Alpharabian tuning

The Alpharabian tuning is an 11-limit version of just intonation- specifically the version that is limited to the 2.3.11 subgroup- that is currently being pioneered in large part by Aura.

Interval Naming Scheme

In the current interval naming scheme, there are several basic premises of Alpharabian tuning:

Intervals that are in the 2.11 subgroup are all considered Alpharabian intervals.
The intervals 3/2, 4/3, 9/8, 16/9, and so forth, have the same functions as in Pythagorean tuning.
Intervals that result from the modification of a Pythagorean interval by 1089/1024 are labeled similarly to those modified in the equivalent fashion by 2187/2048, the only difference being that modification by 1089/1024 results in an Alpharabian interval rather than a Pythagorean interval.
Since 1089/1024 is (33/32)^2, modifying a Pythagorean interval by 33/32 always results in an interval that is considered "Alpharabian".
As both the rastma and 1331/1296 are subchromas that form differences between members of the 2.11 subgroup and Pythagorean intervals, both of these subchromas belong to a set of intervals defining different interval sets within Alpharabian tuning, and subchromas within this particular interval set help define the differences between Pythagorean, Alpharabian and Betarabian intervals.

The following rules are directly derived from the above premises:

Generally, intervals that result from the modification of a Pythagorean interval by 33/32 take either the 'parasuper' or 'parasub' prefixes, however, there are a number of special cases...

Augmentation of a Perfect Fourth or Perfect Fifth by 33/32 results in a Paramajor interval
Dimunition of a Perfect Fourth or Perfect Fifth by 33/32 results in a Paraminor interval
Augmentation of a Pythagorean Minor interval by 33/32 results in a Lesser Neutral interval
Dimunition of a Pythagorean Major interval by 33/32 results in a Greater Neutral interval

Generally, intervals that result that result from the modification of a Pythagorean interval by 1331/1296 take either the 'super' or 'sub' prefixes, with these prefixes generally being stacked where multiple such modifications occur, however, there are some significant caveats...

Augmentation of a Pythagorean Minor interval by a single 1331/1296 results in a Supraminor interval, but a second such augmentation results in a Betarabian Major interval due to said interval differing from the nearby Alpharabian Major (covered under modifications by 1089/1024) by a rastma.
Dimunition of a Pythagorean Major interval by a single 1331/1296 results in a Submajor interval, but a second such dimunition results in a Betarabian Minor interval due to said interval differing from the nearby Alpharabian Minor (covered under modifications by 1089/1024) by a rastma.

Parachromatic-Paradiatonic Contrast

Most music theorists know that there are basically two types of semitones- the diatonic semitone or minor second, and the chromatic semitone or augmented prime. They also know that a diatonic semitone and a chromatic semitone add up to a whole tone. In 3-limit tuning, the diatonic semitone has a ratio of 256/243, and the chromatic semitone- with a ratio of 2187/2048- is otherwise known as the apotome, and these two intervals add up to a 9/8 whole tone. Furthermore, in 5-limit tuning, these same semitones exist alongside other semitones derived through alteration by 81/80. On one hand, adding 81/80 to 256/243 yields 16/15, and adding another 81/80 yields 27/25- two additional diatonic semitones. On the other hand, subtracting 81/80 from the apotome yields 135/128, and subtracting another 81/80 yields 25/24- two additional chromatic semitones. When added up in the proper pairs- 16/15 with 135/128, and 27/25 with 25/24- the additional sets of semitones again yield a 9/8 whole tone. In light of all this, it has been argued that the familiar sharp signs and flat signs- which are used to denote the chromatic semitone- were never meant to denote exactly half of a whole tone, but rather, a whole tone minus a minor second.

Building on this logic, we can then apply similar distinctions among quartertones, and thus make the argument that quartertones don't have to denote exactly one fourth of a whole tone in as of themselves, but rather, they only have to add up to a whole tone when paired up correctly. However, it should be noted that for quartertones, there are sometimes multiple correct options, and thus, things are more complicated. We shall begin to define the musical functions of quartertones by drawing a distinction between the terms "Parachromatic" and "Paradiatonic" for purposes of classifying quartertone intervals. For starters, paradiatonic quartertones are analogous to diatonic semitones in that they are denoted as seconds, albeit subminor seconds, while parachromatic quartertones are denoted as superprimes of some sort. However, the distinction goes further than that- a parachromatic quartertone and a paradiatonic quartertone add up to a diatonic semitone, while two parachromatic quartertones add up to a chromatic semitone. Given both these definitions for "paradiatonic" and "parachromatic", and given that a diatonic semitone and a chromatic semitone add up to a whole tone when paired correctly, we can deduce that a whole tone can be assembled from three parachromatic quartertones and one paradiatonic quartertone. Because there are sometimes multiple correct options for assembling parachromatic and paradiatonic intervals to make a 9/8 whole tone, we have to choose the simplest configuration of paradiatonic and parachromatic intervals to assemble in order to create a 9/8 whole tone- a configuration that only requires one type of parachromatic quartertone and one type of paradiatonic quartertone.