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Dreyblatt tuning system: Difference between revisions

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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: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 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>
<h4>Original Wikitext content:</h4>
<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//
1, 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".
1/1
|| Note || Freq. || Partial || Cents ||
33/32
|| F || 349.2 || 1 || 0 ||
35/32
|| F# || 360.11 || 33 || -47 ||
9/8
|| G || 381.93 || 35 || -45 ||
77/64
|| G# || 392.85 || 9 || +4 ||
5/4
|| G# || 420.13 || 77 || +20 ||
81/64
|| A || 436.5 || 5 || -14 ||
21/16
|| A || 441.95 || 81 || +8 ||
11/8
|| A# || 458.32 || 21 || -29 ||
45/32
|| B || 480.15 || 11 || -49 ||
3/2
|| B || 491.06 || 45 || -10 ||
49/32
|| C || 523.8 || 3 || +2 ||
99/64
|| C || 534.71 || 49 || +38 ||
25/16
|| C# || 540.16 || 99 || -45 ||
27/16
|| C# || 545.62 || 25 || -28 ||
55/32
|| D || 589.27 || 27 || +6 ||
7/4
|| D || 600.18 || 55 || +37 ||
15/8
|| D# || 611.1 || 7 || -31 ||
121/64
|| E || 654.75 || 15 || -12 ||
63/32
|| E || 660.20 || 121 || +2 ||
2/1</pre></div>
|| F || 687.48 || 63 || -27 ||</pre></div>
<h4>Original HTML content:</h4>
<h4>Original HTML content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&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;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;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;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;
1, 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;
&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;
1/1&lt;br /&gt;
 
33/32&lt;br /&gt;
 
35/32&lt;br /&gt;
&lt;table class="wiki_table"&gt;
9/8&lt;br /&gt;
    &lt;tr&gt;
77/64&lt;br /&gt;
        &lt;td&gt;Note&lt;br /&gt;
5/4&lt;br /&gt;
&lt;/td&gt;
81/64&lt;br /&gt;
        &lt;td&gt;Freq.&lt;br /&gt;
21/16&lt;br /&gt;
&lt;/td&gt;
11/8&lt;br /&gt;
        &lt;td&gt;Partial&lt;br /&gt;
45/32&lt;br /&gt;
&lt;/td&gt;
3/2&lt;br /&gt;
        &lt;td&gt;Cents&lt;br /&gt;
49/32&lt;br /&gt;
&lt;/td&gt;
99/64&lt;br /&gt;
    &lt;/tr&gt;
25/16&lt;br /&gt;
    &lt;tr&gt;
27/16&lt;br /&gt;
        &lt;td&gt;F&lt;br /&gt;
55/32&lt;br /&gt;
&lt;/td&gt;
7/4&lt;br /&gt;
        &lt;td&gt;349.2&lt;br /&gt;
15/8&lt;br /&gt;
&lt;/td&gt;
121/64&lt;br /&gt;
        &lt;td&gt;1&lt;br /&gt;
63/32&lt;br /&gt;
&lt;/td&gt;
2/1&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;
        &lt;td&gt;G#&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;392.85&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;+4&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;420.13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;77&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;+20&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;A&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;436.5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-14&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;A&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;441.95&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;81&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;+8&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;A#&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;458.32&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-29&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;B&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;480.15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-49&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;B&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;491.06&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;45&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-10&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;C&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;523.8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;+2&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;C&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;534.71&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;49&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;+38&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;C#&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;540.16&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;99&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-45&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;C#&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;545.62&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;25&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-28&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;D&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;589.27&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;27&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;+6&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;D&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;600.18&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;55&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;+37&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;D#&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;611.1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-31&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;E&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;654.75&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-12&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;E&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;660.20&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;121&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;+2&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;687.48&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;63&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-27&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;/body&gt;&lt;/html&gt;</pre></div>
Retrieved from "https://en.xen.wiki/w/Dreyblatt_tuning_system"