Pentadacus: Difference between revisions
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Pentadacus is a [[nonoctave]] [[regular temperament]] in the 5.7.11 [[subgroup]] which tempers out the comma [[831875/823543]]. It is even more exotic than [[Bohlen-Pierce]], lacking both [[2/1]] and [[3/1]], and typically it would be used with an [[equave]] of [[5/1]]. It is generated by a [[meantone]]-esque small whole tone interval that represents [[54/49]]. Stacking 3 of these tones gives [[7/5]] and 7 of them give [[11/5]]. Pentadacus has both low [[complexity]] (especially by the standards of the 5/1-equivalent world, where scales have lots of notes) and low [[error]] if tuned correctly, providing an [[efficiency|efficient]] traversal of the 5.7.11 subgroup. [[14ed5]] is an inaccurate but important tuning of Pentadacus, because in 14ed5, the whole tone generator corresponds to a single step of 14ed5, although the whole tone is bigger than usual being around [[9/8]]-sized, | Pentadacus is a [[nonoctave]] [[regular temperament]] in the 5.7.11 [[subgroup]] which tempers out the comma [[831875/823543]]. It is even more exotic than [[Bohlen-Pierce]], lacking both [[2/1]] and [[3/1]], and typically it would be used with an [[equave]] of [[5/1]]. It is generated by a [[meantone]]-esque small whole tone interval that represents [[54/49]]. Stacking 3 of these tones gives [[7/5]] and 7 of them give [[11/5]]. Pentadacus has both low [[complexity]] (especially by the standards of the 5/1-equivalent world, where scales have lots of notes) and low [[error]] if tuned correctly, providing an [[efficiency|efficient]] traversal of the 5.7.11 subgroup. [[14ed5]] is an inaccurate but important tuning of Pentadacus, because in 14ed5, the whole tone generator corresponds to a single step of 14ed5, although the whole tone is bigger than usual being around [[9/8]]-sized, causing the approximations of 7/5 and 11/5 to be bad. Basically, pentadacus can be thought of as a compressed 14ed5, at least until you hit [[5/1]]. | ||
Pentadacus is connected to [[didacus]] temperament as both share rheir whole role genweafor | Pentadacus is connected to [[didacus]] temperament as both share rheir whole role genweafor | ||
Revision as of 22:17, 7 March 2026
Pentadacus is a nonoctave regular temperament in the 5.7.11 subgroup which tempers out the comma 831875/823543. It is even more exotic than Bohlen-Pierce, lacking both 2/1 and 3/1, and typically it would be used with an equave of 5/1. It is generated by a meantone-esque small whole tone interval that represents 54/49. Stacking 3 of these tones gives 7/5 and 7 of them give 11/5. Pentadacus has both low complexity (especially by the standards of the 5/1-equivalent world, where scales have lots of notes) and low error if tuned correctly, providing an efficient traversal of the 5.7.11 subgroup. 14ed5 is an inaccurate but important tuning of Pentadacus, because in 14ed5, the whole tone generator corresponds to a single step of 14ed5, although the whole tone is bigger than usual being around 9/8-sized, causing the approximations of 7/5 and 11/5 to be bad. Basically, pentadacus can be thought of as a compressed 14ed5, at least until you hit 5/1.
Pentadacus is connected to didacus temperament as both share rheir whole role genweafor