Lhearne

::::: Ah, great! I was wondering if you had named any of it yet! In this system 33/32 functions as the large step in the 24-note scale, the small step in the 15-note scale, and the chroma in the 9-note scale, so I can see it having it's own identity as a musical interval. Most larger commas do in other contexts. Myself I have called 11/8 and 16/11 the major fourth and minor fifth in a Porcupine[7] system, so I like the idea of calling them the paramajor fourth and the paraminor fifth. I also think this system is a great find! It's remarkably accurate, and not unwieldly complex, and is the first to overtake the simple and powerful Neutral temperament as the 'best' temperament when you look for more accurate temperaments. I think your naming scheme for the tuning works well, and perhaps should exist in its context separately to my naming scheme, which is not designed for this sort of use. Since 11/8 is an alteration of 4/3, 2 11/8s are a double alteration of 16/9, so though the sound a sort of major seventh they in this way instead a type of minor seventh, in order to conserve diatonic interval arithmetic, and named as such in my system: an Up Up minor seventh. If we consider it instead as a type of major seventh, we could consider prefixing it as 243/242 from 243/128, with 243/242 the prefixed comma. In my porcupine system this interval would be labelled an Augmented 7th, where 11/8 * 4/3 = 11/6 is a Perfect seventh (or, alternatively, simply a major seventh) but in my systems for non-fifth based contexts I use the interval logic of the generator, and label the generator a perfect interval (or not, when I tried to advocate for called 3/2 a minor fifth even in meantone to back-generalize calling 121/64 a major seventh haha). However, since you use 'Alpharabian' as a prefix indicating adding 243/242 to the limma, then since a limma is a minor second it follows that 128/121 is an Alphaminor second and 121/64 is an alphamajor seventh. Then the 'paraminor' prefix indicates alteration down by 33/32, 'paramajor' indicates alteration up by 33/32, and 'alpha' indicates alteration by 243/242. Using capitals to indicate alteration upwards and lowercase to indicate prefixing downwards, Alpharabian[9] would be labelled  

::::: This allows us to have well-ordered names for the scale. If I were to build this ability into my system instead, I would add a prefix for 243/242 that begins with a different letter. I'm at a loss for what I would use because 243/242 doesn't have any association to me as a chroma. All my other prefixes are associated with a 'known' meaning.  

::::: --[[User:Lhearne|Lhearne]] ([[User talk:Lhearne|talk]]) 01:58, 3 February 2021 (UTC)