Dreyblatt tuning system: Difference between revisions

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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:guest|guest]] and made on <tt>2007-02-07 21:44:59 UTC</tt>.<br>
: The original revision id was <tt>2696984</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]])


//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 [[harmonic]]s and their multiples in the following pattern:


//1 3 5 7 9 11//
{| class="wikitable"
//3 9 15 21 27 33//
|-
//5 15 25 35 45 55//
| | 1
//7 21 35 49 63 77//
| | 3
//9 27 45 63 81 99//
| | 5
//11 33 55 77 99 121//
| | 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 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//
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:
//order: 1, 33, 35, 9, 77, 5, 81, 21, [11,] 45, 3, 49, 99, 25, 27, 55, 7, 15, 121, 63, (2)//


As ratios:
1, 33, 35, 9, 77, 5, 81, 21, [11,] 45, 3, 49, 99, 25, 27, 55, 7, 15, 121, 63, (2)
1/1
 
33/32
These tones are performed in "[[just intonation]]' based on a fundamental tone of "F".
35/32
 
9/8
{| class="wikitable"
77/64
|-
5/4
| | Note
81/64
| | Freq.
21/16
| | Partial
11/8
| | Cents
45/32
|-
3/2
| | F
49/32
| | 349.2
99/64
| | 1
25/16
| | 0
27/16
|-
55/32
| | F#
7/4
| | 360.11
15/8
| | 33
121/64
| | -47
63/32
|-
2/1</pre></div>
| | G
<h4>Original HTML content:</h4>
| | 381.93
<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;
| | 35
&lt;br /&gt;
| | -45
&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;
|-
&lt;br /&gt;
| | G#
&lt;em&gt;1 3 5 7 9 11&lt;/em&gt;&lt;br /&gt;
| | 392.85
&lt;em&gt;3 9 15 21 27 33&lt;/em&gt;&lt;br /&gt;
| | 9
&lt;em&gt;5 15 25 35 45 55&lt;/em&gt;&lt;br /&gt;
| | +4
&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;
| | G#
&lt;em&gt;11 33 55 77 99 121&lt;/em&gt;&lt;br /&gt;
| | 420.13
&lt;br /&gt;
| | 77
&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;
| | +20
&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;
| | A
As ratios:&lt;br /&gt;
| | 436.5
1/1&lt;br /&gt;
| | 5
33/32&lt;br /&gt;
| | -14
35/32&lt;br /&gt;
|-
9/8&lt;br /&gt;
| | A
77/64&lt;br /&gt;
| | 441.95
5/4&lt;br /&gt;
| | 81
81/64&lt;br /&gt;
| | +8
21/16&lt;br /&gt;
|-
11/8&lt;br /&gt;
| | A#
45/32&lt;br /&gt;
| | 458.32
3/2&lt;br /&gt;
| | 21
49/32&lt;br /&gt;
| | -29
99/64&lt;br /&gt;
|-
25/16&lt;br /&gt;
| | B
27/16&lt;br /&gt;
| | 480.15
55/32&lt;br /&gt;
| | 11
7/4&lt;br /&gt;
| | -49
15/8&lt;br /&gt;
|-
121/64&lt;br /&gt;
| | B
63/32&lt;br /&gt;
| | 491.06
2/1&lt;/body&gt;&lt;/html&gt;</pre></div>
| | 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
|}
 
[[Category:Just intonation]]
[[Category:11-limit]]

Latest revision as of 05:20, 9 January 2024

from Arnold Dreyblatt: Tuning Systems Explanation, http://www.dreyblatt.net/general-information-music#/tuning-system/

The Dreyblatt Tuning System is calculated from the third, fifth, seventh, ninth and eleventh harmonics 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 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)

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
Retrieved from "https://en.xen.wiki/index.php?title=Dreyblatt_tuning_system&oldid=131343"