User:AthiTrydhen/Flippery: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
A '''fixed-frame flip''' is a chord progression of the form a:b:c &lt;-&gt; 1/c:1/b:1/a, where the a of the first chord is the same as the 1/c of the second chord.
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:Praimhin|Praimhin]] and made on <tt>2016-06-06 09:34:36 UTC</tt>.<br>
: The original revision id was <tt>584872051</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">A **fixed-frame flip** is a chord progression of the form a:b:c &lt;-&gt; 1/c:1/b:1/a, where the a of the first chord is the same as the 1/c of the second chord.


A **fixed-center flip** is a chord progression of the form a:b:c &lt;-&gt; 1/c:1/b:1/a, where the b of the first chord is the same as the 1/b of the second chord.
A '''fixed-center flip''' is a chord progression of the form a:b:c &lt;-&gt; 1/c:1/b:1/a, where the b of the first chord is the same as the 1/b of the second chord.


A scale is **flippery** if every step of the scale is part of either a fixed frame flip or a fixed center flip using only notes in the scale.
A scale is '''flippery''' if every step of the scale is part of either a fixed frame flip or a fixed center flip using only notes in the scale.


==Examples==  
==Examples==


The scale [1/1, 9/8, 6/5, 5/4, 45/32, 3/2, 8/5, 5/3, 15/8, 2/1] is flippery.
The scale [1/1, 9/8, 6/5, 5/4, 45/32, 3/2, 8/5, 5/3, 15/8, 2/1] is flippery.


1/1-9/8: part of the fixed frame flip 1/4:1/3:1/2 -&gt; 2:3:4, where 1/1 serves as the 1/3 of the first chord and 9/8 as the 3 of the second chord.
1/1-9/8: part of the fixed frame flip 1/4:1/3:1/2 -&gt; 2:3:4, where 1/1 serves as the 1/3 of the first chord and 9/8 as the 3 of the second chord.
9/8-6/5: part of the fixed center flip 3:4:5 -&gt; 1/5:1/4:1/3, where 9/8 serves as the 3 of the first chord and 6/5 as the 1/5 of the second chord.
9/8-6/5: part of the fixed center flip 3:4:5 -&gt; 1/5:1/4:1/3, where 9/8 serves as the 3 of the first chord and 6/5 as the 1/5 of the second chord.
6/5-5/4: part of the fixed frame flip 1/6:1/5:1/4 -&gt; 4:5:6, where 6/5 serves as the 1/5 of the first chord and 5/4 as the 5 of the second chord.
6/5-5/4: part of the fixed frame flip 1/6:1/5:1/4 -&gt; 4:5:6, where 6/5 serves as the 1/5 of the first chord and 5/4 as the 5 of the second chord.
5/4-45/32: part of the fixed frame flip 1/4:1/3:1/2 -&gt; 2:3:4, where 5/4 serves as the 1/3 of the first chord and 45/32 as the 3 of the second chord.
5/4-45/32: part of the fixed frame flip 1/4:1/3:1/2 -&gt; 2:3:4, where 5/4 serves as the 1/3 of the first chord and 45/32 as the 3 of the second chord.
45/32-3/2: part of the fixed frame flip 1/5:1/4:1/3 -&gt; 3:4:5, where 45/32 serves as the 1/4 of the first chord and 3/2 as the 4 of the second chord.
45/32-3/2: part of the fixed frame flip 1/5:1/4:1/3 -&gt; 3:4:5, where 45/32 serves as the 1/4 of the first chord and 3/2 as the 4 of the second chord.
3/2-8/5: part of the fixed frame flip 1/5:1/4:1/3 -&gt; 3:4:5, where 3/2 serves as the 1/4 of the first chord and 8/5 as the 4 of the second chord.
3/2-8/5: part of the fixed frame flip 1/5:1/4:1/3 -&gt; 3:4:5, where 3/2 serves as the 1/4 of the first chord and 8/5 as the 4 of the second chord.
8/5-5/3: part of the fixed center flip 4:5:6 -&gt; 1/6:1/5:1/4, where 8/5 serves as the 1/4 of the first chord and 5/3 as the 1/6 of the second chord.
8/5-5/3: part of the fixed center flip 4:5:6 -&gt; 1/6:1/5:1/4, where 8/5 serves as the 1/4 of the first chord and 5/3 as the 1/6 of the second chord.
5/3-15/8: part of the fixed frame flip 1/4:1/3:1/2 -&gt; 2:3:4, where 5/3 serves as the 1/3 of the first chord and 15/8 as the 3 of the second chord.
5/3-15/8: part of the fixed frame flip 1/4:1/3:1/2 -&gt; 2:3:4, where 5/3 serves as the 1/3 of the first chord and 15/8 as the 3 of the second chord.
15/8-2/1: part of the fixed frame flip 1/5:1/4:1/3 -&gt; 3:4:5, where 15/8 serves as the 1/4 of the first chord and 2/1 as the 4 of the second chord.
15/8-2/1: part of the fixed frame flip 1/5:1/4:1/3 -&gt; 3:4:5, where 15/8 serves as the 1/4 of the first chord and 2/1 as the 4 of the second chord.


In contrast, the scale [1/1, 9/8, 6/5, 5/4, 45/32, 3/2, 8/5, 5/3, 16/9, 2/1] is not flippery; the step 5/3-16/9 is not part of any flip.
In contrast, the scale [1/1, 9/8, 6/5, 5/4, 45/32, 3/2, 8/5, 5/3, 16/9, 2/1] is not flippery; the step 5/3-16/9 is not part of any flip.
* A hypothetical fixed frame flip involving the step 5/3-16/9 would look like 4/3:5/3:20/9 → 4/3:16/9:20/9, but neither the note 4/3 nor 10/9 (octave reduced 20/9) are in the scale.
 
* A hypothetical fixed center flip involving the step 5/3-16/9 would look either like 1/1:4/3:5/3 → 16/15:4/3:16/9, or 5/3:20/9:50/18 → 16/9:20/9:80/27, which again involve notes outside the scale.</pre></div>
<ul><li>A hypothetical fixed frame flip involving the step 5/3-16/9 would look like 4/3:5/3:20/9 → 4/3:16/9:20/9, but neither the note 4/3 nor 10/9 (octave reduced 20/9) are in the scale.</li><li>A hypothetical fixed center flip involving the step 5/3-16/9 would look either like 1/1:4/3:5/3 → 16/15:4/3:16/9, or 5/3:20/9:50/18 → 16/9:20/9:80/27, which again involve notes outside the scale.</li></ul>
<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;flippery&lt;/title&gt;&lt;/head&gt;&lt;body&gt;A &lt;strong&gt;fixed-frame flip&lt;/strong&gt; is a chord progression of the form a:b:c &amp;lt;-&amp;gt; 1/c:1/b:1/a, where the a of the first chord is the same as the 1/c of the second chord.&lt;br /&gt;
&lt;br /&gt;
A &lt;strong&gt;fixed-center flip&lt;/strong&gt; is a chord progression of the form a:b:c &amp;lt;-&amp;gt; 1/c:1/b:1/a, where the b of the first chord is the same as the 1/b of the second chord.&lt;br /&gt;
&lt;br /&gt;
A scale is &lt;strong&gt;flippery&lt;/strong&gt; if every step of the scale is part of either a fixed frame flip or a fixed center flip using only notes in the scale.&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-Examples"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Examples&lt;/h2&gt;
&lt;br /&gt;
The scale [1/1, 9/8, 6/5, 5/4, 45/32, 3/2, 8/5, 5/3, 15/8, 2/1] is flippery.&lt;br /&gt;
&lt;br /&gt;
1/1-9/8: part of the fixed frame flip 1/4:1/3:1/2 -&amp;gt; 2:3:4, where 1/1 serves as the 1/3 of the first chord and 9/8 as the 3 of the second chord.&lt;br /&gt;
9/8-6/5: part of the fixed center flip 3:4:5 -&amp;gt; 1/5:1/4:1/3, where 9/8 serves as the 3 of the first chord and 6/5 as the 1/5 of the second chord.&lt;br /&gt;
6/5-5/4: part of the fixed frame flip 1/6:1/5:1/4 -&amp;gt; 4:5:6, where 6/5 serves as the 1/5 of the first chord and 5/4 as the 5 of the second chord.&lt;br /&gt;
5/4-45/32: part of the fixed frame flip 1/4:1/3:1/2 -&amp;gt; 2:3:4, where 5/4 serves as the 1/3 of the first chord and 45/32 as the 3 of the second chord.&lt;br /&gt;
45/32-3/2: part of the fixed frame flip 1/5:1/4:1/3 -&amp;gt; 3:4:5, where 45/32 serves as the 1/4 of the first chord and 3/2 as the 4 of the second chord.&lt;br /&gt;
3/2-8/5: part of the fixed frame flip 1/5:1/4:1/3 -&amp;gt; 3:4:5, where 3/2 serves as the 1/4 of the first chord and 8/5 as the 4 of the second chord.&lt;br /&gt;
8/5-5/3: part of the fixed center flip 4:5:6 -&amp;gt; 1/6:1/5:1/4, where 8/5 serves as the 1/4 of the first chord and 5/3 as the 1/6 of the second chord.&lt;br /&gt;
5/3-15/8: part of the fixed frame flip 1/4:1/3:1/2 -&amp;gt; 2:3:4, where 5/3 serves as the 1/3 of the first chord and 15/8 as the 3 of the second chord.&lt;br /&gt;
15/8-2/1: part of the fixed frame flip 1/5:1/4:1/3 -&amp;gt; 3:4:5, where 15/8 serves as the 1/4 of the first chord and 2/1 as the 4 of the second chord.&lt;br /&gt;
&lt;br /&gt;
In contrast, the scale [1/1, 9/8, 6/5, 5/4, 45/32, 3/2, 8/5, 5/3, 16/9, 2/1] is not flippery; the step 5/3-16/9 is not part of any flip.&lt;br /&gt;
&lt;ul&gt;&lt;li&gt;A hypothetical fixed frame flip involving the step 5/3-16/9 would look like 4/3:5/3:20/9 → 4/3:16/9:20/9, but neither the note 4/3 nor 10/9 (octave reduced 20/9) are in the scale.&lt;/li&gt;&lt;li&gt;A hypothetical fixed center flip involving the step 5/3-16/9 would look either like 1/1:4/3:5/3 → 16/15:4/3:16/9, or 5/3:20/9:50/18 → 16/9:20/9:80/27, which again involve notes outside the scale.&lt;/li&gt;&lt;/ul&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>

Revision as of 00:00, 17 July 2018

A fixed-frame flip is a chord progression of the form a:b:c <-> 1/c:1/b:1/a, where the a of the first chord is the same as the 1/c of the second chord.

A fixed-center flip is a chord progression of the form a:b:c <-> 1/c:1/b:1/a, where the b of the first chord is the same as the 1/b of the second chord.

A scale is flippery if every step of the scale is part of either a fixed frame flip or a fixed center flip using only notes in the scale.

Examples

The scale [1/1, 9/8, 6/5, 5/4, 45/32, 3/2, 8/5, 5/3, 15/8, 2/1] is flippery.

1/1-9/8: part of the fixed frame flip 1/4:1/3:1/2 -> 2:3:4, where 1/1 serves as the 1/3 of the first chord and 9/8 as the 3 of the second chord.

9/8-6/5: part of the fixed center flip 3:4:5 -> 1/5:1/4:1/3, where 9/8 serves as the 3 of the first chord and 6/5 as the 1/5 of the second chord.

6/5-5/4: part of the fixed frame flip 1/6:1/5:1/4 -> 4:5:6, where 6/5 serves as the 1/5 of the first chord and 5/4 as the 5 of the second chord.

5/4-45/32: part of the fixed frame flip 1/4:1/3:1/2 -> 2:3:4, where 5/4 serves as the 1/3 of the first chord and 45/32 as the 3 of the second chord.

45/32-3/2: part of the fixed frame flip 1/5:1/4:1/3 -> 3:4:5, where 45/32 serves as the 1/4 of the first chord and 3/2 as the 4 of the second chord.

3/2-8/5: part of the fixed frame flip 1/5:1/4:1/3 -> 3:4:5, where 3/2 serves as the 1/4 of the first chord and 8/5 as the 4 of the second chord.

8/5-5/3: part of the fixed center flip 4:5:6 -> 1/6:1/5:1/4, where 8/5 serves as the 1/4 of the first chord and 5/3 as the 1/6 of the second chord.

5/3-15/8: part of the fixed frame flip 1/4:1/3:1/2 -> 2:3:4, where 5/3 serves as the 1/3 of the first chord and 15/8 as the 3 of the second chord.

15/8-2/1: part of the fixed frame flip 1/5:1/4:1/3 -> 3:4:5, where 15/8 serves as the 1/4 of the first chord and 2/1 as the 4 of the second chord.

In contrast, the scale [1/1, 9/8, 6/5, 5/4, 45/32, 3/2, 8/5, 5/3, 16/9, 2/1] is not flippery; the step 5/3-16/9 is not part of any flip.

  • A hypothetical fixed frame flip involving the step 5/3-16/9 would look like 4/3:5/3:20/9 → 4/3:16/9:20/9, but neither the note 4/3 nor 10/9 (octave reduced 20/9) are in the scale.
  • A hypothetical fixed center flip involving the step 5/3-16/9 would look either like 1/1:4/3:5/3 → 16/15:4/3:16/9, or 5/3:20/9:50/18 → 16/9:20/9:80/27, which again involve notes outside the scale.
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