Purdal: Difference between revisions
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Wikispaces>xenwolf **Imported revision 437743050 - Original comment: ** |
Wikispaces>Osmiorisbendi **Imported revision 438078124 - 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: | : This revision was by author [[User:Osmiorisbendi|Osmiorisbendi]] and made on <tt>2013-06-14 03:34:39 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>438078124</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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[[math]] | [[math]] | ||
<span style="background-color: #ffffff;">The table below show us uniquely the translation of the Purdal values without decimals, to the simple Cent equivalence:</span> | |||
|| **<span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">Harmonic (until the 63º)</span>** || **<span style="color: #0000ff; font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">Purdal entire value</span>** || **<span style="color: #008080; font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">Cent equivalence</span>** || | || **<span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">Harmonic (until the 63º)</span>** || **<span style="color: #0000ff; font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">Purdal entire value</span>** || **<span style="color: #008080; font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">Cent equivalence</span>** || | ||
|| <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">2/1</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">9900</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">1200</span> || | || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">2/1</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">9900</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">1200</span> || | ||
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|| <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">29/16</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">8494</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">1029.__57__</span> || | || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">29/16</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">8494</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">1029.__57__</span> || | ||
|| <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">31/16</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">9447</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">1145.__09__</span> || | || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">31/16</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">9447</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">1145.__09__</span> || | ||
|| <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">33/32</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">440</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">53. | || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">33/32</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">440</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">53.__3__</span> || | ||
|| <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">35/32</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">1280</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">155.__15__</span> || | || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">35/32</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">1280</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">155.__15__</span> || | ||
|| <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">37/32</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">2074</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">251.__39__</span> || | || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">37/32</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">2074</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">251.__39__</span> || | ||
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|| <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">61/32</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">9214</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">1116.__84__</span> || | || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">61/32</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">9214</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">1116.__84__</span> || | ||
|| <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">63/32</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">9675</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">1172.__72__</span> || | || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">63/32</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">9675</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">1172.__72__</span> || | ||
==Links | <span style="background-color: #ffffff; display: block; text-align: center;">If you want real values between Purdal sizes and Cents sizes with any ratios, check them with this [[purdal/Purdal calculator|Purdal calculator]].</span><span style="background-color: #ffffff; display: block; text-align: center;">!!'!!!'!!!!'!!!'!!!!'!!!'!!!!'!!!'!!!!'!!!'!!!!'!!!'!!!!'!!!'!!!!'!!!'!!!!'!!!'!!</span> | ||
<span style="font-size: 1.3em; line-height: 1.5;">**Links**</span> | |||
* [[purdal/purdal]] - where this article was initially copied from</pre></div> | * [[purdal/purdal]] - where this article was initially copied from</pre></div> | ||
<h4>Original HTML content:</h4> | <h4>Original HTML content:</h4> | ||
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--><script type="math/tex">9900 = 2^2 \cdot 3^2 \cdot 5^2 \cdot 11</script><!-- ws:end:WikiTextMathRule:0 --><br /> | --><script type="math/tex">9900 = 2^2 \cdot 3^2 \cdot 5^2 \cdot 11</script><!-- ws:end:WikiTextMathRule:0 --><br /> | ||
<br /> | <br /> | ||
<span style="background-color: #ffffff;">The table below show us uniquely the translation of the Purdal values without decimals, to the simple Cent equivalence:</span><br /> | |||
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<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">440</span><br /> | <td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">440</span><br /> | ||
</td> | </td> | ||
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">53.<u> | <td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">53.<u>3</u></span><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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</table> | </table> | ||
< | <span style="background-color: #ffffff; display: block; text-align: center;">If you want real values between Purdal sizes and Cents sizes with any ratios, check them with this <a class="wiki_link" href="http://purdal.wikispaces.com/Purdal%20calculator">Purdal calculator</a>.</span><span style="background-color: #ffffff; display: block; text-align: center;">!!'!!!'!!!!'!!!'!!!!'!!!'!!!!'!!!'!!!!'!!!'!!!!'!!!'!!!!'!!!'!!!!'!!!'!!!!'!!!'!!</span><br /> | ||
<span style="font-size: 1.3em; line-height: 1.5;"><strong>Links</strong></span><br /> | |||
<ul><li><a class="wiki_link" href="http://purdal.wikispaces.com/purdal">purdal/purdal</a> - where this article was initially copied from</li></ul></body></html></pre></div> | |||
Revision as of 03:34, 14 June 2013
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author Osmiorisbendi and made on 2013-06-14 03:34:39 UTC.
- The original revision id was 438078124.
- The revision comment was:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
<span style="font-size: 13px; line-height: 1.5;"> The </span>**<span style="font-size: 13px; line-height: 1.5;">purdal</span>**<span style="font-size: 13px; line-height: 1.5;"> is a unit of [[interval size measure|measure for musical intervals]], </span><span style="background-color: #ffffff; font-size: 13px; line-height: 1.5;">suggested by [[xenharmonic/Tútim Dennsuul Wafiil|Tútim Dennsuul]], which is the [[purdal/Ditave|Ditave]] (2/1, the 'Octave') divided into </span>**<span style="background-color: #ffffff; font-size: 13px; line-height: 1.5;">9900 equal parts</span>**<span style="background-color: #ffffff; font-size: 13px; line-height: 1.5;">. The Purdals </span><span class="hps" style="background-color: #ffffff; font-size: 13px; line-height: 1.5;">are shown as a reliable and very consistent to idealize any musical system</span><span style="background-color: #ffffff; font-size: 13px; line-height: 1.5;">, </span><span class="hps" style="background-color: #ffffff; font-size: 13px; line-height: 1.5;">whether just or temperate</span><span style="background-color: #ffffff; font-size: 13px; line-height: 1.5;">.</span> <span style="background-color: #ffffff;">The purpose that it have is for the need of precise with better quality in its presentation, those 'EDDs' </span><span class="hps" style="background-color: #ffffff;">who have a quantity equal to a prime number of intervals and systems until 990 steps per Ditave, only requiring 2 decimals for a basic precision.</span><span style="background-color: #ffffff;">The [[purdal/12-EDD|12-EDD]] contains 825 Purdals in each semitone; Each Purdal is equivalent to 4/33 of a Cent (0.121212121.. Cents).</span> <span style="background-color: #ffffff;">The ditaved Purdal (9900) is divisible</span><span style="font-size: 13px; line-height: 1.5;"> by: 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 18, 20, 22, 25, 30, 33, 36, 44, 45, 50, 55, 60, 66, 75, 90, 99, 100, 110, 132, 150, 165, 180, 198, 220, 225, 275, 300, 330, 396, 450, 495, 550, 660, 825, 900, 990, 1100, 1650, 1980, 2475, 3300 & 4950 exact parts.</span> The Purdal's prime factorization is [[math]] 9900 = 2^2 \cdot 3^2 \cdot 5^2 \cdot 11 [[math]] <span style="background-color: #ffffff;">The table below show us uniquely the translation of the Purdal values without decimals, to the simple Cent equivalence:</span> || **<span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">Harmonic (until the 63º)</span>** || **<span style="color: #0000ff; font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">Purdal entire value</span>** || **<span style="color: #008080; font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">Cent equivalence</span>** || || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">2/1</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">9900</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">1200</span> || || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">3/2</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">5791</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">701.__93__</span> || || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">5/4</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">3187</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">386.__30__</span> || || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">7/4</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">7993</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">968.__84__</span> || || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">9/8</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">1682</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">203.__87__</span> || || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">11/8</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">4548</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">551.__27__</span> || || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">13/8</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">6934</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">840.__48__</span> || || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">15/8</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">8978</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">1088.__24__</span> || || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">17/16</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">866</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">104.__96__</span> || || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">19/16</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">2454</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">297.__45__</span> || || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">21/16</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">3884</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">470.__78__</span> || || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">23/16</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">5183</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">628.__24__</span> || || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">25/16</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">6374</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">772.__60__</span> || || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">27/16</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">7473</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">905.__81__</span> || || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">29/16</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">8494</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">1029.__57__</span> || || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">31/16</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">9447</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">1145.__09__</span> || || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">33/32</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">440</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">53.__3__</span> || || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">35/32</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">1280</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">155.__15__</span> || || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">37/32</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">2074</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">251.__39__</span> || || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">39/32</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">2825</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">342.__42__</span> || || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">41/32</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">3540</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">429.__09__</span> || || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">43/32</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">4220</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">511.__51__</span> || || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">45/32</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">4869</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">590.__18__</span> || || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">47/32</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">5490</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">665.__45__</span> || || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">49/32</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">6086</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">737.__69__</span> || || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">51/32</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">6657</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">806.__90__</span> || || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">53/32</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">7206</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">873.__45__</span> || || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">55/32</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">7735</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">937.__57__</span> || || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">57/32</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">8246</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">999.__51__</span> || || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">59/32</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">8738</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">1059.__15__</span> || || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">61/32</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">9214</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">1116.__84__</span> || || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">63/32</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">9675</span> || <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">1172.__72__</span> || <span style="background-color: #ffffff; display: block; text-align: center;">If you want real values between Purdal sizes and Cents sizes with any ratios, check them with this [[purdal/Purdal calculator|Purdal calculator]].</span><span style="background-color: #ffffff; display: block; text-align: center;">!!'!!!'!!!!'!!!'!!!!'!!!'!!!!'!!!'!!!!'!!!'!!!!'!!!'!!!!'!!!'!!!!'!!!'!!!!'!!!'!!</span> <span style="font-size: 1.3em; line-height: 1.5;">**Links**</span> * [[purdal/purdal]] - where this article was initially copied from
Original HTML content:
<html><head><title>Purdal</title></head><body><span style="font-size: 13px; line-height: 1.5;"> The </span><strong><span style="font-size: 13px; line-height: 1.5;">purdal</span></strong><span style="font-size: 13px; line-height: 1.5;"> is a unit of <a class="wiki_link" href="/interval%20size%20measure">measure for musical intervals</a>, </span><span style="background-color: #ffffff; font-size: 13px; line-height: 1.5;">suggested by <a class="wiki_link" href="http://xenharmonic.wikispaces.com/T%C3%BAtim%20Dennsuul%20Wafiil">Tútim Dennsuul</a>, which is the <a class="wiki_link" href="http://purdal.wikispaces.com/Ditave">Ditave</a> (2/1, the 'Octave') divided into </span><strong><span style="background-color: #ffffff; font-size: 13px; line-height: 1.5;">9900 equal parts</span></strong><span style="background-color: #ffffff; font-size: 13px; line-height: 1.5;">. The Purdals </span><span style="background-color: #ffffff; font-size: 13px; line-height: 1.5;" class="hps">are shown as a reliable and very consistent to idealize any musical system</span><span style="background-color: #ffffff; font-size: 13px; line-height: 1.5;">, </span><span style="background-color: #ffffff; font-size: 13px; line-height: 1.5;" class="hps">whether just or temperate</span><span style="background-color: #ffffff; font-size: 13px; line-height: 1.5;">.</span><br />
<span style="background-color: #ffffff;">The purpose that it have is for the need of precise with better quality in its presentation, those 'EDDs' </span><span style="background-color: #ffffff;" class="hps">who have a quantity equal to a prime number of intervals and systems until 990 steps per Ditave, only requiring 2 decimals for a basic precision.</span><span style="background-color: #ffffff;">The <a class="wiki_link" href="http://purdal.wikispaces.com/12-EDD">12-EDD</a> contains 825 Purdals in each semitone; Each Purdal is equivalent to 4/33 of a Cent (0.121212121.. Cents).</span><br />
<br />
<span style="background-color: #ffffff;">The ditaved Purdal (9900) is divisible</span><span style="font-size: 13px; line-height: 1.5;"> by: 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 18, 20, 22, 25, 30, 33, 36, 44, 45, 50, 55, 60, 66, 75, 90, 99, 100, 110, 132, 150, 165, 180, 198, 220, 225, 275, 300, 330, 396, 450, 495, 550, 660, 825, 900, 990, 1100, 1650, 1980, 2475, 3300 & 4950 exact parts.</span><br />
<br />
The Purdal's prime factorization is<br />
<!-- ws:start:WikiTextMathRule:0:
[[math]]<br/>
9900 = 2^2 \cdot 3^2 \cdot 5^2 \cdot 11<br/>[[math]]
--><script type="math/tex">9900 = 2^2 \cdot 3^2 \cdot 5^2 \cdot 11</script><!-- ws:end:WikiTextMathRule:0 --><br />
<br />
<span style="background-color: #ffffff;">The table below show us uniquely the translation of the Purdal values without decimals, to the simple Cent equivalence:</span><br />
<table class="wiki_table">
<tr>
<td><strong><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">Harmonic (until the 63º)</span></strong><br />
</td>
<td><strong><span style="color: #0000ff; font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">Purdal entire value</span></strong><br />
</td>
<td><strong><span style="color: #008080; font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">Cent equivalence</span></strong><br />
</td>
</tr>
<tr>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">2/1</span><br />
</td>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">9900</span><br />
</td>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">1200</span><br />
</td>
</tr>
<tr>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">3/2</span><br />
</td>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">5791</span><br />
</td>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">701.<u>93</u></span><br />
</td>
</tr>
<tr>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">5/4</span><br />
</td>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">3187</span><br />
</td>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">386.<u>30</u></span><br />
</td>
</tr>
<tr>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">7/4</span><br />
</td>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">7993</span><br />
</td>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">968.<u>84</u></span><br />
</td>
</tr>
<tr>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">9/8</span><br />
</td>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">1682</span><br />
</td>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">203.<u>87</u></span><br />
</td>
</tr>
<tr>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">11/8</span><br />
</td>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">4548</span><br />
</td>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">551.<u>27</u></span><br />
</td>
</tr>
<tr>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">13/8</span><br />
</td>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">6934</span><br />
</td>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">840.<u>48</u></span><br />
</td>
</tr>
<tr>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">15/8</span><br />
</td>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">8978</span><br />
</td>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">1088.<u>24</u></span><br />
</td>
</tr>
<tr>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">17/16</span><br />
</td>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">866</span><br />
</td>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">104.<u>96</u></span><br />
</td>
</tr>
<tr>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">19/16</span><br />
</td>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">2454</span><br />
</td>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">297.<u>45</u></span><br />
</td>
</tr>
<tr>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">21/16</span><br />
</td>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">3884</span><br />
</td>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">470.<u>78</u></span><br />
</td>
</tr>
<tr>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">23/16</span><br />
</td>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">5183</span><br />
</td>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">628.<u>24</u></span><br />
</td>
</tr>
<tr>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">25/16</span><br />
</td>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">6374</span><br />
</td>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">772.<u>60</u></span><br />
</td>
</tr>
<tr>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">27/16</span><br />
</td>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">7473</span><br />
</td>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">905.<u>81</u></span><br />
</td>
</tr>
<tr>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">29/16</span><br />
</td>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">8494</span><br />
</td>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">1029.<u>57</u></span><br />
</td>
</tr>
<tr>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">31/16</span><br />
</td>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">9447</span><br />
</td>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">1145.<u>09</u></span><br />
</td>
</tr>
<tr>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">33/32</span><br />
</td>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">440</span><br />
</td>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">53.<u>3</u></span><br />
</td>
</tr>
<tr>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">35/32</span><br />
</td>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">1280</span><br />
</td>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">155.<u>15</u></span><br />
</td>
</tr>
<tr>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">37/32</span><br />
</td>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">2074</span><br />
</td>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">251.<u>39</u></span><br />
</td>
</tr>
<tr>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">39/32</span><br />
</td>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">2825</span><br />
</td>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">342.<u>42</u></span><br />
</td>
</tr>
<tr>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">41/32</span><br />
</td>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">3540</span><br />
</td>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">429.<u>09</u></span><br />
</td>
</tr>
<tr>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">43/32</span><br />
</td>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">4220</span><br />
</td>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">511.<u>51</u></span><br />
</td>
</tr>
<tr>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">45/32</span><br />
</td>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">4869</span><br />
</td>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">590.<u>18</u></span><br />
</td>
</tr>
<tr>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">47/32</span><br />
</td>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">5490</span><br />
</td>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">665.<u>45</u></span><br />
</td>
</tr>
<tr>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">49/32</span><br />
</td>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">6086</span><br />
</td>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">737.<u>69</u></span><br />
</td>
</tr>
<tr>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">51/32</span><br />
</td>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">6657</span><br />
</td>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">806.<u>90</u></span><br />
</td>
</tr>
<tr>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">53/32</span><br />
</td>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">7206</span><br />
</td>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">873.<u>45</u></span><br />
</td>
</tr>
<tr>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">55/32</span><br />
</td>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">7735</span><br />
</td>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">937.<u>57</u></span><br />
</td>
</tr>
<tr>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">57/32</span><br />
</td>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">8246</span><br />
</td>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">999.<u>51</u></span><br />
</td>
</tr>
<tr>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">59/32</span><br />
</td>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">8738</span><br />
</td>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">1059.<u>15</u></span><br />
</td>
</tr>
<tr>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">61/32</span><br />
</td>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">9214</span><br />
</td>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">1116.<u>84</u></span><br />
</td>
</tr>
<tr>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">63/32</span><br />
</td>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">9675</span><br />
</td>
<td><span style="font-family: 'Times New Roman',Times,serif; font-size: 14.545454025268555px;">1172.<u>72</u></span><br />
</td>
</tr>
</table>
<span style="background-color: #ffffff; display: block; text-align: center;">If you want real values between Purdal sizes and Cents sizes with any ratios, check them with this <a class="wiki_link" href="http://purdal.wikispaces.com/Purdal%20calculator">Purdal calculator</a>.</span><span style="background-color: #ffffff; display: block; text-align: center;">!!'!!!'!!!!'!!!'!!!!'!!!'!!!!'!!!'!!!!'!!!'!!!!'!!!'!!!!'!!!'!!!!'!!!'!!!!'!!!'!!</span><br />
<span style="font-size: 1.3em; line-height: 1.5;"><strong>Links</strong></span><br />
<ul><li><a class="wiki_link" href="http://purdal.wikispaces.com/purdal">purdal/purdal</a> - where this article was initially copied from</li></ul></body></html>