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

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In answering these questions one should note that the Prime and the Octave are the fundamental intervals in both my system and conventional music systems. Furthermore, it doesn't make sense to have dedicated names for intervals that go in the opposite direction from of a given tonality's direction of construction, such as "Paraminor Unison", and, since a term like "Paramajor Unison" would imply the existence of the nonsensical "Paraminor Unison" by definition, we can discard the idea of a "Paramajor Unison" also. Therefore, we can reuse the term "Superprime", as well as the terms "Suboctave", and "Superoctave", as the "Super-" and "Sub-" prefixes imply widening and narrowing respectively. For the same reason, we should additionally use the "Super-" prefix for the augmentation of Major intervals by 33/32, and the dimunition of Minor intervals by 33/32. While the "Super-" and "Sub-" prefixes are often associated with the 7-limit, it should be remembered that in this system, the 7-limit versions of these intervals are variations on the standard intervals as opposed to being the standard intervals themselves. Furthermore, while I have [[User talk:Aura #Getting Started|previously]] advocated for the use of "Parasuper-" and "Parasub-" to refer to these 11-limit intervals, I now realize that such a distinction is largely untenable in light of the the 11-limit's status as a navigational prime, and the higher priority it thus carries over the 7-limit. Nevertheless, because the dimunition of a major interval by 33/32 does not result in the same interval as does the augmentation of a minor interval by 33/32, as these intervals differ by the rastma, I find it prudent to use the term "Greater Neutral" to refer to dimunition of a major interval by 33/32, and the term "Lesser Neutral" to refer to the augmentation of a minor interval by 33/32.

Now, if one does the math, they will realize that an Alpharabian Supermajor Second, having a ratio of [[297/256]], is larger than an Alpharabian Subminor Third with its ratio of [[1024/891]], and that the difference between these two intervals is 264627/262144- a comma ~~that~~ is ~~also the sum of the rastma and the Alpharabian comma~~.

Now, if one does the math, they will realize that an Alpharabian Supermajor Second, having a ratio of [[297/256]], is larger than an Alpharabian Subminor Third with its ratio of [[1024/891]], and that the difference between these two intervals is 264627/262144- a comma which similarly separates other enharmonic quartertone-based interval pairs and is tempered out in 24edo.

== Measuring EDO Approximation Quality ==

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 In answering these questions one should note that the Prime and the Octave are the fundamental intervals in both my system and conventional music systems.  Furthermore, it doesn't make sense to have dedicated names for intervals that go in the opposite direction from of a given tonality's direction of construction, such as "Paraminor Unison", and, since a term like "Paramajor Unison" would imply the existence of the nonsensical "Paraminor Unison" by definition, we can discard the idea of a "Paramajor Unison" also.  Therefore, we can reuse the term "Superprime", as well as the terms "Suboctave", and "Superoctave", as the "Super-" and "Sub-" prefixes imply widening and narrowing respectively.  For the same reason, we should additionally use the "Super-" prefix for the augmentation of Major intervals by 33/32, and the dimunition of Minor intervals by 33/32.  While the "Super-" and "Sub-" prefixes are often associated with the 7-limit, it should be remembered that in this system, the 7-limit versions of these intervals are variations on the standard intervals as opposed to being the standard intervals themselves.  Furthermore, while I have [[User talk:Aura #Getting Started|previously]] advocated for the use of "Parasuper-" and "Parasub-" to refer to these 11-limit intervals, I now realize that such a distinction is largely untenable in light of the the 11-limit's status as a navigational prime, and the higher priority it thus carries over the 7-limit.  Nevertheless, because the dimunition of a major interval by 33/32 does not result in the same interval as does the augmentation of a minor interval by 33/32, as these intervals differ by the rastma, I find it prudent to use the term "Greater Neutral" to refer to dimunition of a major interval by 33/32, and the term "Lesser Neutral" to refer to the augmentation of a minor interval by 33/32.
-Now, if one does the math, they will realize that an Alpharabian Supermajor Second, having a ratio of [[297/256]], is larger than an Alpharabian Subminor Third with its ratio of [[1024/891]], and that the difference between these two intervals is 264627/262144- a comma that is also the sum of the rastma and the Alpharabian comma.
+Now, if one does the math, they will realize that an Alpharabian Supermajor Second, having a ratio of [[297/256]], is larger than an Alpharabian Subminor Third with its ratio of [[1024/891]], and that the difference between these two intervals is 264627/262144- a comma which similarly separates other enharmonic quartertone-based interval pairs and is tempered out in 24edo.
 == Measuring EDO Approximation Quality ==