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:~~guest~~|~~guest~~]] and made on <tt>~~2012~~-04-~~04 15~~:09:38 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2014-02-26 10:52:29 UTC</tt>.<br>

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

: The original revision id was <tt>492166238</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 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~~]].

<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 of a given [[periodic scale]]. Mike Battaglia proposed the term (a permutation of the letters of "mode) to discuss [[Fokker blocks]].

<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>

<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>

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 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 /&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"><html><head><title>Dome</title></head><body>A <strong>dome</strong> is the collection of modal variants 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) to discuss <a class="wiki_link" href="/Fokker%20blocks">Fokker blocks</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 &amp~~;~~quot~~;~~mode~~&~~amp~~;~~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>

<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>

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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:guest|guest]] and made on <tt>2012-04-04 15:09:38 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2014-02-26 10:52:29 UTC</tt>.<br>
-: The original revision id was <tt>317697486</tt>.<br>
+: The original revision id was <tt>492166238</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 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]].
+<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 of a given [[periodic scale]]. Mike Battaglia proposed the term (a permutation of the letters of "mode) to discuss [[Fokker blocks]].
-&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;
+&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 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.&lt;/span&gt;
+</pre></div>
-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 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;
+<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 the collection of modal variants of a given &lt;a class="wiki_link" href="/periodic%20scale"&gt;periodic scale&lt;/a&gt;. Mike Battaglia proposed the term (a permutation of the letters of &amp;quot;mode) to discuss &lt;a class="wiki_link" href="/Fokker%20blocks"&gt;Fokker blocks&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>
+&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 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.&lt;/span&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>