Unidec: Difference between revisions

Revision as of 13:32, 16 November 2025

Unidec is a temperament generated by a wide major third representing 80/63 which can be taken as 14/11 from the 11-limit onwards. Two generators minus a semi-octave period make a ~8/7, and three ~8/7's make a perfect fifth of 3/2, tempering out 1029/1024, the gamelisma, and 4375/4374, the ragisma, with the 11-limit extension adding 385/384 or 441/440 to the comma list.

Unidec has two viable 13-limit extensions: hendec and ekadash.

See Gamelismic clan #Unidec for technical data.

See also: Chords of unidec

Eigenmonzo (unchanged interval)	Generator (¢)	Comments
13/12	415.357
7/4	415.587
13/10	416.198
11/8	416.227
13/9	416.338
15/13	416.516
7/6	416.641
7/5	416.730	7-odd-limit minimax
11/6	416.737
11/10	416.785
9/7	416.792	9- and 11-odd-limit minimax
15/14	416.813
11/9	416.839
15/11	416.848
5/3	416.872
5/4	416.938	5-, 13- and 15-odd-limit minimax
15/8	416.957
3/2	416.993
11/7	417.508
9/5	417.596
13/11	417.842
13/7	417.925
13/8	420.264

Revision as of 13:26, 16 November 2025 view source FloraC (talk \| contribs) autopatrolled, Bureaucrats, Interface administrators, Sysops 24,102 edits →Tunings: invert the gen and simplify the ratios ← Older edit		Revision as of 13:32, 16 November 2025 view source FloraC (talk \| contribs) autopatrolled, Bureaucrats, Interface administrators, Sysops 24,102 edits Rework on intro Newer edit →
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	'''Unidec''' is ~~the~~ [[regular temperament]] ~~defined in~~ the 7-limit by [[tempering out]] [[1029/1024]], the gamelisma, and [[4375/4374]], the ragisma, with the 11-limit extension adding [[385/384]] or [[441/440]] to the comma list~~, featuring a period of a semioctave and a generator of a classic whole tone~~.		'''Unidec''' is a [[regular temperament\|temperament]] [[generator\|generated]] by a wide major third representing [[80/63]] which can be taken as [[14/11]] from the 11-limit onwards. Two generators minus a [[semi-octave]] [[period]] make a [[~]][[8/7]], and three ~8/7's make a perfect fifth of [[3/2]], [[tempering out]] [[1029/1024]], the gamelisma, and [[4375/4374]], the ragisma, with the [[11-limit]] [[extension]] adding [[385/384]] or [[441/440]] to the comma list.

	Unidec has two viable 13-limit extensions: '''hendec''' and '''ekadash'''.		Unidec has two viable 13-limit extensions: '''hendec''' and '''ekadash'''.