Unidec: Difference between revisions
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'''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 | '''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: | Unidec has two viable 13-limit extensions: hendec and ekadash, discussed in [[Unidec extensions]]. | ||
See [[Gamelismic clan #Unidec]] for technical data. | See [[Gamelismic clan #Unidec]] for technical data. | ||
== Interval chain == | |||
In the following table, odd harmonics 1–21 and their inverses are in '''bold'''. | |||
{| class="wikitable center-1 right-2 right-4" | |||
|- | |||
! rowspan="2" | # | |||
! colspan="2" | Period 0 | |||
! colspan="2" | Period 1 | |||
|- | |||
! Cents* | |||
! Approximate ratios | |||
! Cents* | |||
! Approximate ratios | |||
|- | |||
| 0 | |||
| 0.00 | |||
| '''1/1''' | |||
| 600.00 | |||
| 99/70, 140/99 | |||
|- | |||
| 1 | |||
| 416.85 | |||
| 14/11 | |||
| 1016.80 | |||
| 9/5 | |||
|- | |||
| 2 | |||
| 833.71 | |||
| 81/50, 160/99 | |||
| 233.71 | |||
| '''8/7''' | |||
|- | |||
| 3 | |||
| 50.56 | |||
| 33/32, 36/35 | |||
| 650.56 | |||
| '''16/11''' | |||
|- | |||
| 4 | |||
| 467.42 | |||
| '''21/16''' | |||
| 1067.42 | |||
| 50/27 | |||
|- | |||
| 5 | |||
| 884.27 | |||
| 5/3 | |||
| 284.27 | |||
| 33/28 | |||
|- | |||
| 6 | |||
| 101.13 | |||
| 35/33 | |||
| 701.13 | |||
| '''3/2''' | |||
|- | |||
| 7 | |||
| 517.98 | |||
| 27/20 | |||
| 1117.98 | |||
| 21/11, 40/21 | |||
|- | |||
| 8 | |||
| 934.83 | |||
| 12/7 | |||
| 334.83 | |||
| 40/33 | |||
|- | |||
| 9 | |||
| 151.69 | |||
| 12/11 | |||
| 751.69 | |||
| 54/35 | |||
|- | |||
| 10 | |||
| 568.54 | |||
| 25/18 | |||
| 1168.54 | |||
| 55/28, 63/32, 96/49, 108/55 | |||
|- | |||
| 11 | |||
| 985.40 | |||
| 99/56 | |||
| 385.40 | |||
| '''5/4''' | |||
|- | |||
| 12 | |||
| 202.25 | |||
| '''9/8''' | |||
| 802.25 | |||
| 35/22 | |||
|- | |||
| 13 | |||
| 619.11 | |||
| 10/7 | |||
| 19.11 | |||
| 81/80, 99/98, 100/99 | |||
|} | |||
<nowiki/>* In 11-limit CWE tuning, octave reduced | |||
== Chords and harmony == | == Chords and harmony == | ||