Armodue theory: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

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: This revision was by author [[User:~~Osmiorisbendi~~|~~Osmiorisbendi~~]] and made on <tt>2011-07-13 03:~~37:46~~ UTC</tt>.<br>

: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2011-07-13 05:03:51 UTC</tt>.<br>

: The original revision id was <tt>~~241126281~~</tt>.<br>

: The original revision id was <tt>241131115</tt>.<br>

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

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=Semi-equalized Armodue=

One step of 16edo (75 cents) is nearly equal to two steps (2\31) of [[31edo]] (77.42 cents). If we take the latter as a base, we get semi-equalized Armodue. In this temperament there is inevitably a smaller microtone (eka between the notes '7#' and '8'). leading to the 16 note MOS Valentine[16] of [[Starling temperaments#Valentine|valentine temperament]]. Similarly we might use three steps of [[46edo]], 3\46, 78.26 cents, or five steps of [[77edo]], 77.92 cents.

One step of 16edo (75 cents) is nearly equal to two steps (2\31) of [[31edo]] (77.42 cents). If we take the latter as a base, we get semi-equalized Armodue. In this temperament there is inevitably a smaller microtone (eka between the notes '7#' and '8'). leading to the 16 note MOS Valentine[16] of [[Starling temperaments#Valentine temperament|valentine temperament]]. Similarly we might use three steps of [[46edo]], 3\46, 78.26 cents, or five steps of [[77edo]], 77.92 cents.

Semi-equalized Armodue provides a balance between the symmetry of the equalized system and the purity of natural intervals (intervals of semi-equalized Armodue are very pure, and at the same time it preserves the symmetry of the equalized system and its interval sizes almost unchanged).

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<h1 id="toc2"><a name="Semi-equalized Armodue"></a>Semi-equalized Armodue</h1>

<br />

One step of 16edo (75 cents) is nearly equal to two steps (2\31) of <a class="wiki_link" href="/31edo">31edo</a> (77.42 cents). If we take the latter as a base, we get semi-equalized Armodue. In this temperament there is inevitably a smaller microtone (eka between the notes '7#' and '8'). leading to the 16 note MOS Valentine[16] of <a class="wiki_link" href="/Starling%20temperaments#Valentine">valentine temperament</a>. Similarly we might use three steps of <a class="wiki_link" href="/46edo">46edo</a>, 3\46, 78.26 cents, or five steps of <a class="wiki_link" href="/77edo">77edo</a>, 77.92 cents.<br />

One step of 16edo (75 cents) is nearly equal to two steps (2\31) of <a class="wiki_link" href="/31edo">31edo</a> (77.42 cents). If we take the latter as a base, we get semi-equalized Armodue. In this temperament there is inevitably a smaller microtone (eka between the notes '7#' and '8'). leading to the 16 note MOS Valentine[16] of <a class="wiki_link" href="/Starling%20temperaments#Valentine temperament">valentine temperament</a>. Similarly we might use three steps of <a class="wiki_link" href="/46edo">46edo</a>, 3\46, 78.26 cents, or five steps of <a class="wiki_link" href="/77edo">77edo</a>, 77.92 cents.<br />

<br />

Semi-equalized Armodue provides a balance between the symmetry of the equalized system and the purity of natural intervals (intervals of semi-equalized Armodue are very pure, and at the same time it preserves the symmetry of the equalized system and its interval sizes almost unchanged).<br />

@@ 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:Osmiorisbendi|Osmiorisbendi]] and made on <tt>2011-07-13 03:37:46 UTC</tt>.<br>
+: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2011-07-13 05:03:51 UTC</tt>.<br>
-: The original revision id was <tt>241126281</tt>.<br>
+: The original revision id was <tt>241131115</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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 =Semi-equalized Armodue=
-One step of 16edo (75 cents) is nearly equal to two steps (2\31) of [[31edo]] (77.42 cents). If we take the latter as a base, we get semi-equalized Armodue. In this temperament there is inevitably a smaller microtone (eka between the notes '7#' and '8'). leading to the 16 note MOS Valentine[16] of [[Starling temperaments#Valentine|valentine temperament]]. Similarly we might use three steps of [[46edo]], 3\46, 78.26 cents, or five steps of [[77edo]], 77.92 cents.
+One step of 16edo (75 cents) is nearly equal to two steps (2\31) of [[31edo]] (77.42 cents). If we take the latter as a base, we get semi-equalized Armodue. In this temperament there is inevitably a smaller microtone (eka between the notes '7#' and '8'). leading to the 16 note MOS Valentine[16] of [[Starling temperaments#Valentine temperament|valentine temperament]]. Similarly we might use three steps of [[46edo]], 3\46, 78.26 cents, or five steps of [[77edo]], 77.92 cents.
 Semi-equalized Armodue provides a balance between the symmetry of the equalized system and the purity of natural intervals (intervals of semi-equalized Armodue are very pure, and at the same time it preserves the symmetry of the equalized system and its interval sizes almost unchanged).
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 &lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="Semi-equalized Armodue"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Semi-equalized Armodue&lt;/h1&gt;
   &lt;br /&gt;
-One step of 16edo (75 cents) is nearly equal to two steps (2\31) of &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt; (77.42 cents). If we take the latter as a base, we get semi-equalized Armodue. In this temperament there is inevitably a smaller microtone (eka between the notes '7#' and '8'). leading to the 16 note MOS Valentine[16] of &lt;a class="wiki_link" href="/Starling%20temperaments#Valentine"&gt;valentine temperament&lt;/a&gt;. Similarly we might use three steps of &lt;a class="wiki_link" href="/46edo"&gt;46edo&lt;/a&gt;, 3\46, 78.26 cents, or five steps of &lt;a class="wiki_link" href="/77edo"&gt;77edo&lt;/a&gt;, 77.92 cents.&lt;br /&gt;
+One step of 16edo (75 cents) is nearly equal to two steps (2\31) of &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt; (77.42 cents). If we take the latter as a base, we get semi-equalized Armodue. In this temperament there is inevitably a smaller microtone (eka between the notes '7#' and '8'). leading to the 16 note MOS Valentine[16] of &lt;a class="wiki_link" href="/Starling%20temperaments#Valentine temperament"&gt;valentine temperament&lt;/a&gt;. Similarly we might use three steps of &lt;a class="wiki_link" href="/46edo"&gt;46edo&lt;/a&gt;, 3\46, 78.26 cents, or five steps of &lt;a class="wiki_link" href="/77edo"&gt;77edo&lt;/a&gt;, 77.92 cents.&lt;br /&gt;
 &lt;br /&gt;
 Semi-equalized Armodue provides a balance between the symmetry of the equalized system and the purity of natural intervals (intervals of semi-equalized Armodue are very pure, and at the same time it preserves the symmetry of the equalized system and its interval sizes almost unchanged).&lt;br /&gt;