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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:keenanpepper|keenanpepper]] and made on <tt>2011-11-14 12:43:13 UTC</tt>.<br>
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| : The original revision id was <tt>275226540</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 any "alternate form" of a scale that is not a [[mode]]. It might consist of the same steps in a different cyclic order, or it might consist of a different set of steps but very similar interval inventory. To be called "domes", however, two scales must be very closely related; so closely related that it's better to think of them as different versions of the same scale. (The term is thus subjective, and really describes how the writer is thinking of some scales rather than anything about the scales themselves.)
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| The term (which is a permutation of the letters of the word "mode") was invented by Mike Battaglia to describe the way different [[Fokker blocks]] with the same unison vectors (that are not modes) are related to each other.</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 any &quot;alternate form&quot; of a scale that is not a <a class="wiki_link" href="/mode">mode</a>. It might consist of the same steps in a different cyclic order, or it might consist of a different set of steps but very similar interval inventory. To be called &quot;domes&quot;, however, two scales must be very closely related; so closely related that it's better to think of them as different versions of the same scale. (The term is thus subjective, and really describes how the writer is thinking of some scales rather than anything about the scales themselves.)<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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| The term (which is a permutation of the letters of the word &quot;mode&quot;) was invented by Mike Battaglia to describe the way different <a class="wiki_link" href="/Fokker%20blocks">Fokker blocks</a> with the same unison vectors (that are not modes) are related to each other.</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.