 times per octave. This is followed by listings of some important rational intervals that are possible in this tuning, mainly in the range of a fourth (the range where the ajnas - maqam tetrachords - reside),<br />		The tuning systems are all described by a series of cent values, which describe the subdivision of one apotome. According to the system sketched above, the first and the last value are always 22 cents (or 21.5 cents). This subdivision pattern occurs twice on each string, altogether 14 times per octave. This is followed by listings of some important rational intervals that are possible in this tuning, mainly in the range of a fourth (the range where the ajnas - maqam <a class="wiki_link" href="/tetrachord">tetrachords</a> - reside),<br />
	<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 (the <a class="wiki_link" href="/135_128">major limma</a>), while the lowest mandal position on the following string (D in the example) is 214 (one wholetone above C) - 114 = 90 cents (the <a class="wiki_link" href="/256_243">pythagorean limma</a>, the same interval as between E and F) - we have two notes differing by one <a class="wiki_link" href="/32805_32768">schisma (2 cents)</a>. So the interval of the schisma is present and can be played on a qanun in any of the tuning systems described here.<br />		An notable property (of all systems) is that the second-highest mandal position of, say, the C string is 114-22=92 cents (the <a class="wiki_link" href="/135_128">major limma</a>), while the lowest mandal position on the following string (D in the example) is 214 (one wholetone above C) - 114 = 90 cents (the <a class="wiki_link" href="/256_243">pythagorean limma</a>, the same interval as between E and F) - we have two notes differing by one <a class="wiki_link" href="/32805_32768">schisma (2 cents)</a>. So the interval of the schisma is present and can be played on a qanun in any of the tuning systems described here.<br />

← Older revision		Revision as of 18:34, 1 November 2016
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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>~~2015~~-11-~~19 04~~:26:04 UTC</tt>.<br>		: This revision was by author [[User:xenwolf\|xenwolf]] and made on <tt>2016-11-01 18:34:52 UTC</tt>.<br>
	: The original revision id was <tt>~~567029271~~</tt>.<br>		: The original revision id was <tt>597692908</tt>.<br>
	: The revision comment was: <tt></tt><br>		: The revision comment was: <tt>removed tel links</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>
	<h4>Original Wikitext content:</h4>		<h4>Original Wikitext content:</h4>
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	Interval ratios, ascending from C:		Interval ratios, ascending from C:
	* On the D string (from Db to D):		* On the D string (from Db to D):
	> 256/243 (90), ~~[[tel:~~16/15/112~~\|16/15/112]]~~), 14/13 (128), 64/59 (141), ~~[[tel:59/54 /153\|~~59/54 /153]]), 209/189 (166), 10(9 (182), 9/8 (204)		> 256/243 (90), 16/15/112), 14/13 (128), 64/59 (141), 59/54 /153), 209/189 (166), 10(9 (182), 9/8 (204)
	* On the E string (from Eb to E):		* On the E string (from Eb to E):
	> 32/27 (294), 6/5 (316), 63/52 (332), 72/59 (345), 59/48 (357), 26/21 (370), 5/4 (386), 81/64 (408)</pre></div>		> 32/27 (294), 6/5 (316), 63/52 (332), 72/59 (345), 59/48 (357), 26/21 (370), 5/4 (386), 81/64 (408)</pre></div>
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	Interval ratios, ascending from C:<br />		Interval ratios, ascending from C:<br />
	<ul><li>On the D string (from Db to D):<br />		<ul><li>On the D string (from Db to D):<br />
	256/243 (90), ~~[[tel:~~16/15/112~~\|16/15/112]]~~), 14/13 (128), 64/59 (141), ~~[[tel:59/54 /153\|~~59/54 /153]]), 209/189 (166), 10(9 (182), 9/8 (204)</li><li>On the E string (from Eb to E):<br />		256/243 (90), 16/15/112), 14/13 (128), 64/59 (141), 59/54 /153), 209/189 (166), 10(9 (182), 9/8 (204)</li><li>On the E string (from Eb to E):<br />
	32/27 (294), 6/5 (316), 63/52 (332), 72/59 (345), 59/48 (357), 26/21 (370), 5/4 (386), 81/64 (408)</li></ul></body></html></pre></div>		32/27 (294), 6/5 (316), 63/52 (332), 72/59 (345), 59/48 (357), 26/21 (370), 5/4 (386), 81/64 (408)</li></ul></body></html></pre></div>

Tuning systems for qanun - Revision history

ArrowHead294 at 18:26, 11 February 2025

BudjarnLambeth: {{Notation navbox}}

FloraC: Recategorize

Wikispaces>FREEZE at 00:00, 17 July 2018

Wikispaces>xenwolf: **Imported revision 597692908 - Original comment: removed tel links**

Wikispaces>hstraub: **Imported revision 567029271 - Original comment: **

Wikispaces>hstraub: **Imported revision 557870945 - Original comment: **

Wikispaces>JosephRuhf: **Imported revision 341825802 - Original comment: **