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Ptolemismic chords

Revision as of 08:59, 1 June 2023 by FloraC (talk | contribs) (+tetrads and pentads)

Ptolemismic chords are essentially tempered chords tempered by the ptolemisma, 100/99.

The ptolemismic triad consists of 11/8 and a stack of two 6/5's closing at the octave:

  • 1-11/8-5/3 with steps of 11/8-6/5-6/5.

It can be extended to tetrads as

  • 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;
  • 1-5/4-11/8-5/3 with steps 5/4-11/10-6/5-6/5, and its inverse
  • 1-11/10-11/8-5/3 with steps 11/10-5/4-6/5-6/5.

They can be extended to pentads as

  • 1-5/4-11/8-3/2-5/3 with steps 5/4-11/10-12/11-11/10-6/5, and its inverse
  • 1-11/10-11/8-5/3-11/6 with steps 11/10-5/4-6/5-11/10-12/11.

Equal divisions with ptolemismic triads include 19edo, 22edo, 37edo, 41edo and 104edo.

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