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

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When two EDOs are both given a "P" rating in the Hunt system for representation quality, the tie between them is broken by which EDO-tempered version has the smaller absolute error. Furthermore, when the best representation of an interval in a given p-limit sequence cannot be reached by stacking tempered versions of the preceding intervals in that same p-limit sequence, the disconnected interval and any intervals following it in the same sequence are disqualified under my standards, no matter how good their representation rating in the Hunt system is.

== Navigational Primes and Key Signatures ==

Now, many if not most musicians who are not microtonalists are acquainted with standard music notation, with its clefs and staves, key signatures and time signatures. However, when you take this into the microtonal realm, it becomes readily apparent that- in all of the most intuitive systems- it is the 3-limit that defines both the standard location and structure of the various notes and key signatures. This makes even more sense when you consider that the standard sharp and flat accidentals modify the base note by an [[apotome]].

== 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. There's also the matter of good 11-limit representation in particular, and 159edo surpasses both 171edo and 205edo on this point, and as if that weren't enough, I've since found out that the deal is made even sweeter by the fact that the 3-limit and the 11-limit are joined in this EDO by the tempering out of 1771561/1769472- a feature that is absent from both 171edo and 205edo.

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 When two EDOs are both given a "P" rating in the Hunt system for representation quality, the tie between them is broken by which EDO-tempered version has the smaller absolute error.  Furthermore, when the best representation of an interval in a given p-limit sequence cannot be reached by stacking tempered versions of the preceding intervals in that same p-limit sequence, the disconnected interval and any intervals following it in the same sequence are disqualified under my standards, no matter how good their representation rating in the Hunt system is.
+== Navigational Primes and Key Signatures ==
+Now, many if not most musicians who are not microtonalists are acquainted with standard music notation, with its clefs and staves, key signatures and time signatures.  However, when you take this into the microtonal realm, it becomes readily apparent that- in all of the most intuitive systems- it is the 3-limit that defines both the standard location and structure of the various notes and key signatures.  This makes even more sense when you consider that the standard sharp and flat accidentals modify the base note by an [[apotome]].
 == 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.  There's also the matter of good 11-limit representation in particular, and 159edo surpasses both 171edo and 205edo on this point, and as if that weren't enough, I've since found out that the deal is made even sweeter by the fact that the 3-limit and the 11-limit are joined in this EDO by the tempering out of 1771561/1769472- a feature that is absent from both 171edo and 205edo.