159edo: Difference between revisions

The approximations of everything in the 17-odd-limit and even the approximations of 19/16, 29/16 and 31/16 all fall within the boundaries of the harmonic [http://musictheory.zentral.zone/huntsystem2.html#2 JND], and similarly this system can approximate the sounds of other systems such as [[10edo]], [[13edo]], [[22edo]] and [[31edo]].  Furthermore, the step size of 159edo is simultaneously above the average peak melodic JND and small enough to be well within the margin of error between Just 5-limit intervals and their [[12edo]] counterparts, 159edo offers a decent balance between allowing the possibility of seamless modulation to keys that are not in the same series of fifths, and not having a step-size so small as to have individual steps blend completely into one another, even as it also allows one to also control the bandwidth of certain sounds.  As a result of tempering out some of the commas, it allows [[essentially tempered chord]]s including [[marveltwin chords]], [[gentle chords]], [[keenanismic chords]], [[werckismic chords]], and [[sinbadmic chords]] in the 13-odd-limit, in addition to [[island chords]] and [[nicolic chords]] in the 15-odd-limit.

No less than five possible generators for the [[5L 2s|diatonic]] [[MOS]] Scale are supported by 159edo, though these different diatonic scales have different descendants. The 91\159 generator results in large and small scale steps at 23\159 and 22\159 respectively, making for a quasi-equalized diatonic scale, which can be extended to a [[7L 26s|siskontyttonic]] MOS, while the 95\159 results in large and small scale steps at 31\159 and 2\159 respectively, making for a version approaching paucitonic, which can be extended to a [[5L 22s|reinatonic]] MOS. The 92\159 generator results in large and small scale steps at 25\159 and 17\159 respectively, and this makes for a very meantone-like diatonic scale perfect for xenharmonic pieces that follow in the classical tradition, though this can be extended to a [[19L 26s|veljentyttonic]] MOS. Conversely, the 94\159 generator results in results in large and small scale steps at 29\159 and 7\159 respectively, and this makes for a superpyth diatonic scale that is slightly harder and better than that of [[22edo]], which can be extended to an [[22L 5s|antireinatonic]] MOS. Finally, the patent 93\159 generator results in the same diatonic MOS scale found in 53edo, which, despite now having competition from other possible generators, is still the go-to for those looking for something more akin to the classic [[Pythagorean tuning]], as well as for those looking to deal with good approximations of related 5-limit scales, or even just the basic form of the [[12L 29s|pythamystonic]] MOS.