User:Eufalesio/PLIN: Difference between revisions

Short for '''Pythagoreanoid Loose Interval Notation''', it's a type of [[2.3-equivalent class and Pythagorean-commatic interval naming system|2.3-equivalent class]]. It attempts to provide precision tiers to name intervals, based on a chain of '''pure''' fifths. The reason of why to use a chain of fifths, apart from tradition and my biases, is that it provides the simplest framefork for building scales, and because it is the most widely used worldwide. Why to use pure fifths and not an edo's best approximation of a fifth is to have a retrocompatible sistem. Among the lower primes, it makes the best small MOS scales (2,3,5,(7),12,(17),(29),41,53), second in place to 11 (2,5,(7),(9),11,13,24,37). An argument could be made to make a system based on 11 to build scales, but that's beyond the scope of this article. After all, this is about a ''pythagoreanoid'' notation, not a ''hendecoid'' notation.

Any single region has infinite intervals represented in it, and thus it is important to distinguish the breadth of the buckets any JI interval can fall into. So, while there are an infinite amount of minor thirds, and of superminor thirds, and of qu superminorthirds, and of twomins qu superminor thirds, all of them will 6/5; with 12-PLIN being quite rough, 53-PLIN being very accurate, and 665-PLIN and 7315-PLIN further refining the accuracy to extreme levels to the point where all of those will sound indistinguishable from 6/5, since the difference will be only of 0.16 c per region in 7315-PLIN.

12-PLIN, 53-PLIN and 665-PLIN are MOSses, more concretely, 5L 7s 6|5 1.260, 41L 12s 26|26 H=1.1822, and 306L 359s H=1.0427, but 159-PLIN and 7315 are not, as they modify the two last MOSses respectively with fractions of the telic commas. As such, to make things easier, '''EPLIN'''s may be used to have exactly equal regions, which will make things easier to work with. by default, PLINs are not equal, so it needs to be specified when an equalized PLIN is being used, because it can change the region an interval falls into. For example, 31/16 is a rough octave, but in 12-EPLIN, a '''eq'''rough major seventh. 7/4 is a fixsubminor seventh, but in 159-EPLIN, an '''equwee'''subminor seventh.  

For two, is 11/9 a minor third or a major third? Or 13/10 a major third or a fourth? That depends on how you treat it. Augmented/diminished, and '''chromas''' have the same logic in that they are '''''functional''''' in this system. Using ''perfect'' is also redundant and ambiguous, so use different coinages to refer specifically to the centers of regions of the different PLINs. An interval is not a chroma, but rather, '''''works''''' as a chroma. When you are dealing with intervals inside a scale and a piece, it may be useful to refer to 25/16 as an augmented fifth, but '''sonically''' speaking, it is a rough minor sixth. Or a hypominor sixth. Or a mi hypominor sixth. Or a fourplus mi hypominor sixth... you get the point.  

Also, no words for other primes. So no ptolemaic/pental/classical, septimal, undecimal... etc. Everything stays in the 3-limit. Minimum complexity, reducing the amount of classes and descriptors to worry about to the absolute minimum.

The choice of giving no center descriptor to 53-PLIN is that I believe that for the average xennie, 53 regions is precise enough to accurately name most intervals, and simple enough that the regions cannot be confused.

Of course, the names would have many synonyms, so hypo/hyper = infra/ultra, minor second = limma, major second = tone, unison = prime, major third = ditone. Extending my rules; apotome = superminor second; superlimma.  

|+ 159-PLIN; 41L 12s 26 |159-PLIN up to the first major second; MOS 41L 12s 26|26; tolerance = '''3.91c'''