User:Aura/Aura's Ideas on Tonality: Difference between revisions

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== Choice of EDO for Microtonal Systems ==

While Hunt's microtonal system is based on [[205edo]], my microtonal system is built on [[159edo]]. Why this difference? Well, even though 205edo has better interval representation in a number of cases, the step size of 205edo is too small, as half of the distance between individual steps- that is, the distance between the center of a given step and the edge of that same step- is less than 3.5 cents, which is less than the average peak [http://musictheory.zentral.zone/huntsystem2.html#2 JND] of human pitch perception. This results in individual steps blending into one another and thus being hard to tell apart- a problem which all EDOs higher than 171 have, and a significant deterrent for me. Secondly, while 171edo itself also has better representation in a number of cases, the comma created by one of 159edo's three circles of fifths is smaller than that created by one of 205edo's five circles of fifths or even that created by the 171edo circle of fifths- yes, closing the circle of fifths with the least amount of error possible was one consideration.

While Hunt's microtonal system is based on [[205edo]], my microtonal system is built on [[159edo]]. Why this difference? Well, even though 205edo has better interval representation in a number of cases, the step size of 205edo is too small, as half of the distance between individual steps- that is, the distance between the center of a given step and the edge of that same step- is less than 3.5 cents, which is less than the average peak [http://musictheory.zentral.zone/huntsystem2.html#2 JND] of human pitch perception. This results in individual steps blending into one another and thus being hard to tell apart- a problem which all EDOs higher than 171 have, and a significant deterrent for me. Secondly, while 171edo itself also has better representation in a number of cases, the comma created by one of 159edo's three circles of fifths is smaller than that created by one of 205edo's five circles of fifths, or even that created by the 171edo circle of fifths- yes, closing the circle of fifths with the least amount of error possible was one consideration. There's also the matter of good 11-limit representation in particular, and 159edo suspasses both 171edo and 205edo on this point.

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	== Choice of EDO for Microtonal Systems ==		== Choice of EDO for Microtonal Systems ==

	While Hunt's microtonal system is based on [[205edo]], my microtonal system is built on [[159edo]]. Why this difference? Well, even though 205edo has better interval representation in a number of cases, the step size of 205edo is too small, as half of the distance between individual steps- that is, the distance between the center of a given step and the edge of that same step- is less than 3.5 cents, which is less than the average peak [http://musictheory.zentral.zone/huntsystem2.html#2 JND] of human pitch perception. This results in individual steps blending into one another and thus being hard to tell apart- a problem which all EDOs higher than 171 have, and a significant deterrent for me. Secondly, while 171edo itself also has better representation in a number of cases, the comma created by one of 159edo's three circles of fifths is smaller than that created by one of 205edo's five circles of fifths or even that created by the 171edo circle of fifths- yes, closing the circle of fifths with the least amount of error possible was one consideration.		While Hunt's microtonal system is based on [[205edo]], my microtonal system is built on [[159edo]]. Why this difference? Well, even though 205edo has better interval representation in a number of cases, the step size of 205edo is too small, as half of the distance between individual steps- that is, the distance between the center of a given step and the edge of that same step- is less than 3.5 cents, which is less than the average peak [http://musictheory.zentral.zone/huntsystem2.html#2 JND] of human pitch perception. This results in individual steps blending into one another and thus being hard to tell apart- a problem which all EDOs higher than 171 have, and a significant deterrent for me. Secondly, while 171edo itself also has better representation in a number of cases, the comma created by one of 159edo's three circles of fifths is smaller than that created by one of 205edo's five circles of fifths, or even that created by the 171edo circle of fifths- yes, closing the circle of fifths with the least amount of error possible was one consideration. There's also the matter of good 11-limit representation in particular, and 159edo suspasses both 171edo and 205edo on this point.