Ptolemismic chords: Difference between revisions

m Improve readability; recategorize
Adjust the rotation of certain chords to expose the perfect fifth
 
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The inversely related pairs of chords are
The inversely related pairs of chords are
* 1–11/8–3/2–5/3 with steps 11/8, 12/11, 11/10, 6/5, and its inverse
* 1–11/8–3/2–5/3 with steps 11/8, 12/11, 11/10, 6/5, and its inverse
* 1–11/8–5/3–11/6 with steps 11/8, 6/5, 11/10, 12/11;  
* 1–12/11–3/2–9/5 with steps 12/11, 11/8, 6/5, 11/10;  
* 1–5/4–11/8–5/3 with steps 5/4, 11/10, 6/5, 6/5, and its inverse
* 1–5/4–3/2–9/5 with steps 5/4, 6/5, 6/5, 11/10, and its inverse
* 1–11/10–11/8–5/3 with steps 11/10, 5/4, 6/5, 6/5.  
* 1–6/5–3/2–5/3 with steps 6/5, 5/4, 11/10, 6/5.  


For pentads, there are two palindromic chords and a pair of chords in inverse relationship. The palindromic chords are
For pentads, there are two palindromic chords and a pair of chords in inverse relationship. The palindromic chords are
* 1–11/8–3/2–5/3–11/6 with steps 11/8, 12/11, 11/10, 11/10, 12/11;
* 1–9/8–5/4–3/2–9/5 with steps 9/8, 11/10, 6/5, 6/5, 11/10;
* 1–9/8–5/4–3/2–9/5 with steps 9/8, 11/10, 6/5, 6/5, 11/10.
* 1–11/8–3/2–5/3–11/6 with steps 11/8, 12/11, 11/10, 11/10, 12/11.


The inversely related pair of chords is
The inversely related pair of chords is
* 1–5/4–11/8–3/2–5/3 with steps 5/4, 11/10, 12/11, 11/10, 6/5, and its inverse
* 1–5/4–3/2–5/3–9/5 with steps 5/4, 6/5, 11/10, 12/11, 11/10, and its inverse
* 1–11/10–11/8–5/3–11/6 with steps 11/10, 5/4, 6/5, 11/10, 12/11.  
* 1–6/5–3/2–5/3–9/5 with steps 6/5, 5/4, 11/10, 12/11, 11/10.  


[[Equal temperament]]s with ptolemismic chords include {{EDOs| 19, 22, 37, 41, and 104 }}.
[[Equal temperament]]s with ptolemismic chords include {{EDOs| 19, 22, 37, 41, and 104 }}.