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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | '''Singtervals''' is a series of [[Ear training|ear-training]] exercises originated by [[Andrew Heathwaite]] around 2011. |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | [[File:9-limit Singtervals.png|thumb]] |
| : This revision was by author [[User:xenjacob|xenjacob]] and made on <tt>2014-11-30 22:32:14 UTC</tt>.<br>
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| : The original revision id was <tt>533247350</tt>.<br> | | == A rundown of 9-odd-limit Singtervals == |
| : The revision comment was: <tt></tt><br>
| | * The order of [[interval]]s as they correspond to the chart begin going down the left column, and back up from the bottom of the right column. This way, octave inversions of intervals are lined up next to one another. |
| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
| | * Whenever the [[solfege]] appears, that is referring to a transposition of the harmonic series. do = 1/1, re = 9/8, mi = 5/4, so = 3/2, ta = 7/4. |
| <h4>Original Wikitext content:</h4>
| | * The transpositions of do are by subharmonic intervals. (The [[subharmonic series]] is the harmonic series turned upside down i.e. 1/1, 1/2, 1/3, 1/4, etc.) |
| <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">[[media type="custom" key="26967518"]]
| | * This is to facilitate changes of function of the 1/1. For example, in the first singterval, labeled [[10/9]], the tonic of the harmonic series is transposed to the 9th subharmonic, or 16/9, so that 1/1 functions as 9/8 (re) and 10/9 functions as 5/4 (mi). |
| [[file:singtervals9 visualization.pdf]]</pre></div> | | * This exercise is exhaustive of the [[9-odd-limit]], i.e. it contains every possible (octave-reduced) interval that can be expressed by a fraction between whole numbers 1 through 9. |
| <h4>Original HTML content:</h4>
| | * The resulting intervals ''between'' the intervals being sung can be calculated by dividing the consecutive fractions. For example, the microtone between 10/9 and 9/8 is [[81/80]]. Other intervals encountered include 64/63, 36/35, 25/24, 28/27, 21/20, and 49/48. Since all of these intervals are of the form (''n'' + 1)/''n'', they fall within the category of [[superparticular interval]]s. |
| <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>singtervals</title></head><body><!-- ws:start:WikiTextMediaRule:0:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/custom/26967518?h=0&amp;w=0&quot; class=&quot;WikiMedia WikiMediaCustom&quot; id=&quot;wikitext@@media@@type=&amp;quot;custom&amp;quot; key=&amp;quot;26967518&amp;quot;&quot; title=&quot;Custom Media&quot;/&gt; --><iframe width="100%" height="166" scrolling="no" frameborder="no" src="https://w.soundcloud.com/player/?url=https%3A//api.soundcloud.com/tracks/70692657&amp;color=ff5500&amp;auto_play=false&amp;hide_related=false&amp;show_comments=true&amp;show_user=true&amp;show_reposts=false"></iframe><!-- ws:end:WikiTextMediaRule:0 --><br />
| | * A handy way to convert a ratio ''a''/''b'' to cents is to Google <code>log(a/b)/log(2)*1200</code>. For example, typing <code>log(10/9)/log(2)*1200</code> into Google yields 182.403712134! |
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| | == 9-odd-limit singtervals == |
| | <soundcloud>https://soundcloud.com/andrew_heathwaite/9-limit-singtervals</soundcloud> |
| | |
| | [[Category:todo:intro]] |
| | [[File:Singtervals9 visualization.pdf|thumb]] |
| | [https://soundcloud.com/metaclown/jacob-barton-singing-andrew-heathwaites-singtervals-9limit Jacob Barton singing 9-limit singtervals] |
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| | == And beyond == |
| | <soundcloud>https://soundcloud.com/andrew_heathwaite/11-limit-singtervals</soundcloud> |
| | [https://archive.org/details/singtervals-through-15-limit-pure Casey Hale's 15-odd-limit Singtervals notated in Revo Sagittal] |