Augmented family: Difference between revisions

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:xenwolf|xenwolf]] and made on <tt>2011-03-~~05 16~~:00:03 UTC</tt>.<br>

: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2011-07-01 11:19:07 UTC</tt>.<br>

: The original revision id was <tt>~~207626542~~</tt>.<br>

: The original revision id was <tt>239658611</tt>.<br>

: The revision comment was: <tt>~~some edo links added. What means "Badness" ?~~</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">The 5-limit parent comma for the augmented family is 128/125, the diesis. Its [[monzo]] is |7 0 -3>, and flipping that yields <<3 0 -7|| for the [[wedgie]]. Hence the period is 1/3 octave, and this is what is used for a major third. The [[generator]] can be taken as a fifth or a semitone, and [[12edo]], with its excellent fifth, is an obvious tuning for 5-limit augmented, though a sharper fifth might be preferred to go with the sharp third.

<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">The 5-limit parent comma for the **augmented family** is 128/125, the [[diesis]]. Its [[monzo]] is |7 0 -3>, and flipping that yields <<3 0 -7|| for the [[wedgie]]. Hence the period is 1/3 octave, and this is what is used for a major third. The [[generator]] can be taken as a fifth or a semitone, and [[12edo]], with its excellent fifth, is an obvious tuning for [[5-limit]] augmented, though a sharper fifth might be preferred to go with the sharp third.

==Seven limit children==

The second comma of the [[Normal lists|normal comma list]] defines which 7-limit family member we are looking at. August adds 36/35, augene 64/63, hexe 256/245, hemiaug 245/243, and hemis 49/48. Hexe splits the period to 1/6 octave, and hemiaug the generator, giving quarter-tones instead of semitones.

The second comma of the [[Normal lists|normal comma list]] defines which [[7-limit]] family member we are looking at. August adds 36/35, augene 64/63, hexe 256/245, hemiaug 245/243, and hemis 49/48. Hexe splits the period to 1/6 octave, and hemiaug the generator, giving quarter-tones instead of semitones.

==August==

Line 36:

Map: [<3 0 7 -1 1 -3|, <0 1 0 2 2 3|]

EDOs: 9, 12, 21, 54

EDOs: 9, 12, [[21edo|21]], [[54edo|54]]

Badness: 0.0184

Line 76:

Map: [<3 0 7 6|, <0 2 0 1|]

Wedgie: <<6 0 3 -14 -12 7||

EDOs: 6, 9, 15, 24, 39, 102

EDOs: 6, 9, [[15edo|15]], [[24edo|24]], [[39edo|39]], [[102edo|102]]

Badness: 0.0202

Line 85:

Map: [<3 0 7 6 8|, <0 2 0 1 1|]

EDOs: 6, 9, 15, 24, 39, 63, 102

EDOs: 6, 9, 15, 24, 39, [[63edo|63]], 102

Badness: 0.0262

Line 94:

Map: [<3 0 7 6 8 4|, <0 2 0 1 1 3|]

EDOs: 6, 9, 15, 24, 87

EDOs: 6, 9, 15, 24, [[87edo|87]]

Badness: 0.0202</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>Augmented family</title></head><body>The 5-limit parent comma for the augmented family is 128/125, the diesis. Its <a class="wiki_link" href="/monzo">monzo</a> is |7 0 -3&gt;, and flipping that yields &lt;&lt;3 0 -7|| for the <a class="wiki_link" href="/wedgie">wedgie</a>. Hence the period is 1/3 octave, and this is what is used for a major third. The <a class="wiki_link" href="/generator">generator</a> can be taken as a fifth or a semitone, and <a class="wiki_link" href="/12edo">12edo</a>, with its excellent fifth, is an obvious tuning for 5-limit augmented, though a sharper fifth might be preferred to go with the sharp third. <br />

<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>Augmented family</title></head><body>The 5-limit parent comma for the <strong>augmented family</strong> is 128/125, the <a class="wiki_link" href="/diesis">diesis</a>. Its <a class="wiki_link" href="/monzo">monzo</a> is |7 0 -3&gt;, and flipping that yields &lt;&lt;3 0 -7|| for the <a class="wiki_link" href="/wedgie">wedgie</a>. Hence the period is 1/3 octave, and this is what is used for a major third. The <a class="wiki_link" href="/generator">generator</a> can be taken as a fifth or a semitone, and <a class="wiki_link" href="/12edo">12edo</a>, with its excellent fifth, is an obvious tuning for <a class="wiki_link" href="/5-limit">5-limit</a> augmented, though a sharper fifth might be preferred to go with the sharp third. <br />

<br />

<h2 id="toc0"><a name="x-Seven limit children"></a>Seven limit children</h2>

The second comma of the <a class="wiki_link" href="/Normal%20lists">normal comma list</a> defines which 7-limit family member we are looking at. August adds 36/35, augene 64/63, hexe 256/245, hemiaug 245/243, and hemis 49/48. Hexe splits the period to 1/6 octave, and hemiaug the generator, giving quarter-tones instead of semitones.<br />

The second comma of the <a class="wiki_link" href="/Normal%20lists">normal comma list</a> defines which <a class="wiki_link" href="/7-limit">7-limit</a> family member we are looking at. August adds 36/35, augene 64/63, hexe 256/245, hemiaug 245/243, and hemis 49/48. Hexe splits the period to 1/6 octave, and hemiaug the generator, giving quarter-tones instead of semitones.<br />

<br />

<h2 id="toc1"><a name="x-August"></a>August</h2>

Line 127:

<br />

Map: [&lt;3 0 7 -1 1 -3|, &lt;0 1 0 2 2 3|]<br />

EDOs: 9, 12, 21, 54<br />

EDOs: 9, 12, <a class="wiki_link" href="/21edo">21</a>, <a class="wiki_link" href="/54edo">54</a><br />

Badness: 0.0184<br />

<br />

Line 167:

Map: [&lt;3 0 7 6|, &lt;0 2 0 1|]<br />

Wedgie: &lt;&lt;6 0 3 -14 -12 7||<br />

EDOs: 6, 9, 15, 24, 39, 102<br />

EDOs: 6, 9, <a class="wiki_link" href="/15edo">15</a>, <a class="wiki_link" href="/24edo">24</a>, <a class="wiki_link" href="/39edo">39</a>, <a class="wiki_link" href="/102edo">102</a><br />

Badness: 0.0202<br />

<br />

Line 176:

<br />

Map: [&lt;3 0 7 6 8|, &lt;0 2 0 1 1|]<br />

EDOs: 6, 9, 15, 24, 39, 63, 102<br />

EDOs: 6, 9, 15, 24, 39, <a class="wiki_link" href="/63edo">63</a>, 102<br />

Badness: 0.0262<br />

<br />

Line 185:

<br />

Map: [&lt;3 0 7 6 8 4|, &lt;0 2 0 1 1 3|]<br />

EDOs: 6, 9, 15, 24, 87<br />

EDOs: 6, 9, 15, 24, <a class="wiki_link" href="/87edo">87</a><br />

Badness: 0.0202</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:xenwolf|xenwolf]] and made on <tt>2011-03-05 16:00:03 UTC</tt>.<br>
+: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2011-07-01 11:19:07 UTC</tt>.<br>
-: The original revision id was <tt>207626542</tt>.<br>
+: The original revision id was <tt>239658611</tt>.<br>
-: The revision comment was: <tt>some edo links added. What means "Badness" ?</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">The 5-limit parent comma for the augmented family is 128/125, the diesis. Its [[monzo]] is |7 0 -3&gt;, and flipping that yields &lt;&lt;3 0 -7|| for the [[wedgie]]. Hence the period is 1/3 octave, and this is what is used for a major third. The [[generator]] can be taken as a fifth or a semitone, and [[12edo]], with its excellent fifth, is an obvious tuning for 5-limit augmented, though a sharper fifth might be preferred to go with the sharp third.
+<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">The 5-limit parent comma for the **augmented family** is 128/125, the [[diesis]]. Its [[monzo]] is |7 0 -3&gt;, and flipping that yields &lt;&lt;3 0 -7|| for the [[wedgie]]. Hence the period is 1/3 octave, and this is what is used for a major third. The [[generator]] can be taken as a fifth or a semitone, and [[12edo]], with its excellent fifth, is an obvious tuning for [[5-limit]] augmented, though a sharper fifth might be preferred to go with the sharp third.
 ==Seven limit children==
-The second comma of the [[Normal lists|normal comma list]] defines which 7-limit family member we are looking at. August adds 36/35, augene 64/63, hexe 256/245, hemiaug 245/243, and hemis 49/48. Hexe splits the period to 1/6 octave, and hemiaug the generator, giving quarter-tones instead of semitones.
+The second comma of the [[Normal lists|normal comma list]] defines which [[7-limit]] family member we are looking at. August adds 36/35, augene 64/63, hexe 256/245, hemiaug 245/243, and hemis 49/48. Hexe splits the period to 1/6 octave, and hemiaug the generator, giving quarter-tones instead of semitones.
 ==August==
@@ Line 36: / Line 36: @@
 Map: [&lt;3 0 7 -1 1 -3|, &lt;0 1 0 2 2 3|]
-EDOs: 9, 12, 21, 54
+EDOs: 9, 12, [[21edo|21]], [[54edo|54]]
 Badness: 0.0184
@@ Line 76: / Line 76: @@
 Map: [&lt;3 0 7 6|, &lt;0 2 0 1|]
 Wedgie: &lt;&lt;6 0 3 -14 -12 7||
-EDOs: 6, 9, 15, 24, 39, 102
+EDOs: 6, 9, [[15edo|15]], [[24edo|24]], [[39edo|39]], [[102edo|102]]
 Badness: 0.0202
@@ Line 85: / Line 85: @@
 Map: [&lt;3 0 7 6 8|, &lt;0 2 0 1 1|]
-EDOs: 6, 9, 15, 24, 39, 63, 102
+EDOs: 6, 9, 15, 24, 39, [[63edo|63]], 102
 Badness: 0.0262
@@ Line 94: / Line 94: @@
 Map: [&lt;3 0 7 6 8 4|, &lt;0 2 0 1 1 3|]
-EDOs: 6, 9, 15, 24, 87
+EDOs: 6, 9, 15, 24, [[87edo|87]]
 Badness: 0.0202</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;Augmented family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The 5-limit parent comma for the augmented family is 128/125, the diesis. Its &lt;a class="wiki_link" href="/monzo"&gt;monzo&lt;/a&gt; is |7 0 -3&amp;gt;, and flipping that yields &amp;lt;&amp;lt;3 0 -7|| for the &lt;a class="wiki_link" href="/wedgie"&gt;wedgie&lt;/a&gt;. Hence the period is 1/3 octave, and this is what is used for a major third. The &lt;a class="wiki_link" href="/generator"&gt;generator&lt;/a&gt; can be taken as a fifth or a semitone, and &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt;, with its excellent fifth, is an obvious tuning for 5-limit augmented, though a sharper fifth might be preferred to go with the sharp third. &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;Augmented family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The 5-limit parent comma for the &lt;strong&gt;augmented family&lt;/strong&gt; is 128/125, the &lt;a class="wiki_link" href="/diesis"&gt;diesis&lt;/a&gt;. Its &lt;a class="wiki_link" href="/monzo"&gt;monzo&lt;/a&gt; is |7 0 -3&amp;gt;, and flipping that yields &amp;lt;&amp;lt;3 0 -7|| for the &lt;a class="wiki_link" href="/wedgie"&gt;wedgie&lt;/a&gt;. Hence the period is 1/3 octave, and this is what is used for a major third. The &lt;a class="wiki_link" href="/generator"&gt;generator&lt;/a&gt; can be taken as a fifth or a semitone, and &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt;, with its excellent fifth, is an obvious tuning for &lt;a class="wiki_link" href="/5-limit"&gt;5-limit&lt;/a&gt; augmented, though a sharper fifth might be preferred to go with the sharp third. &lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Seven limit children"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Seven limit children&lt;/h2&gt;
-The second comma of the &lt;a class="wiki_link" href="/Normal%20lists"&gt;normal comma list&lt;/a&gt; defines which 7-limit family member we are looking at. August adds 36/35, augene 64/63, hexe 256/245, hemiaug 245/243, and hemis 49/48. Hexe splits the period to 1/6 octave, and hemiaug the generator, giving quarter-tones instead of semitones.&lt;br /&gt;
+The second comma of the &lt;a class="wiki_link" href="/Normal%20lists"&gt;normal comma list&lt;/a&gt; defines which &lt;a class="wiki_link" href="/7-limit"&gt;7-limit&lt;/a&gt; family member we are looking at. August adds 36/35, augene 64/63, hexe 256/245, hemiaug 245/243, and hemis 49/48. Hexe splits the period to 1/6 octave, and hemiaug the generator, giving quarter-tones instead of semitones.&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="x-August"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;August&lt;/h2&gt;
@@ Line 127: / Line 127: @@
 &lt;br /&gt;
 Map: [&amp;lt;3 0 7 -1 1 -3|, &amp;lt;0 1 0 2 2 3|]&lt;br /&gt;
-EDOs: 9, 12, 21, 54&lt;br /&gt;
+EDOs: 9, 12, &lt;a class="wiki_link" href="/21edo"&gt;21&lt;/a&gt;, &lt;a class="wiki_link" href="/54edo"&gt;54&lt;/a&gt;&lt;br /&gt;
 Badness: 0.0184&lt;br /&gt;
 &lt;br /&gt;
@@ Line 167: / Line 167: @@
 Map: [&amp;lt;3 0 7 6|, &amp;lt;0 2 0 1|]&lt;br /&gt;
 Wedgie: &amp;lt;&amp;lt;6 0 3 -14 -12 7||&lt;br /&gt;
-EDOs: 6, 9, 15, 24, 39, 102&lt;br /&gt;
+EDOs: 6, 9, &lt;a class="wiki_link" href="/15edo"&gt;15&lt;/a&gt;, &lt;a class="wiki_link" href="/24edo"&gt;24&lt;/a&gt;, &lt;a class="wiki_link" href="/39edo"&gt;39&lt;/a&gt;, &lt;a class="wiki_link" href="/102edo"&gt;102&lt;/a&gt;&lt;br /&gt;
 Badness: 0.0202&lt;br /&gt;
 &lt;br /&gt;
@@ Line 176: / Line 176: @@
 &lt;br /&gt;
 Map: [&amp;lt;3 0 7 6 8|, &amp;lt;0 2 0 1 1|]&lt;br /&gt;
-EDOs: 6, 9, 15, 24, 39, 63, 102&lt;br /&gt;
+EDOs: 6, 9, 15, 24, 39, &lt;a class="wiki_link" href="/63edo"&gt;63&lt;/a&gt;, 102&lt;br /&gt;
 Badness: 0.0262&lt;br /&gt;
 &lt;br /&gt;
@@ Line 185: / Line 185: @@
 &lt;br /&gt;
 Map: [&amp;lt;3 0 7 6 8 4|, &amp;lt;0 2 0 1 1 3|]&lt;br /&gt;
-EDOs: 6, 9, 15, 24, 87&lt;br /&gt;
+EDOs: 6, 9, 15, 24, &lt;a class="wiki_link" href="/87edo"&gt;87&lt;/a&gt;&lt;br /&gt;
 Badness: 0.0202&lt;/body&gt;&lt;/html&gt;</pre></div>