Wikispaces>Andrew_Heathwaite |
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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | #redirect [[8afdo]] |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
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| : This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-03-25 19:52:15 UTC</tt>.<br>
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| : The original revision id was <tt>214110848</tt>.<br>
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| : The revision comment was: <tt></tt><br>
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| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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| <h4>Original Wikitext content:</h4>
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| <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.
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| Otones 8-16 contains eight tones in the octave and eight different step sizes. The steps get smaller as the scale ascends:
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| || harmonic || ratio from 1/1 || ratio in between ("step") || names || cents value, scale member || cents value, step ||
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| || 8 || 1/1 || || unison, perfect prime || 0.00 || ||
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| || || || 9:8 || large whole step; Pythagorean whole step; major whole tone || || 203.91 ||
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| || 9 || 9/8 || || large whole step; Pythagorean whole step; major whole tone || 203.91 || ||
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| || || || 10:9 || small whole step; 5-limit whole step; minor whole tone || || 182.40 ||
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| || 10 || 5/4 || || 5-limit major third || 386.31 || ||
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| || || || 11:10 || large undecimal neutral second, 4/5-tone, Ptolemy's second || || 165.00 ||
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| || 11 || 11/8 || || undecimal semi-augmented fourth || 551.32 || ||
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| || || || 12:11 || small undecimal neutral second, 3/4-tone || || 150.64 ||
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| || 12 || 3/2 || || just perfect fifth || 701.955 || ||
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| || || || 13:12 || large tridecimal neutral second, tridecimal 2/3 tone || || 138.57 ||
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| || 13 || 13/8 || || tridecimal neutral sixth || 840.53 || ||
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| || || || 14:13 || small tridecimal neutral second; lesser tridecimal 2/3 tone || || 128.30 ||
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| || 14 || 7/4 || || harmonic seventh || 968.83 || ||
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| || || || 15:14 || septimal minor second; major diatonic semitone || || 119.44 ||
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| || 15 || 15/8 || || 5-limit major seventh; classic major seventh || 1088.27 || ||
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| || || || 16:15 || 5-limit minor second; classic minor second; minor diatonic semitone || || 111.73 ||
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| || 16 || 2/1 || || perfect octave || 1200.00 || ||</pre></div>
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| <h4>Original HTML content:</h4>
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| <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"><html><head><title>otones8-16</title></head><body>&quot;Otones 8-16&quot; refers to a scale generated by taking the 8th through 16th overtone over some fundamental. Dante Rosati calls this the &quot;Diatonic Harmonic Series Scale&quot; and Denny Genovese calls this &quot;Mode 8 of the Harmonic Series&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.<br />
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| <br />
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| Otones 8-16 contains eight tones in the octave and eight different step sizes. The steps get smaller as the scale ascends:<br />
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| <br />
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| <table class="wiki_table">
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| <tr>
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| <td>harmonic<br />
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| </td>
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| <td>ratio from 1/1<br />
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| </td>
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| <td>ratio in between (&quot;step&quot;)<br />
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| </td>
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| <td>names<br />
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| </td>
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| <td>cents value, scale member<br />
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| </td>
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| <td>cents value, step<br />
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| </td>
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| </tr>
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| <tr>
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| <td>8<br />
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| </td>
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| <td>1/1<br />
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| </td>
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| <td><br />
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| </td>
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| <td>unison, perfect prime<br />
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| </td>
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| <td>0.00<br />
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| </td>
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| <td><br />
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| </td>
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| </tr>
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| <tr>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td>9:8<br />
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| </td>
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| <td>large whole step; Pythagorean whole step; major whole tone<br />
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| </td>
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| <td><br />
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| </td>
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| <td>203.91<br />
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| </td>
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| </tr>
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| <tr>
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| <td>9<br />
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| </td>
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| <td>9/8<br />
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| </td>
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| <td><br />
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| </td>
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| <td>large whole step; Pythagorean whole step; major whole tone<br />
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| </td>
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| <td>203.91<br />
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| </td>
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| <td><br />
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| </td>
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| </tr>
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| <tr>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td>10:9<br />
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| </td>
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| <td>small whole step; 5-limit whole step; minor whole tone<br />
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| </td>
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| <td><br />
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| </td>
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| <td>182.40<br />
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| </td>
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| </tr>
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| <tr>
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| <td>10<br />
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| </td>
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| <td>5/4<br />
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| </td>
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| <td><br />
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| </td>
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| <td>5-limit major third<br />
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| </td>
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| <td>386.31<br />
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| </td>
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| <td><br />
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| </td>
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| </tr>
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| <tr>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td>11:10<br />
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| </td>
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| <td>large undecimal neutral second, 4/5-tone, Ptolemy's second<br />
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| </td>
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| <td><br />
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| </td>
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| <td>165.00<br />
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| </td>
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| </tr>
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| <tr>
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| <td>11<br />
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| </td>
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| <td>11/8<br />
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| </td>
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| <td><br />
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| </td>
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| <td>undecimal semi-augmented fourth<br />
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| </td>
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| <td>551.32<br />
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| </td>
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| <td><br />
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| </td>
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| </tr>
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| <tr>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td>12:11<br />
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| </td>
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| <td>small undecimal neutral second, 3/4-tone<br />
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| </td>
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| <td><br />
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| </td>
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| <td>150.64<br />
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| </td>
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| </tr>
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| <tr>
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| <td>12<br />
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| </td>
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| <td>3/2<br />
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| </td>
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| <td><br />
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| </td>
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| <td>just perfect fifth<br />
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| </td>
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| <td>701.955<br />
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| </td>
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| <td><br />
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| </td>
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| </tr>
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| <tr>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td>13:12<br />
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| </td>
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| <td>large tridecimal neutral second, tridecimal 2/3 tone<br />
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| </td>
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| <td><br />
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| </td>
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| <td>138.57<br />
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| </td>
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| </tr>
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| <tr>
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| <td>13<br />
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| </td>
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| <td>13/8<br />
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| </td>
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| <td><br />
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| </td>
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| <td>tridecimal neutral sixth<br />
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| </td>
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| <td>840.53<br />
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| </td>
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| <td><br />
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| </td>
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| </tr>
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| <tr>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td>14:13<br />
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| </td>
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| <td>small tridecimal neutral second; lesser tridecimal 2/3 tone<br />
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| </td>
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| <td><br />
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| </td>
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| <td>128.30<br />
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| </td>
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| </tr>
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| <tr>
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| <td>14<br />
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| </td>
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| <td>7/4<br />
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| </td>
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| <td><br />
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| </td>
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| <td>harmonic seventh<br />
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| </td>
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| <td>968.83<br />
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| </td>
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| <td><br />
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| </td>
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| </tr>
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| <tr>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td>15:14<br />
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| </td>
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| <td>septimal minor second; major diatonic semitone<br />
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| </td>
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| <td><br />
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| </td>
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| <td>119.44<br />
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| </td>
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| </tr>
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| <tr>
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| <td>15<br />
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| </td>
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| <td>15/8<br />
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| </td>
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| <td><br />
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| </td>
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| <td>5-limit major seventh; classic major seventh<br />
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| </td>
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| <td>1088.27<br />
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| </td>
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| <td><br />
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| </td>
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| </tr>
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| <tr>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td>16:15<br />
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| </td>
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| <td>5-limit minor second; classic minor second; minor diatonic semitone<br />
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| </td>
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| <td><br />
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| </td>
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| <td>111.73<br />
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| </td>
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| </tr>
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| <tr>
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| <td>16<br />
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| </td>
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| <td>2/1<br />
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| </td>
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| <td><br />
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| </td>
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| <td>perfect octave<br />
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| </td>
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| <td>1200.00<br />
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| </td>
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| <td><br />
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| </td>
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| </tr>
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| </table>
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| </body></html></pre></div>
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