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

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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 all of 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 standard notes and key signatures that one finds in [[12edo]]. This even extends to the fact that the standard sharp and flat accidentals modify the base note by an [[2187/2048|apotome]], and how the double sharp and double flat accidentals modify the base note by two apotomes. When one comes from a background in 24edo as I have, and has even used quartertone-based keys signatures as I have, it becomes apparent that the 11-limit joins together with the 3-limit in defining the standard location and structure of the various notes and quartertone-based key signatures that one would see in 24edo.

Because the 3-limit and the 11-limit are the primes that have all of this foundational functionality, they are naturally very important in musical systems that have their roots in 24edo, and their pivotal role in laying the groundwork for key signatures means that they can be referred as the "navigational primes". In both the traditional and quartertone-based key signatures, it is the Pythagorean Diatonic Scales that arise as the standard variants for the various key signatures, as these are the simplest diatonic scales that can be formed with the 3-limit, and the pure 11-limit is not capable of forming diatonic scales. Although the 5-limit, 7-limit and 13-limit also play a role in defining key signatures, these primes define variations on the standard key signatures as opposed to the standard key signatures themselves. For the sake of simplicity, it can generally be assumed that that higher primes are ill-suited for serving as anything other than accidentals.

Because the 3-limit and the 11-limit are the primes that have all of this foundational functionality, they are naturally very important in musical systems that have their roots in 24edo, and their pivotal role in laying the groundwork for key signatures means that they can be referred as the "navigational primes". In both the traditional and quartertone-based key signatures, it is the Pythagorean Diatonic Scales that arise as the standard variants for the various key signatures, as these are the simplest diatonic scales that can be formed with the 3-limit, and the pure 11-limit is not capable of forming diatonic scales at all. Although the 5-limit, 7-limit and 13-limit also play a role in defining key signatures, these primes define variations on the standard key signatures as opposed to the standard key signatures themselves. For the sake of simplicity, it can generally be assumed that that higher primes are ill-suited for serving as anything other than accidentals.

== Measuring EDO Approximation Quality ==

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 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 all of 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 standard notes and key signatures that one finds in [[12edo]].  This even extends to the fact that the standard sharp and flat accidentals modify the base note by an [[2187/2048|apotome]], and how the double sharp and double flat accidentals modify the base note by two apotomes.  When one comes from a background in 24edo as I have, and has even used quartertone-based keys signatures as I have, it becomes apparent that the 11-limit joins together with the 3-limit in defining the standard location and structure of the various notes and quartertone-based key signatures that one would see in 24edo.
-Because the 3-limit and the 11-limit are the primes that have all of this foundational functionality, they are naturally very important in musical systems that have their roots in 24edo, and their pivotal role in laying the groundwork for key signatures means that they can be referred as the "navigational primes".  In both the traditional and quartertone-based key signatures, it is the Pythagorean Diatonic Scales that arise as the standard variants for the various key signatures, as these are the simplest diatonic scales that can be formed with the 3-limit, and the pure 11-limit is not capable of forming diatonic scales.  Although the 5-limit, 7-limit and 13-limit also play a role in defining key signatures, these primes define variations on the standard key signatures as opposed to the standard key signatures themselves.  For the sake of simplicity, it can generally be assumed that that higher primes are ill-suited for serving as anything other than accidentals.
+Because the 3-limit and the 11-limit are the primes that have all of this foundational functionality, they are naturally very important in musical systems that have their roots in 24edo, and their pivotal role in laying the groundwork for key signatures means that they can be referred as the "navigational primes".  In both the traditional and quartertone-based key signatures, it is the Pythagorean Diatonic Scales that arise as the standard variants for the various key signatures, as these are the simplest diatonic scales that can be formed with the 3-limit, and the pure 11-limit is not capable of forming diatonic scales at all.  Although the 5-limit, 7-limit and 13-limit also play a role in defining key signatures, these primes define variations on the standard key signatures as opposed to the standard key signatures themselves.  For the sake of simplicity, it can generally be assumed that that higher primes are ill-suited for serving as anything other than accidentals.
 == Measuring EDO Approximation Quality ==