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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
from [[Arnold Dreyblatt]]: ''Tuning Systems Explanation'', http://www.dreyblatt.net/general-information-music#/tuning-system/
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>2007-09-14 13:51:07 UTC</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 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:
The ''Dreyblatt Tuning System'' is calculated from the third, fifth, seventh, ninth and eleventh [[harmonic]]s 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:
{| class="wikitable"
|-
| | 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 harmonics 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 harmonic 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)
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".  
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 ||</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 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;
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;
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;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;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;
 


&lt;table class="wiki_table"&gt;
{| class="wikitable"
    &lt;tr&gt;
|-
        &lt;td&gt;Note&lt;br /&gt;
| | Note
&lt;/td&gt;
| | Freq.
        &lt;td&gt;Freq.&lt;br /&gt;
| | Partial
&lt;/td&gt;
| | Cents
        &lt;td&gt;Partial&lt;br /&gt;
|-
&lt;/td&gt;
| | F
        &lt;td&gt;Cents&lt;br /&gt;
| | 349.2
&lt;/td&gt;
| | 1
    &lt;/tr&gt;
| | 0
    &lt;tr&gt;
|-
        &lt;td&gt;F&lt;br /&gt;
| | F#
&lt;/td&gt;
| | 360.11
        &lt;td&gt;349.2&lt;br /&gt;
| | 33
&lt;/td&gt;
| | -47
        &lt;td&gt;1&lt;br /&gt;
|-
&lt;/td&gt;
| | G
        &lt;td&gt;0&lt;br /&gt;
| | 381.93
&lt;/td&gt;
| | 35
    &lt;/tr&gt;
| | -45
    &lt;tr&gt;
|-
        &lt;td&gt;F#&lt;br /&gt;
| | G#
&lt;/td&gt;
| | 392.85
        &lt;td&gt;360.11&lt;br /&gt;
| | 9
&lt;/td&gt;
| | +4
        &lt;td&gt;33&lt;br /&gt;
|-
&lt;/td&gt;
| | G#
        &lt;td&gt;-47&lt;br /&gt;
| | 420.13
&lt;/td&gt;
| | 77
    &lt;/tr&gt;
| | +20
    &lt;tr&gt;
|-
        &lt;td&gt;G&lt;br /&gt;
| | A
&lt;/td&gt;
| | 436.5
        &lt;td&gt;381.93&lt;br /&gt;
| | 5
&lt;/td&gt;
| | -14
        &lt;td&gt;35&lt;br /&gt;
|-
&lt;/td&gt;
| | A
        &lt;td&gt;-45&lt;br /&gt;
| | 441.95
&lt;/td&gt;
| | 81
    &lt;/tr&gt;
| | +8
    &lt;tr&gt;
|-
        &lt;td&gt;G#&lt;br /&gt;
| | A#
&lt;/td&gt;
| | 458.32
        &lt;td&gt;392.85&lt;br /&gt;
| | 21
&lt;/td&gt;
| | -29
        &lt;td&gt;9&lt;br /&gt;
|-
&lt;/td&gt;
| | B
        &lt;td&gt;+4&lt;br /&gt;
| | 480.15
&lt;/td&gt;
| | 11
    &lt;/tr&gt;
| | -49
    &lt;tr&gt;
|-
        &lt;td&gt;G#&lt;br /&gt;
| | B
&lt;/td&gt;
| | 491.06
        &lt;td&gt;420.13&lt;br /&gt;
| | 45
&lt;/td&gt;
| | -10
        &lt;td&gt;77&lt;br /&gt;
|-
&lt;/td&gt;
| | C
        &lt;td&gt;+20&lt;br /&gt;
| | 523.8
&lt;/td&gt;
| | 3
    &lt;/tr&gt;
| | +2
    &lt;tr&gt;
|-
        &lt;td&gt;A&lt;br /&gt;
| | C
&lt;/td&gt;
| | 534.71
        &lt;td&gt;436.5&lt;br /&gt;
| | 49
&lt;/td&gt;
| | +38
        &lt;td&gt;5&lt;br /&gt;
|-
&lt;/td&gt;
| | C#
        &lt;td&gt;-14&lt;br /&gt;
| | 540.16
&lt;/td&gt;
| | 99
    &lt;/tr&gt;
| | -45
    &lt;tr&gt;
|-
        &lt;td&gt;A&lt;br /&gt;
| | C#
&lt;/td&gt;
| | 545.62
        &lt;td&gt;441.95&lt;br /&gt;
| | 25
&lt;/td&gt;
| | -28
        &lt;td&gt;81&lt;br /&gt;
|-
&lt;/td&gt;
| | D
        &lt;td&gt;+8&lt;br /&gt;
| | 589.27
&lt;/td&gt;
| | 27
    &lt;/tr&gt;
| | +6
    &lt;tr&gt;
|-
        &lt;td&gt;A#&lt;br /&gt;
| | D
&lt;/td&gt;
| | 600.18
        &lt;td&gt;458.32&lt;br /&gt;
| | 55
&lt;/td&gt;
| | +37
        &lt;td&gt;21&lt;br /&gt;
|-
&lt;/td&gt;
| | D#
        &lt;td&gt;-29&lt;br /&gt;
| | 611.1
&lt;/td&gt;
| | 7
    &lt;/tr&gt;
| | -31
    &lt;tr&gt;
|-
        &lt;td&gt;B&lt;br /&gt;
| | E
&lt;/td&gt;
| | 654.75
        &lt;td&gt;480.15&lt;br /&gt;
| | 15
&lt;/td&gt;
| | -12
        &lt;td&gt;11&lt;br /&gt;
|-
&lt;/td&gt;
| | E
        &lt;td&gt;-49&lt;br /&gt;
| | 660.20
&lt;/td&gt;
| | 121
    &lt;/tr&gt;
| | +2
    &lt;tr&gt;
|-
        &lt;td&gt;B&lt;br /&gt;
| | F
&lt;/td&gt;
| | 687.48
        &lt;td&gt;491.06&lt;br /&gt;
| | 63
&lt;/td&gt;
| | -27
        &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>
[[Category:Just intonation]]
[[Category:11-limit]]
Retrieved from "https://en.xen.wiki/w/Dreyblatt_tuning_system"