User:Lucius Chiaraviglio/Keyboard Layout Lab: Difference between revisions

[[Bryan Deister]] has demonstrated a [[2L 6s]] (14:5 step ratio) mapping for [[58edo]] in [https://www.youtube.com/shorts/7gkRyld5OU8 ''Waltz in 58edo''] (2025). The rightward generator 5\58 functions as the classic diatonmic semitone ~[[16/15]], the large septendecimal semitone ~[[17/16]], and the small septendecimal semitone ~[[18/17]], meaning that the charisma [[256/255]] and the semitonisma ([289/288]] are both tempered out. The rightward generator is also the [[normal forms|minimal form]] of the [[Diaschismic]] generator, and indeed the [[diaschisma]] 2048/2045 is also tempered out. This generator makes a slew of intervals of reasonable prime limit that are not far from just: two of them make a near-just whole tone ~[[9/8]]; three of them make a mildly flat classic minor third ~[[6/5]]; four of them make a mildly flat undecimal major third ~[[14/11]]; five of them make a near-just classic acute fourth ~[[27/20]]; six of them pass the [[semioctave]] to make a slightly flat greater septimal tritone ~[[10/7]]; seven of them make a slightly flat septimal superfifth ~[[32/21]]; eight of them make a slightly flat tridecimal supraminor sixth ~[[21/13]]; nine of them make a near-just septimal major sixth ~[[12/7]]; and ten of them make an extremely accurate undecimal supraminor seventh ~[[20/11]]. Other common intervals such as the moderately sharp (although high in relative error) classic major third ~[[5/4]], the near-just perfect fourth ~[[4/3]], and the near-just perfect fifth ~[[3/2]] are in very easy reach of the chain of rightward generators, and not very distant from the root note. This may be sufficient compensation for the reverse chroma and the range of only three full octaves (which slope only slightly upward), with large partial octaves being chopped off by the upper left and lower right corners.

Last modified:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 21:14, 19 August 2025 (UTC)