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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | {{About|a collection of scales|a type of scale|Modal union}} |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | A '''dome''' is a collection of [[Periodic scale #Rotations|rotations]] of a scale that comes from a given [[Fokker block]] recipe. [[Mike Battaglia]] coined the term (a permutation of the letters of "mode"). |
| : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2014-05-13 12:19:00 UTC</tt>.<br>
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| : The original revision id was <tt>508620762</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">A **dome** is the collection of modal variants, ie of [[Periodic scale#Definition-Rotations|rotations]], of a given [[periodic scale]]. Mike Battaglia proposed the term (a permutation of the letters of "mode") to discuss [[Fokker blocks]].
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| <span style="background-color: rgba(255,255,255,0.917969); color: #222222; font-family: arial,sans-serif;">For example, if you look at all of the scales that you can get with the 25/24 and </span><span style="background-color: rgba(255,255,255,0.917969); color: #222222; font-family: arial,sans-serif;">81/80 unison vectors which contain 1/1, you'll find that you get 49 different scales. If we consider scales which are modally equivalent to be in the same dome, then the playing field reduces to seven domes obtainable from the 25/24 and 81/80 Fokker block. Each dome of this block is a collection of seven scales which are modally equivalent. However, every dome is modally independent from every other dome of the block; the domes partition the set of scales of the block into disjoint sets.</span></pre></div>
| | For example, if you look at all Fokker block scales that you can get with the 25/24 and 81/80 chromas, you will find that you get 49 different scales. If we consider scales which are modally equivalent to be in the same dome, then the playing field reduces to seven (heptatonic) domes obtainable from the 25/24 and 81/80 [[Fokker arena]]. Each dome of this arena is a collection of seven periodic scales which are modally equivalent, which is to say, rotations of each other. However, every dome is independent from every other dome of the arena; the domes partition the set of scales of the arena into disjoint sets. |
| <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>Dome</title></head><body>A <strong>dome</strong> is the collection of modal variants, ie of <a class="wiki_link" href="/Periodic%20scale#Definition-Rotations">rotations</a>, of a given <a class="wiki_link" href="/periodic%20scale">periodic scale</a>. Mike Battaglia proposed the term (a permutation of the letters of &quot;mode&quot;) to discuss <a class="wiki_link" href="/Fokker%20blocks">Fokker blocks</a>.<br />
| | While we have defined a dome as a set, it should be noted it has a natural cyclic group structure. |
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| <span style="background-color: rgba(255,255,255,0.917969); color: #222222; font-family: arial,sans-serif;">For example, if you look at all of the scales that you can get with the 25/24 and </span><span style="background-color: rgba(255,255,255,0.917969); color: #222222; font-family: arial,sans-serif;">81/80 unison vectors which contain 1/1, you'll find that you get 49 different scales. If we consider scales which are modally equivalent to be in the same dome, then the playing field reduces to seven domes obtainable from the 25/24 and 81/80 Fokker block. Each dome of this block is a collection of seven scales which are modally equivalent. However, every dome is modally independent from every other dome of the block; the domes partition the set of scales of the block into disjoint sets.</span></body></html></pre></div>
| | [[Category:Scale]] |
| | [[Category:Math]] |
| | [[Category:Fokker block]] |
| | [[Category:Terms]] |
- This page is about a collection of scales. For a type of scale, see Modal union.
A dome is a collection of rotations of a scale that comes from a given Fokker block recipe. Mike Battaglia coined the term (a permutation of the letters of "mode").
For example, if you look at all Fokker block scales that you can get with the 25/24 and 81/80 chromas, you will find that you get 49 different scales. If we consider scales which are modally equivalent to be in the same dome, then the playing field reduces to seven (heptatonic) domes obtainable from the 25/24 and 81/80 Fokker arena. Each dome of this arena is a collection of seven periodic scales which are modally equivalent, which is to say, rotations of each other. However, every dome is independent from every other dome of the arena; the domes partition the set of scales of the arena into disjoint sets.
While we have defined a dome as a set, it should be noted it has a natural cyclic group structure.