Otones8-16: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
"Otones 8-16" refers to a scale generated by taking the 8th through 16th overtone over some fundamental. Dante Rosati calls this the "Diatonic Harmonic Series Scale" and Denny Genovese calls this "Mode 8 of the Harmonic Series". It may be treated as octave-repeating, or not. The frequency ratio between the steps of the scale can be represented as 8:9:10:11:12:13:14:15:16. Note that 16, being a doubling of 8, is an octave above the first tone.
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-10-08 23:12:13 UTC</tt>.<br>
: The original revision id was <tt>262909310</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">"Otones 8-16" refers to a scale generated by taking the 8th through 16th overtone over some fundamental. Dante Rosati calls this the "Diatonic Harmonic Series Scale" and Denny Genovese calls this "Mode 8 of the Harmonic Series". It may be treated as octave-repeating, or not. The frequency ratio between the steps of the scale can be represented as 8:9:10:11:12:13:14:15:16. Note that 16, being a doubling of 8, is an octave above the first tone.


Otones 8-16 contains eight tones in the octave and eight different step sizes. The steps get smaller as the scale ascends:
Otones 8-16 contains eight tones in the octave and eight different step sizes. The steps get smaller as the scale ascends:


|| harmonic || ratio from 1/1 || ratio in between ("step") || names || cents value, scale member || cents value, step ||
{| class="wikitable"
|| 8 || 1/1 ||   || unison, perfect prime || 0.00 ||   ||
|-
||   ||   || 9:8 || large whole step; Pythagorean whole step; major whole tone ||   || 203.91 ||
| | harmonic
|| 9 || 9/8 ||   || large whole step; Pythagorean whole step; major whole tone || 203.91 ||   ||
| | ratio from 1/1
||   ||   || 10:9 || small whole step; 5-limit whole step; minor whole tone ||   || 182.40 ||
| | ratio in between ("step")
|| 10 || 5/4 ||   || 5-limit major third || 386.31 ||   ||
| | names
||   ||   || 11:10 || large undecimal neutral second, 4/5-tone, Ptolemy's second ||   || 165.00 ||
| | cents value, scale member
|| 11 || 11/8 ||   || undecimal semi-augmented fourth || 551.32 ||   ||
| | cents value, step
||   ||   || 12:11 || small undecimal neutral second, 3/4-tone ||   || 150.64 ||
|-
|| 12 || 3/2 ||   || just perfect fifth || 701.955 ||   ||
| | 8
||   ||   || 13:12 || large tridecimal neutral second, tridecimal 2/3 tone ||   || 138.57 ||
| | 1/1
|| 13 || 13/8 ||   || tridecimal neutral sixth || 840.53 ||   ||
| |  
||   ||   || 14:13 || small tridecimal neutral second; lesser tridecimal 2/3 tone ||   || 128.30 ||
| | unison, perfect prime
|| 14 || 7/4 ||   || harmonic seventh || 968.83 ||   ||
| | 0.00
||   ||   || 15:14 || septimal minor second; major diatonic semitone ||   || 119.44 ||
| |  
|| 15 || 15/8 ||   || 5-limit major seventh; classic major seventh || 1088.27 ||   ||
|-
||   ||   || 16:15 || 5-limit minor second; classic minor second; minor diatonic semitone ||   || 111.73 ||
| |  
|| 16 || 2/1 ||   || perfect octave || 1200.00 ||   ||
| |  
| | 9:8
| | large whole step; Pythagorean whole step; major whole tone
| |  
| | 203.91
|-
| | 9
| | 9/8
| |  
| | large whole step; Pythagorean whole step; major whole tone
| | 203.91
| |  
|-
| |  
| |  
| | 10:9
| | small whole step; 5-limit whole step; minor whole tone
| |  
| | 182.40
|-
| | 10
| | 5/4
| |  
| | 5-limit major third
| | 386.31
| |  
|-
| |  
| |  
| | 11:10
| | large undecimal neutral second, 4/5-tone, Ptolemy's second
| |  
| | 165.00
|-
| | 11
| | 11/8
| |  
| | undecimal semi-augmented fourth
| | 551.32
| |  
|-
| |  
| |  
| | 12:11
| | small undecimal neutral second, 3/4-tone
| |  
| | 150.64
|-
| | 12
| | 3/2
| |  
| | just perfect fifth
| | 701.955
| |  
|-
| |  
| |  
| | 13:12
| | large tridecimal neutral second, tridecimal 2/3 tone
| |  
| | 138.57
|-
| | 13
| | 13/8
| |  
| | tridecimal neutral sixth
| | 840.53
| |  
|-
| |  
| |  
| | 14:13
| | small tridecimal neutral second; lesser tridecimal 2/3 tone
| |  
| | 128.30
|-
| | 14
| | 7/4
| |  
| | harmonic seventh
| | 968.83
| |  
|-
| |  
| |  
| | 15:14
| | septimal minor second; major diatonic semitone
| |  
| | 119.44
|-
| | 15
| | 15/8
| |  
| | 5-limit major seventh; classic major seventh
| | 1088.27
| |  
|-
| |  
| |  
| | 16:15
| | 5-limit minor second; classic minor second; minor diatonic semitone
| |  
| | 111.73
|-
| | 16
| | 2/1
| |  
| | perfect octave
| | 1200.00
| |  
|}


===Compositions:===  
===Compositions:===
[[http://www.youtube.com/watch?v=FlwN7qSGz9U|Paracelsus for Diatonic Harmonic Guitar by Dante Rosati]]
[http://www.youtube.com/watch?v=FlwN7qSGz9U Paracelsus for Diatonic Harmonic Guitar by Dante Rosati]
[[http://www.youtube.com/watch?v=U6ElPRoIZak|No Snow for Diatonic Harmonic Guitar by Dante Rosati]]</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;otones8-16&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&amp;quot;Otones 8-16&amp;quot; refers to a scale generated by taking the 8th through 16th overtone over some fundamental. Dante Rosati calls this the &amp;quot;Diatonic Harmonic Series Scale&amp;quot; and Denny Genovese calls this &amp;quot;Mode 8 of the Harmonic Series&amp;quot;. It may be treated as octave-repeating, or not. The frequency ratio between the steps of the scale can be represented as 8:9:10:11:12:13:14:15:16. Note that 16, being a doubling of 8, is an octave above the first tone.&lt;br /&gt;
&lt;br /&gt;
Otones 8-16 contains eight tones in the octave and eight different step sizes. The steps get smaller as the scale ascends:&lt;br /&gt;
&lt;br /&gt;


 
[http://www.youtube.com/watch?v=U6ElPRoIZak No Snow for Diatonic Harmonic Guitar by Dante Rosati]
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;td&gt;harmonic&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;ratio from 1/1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;ratio in between (&amp;quot;step&amp;quot;)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;names&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;cents value, scale member&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;cents value, step&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1/1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;unison, perfect prime&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0.00&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9:8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;large whole step; Pythagorean whole step; major whole tone&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;203.91&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;9/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;large whole step; Pythagorean whole step; major whole tone&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;203.91&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;10:9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;small whole step; 5-limit whole step; minor whole tone&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;182.40&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5/4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5-limit major third&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;386.31&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11:10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;large undecimal neutral second, 4/5-tone, Ptolemy's second&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;165.00&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;11/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;undecimal semi-augmented fourth&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;551.32&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;12:11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;small undecimal neutral second, 3/4-tone&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;150.64&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;12&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;just perfect fifth&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;701.955&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;13:12&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;large tridecimal neutral second, tridecimal 2/3 tone&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;138.57&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;13/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;tridecimal neutral sixth&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;840.53&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;14:13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;small tridecimal neutral second; lesser tridecimal 2/3 tone&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;128.30&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7/4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;harmonic seventh&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;968.83&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;15:14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;septimal minor second; major diatonic semitone&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;119.44&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;15/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5-limit major seventh; classic major seventh&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1088.27&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;16:15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5-limit minor second; classic minor second; minor diatonic semitone&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;111.73&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;16&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;2/1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;perfect octave&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1200.00&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc0"&gt;&lt;a name="x--Compositions:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Compositions:&lt;/h3&gt;
&lt;a class="wiki_link_ext" href="http://www.youtube.com/watch?v=FlwN7qSGz9U" rel="nofollow"&gt;Paracelsus for Diatonic Harmonic Guitar by Dante Rosati&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://www.youtube.com/watch?v=U6ElPRoIZak" rel="nofollow"&gt;No Snow for Diatonic Harmonic Guitar by Dante Rosati&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>

Revision as of 00:00, 17 July 2018

"Otones 8-16" refers to a scale generated by taking the 8th through 16th overtone over some fundamental. Dante Rosati calls this the "Diatonic Harmonic Series Scale" and Denny Genovese calls this "Mode 8 of the Harmonic Series". It may be treated as octave-repeating, or not. The frequency ratio between the steps of the scale can be represented as 8:9:10:11:12:13:14:15:16. Note that 16, being a doubling of 8, is an octave above the first tone.

Otones 8-16 contains eight tones in the octave and eight different step sizes. The steps get smaller as the scale ascends:

harmonic ratio from 1/1 ratio in between ("step") names cents value, scale member cents value, step
8 1/1 unison, perfect prime 0.00
9:8 large whole step; Pythagorean whole step; major whole tone 203.91
9 9/8 large whole step; Pythagorean whole step; major whole tone 203.91
10:9 small whole step; 5-limit whole step; minor whole tone 182.40
10 5/4 5-limit major third 386.31
11:10 large undecimal neutral second, 4/5-tone, Ptolemy's second 165.00
11 11/8 undecimal semi-augmented fourth 551.32
12:11 small undecimal neutral second, 3/4-tone 150.64
12 3/2 just perfect fifth 701.955
13:12 large tridecimal neutral second, tridecimal 2/3 tone 138.57
13 13/8 tridecimal neutral sixth 840.53
14:13 small tridecimal neutral second; lesser tridecimal 2/3 tone 128.30
14 7/4 harmonic seventh 968.83
15:14 septimal minor second; major diatonic semitone 119.44
15 15/8 5-limit major seventh; classic major seventh 1088.27
16:15 5-limit minor second; classic minor second; minor diatonic semitone 111.73
16 2/1 perfect octave 1200.00

Compositions:

Paracelsus for Diatonic Harmonic Guitar by Dante Rosati

No Snow for Diatonic Harmonic Guitar by Dante Rosati

Retrieved from "https://en.xen.wiki/index.php?title=Otones8-16&oldid=2996"