Dome: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>

: This revision was by author [[User:~~keenanpepper~~|~~keenanpepper~~]] and made on <tt>~~2011~~-11-~~14 12~~:43:13 UTC</tt>.<br>

: This revision was by author [[User:guest|guest]] and made on <tt>2012-04-04 15:09:38 UTC</tt>.<br>

: The original revision id was <tt>~~275226540~~</tt>.<br>

: The original revision id was <tt>317697486</tt>.<br>

: The revision comment was: <tt></tt><br>

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>

<h4>Original Wikitext content:</h4>

<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~~.)

<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 a collection of scales, which are equivalent up to modal rotation, which is produced by shifting the lattice coset of unison vectors around on a [[Fokker blocks|Fokker block]].

<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 the same "dome," then the playing field reduces to 7 fundamental "domes" which you can get out of the 25/24 and 81/80 Fokker block. Each dome of this block is a collection of 7 scales which are modally equivalent. However, every dome is modally independent from every other dome of the block.</span>

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>

<h4>Original HTML content:</h4>

<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 />

<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 a collection of scales, which are equivalent up to modal rotation, which is produced by shifting the lattice coset of unison vectors around on a <a class="wiki_link" href="/Fokker%20blocks">Fokker block</a>.<br />

<br />

<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 the same &quot;dome,&quot; then the playing field reduces to 7 fundamental &quot;domes&quot; which you can get out of the 25/24 and 81/80 Fokker block. Each dome of this block is a collection of 7 scales which are modally equivalent. However, every dome is modally independent from every other dome of the block.</span><br />

<br />

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>

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 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2011-11-14 12:43:13 UTC</tt>.<br>
+: This revision was by author [[User:guest|guest]] and made on <tt>2012-04-04 15:09:38 UTC</tt>.<br>
-: The original revision id was <tt>275226540</tt>.<br>
+: The original revision id was <tt>317697486</tt>.<br>
 : The revision comment was: <tt></tt><br>
 The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
 <h4>Original Wikitext content:</h4>
-<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.)
+<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 a collection of scales, which are equivalent up to modal rotation, which is produced by shifting the lattice coset of unison vectors around on a [[Fokker blocks|Fokker block]].
+&lt;span style="background-color: rgba(255,255,255,0.917969); color: #222222; font-family: arial,sans-serif;"&gt;For example, if you look at all of the scales that you can get with the 25/24 and &lt;/span&gt;&lt;span style="background-color: rgba(255,255,255,0.917969); color: #222222; font-family: arial,sans-serif;"&gt;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 the same "dome," then the playing field reduces to 7 fundamental "domes" which you can get out of the 25/24 and 81/80 Fokker block. Each dome of this block is a collection of 7 scales which are modally equivalent. However, every dome is modally independent from every other dome of the block.&lt;/span&gt;
 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>
 <h4>Original HTML content:</h4>
-<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Dome&lt;/title&gt;&lt;/head&gt;&lt;body&gt;A &lt;strong&gt;dome&lt;/strong&gt; is any &amp;quot;alternate form&amp;quot; of a scale that is not a &lt;a class="wiki_link" href="/mode"&gt;mode&lt;/a&gt;. 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 &amp;quot;domes&amp;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.)&lt;br /&gt;
+<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Dome&lt;/title&gt;&lt;/head&gt;&lt;body&gt;A &lt;strong&gt;dome&lt;/strong&gt; is a collection of scales, which are equivalent up to modal rotation, which is produced by shifting the lattice coset of unison vectors around on a &lt;a class="wiki_link" href="/Fokker%20blocks"&gt;Fokker block&lt;/a&gt;.&lt;br /&gt;
+&lt;br /&gt;
+&lt;span style="background-color: rgba(255,255,255,0.917969); color: #222222; font-family: arial,sans-serif;"&gt;For example, if you look at all of the scales that you can get with the 25/24 and &lt;/span&gt;&lt;span style="background-color: rgba(255,255,255,0.917969); color: #222222; font-family: arial,sans-serif;"&gt;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 the same &amp;quot;dome,&amp;quot; then the playing field reduces to 7 fundamental &amp;quot;domes&amp;quot; which you can get out of the 25/24 and 81/80 Fokker block. Each dome of this block is a collection of 7 scales which are modally equivalent. However, every dome is modally independent from every other dome of the block.&lt;/span&gt;&lt;br /&gt;
 &lt;br /&gt;
 The term (which is a permutation of the letters of the word &amp;quot;mode&amp;quot;) was invented by Mike Battaglia to describe the way different &lt;a class="wiki_link" href="/Fokker%20blocks"&gt;Fokker blocks&lt;/a&gt; with the same unison vectors (that are not modes) are related to each other.&lt;/body&gt;&lt;/html&gt;</pre></div>