Xenharmonic Wiki

User:FloraC/Workbench

< User:FloraC
Revision as of 11:15, 9 April 2026 by FloraC (talk | contribs) (Created page with "== Temperament pages == Notes: # Order: subgroup, comma list, mapping (mapping generators) / subgroup-val mapping & gencom mapping, lattice basis, optimal tunings (WE and CWE), minimax tuning, tuning ranges, algebraic generator (?), optimal ET sequence, badness, complexity spectrum, and others. # Comma list should be the Tenney-minimal commas sufficient to define the temperament, stated in Normal forms #Normal forms for...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Temperament pages

Notes:

  1. Order: subgroup, comma list, mapping (mapping generators) / subgroup-val mapping & gencom mapping, lattice basis, optimal tunings (WE and CWE), minimax tuning, tuning ranges, algebraic generator (?), optimal ET sequence, badness, complexity spectrum, and others.
  2. Comma list should be the Tenney-minimal commas sufficient to define the temperament, stated in Normal forms #Normal forms for commas.
  3. In mapping generators, show all the ratios as used in the mapping, including the period.
  4. For subgroup temperaments, "mapping" becomes "subgroup-val mapping" and "gencom mapping"".
    • If the subgroup is trivial, simply show "WE"/"CWE", otherwise show "subgroup/inharmonic WE/CWE" instead.
  5. Cent symbols.
  6. Since minimax tunings are based on tonality diamonds, it should explicitly state the odd limit, or a diamond function of ratios.
  7. Algebraic generators are to be discussed later.

Get a family for:

  • Ripple (3 different 7-limit extensions) done
  • Smate (2 different 7-limit extensions) done
  • Passion (4 different 7-limit extensions, 3 strong and 1 weak) done
  • Undim done
  • Quintaleap done
  • Quindromeda done
  • Parakleismic (many reasonable but unnamed 7-limit extensions)
  • Schismatic rank-3 family (perhaps)

Progress:

Scale trees

6-tone
1L 5s, 2L 4s, 3L 3s, 4L 2s, 5L 1s
7-tone
1L 6s, 2L 5s, 3L 4s, 4L 3s, 5L 2s, 6L 1s
8-tone
1L 7s, 2L 6s, 3L 5s, 4L 4s, 5L 3s, 6L 2s, 7L 1s
9-tone
1L 8s, 2L 7s, 3L 6s, 4L 5s, 5L 4s, 6L 3s, 7L 2s, 8L 1s
10-tone
1L 9s, 2L 8s, 3L 7s, 4L 6s, 5L 5s, 6L 4s, 7L 3s, 8L 2s, 9L 1s
11-tone
1L 10s, 2L 9s, 3L 8s, 4L 7s, 5L 6s, 6L 5s, 7L 4s, 8L 3s, 9L 2s, 10L 1s
12-tone
1L 11s, 2L 10s, 3L 9s, 4L 8s, 5L 7s, 6L 6s, 7L 5s, 8L 4s, 9L 3s, 10L 2s, 11L 1s
Retrieved from "https://en.xen.wiki/index.php?title=User:FloraC/Workbench&oldid=227528"