Dreyblatt tuning system: Difference between revisions

Revision as of 13:51, 14 September 2007

IMPORTED REVISION FROM WIKISPACES

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

This revision was by author xenjacob and made on 2007-09-14 13:51:07 UTC.

The original revision id was 7975019.

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:

from Arnold Dreyblatt: //Tuning Systems Explanation//, [[http://www.dreyblatt.net/html/music.php?id=67|www.dreyblatt.net/html/music.php?id=67]]

The //Dreyblatt Tuning System// is calculated from the third, fifth, seventh, ninth and eleventh overtones and their multiples in the following pattern:
|| 1 || 3 || 5 || 7 || 9 || 11 ||
|| 3 || 9 || 15 || 21 || 27 || 33 ||
|| 5 || 15 || 25 || 35 || 45 || 55 ||
|| 7 || 21 || 35 || 49 || 63 || 77 ||
|| 9 || 27 || 45 || 63 || 81 || 99 ||
|| 11 || 33 || 55 || 77 || 99 || 121 ||

These mathematically related overtones are heard as tonal relationships when they are transposed and sounded above a fundamental tone. In this process of transposition from their position in the natural overtone series, these tones fall (unequally) in the span of one octave in the following order:

1, 33, 35, 9, 77, 5, 81, 21, [11,] 45, 3, 49, 99, 25, 27, 55, 7, 15, 121, 63, (2)

These tones are performed in "just intonation' based on a fundamental tone of "F". 
|| Note || Freq. || Partial || Cents ||
|| F || 349.2 || 1 || 0 ||
|| F# || 360.11 || 33 || -47 ||
|| G || 381.93 || 35 || -45 ||
|| G# || 392.85 || 9 || +4 ||
|| G# || 420.13 || 77 || +20 ||
|| A || 436.5 || 5 || -14 ||
|| A || 441.95 || 81 || +8 ||
|| A# || 458.32 || 21 || -29 ||
|| B || 480.15 || 11 || -49 ||
|| B || 491.06 || 45 || -10 ||
|| C || 523.8 || 3 || +2 ||
|| C || 534.71 || 49 || +38 ||
|| C# || 540.16 || 99 || -45 ||
|| C# || 545.62 || 25 || -28 ||
|| D || 589.27 || 27 || +6 ||
|| D || 600.18 || 55 || +37 ||
|| D# || 611.1 || 7 || -31 ||
|| E || 654.75 || 15 || -12 ||
|| E || 660.20 || 121 || +2 ||
|| F || 687.48 || 63 || -27 ||

Original HTML content:

<html><head><title>Arnold Dreyblatt</title></head><body>from Arnold Dreyblatt: <em>Tuning Systems Explanation</em>, <a class="wiki_link_ext" href="http://www.dreyblatt.net/html/music.php?id=67" rel="nofollow">www.dreyblatt.net/html/music.php?id=67</a><br />
<br />
The <em>Dreyblatt Tuning System</em> is calculated from the third, fifth, seventh, ninth and eleventh overtones and their multiples in the following pattern:<br />


<table class="wiki_table">
    <tr>
        <td>1<br />
</td>
        <td>3<br />
</td>
        <td>5<br />
</td>
        <td>7<br />
</td>
        <td>9<br />
</td>
        <td>11<br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>9<br />
</td>
        <td>15<br />
</td>
        <td>21<br />
</td>
        <td>27<br />
</td>
        <td>33<br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>15<br />
</td>
        <td>25<br />
</td>
        <td>35<br />
</td>
        <td>45<br />
</td>
        <td>55<br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td>21<br />
</td>
        <td>35<br />
</td>
        <td>49<br />
</td>
        <td>63<br />
</td>
        <td>77<br />
</td>
    </tr>
    <tr>
        <td>9<br />
</td>
        <td>27<br />
</td>
        <td>45<br />
</td>
        <td>63<br />
</td>
        <td>81<br />
</td>
        <td>99<br />
</td>
    </tr>
    <tr>
        <td>11<br />
</td>
        <td>33<br />
</td>
        <td>55<br />
</td>
        <td>77<br />
</td>
        <td>99<br />
</td>
        <td>121<br />
</td>
    </tr>
</table>

<br />
These mathematically related overtones are heard as tonal relationships when they are transposed and sounded above a fundamental tone. In this process of transposition from their position in the natural overtone series, these tones fall (unequally) in the span of one octave in the following order:<br />
<br />
1, 33, 35, 9, 77, 5, 81, 21, [11,] 45, 3, 49, 99, 25, 27, 55, 7, 15, 121, 63, (2)<br />
<br />
These tones are performed in &quot;just intonation' based on a fundamental tone of &quot;F&quot;. <br />


<table class="wiki_table">
    <tr>
        <td>Note<br />
</td>
        <td>Freq.<br />
</td>
        <td>Partial<br />
</td>
        <td>Cents<br />
</td>
    </tr>
    <tr>
        <td>F<br />
</td>
        <td>349.2<br />
</td>
        <td>1<br />
</td>
        <td>0<br />
</td>
    </tr>
    <tr>
        <td>F#<br />
</td>
        <td>360.11<br />
</td>
        <td>33<br />
</td>
        <td>-47<br />
</td>
    </tr>
    <tr>
        <td>G<br />
</td>
        <td>381.93<br />
</td>
        <td>35<br />
</td>
        <td>-45<br />
</td>
    </tr>
    <tr>
        <td>G#<br />
</td>
        <td>392.85<br />
</td>
        <td>9<br />
</td>
        <td>+4<br />
</td>
    </tr>
    <tr>
        <td>G#<br />
</td>
        <td>420.13<br />
</td>
        <td>77<br />
</td>
        <td>+20<br />
</td>
    </tr>
    <tr>
        <td>A<br />
</td>
        <td>436.5<br />
</td>
        <td>5<br />
</td>
        <td>-14<br />
</td>
    </tr>
    <tr>
        <td>A<br />
</td>
        <td>441.95<br />
</td>
        <td>81<br />
</td>
        <td>+8<br />
</td>
    </tr>
    <tr>
        <td>A#<br />
</td>
        <td>458.32<br />
</td>
        <td>21<br />
</td>
        <td>-29<br />
</td>
    </tr>
    <tr>
        <td>B<br />
</td>
        <td>480.15<br />
</td>
        <td>11<br />
</td>
        <td>-49<br />
</td>
    </tr>
    <tr>
        <td>B<br />
</td>
        <td>491.06<br />
</td>
        <td>45<br />
</td>
        <td>-10<br />
</td>
    </tr>
    <tr>
        <td>C<br />
</td>
        <td>523.8<br />
</td>
        <td>3<br />
</td>
        <td>+2<br />
</td>
    </tr>
    <tr>
        <td>C<br />
</td>
        <td>534.71<br />
</td>
        <td>49<br />
</td>
        <td>+38<br />
</td>
    </tr>
    <tr>
        <td>C#<br />
</td>
        <td>540.16<br />
</td>
        <td>99<br />
</td>
        <td>-45<br />
</td>
    </tr>
    <tr>
        <td>C#<br />
</td>
        <td>545.62<br />
</td>
        <td>25<br />
</td>
        <td>-28<br />
</td>
    </tr>
    <tr>
        <td>D<br />
</td>
        <td>589.27<br />
</td>
        <td>27<br />
</td>
        <td>+6<br />
</td>
    </tr>
    <tr>
        <td>D<br />
</td>
        <td>600.18<br />
</td>
        <td>55<br />
</td>
        <td>+37<br />
</td>
    </tr>
    <tr>
        <td>D#<br />
</td>
        <td>611.1<br />
</td>
        <td>7<br />
</td>
        <td>-31<br />
</td>
    </tr>
    <tr>
        <td>E<br />
</td>
        <td>654.75<br />
</td>
        <td>15<br />
</td>
        <td>-12<br />
</td>
    </tr>
    <tr>
        <td>E<br />
</td>
        <td>660.20<br />
</td>
        <td>121<br />
</td>
        <td>+2<br />
</td>
    </tr>
    <tr>
        <td>F<br />
</td>
        <td>687.48<br />
</td>
        <td>63<br />
</td>
        <td>-27<br />
</td>
    </tr>
</table>

</body></html>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:guest|guest]] and made on <tt>2007-02-07 21:44:59 UTC</tt>.<br>
+: This revision was by author [[User:xenjacob|xenjacob]] and made on <tt>2007-09-14 13:51:07 UTC</tt>.<br>
-: The original revision id was <tt>2696984</tt>.<br>
+: The original revision id was <tt>7975019</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>
 <h4>Original Wikitext content:</h4>
-<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">(from [[http://www.dreyblatt.net/html/music.php?id=67|Arnold Dreyblatt's website]])
+<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">from Arnold Dreyblatt: //Tuning Systems Explanation//, [[http://www.dreyblatt.net/html/music.php?id=67|www.dreyblatt.net/html/music.php?id=67]]
-//The tuning system used in my music is calculated from the third, fifth, seventh, ninth and eleventh overtones and their multiples in the following pattern://
+The //Dreyblatt Tuning System// is calculated from the third, fifth, seventh, ninth and eleventh overtones and their multiples in the following pattern:
+|| 1 || 3 || 5 || 7 || 9 || 11 ||
+|| 3 || 9 || 15 || 21 || 27 || 33 ||
+|| 5 || 15 || 25 || 35 || 45 || 55 ||
+|| 7 || 21 || 35 || 49 || 63 || 77 ||
+|| 9 || 27 || 45 || 63 || 81 || 99 ||
+|| 11 || 33 || 55 || 77 || 99 || 121 ||
-//1 3 5 7 9 11//
+These mathematically related overtones are heard as tonal relationships when they are transposed and sounded above a fundamental tone. In this process of transposition from their position in the natural overtone series, these tones fall (unequally) in the span of one octave in the following order:
-//3 9 15 21 27 33//
-//5 15 25 35 45 55//
-//7 21 35 49 63 77//
-//9 27 45 63 81 99//
-//11 33 55 77 99 121//
-//These mathematically related overones are heard as a tonal relation when they are transposed and sounded above a fundamental tone. In this process of transposition from their position in the natural overtone series, these tones fall in the span of one octave in the following//
+, 33, 35, 9, 77, 5, 81, 21, [11,] 45, 3, 49, 99, 25, 27, 55, 7, 15, 121, 63, (2)
-//order: 1, 33, 35, 9, 77, 5, 81, 21, [11,] 45, 3, 49, 99, 25, 27, 55, 7, 15, 121, 63, (2)//
-As ratios:
+These tones are performed in "just intonation' based on a fundamental tone of "F".
-/1
+|| Note || Freq. || Partial || Cents ||
-/32
+|| F || 349.2 || 1 || 0 ||
-/32
+|| F# || 360.11 || 33 || -47 ||
-/8
+|| G || 381.93 || 35 || -45 ||
-/64
+|| G# || 392.85 || 9 || +4 ||
-/4
+|| G# || 420.13 || 77 || +20 ||
-/64
+|| A || 436.5 || 5 || -14 ||
-/16
+|| A || 441.95 || 81 || +8 ||
-/8
+|| A# || 458.32 || 21 || -29 ||
-/32
+|| B || 480.15 || 11 || -49 ||
-/2
+|| B || 491.06 || 45 || -10 ||
-/32
+|| C || 523.8 || 3 || +2 ||
-/64
+|| C || 534.71 || 49 || +38 ||
-/16
+|| C# || 540.16 || 99 || -45 ||
-/16
+|| C# || 545.62 || 25 || -28 ||
-/32
+|| D || 589.27 || 27 || +6 ||
-/4
+|| D || 600.18 || 55 || +37 ||
-/8
+|| D# || 611.1 || 7 || -31 ||
-/64
+|| E || 654.75 || 15 || -12 ||
-/32
+|| E || 660.20 || 121 || +2 ||
-/1</pre></div>
+|| F || 687.48 || 63 || -27 ||</pre></div>
 <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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Arnold Dreyblatt&lt;/title&gt;&lt;/head&gt;&lt;body&gt;(from &lt;a class="wiki_link_ext" href="http://www.dreyblatt.net/html/music.php?id=67" rel="nofollow"&gt;Arnold Dreyblatt's website&lt;/a&gt;)&lt;br /&gt;
+<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Arnold Dreyblatt&lt;/title&gt;&lt;/head&gt;&lt;body&gt;from Arnold Dreyblatt: &lt;em&gt;Tuning Systems Explanation&lt;/em&gt;, &lt;a class="wiki_link_ext" href="http://www.dreyblatt.net/html/music.php?id=67" rel="nofollow"&gt;www.dreyblatt.net/html/music.php?id=67&lt;/a&gt;&lt;br /&gt;
 &lt;br /&gt;
-&lt;em&gt;The tuning system used in my music is calculated from the third, fifth, seventh, ninth and eleventh overtones and their multiples in the following pattern:&lt;/em&gt;&lt;br /&gt;
+The &lt;em&gt;Dreyblatt Tuning System&lt;/em&gt; is calculated from the third, fifth, seventh, ninth and eleventh overtones and their multiples in the following pattern:&lt;br /&gt;
+&lt;table class="wiki_table"&gt;
+    &lt;tr&gt;
+        &lt;td&gt;1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;3&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;5&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;7&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;9&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;11&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;3&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;9&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;15&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;21&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;27&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;33&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;5&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;15&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;25&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;35&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;45&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;55&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;7&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;21&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;35&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;49&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;63&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;77&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;9&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;27&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;45&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;63&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;81&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;99&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;11&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;33&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;55&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;77&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;99&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;121&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+&lt;/table&gt;
 &lt;br /&gt;
-&lt;em&gt;1 3 5 7 9 11&lt;/em&gt;&lt;br /&gt;
+These mathematically related overtones are heard as tonal relationships when they are transposed and sounded above a fundamental tone. In this process of transposition from their position in the natural overtone series, these tones fall (unequally) in the span of one octave in the following order:&lt;br /&gt;
-&lt;em&gt;3 9 15 21 27 33&lt;/em&gt;&lt;br /&gt;
-&lt;em&gt;5 15 25 35 45 55&lt;/em&gt;&lt;br /&gt;
-&lt;em&gt;7 21 35 49 63 77&lt;/em&gt;&lt;br /&gt;
-&lt;em&gt;9 27 45 63 81 99&lt;/em&gt;&lt;br /&gt;
-&lt;em&gt;11 33 55 77 99 121&lt;/em&gt;&lt;br /&gt;
 &lt;br /&gt;
-&lt;em&gt;These mathematically related overones are heard as a tonal relation when they are transposed and sounded above a fundamental tone. In this process of transposition from their position in the natural overtone series, these tones fall in the span of one octave in the following&lt;/em&gt;&lt;br /&gt;
+, 33, 35, 9, 77, 5, 81, 21, [11,] 45, 3, 49, 99, 25, 27, 55, 7, 15, 121, 63, (2)&lt;br /&gt;
-&lt;em&gt;order: 1, 33, 35, 9, 77, 5, 81, 21, [11,] 45, 3, 49, 99, 25, 27, 55, 7, 15, 121, 63, (2)&lt;/em&gt;&lt;br /&gt;
 &lt;br /&gt;
-As ratios:&lt;br /&gt;
+These tones are performed in &amp;quot;just intonation' based on a fundamental tone of &amp;quot;F&amp;quot;. &lt;br /&gt;
-/1&lt;br /&gt;
-/32&lt;br /&gt;
-/32&lt;br /&gt;
+&lt;table class="wiki_table"&gt;
-/8&lt;br /&gt;
+    &lt;tr&gt;
-/64&lt;br /&gt;
+        &lt;td&gt;Note&lt;br /&gt;
-/4&lt;br /&gt;
+&lt;/td&gt;
-/64&lt;br /&gt;
+        &lt;td&gt;Freq.&lt;br /&gt;
-/16&lt;br /&gt;
+&lt;/td&gt;
-/8&lt;br /&gt;
+        &lt;td&gt;Partial&lt;br /&gt;
-/32&lt;br /&gt;
+&lt;/td&gt;
-/2&lt;br /&gt;
+        &lt;td&gt;Cents&lt;br /&gt;
-/32&lt;br /&gt;
+&lt;/td&gt;
-/64&lt;br /&gt;
+    &lt;/tr&gt;
-/16&lt;br /&gt;
+    &lt;tr&gt;
-/16&lt;br /&gt;
+        &lt;td&gt;F&lt;br /&gt;
-/32&lt;br /&gt;
+&lt;/td&gt;
-/4&lt;br /&gt;
+        &lt;td&gt;349.2&lt;br /&gt;
-/8&lt;br /&gt;
+&lt;/td&gt;
-/64&lt;br /&gt;
+        &lt;td&gt;1&lt;br /&gt;
-/32&lt;br /&gt;
+&lt;/td&gt;
-/1&lt;/body&gt;&lt;/html&gt;</pre></div>
+        &lt;td&gt;0&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;F#&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;360.11&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;33&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;-47&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;G&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;381.93&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;35&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;-45&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
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+&lt;/td&gt;
+    &lt;/tr&gt;
+&lt;/table&gt;
+&lt;/body&gt;&lt;/html&gt;</pre></div>

Dreyblatt tuning system: Difference between revisions

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