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

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 I'm not a fan of using large edos to measure everything else, so I'll skip the 159edo vs. 205edo discussion.
+: "Conventionally, there is an aug unison but not a dim unison. So it seems a Paramajor Unison would be valid? What ratio would that be?" Well, Major and Minor never occur unpaired in conventional music, and "Paramajor" and "Paraminor" are coined in analogy to Major and Minor respectively.  This is why I reject the idea of a "Paramajor Unison".  Rather, I refer to a "Parasuperprime", which, ideally, has 33/32 as the ratio.
+: "Seems like dividing 9/8 into a diatonic quartertone and 3 ''identical'' chromatic quartertones will always make huge ratios. Maybe better to have unequal steps."  Nope.  Why?  Because the Apotome has a ratio of 2187/2048- that's four digits for each number, just like with the ratios in my current system.
+: "Greater/Lesser is a problem because one can always add or subtract a rastma and get a new ratio slightly larger or smaller. I guess you solve this with Betarabic vs Alpharabic? This is the problem with cents-based nomenclatures. There's always more ratios in that cents range to deal with, and the nomenclature eventually breaks. I prefer monzo-based nomenclatures that don't break."  I can understand that.
+: "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 people who can hear a difference between 440 Hz and 438Hz, and I know that 7¢ is above the average JND. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 10:19, 1 November 2020 (UTC)