User:AthiTrydhen/Flippery
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IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author Praimhin and made on 2016-06-06 09:34:36 UTC.
- The original revision id was 584872051.
- The revision comment was:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
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.
Original HTML content:
<html><head><title>flippery</title></head><body>A <strong>fixed-frame flip</strong> 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.<br /> <br /> A <strong>fixed-center flip</strong> 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.<br /> <br /> A scale is <strong>flippery</strong> 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.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h2> --><h2 id="toc0"><a name="x-Examples"></a><!-- ws:end:WikiTextHeadingRule:0 -->Examples</h2> <br /> The scale [1/1, 9/8, 6/5, 5/4, 45/32, 3/2, 8/5, 5/3, 15/8, 2/1] is flippery.<br /> <br /> 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.<br /> 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.<br /> 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.<br /> 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.<br /> 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.<br /> 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.<br /> 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.<br /> 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.<br /> 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.<br /> <br /> 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.<br /> <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></body></html>