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:hstraub|hstraub]] and made on <tt>2013-07-16 08:06:17 UTC</tt>.

: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2013-07-16 08:07:24 UTC</tt>.

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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%20temperament|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).

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.

||~ Armodue note ||~ cents (16edo) ||~ cents (semi-equalized Armodue based on [[31edo]]) ||

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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%20temperament">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.

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).

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.

@@ 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:hstraub|hstraub]] and made on <tt>2013-07-16 08:06:17 UTC</tt>.<br>
+: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2013-07-16 08:07:24 UTC</tt>.<br>
-: The original revision id was <tt>441460282</tt>.<br>
+: The original revision id was <tt>441460332</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 82: / Line 82: @@
 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%20temperament|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).
+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.
 ||~ Armodue note ||~ cents (16edo) ||~ cents (semi-equalized Armodue based on [[31edo]]) ||
@@ Line 369: / Line 369: @@
 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%20temperament"&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;
+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;
 &lt;br /&gt;