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 interval 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, leading to 159edo generally having better representations of the 3-limit and 11-limit in general- something which is ~~especially important~~ in light of the aforementioned highly important functions of these two prime limits in particular.

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 interval 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, leading to 159edo generally having better representations of the 3-limit and 11-limit in general- something which is of major significance in light of the aforementioned highly important functions of these two prime limits in particular.

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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 interval 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, leading to 159edo generally having better representations of the 3-limit and 11-limit in general- something which is ~~especially important~~ in light of the aforementioned highly important functions of these two prime limits in particular.		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 interval 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, leading to 159edo generally having better representations of the 3-limit and 11-limit in general- something which is of major significance in light of the aforementioned highly important functions of these two prime limits in particular.