User talk:Aura/Aura's Ideas on Tonality: Difference between revisions
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: "There should also be a simple process to get from the ratio to the name. Why are some ratios Alpharabian and some Betarabian? What simple test can be applied to say 729/704 to determine which category it falls into? What happens to the intervals that don't fit into either category?" The terms are "Alpharabian" and "Betarabian", and yes, there is a rudamentary test in place. Alpharabian intervals are generally either directly in the 2.11 subgroup, or, they differ from a nearby Pythagorean interval by either 33/32, 1331/1296, 8192/8019, 4096/3993, or 243/242. The system for denoting Betarabian intervals is less complete, but so far, Betarabian intervals usually differ from Alpharabian intervals by a rastma. When dealing with intervals that are distant by additionl rastmas, I would just use "Rastimic", "Birastmic", "Trirastmic", and so on. | : "There should also be a simple process to get from the ratio to the name. Why are some ratios Alpharabian and some Betarabian? What simple test can be applied to say 729/704 to determine which category it falls into? What happens to the intervals that don't fit into either category?" The terms are "Alpharabian" and "Betarabian", and yes, there is a rudamentary test in place. Alpharabian intervals are generally either directly in the 2.11 subgroup, or, they differ from a nearby Pythagorean interval by either 33/32, 1331/1296, 8192/8019, 4096/3993, or 243/242. The system for denoting Betarabian intervals is less complete, but so far, Betarabian intervals usually differ from Alpharabian intervals by a rastma. When dealing with intervals that are distant by additionl rastmas, I would just use "Rastimic", "Birastmic", "Trirastmic", and so on. | ||
: "As a practical matter, if some violinists or vocalists were performing 2.3.11 JI music, they would constantly be fudging the rastma. They might shift a pitch by 7¢, or let the tonic drift by 7¢. The neutral triad is an innate-comma chord (aka essentially tempered chord), and the 3rd might fall between 11/9 and 27/22. No listener would notice these slight discrepancies. The rastma would effectively be tempered out, and the notation could reflect this. Simply notate two notes only a rastma apart as the same note, and trust the performers' ears." On the contrary, I've met a music director who can hear a difference between 440 Hz and 438 Hz- a difference of less than 8¢, and I know that 7¢ is above the average JND, so performers fudging the rastma would likely drive this director batty | : "As a practical matter, if some violinists or vocalists were performing 2.3.11 JI music, they would constantly be fudging the rastma. They might shift a pitch by 7¢, or let the tonic drift by 7¢. The neutral triad is an innate-comma chord (aka essentially tempered chord), and the 3rd might fall between 11/9 and 27/22. No listener would notice these slight discrepancies. The rastma would effectively be tempered out, and the notation could reflect this. Simply notate two notes only a rastma apart as the same note, and trust the performers' ears." On the contrary, I've met a music director who can hear a difference between 440 Hz and 438 Hz- a difference of less than 8¢, and I know that 7¢ is above the average JND, so performers fudging the rastma would likely drive this director batty. The main reason for me not tempering out the rastma is that it is useful in modulating to quartertone-based keys Jacob-Collier-style. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 11:03, 1 November 2020 (UTC) | ||