159edo: Difference between revisions

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=== Additional Properties of 159-tone equal temperament ===

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.

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]], [[minor minthmic 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.

=== MOSes and other scales ===

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 === Additional Properties of 159-tone equal temperament ===
-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.
+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]], [[minor minthmic 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.
 === MOSes and other scales ===