Otones8-16
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"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:===
[[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]]Original HTML content:
<html><head><title>otones8-16</title></head><body>"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.<br />
<br />
Otones 8-16 contains eight tones in the octave and eight different step sizes. The steps get smaller as the scale ascends:<br />
<br />
<table class="wiki_table">
<tr>
<td>harmonic<br />
</td>
<td>ratio from 1/1<br />
</td>
<td>ratio in between ("step")<br />
</td>
<td>names<br />
</td>
<td>cents value, scale member<br />
</td>
<td>cents value, step<br />
</td>
</tr>
<tr>
<td>8<br />
</td>
<td>1/1<br />
</td>
<td><br />
</td>
<td>unison, perfect prime<br />
</td>
<td>0.00<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td>9:8<br />
</td>
<td>large whole step; Pythagorean whole step; major whole tone<br />
</td>
<td><br />
</td>
<td>203.91<br />
</td>
</tr>
<tr>
<td>9<br />
</td>
<td>9/8<br />
</td>
<td><br />
</td>
<td>large whole step; Pythagorean whole step; major whole tone<br />
</td>
<td>203.91<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td>10:9<br />
</td>
<td>small whole step; 5-limit whole step; minor whole tone<br />
</td>
<td><br />
</td>
<td>182.40<br />
</td>
</tr>
<tr>
<td>10<br />
</td>
<td>5/4<br />
</td>
<td><br />
</td>
<td>5-limit major third<br />
</td>
<td>386.31<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td>11:10<br />
</td>
<td>large undecimal neutral second, 4/5-tone, Ptolemy's second<br />
</td>
<td><br />
</td>
<td>165.00<br />
</td>
</tr>
<tr>
<td>11<br />
</td>
<td>11/8<br />
</td>
<td><br />
</td>
<td>undecimal semi-augmented fourth<br />
</td>
<td>551.32<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td>12:11<br />
</td>
<td>small undecimal neutral second, 3/4-tone<br />
</td>
<td><br />
</td>
<td>150.64<br />
</td>
</tr>
<tr>
<td>12<br />
</td>
<td>3/2<br />
</td>
<td><br />
</td>
<td>just perfect fifth<br />
</td>
<td>701.955<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td>13:12<br />
</td>
<td>large tridecimal neutral second, tridecimal 2/3 tone<br />
</td>
<td><br />
</td>
<td>138.57<br />
</td>
</tr>
<tr>
<td>13<br />
</td>
<td>13/8<br />
</td>
<td><br />
</td>
<td>tridecimal neutral sixth<br />
</td>
<td>840.53<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td>14:13<br />
</td>
<td>small tridecimal neutral second; lesser tridecimal 2/3 tone<br />
</td>
<td><br />
</td>
<td>128.30<br />
</td>
</tr>
<tr>
<td>14<br />
</td>
<td>7/4<br />
</td>
<td><br />
</td>
<td>harmonic seventh<br />
</td>
<td>968.83<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td>15:14<br />
</td>
<td>septimal minor second; major diatonic semitone<br />
</td>
<td><br />
</td>
<td>119.44<br />
</td>
</tr>
<tr>
<td>15<br />
</td>
<td>15/8<br />
</td>
<td><br />
</td>
<td>5-limit major seventh; classic major seventh<br />
</td>
<td>1088.27<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td>16:15<br />
</td>
<td>5-limit minor second; classic minor second; minor diatonic semitone<br />
</td>
<td><br />
</td>
<td>111.73<br />
</td>
</tr>
<tr>
<td>16<br />
</td>
<td>2/1<br />
</td>
<td><br />
</td>
<td>perfect octave<br />
</td>
<td>1200.00<br />
</td>
<td><br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:0:<h3> --><h3 id="toc0"><a name="x--Compositions:"></a><!-- ws:end:WikiTextHeadingRule:0 -->Compositions:</h3>
<a class="wiki_link_ext" href="http://www.youtube.com/watch?v=FlwN7qSGz9U" rel="nofollow">Paracelsus for Diatonic Harmonic Guitar by Dante Rosati</a><br />
<a class="wiki_link_ext" href="http://www.youtube.com/watch?v=U6ElPRoIZak" rel="nofollow">No Snow for Diatonic Harmonic Guitar by Dante Rosati</a></body></html>