49ed6: 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:MasonGreen1|MasonGreen1]] and made on <tt>2016-04-~~18 02~~:30:10 UTC</tt>.<br>

: This revision was by author [[User:MasonGreen1|MasonGreen1]] and made on <tt>2016-04-20 15:40:26 UTC</tt>.<br>

: The original revision id was <tt>~~580364841~~</tt>.<br>

: The original revision id was <tt>580722411</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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<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">**49ed6** divides the just 6:1 into 49 equal parts, resulting in a step size of about 63.3053 cents and an octave approximately 3 cents sharp. It is a stretched version of [[19edo]] and extremely close to the [[The Riemann Zeta Function and Tuning|zeta peak]], thus minimizing relative error as much as possible. Because 19edo itself is a flat-tending system, stretching the octave by this much improves the overall tuning accuracy.

The fifth is ~ 696.36 cents; about 1/4 of a cent flatter than the fifth of quarter-comma meantone, or half a cent flatter than the fifth of [[31edo]]. Minor thirds are still excellent, only slightly less accurate than they are in standard 19edo.

The fifth is ~ 696.36 cents; about 1/4 of a cent flatter than the fifth of quarter-comma meantone, or half a cent flatter than the fifth of [[31edo]]. The fourth is less accurate than in 19edo, and is close in size to a [[flattone]] fourth.

Minor thirds are still excellent, only slightly less accurate than they are in standard 19edo.

Usable prime harmonics include the 3:1 (about 3 cents flat), the 5:1 (about a cent flat), and the 7:1 and 13:1 (around 12 and 9 cents flat, respectively). The 7:1 and 13:1 in particular are much improved; with pure octaves they are too far out of tune to be usable for most, but the situation changes with the stretched version.

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<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>49ed6</title></head><body><strong>49ed6</strong> divides the just 6:1 into 49 equal parts, resulting in a step size of about 63.3053 cents and an octave approximately 3 cents sharp. It is a stretched version of <a class="wiki_link" href="/19edo">19edo</a> and extremely close to the <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning">zeta peak</a>, thus minimizing relative error as much as possible. Because 19edo itself is a flat-tending system, stretching the octave by this much improves the overall tuning accuracy.<br />

<br />

The fifth is ~ 696.36 cents; about 1/4 of a cent flatter than the fifth of quarter-comma meantone, or half a cent flatter than the fifth of <a class="wiki_link" href="/31edo">31edo</a>. Minor thirds are still excellent, only slightly less accurate than they are in standard 19edo.<br />

The fifth is ~ 696.36 cents; about 1/4 of a cent flatter than the fifth of quarter-comma meantone, or half a cent flatter than the fifth of <a class="wiki_link" href="/31edo">31edo</a>. The fourth is less accurate than in 19edo, and is close in size to a <a class="wiki_link" href="/flattone">flattone</a> fourth.<br />

<br />

Minor thirds are still excellent, only slightly less accurate than they are in standard 19edo.<br />

<br />

Usable prime harmonics include the 3:1 (about 3 cents flat), the 5:1 (about a cent flat), and the 7:1 and 13:1 (around 12 and 9 cents flat, respectively). The 7:1 and 13:1 in particular are much improved; with pure octaves they are too far out of tune to be usable for most, but the situation changes with the stretched version.<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:MasonGreen1|MasonGreen1]] and made on <tt>2016-04-18 02:30:10 UTC</tt>.<br>
+: This revision was by author [[User:MasonGreen1|MasonGreen1]] and made on <tt>2016-04-20 15:40:26 UTC</tt>.<br>
-: The original revision id was <tt>580364841</tt>.<br>
+: The original revision id was <tt>580722411</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 8: / Line 8: @@
 <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">**49ed6** divides the just 6:1 into 49 equal parts, resulting in a step size of about 63.3053 cents and an octave approximately 3 cents sharp. It is a stretched version of [[19edo]] and extremely close to the [[The Riemann Zeta Function and Tuning|zeta peak]], thus minimizing relative error as much as possible. Because 19edo itself is a flat-tending system, stretching the octave by this much improves the overall tuning accuracy.
-The fifth is ~ 696.36 cents; about 1/4 of a cent flatter than the fifth of quarter-comma meantone, or half a cent flatter than the fifth of [[31edo]]. Minor thirds are still excellent, only slightly less accurate than they are in standard 19edo.
+The fifth is ~ 696.36 cents; about 1/4 of a cent flatter than the fifth of quarter-comma meantone, or half a cent flatter than the fifth of [[31edo]]. The fourth is less accurate than in 19edo, and is close in size to a [[flattone]] fourth.
+Minor thirds are still excellent, only slightly less accurate than they are in standard 19edo.
 Usable prime harmonics include the 3:1 (about 3 cents flat), the 5:1 (about a cent flat), and the 7:1 and 13:1 (around 12 and 9 cents flat, respectively). The 7:1 and 13:1 in particular are much improved; with pure octaves they are too far out of tune to be usable for most, but the situation changes with the stretched version.
@@ Line 18: / Line 20: @@
 <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;49ed6&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;strong&gt;49ed6&lt;/strong&gt; divides the just 6:1 into 49 equal parts, resulting in a step size of about 63.3053 cents and an octave approximately 3 cents sharp. It is a stretched version of &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt; and extremely close to the &lt;a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning"&gt;zeta peak&lt;/a&gt;, thus minimizing relative error as much as possible. Because 19edo itself is a flat-tending system, stretching the octave by this much improves the overall tuning accuracy.&lt;br /&gt;
 &lt;br /&gt;
-The fifth is ~ 696.36 cents; about 1/4 of a cent flatter than the fifth of quarter-comma meantone, or half a cent flatter than the fifth of &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt;. Minor thirds are still excellent, only slightly less accurate than they are in standard 19edo.&lt;br /&gt;
+The fifth is ~ 696.36 cents; about 1/4 of a cent flatter than the fifth of quarter-comma meantone, or half a cent flatter than the fifth of &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt;. The fourth is less accurate than in 19edo, and is close in size to a &lt;a class="wiki_link" href="/flattone"&gt;flattone&lt;/a&gt; fourth.&lt;br /&gt;
+&lt;br /&gt;
+Minor thirds are still excellent, only slightly less accurate than they are in standard 19edo.&lt;br /&gt;
 &lt;br /&gt;
 Usable prime harmonics include the 3:1 (about 3 cents flat), the 5:1 (about a cent flat), and the 7:1 and 13:1 (around 12 and 9 cents flat, respectively). The 7:1 and 13:1 in particular are much improved; with pure octaves they are too far out of tune to be usable for most, but the situation changes with the stretched version.&lt;br /&gt;