Omnitetrachordality: 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~~-06~~-27~~ 13:57:44 UTC</tt>.<br>

: This revision was by author [[User:spt3125|spt3125]] and made on <tt>2016-08-06 13:49:43 UTC</tt>.<br>

: The original revision id was <tt>~~348622440~~</tt>.<br>

: The original revision id was <tt>588867276</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>

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E F G A B C D E = (E F G A) + 9/8 + (B C D E) (both tetrachords are sLL)

F G A B C D E F = 9/8 + (G A B C) + (C D E F) (both tetrachords are LLs)

G A B C D E F G = 9/8 + (A B C D) + (D E F G) (both tetrachords are LsL) ~~OR ALTERNATIVELY~~ (G A B C) + (C D E F) + 9/8 (both tetrachords are LLs)

G A B C D E F G = 9/8 + (A B C D) + (D E F G) (both tetrachords are LsL) //or alternatively// (G A B C) + (C D E F) + 9/8 (both tetrachords are LLs)

A B C D E F G A = 9/8 + (B C D E) + (E F G A) (both tetrachords are sLL) ~~OR ALTERNATIVELY~~ (A B C D) + (D E F G) + 9/8 (both tetrachords are LsL)

A B C D E F G A = 9/8 + (B C D E) + (E F G A) (both tetrachords are sLL) //or alternatively// (A B C D) + (D E F G) + 9/8 (both tetrachords are LsL)

B C D E F G A B = (B C D E) + (E F G A) + 9/8 (both tetrachords are sLL)

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(sLss)(sLss)(ss)

In this case, each 4/3 is spanned by a 5-note scale segment rather than a 4-note one, so they are more properly called "pentachords". However, the property is still called "omnitetrachordality" (unless someone proposes a better name and it sticks). ~~This is why this specific MODMOS of pajara was named the "pentachordal decatonic scale" by~~ [[~~Paul Erlich~~]].</pre></div>

In this case, each 4/3 is spanned by a 5-note scale segment rather than a 4-note one, so they are more properly called "pentachords". This is why this specific MODMOS of pajara was named the "pentachordal decatonic scale" by [[Paul Erlich]] (who is believed to have originated the concept of omnitetrachordality, circa 2002). However, the property is still called "omnitetrachordality" (unless someone proposes a better name and it sticks).

See also [[Gallery of omnitetrachordal scales]].</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>Omnitetrachordality</title></head><body>A scale is <strong>omnitetrachordal</strong> if any mode of the scale (that is, any particular octave span of the infinite scale) can be expressed as two identical sequences of steps (&quot;tetrachords&quot;) each spanning <a class="wiki_link" href="/4_3">4/3</a>, plus a <a class="wiki_link" href="/9_8">9/8</a> that may or may not be divided into smaller steps. The definition can of course be generalized to intervals of quasi-equivalence other than 4/3, but the original version is with 4/3.<br />

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E F G A B C D E = (E F G A) + 9/8 + (B C D E) (both tetrachords are sLL)<br />

F G A B C D E F = 9/8 + (G A B C) + (C D E F) (both tetrachords are LLs)<br />

G A B C D E F G = 9/8 + (A B C D) + (D E F G) (both tetrachords are LsL) ~~OR ALTERNATIVELY~~ (G A B C) + (C D E F) + 9/8 (both tetrachords are LLs)<br />

G A B C D E F G = 9/8 + (A B C D) + (D E F G) (both tetrachords are LsL) <em>or alternatively</em> (G A B C) + (C D E F) + 9/8 (both tetrachords are LLs)<br />

A B C D E F G A = 9/8 + (B C D E) + (E F G A) (both tetrachords are sLL) ~~OR ALTERNATIVELY~~ (A B C D) + (D E F G) + 9/8 (both tetrachords are LsL)<br />

A B C D E F G A = 9/8 + (B C D E) + (E F G A) (both tetrachords are sLL) <em>or alternatively</em> (A B C D) + (D E F G) + 9/8 (both tetrachords are LsL)<br />

B C D E F G A B = (B C D E) + (E F G A) + 9/8 (both tetrachords are sLL)<br />

<br />

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(sLss)(sLss)(ss)<br />

<br />

In this case, each 4/3 is spanned by a 5-note scale segment rather than a 4-note one, so they are more properly called &quot;pentachords&quot;. However, the property is still called &quot;omnitetrachordality&quot; (unless someone proposes a better name and it sticks). ~~This is why this specific MODMOS of pajara was named the~~ &~~amp~~;~~quot~~;~~pentachordal decatonic scale~~&~~amp~~;~~quot~~; by <a class="wiki_link" href="/~~Paul~~%~~20Erlich~~">~~Paul Erlich~~</a>.</body></html></pre></div>

In this case, each 4/3 is spanned by a 5-note scale segment rather than a 4-note one, so they are more properly called &quot;pentachords&quot;. This is why this specific MODMOS of pajara was named the &quot;pentachordal decatonic scale&quot; by <a class="wiki_link" href="/Paul%20Erlich">Paul Erlich</a> (who is believed to have originated the concept of omnitetrachordality, circa 2002). However, the property is still called &quot;omnitetrachordality&quot; (unless someone proposes a better name and it sticks).<br />

<br />

See also <a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales">Gallery of omnitetrachordal scales</a>.</body></html></pre></div>

@@ Line 1: / Line 1: @@
 <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>2012-06-27 13:57:44 UTC</tt>.<br>
+: This revision was by author [[User:spt3125|spt3125]] and made on <tt>2016-08-06 13:49:43 UTC</tt>.<br>
-: The original revision id was <tt>348622440</tt>.<br>
+: The original revision id was <tt>588867276</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>
@@ Line 14: / Line 14: @@
 E F G A B C D E = (E F G A) + 9/8 + (B C D E) (both tetrachords are sLL)
 F G A B C D E F = 9/8 + (G A B C) + (C D E F) (both tetrachords are LLs)
-G A B C D E F G = 9/8 + (A B C D) + (D E F G) (both tetrachords are LsL) OR ALTERNATIVELY (G A B C) + (C D E F) + 9/8 (both tetrachords are LLs)
+G A B C D E F G = 9/8 + (A B C D) + (D E F G) (both tetrachords are LsL) //or alternatively// (G A B C) + (C D E F) + 9/8 (both tetrachords are LLs)
-A B C D E F G A = 9/8 + (B C D E) + (E F G A) (both tetrachords are sLL) OR ALTERNATIVELY (A B C D) + (D E F G) + 9/8 (both tetrachords are LsL)
+A B C D E F G A = 9/8 + (B C D E) + (E F G A) (both tetrachords are sLL) //or alternatively// (A B C D) + (D E F G) + 9/8 (both tetrachords are LsL)
 B C D E F G A B = (B C D E) + (E F G A) + 9/8 (both tetrachords are sLL)
@@ Line 33: / Line 33: @@
 (sLss)(sLss)(ss)
-In this case, each 4/3 is spanned by a 5-note scale segment rather than a 4-note one, so they are more properly called "pentachords". However, the property is still called "omnitetrachordality" (unless someone proposes a better name and it sticks). This is why this specific MODMOS of pajara was named the "pentachordal decatonic scale" by [[Paul Erlich]].</pre></div>
+In this case, each 4/3 is spanned by a 5-note scale segment rather than a 4-note one, so they are more properly called "pentachords". This is why this specific MODMOS of pajara was named the "pentachordal decatonic scale" by [[Paul Erlich]] (who is believed to have originated the concept of omnitetrachordality, circa 2002).  However, the property is still called "omnitetrachordality" (unless someone proposes a better name and it sticks).
+See also [[Gallery of omnitetrachordal scales]].</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;Omnitetrachordality&lt;/title&gt;&lt;/head&gt;&lt;body&gt;A scale is &lt;strong&gt;omnitetrachordal&lt;/strong&gt; if any mode of the scale (that is, any particular octave span of the infinite scale) can be expressed as two identical sequences of steps (&amp;quot;tetrachords&amp;quot;) each spanning &lt;a class="wiki_link" href="/4_3"&gt;4/3&lt;/a&gt;, plus a &lt;a class="wiki_link" href="/9_8"&gt;9/8&lt;/a&gt; that may or may not be divided into smaller steps. The definition can of course be generalized to intervals of quasi-equivalence other than 4/3, but the original version is with 4/3.&lt;br /&gt;
@@ Line 43: / Line 45: @@
 E F G A B C D E = (E F G A) + 9/8 + (B C D E) (both tetrachords are sLL)&lt;br /&gt;
 F G A B C D E F = 9/8 + (G A B C) + (C D E F) (both tetrachords are LLs)&lt;br /&gt;
-G A B C D E F G = 9/8 + (A B C D) + (D E F G) (both tetrachords are LsL) OR ALTERNATIVELY (G A B C) + (C D E F) + 9/8 (both tetrachords are LLs)&lt;br /&gt;
+G A B C D E F G = 9/8 + (A B C D) + (D E F G) (both tetrachords are LsL) &lt;em&gt;or alternatively&lt;/em&gt; (G A B C) + (C D E F) + 9/8 (both tetrachords are LLs)&lt;br /&gt;
-A B C D E F G A = 9/8 + (B C D E) + (E F G A) (both tetrachords are sLL) OR ALTERNATIVELY (A B C D) + (D E F G) + 9/8 (both tetrachords are LsL)&lt;br /&gt;
+A B C D E F G A = 9/8 + (B C D E) + (E F G A) (both tetrachords are sLL) &lt;em&gt;or alternatively&lt;/em&gt; (A B C D) + (D E F G) + 9/8 (both tetrachords are LsL)&lt;br /&gt;
 B C D E F G A B = (B C D E) + (E F G A) + 9/8 (both tetrachords are sLL)&lt;br /&gt;
 &lt;br /&gt;
@@ Line 62: / Line 64: @@
 (sLss)(sLss)(ss)&lt;br /&gt;
 &lt;br /&gt;
-In this case, each 4/3 is spanned by a 5-note scale segment rather than a 4-note one, so they are more properly called &amp;quot;pentachords&amp;quot;. However, the property is still called &amp;quot;omnitetrachordality&amp;quot; (unless someone proposes a better name and it sticks). This is why this specific MODMOS of pajara was named the &amp;quot;pentachordal decatonic scale&amp;quot; by &lt;a class="wiki_link" href="/Paul%20Erlich"&gt;Paul Erlich&lt;/a&gt;.&lt;/body&gt;&lt;/html&gt;</pre></div>
+In this case, each 4/3 is spanned by a 5-note scale segment rather than a 4-note one, so they are more properly called &amp;quot;pentachords&amp;quot;. This is why this specific MODMOS of pajara was named the &amp;quot;pentachordal decatonic scale&amp;quot; by &lt;a class="wiki_link" href="/Paul%20Erlich"&gt;Paul Erlich&lt;/a&gt; (who is believed to have originated the concept of omnitetrachordality, circa 2002).  However, the property is still called &amp;quot;omnitetrachordality&amp;quot; (unless someone proposes a better name and it sticks).&lt;br /&gt;
+&lt;br /&gt;
+See also &lt;a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales"&gt;Gallery of omnitetrachordal scales&lt;/a&gt;.&lt;/body&gt;&lt;/html&gt;</pre></div>