Okay, so I'm new here, and I'm new to editing wikis in general, so I need to learn some of the ropes around here. Also, I do have some ideas for interval names and notations, building off of both the SHEFKHED interval naming system and ups and downs notation, and I would like to discuss this. I mean, seeing as I've taken a shine to 159edo, I need a better way of notating this kind of stuff in my music- something that still manages to be diatonic-based... --Aura (talk) 19:41, 31 August 2020 (UTC)

Howdy here! If you want help with editing the wiki, there's a Conventions page on the left side of the wiki that you can refer to, though as a relatively new editor myself, its pretty easy to get the hang of things if you just look at what other people do while editing. On the topic of notation, I'd be happy to talk about it (and perhaps about 159EDO as well!). --CritDeathX (talk) 02:26, 1 September 2020 (UTC)
I'm glad to see that someone has noticed what I'm doing! For the record, I do have distinct names for intervals like 11/8 and 16/11. I call the 11/8 interval the "paramajor fourth" and the 16/11 interval the "paraminor fifth" in part as a reference to this [1]. Similarly, I call 128/99 the "paraminor fourth" and 99/64 the "paramajor fifth". For the record, I do use "parasuper" and "parasub" as prefixes not only for the alteration of perfect primes and perfect octaves by 33/32, but also for the augmentation of major intervals and the dimunition of minor intervals by 33/32. Because the dimunition of a major interval by 33/32 does not result in the same interval as does the augmentation of a minor interval by 33/32, especially in those equal divisions of the octave where 243/242 is not tempered out, I use the term "greater neutral" to refer to dimunition of a major interval by 33/32, and the term "lesser neutral" to refer to the augmentation of a minor interval by 33/32. Do note that I use the Pythagorian chain of fifths as a base. --Aura (talk) 02:51, 1 September 2020 (UTC)
Okay, I like the sound of this so far. I assume you use super/sub and major/minor for 7- & 5-limit intervals respectively, yes? --CritDeathX (talk) 03:32, 1 September 2020 (UTC)
Yes, I do. However, this raises the question of what to do for intervals like 256/225, which naturally occurs between the seventh and second scale degrees in the just versions of the Greater Neapolitan and Lesser Neapolitan scales- otherwise known as the Neapolitan Major and Neapolitan Minor scales respectively. --Aura (talk) 03:44, 1 September 2020 (UTC)
Okay... I have an idea... So, I'm looking at this page [[2]], as well as this page [[3]], and I notice that there's more than one "minor third" and more than one "major third". The same is true of intervals such as supermajor thirds and subminor thirds- particularly for equal divisions of the octave where the septimal kleisma is not tempered out, such as in 159edo. With that in mind, I'm thinking we should disambiguate between different intervals in the same general range. We can build directly off of the SHEFKHED interval naming system for the basics, though with the difference that any Pythagorean interval other than the Perfect Prime, the Perfect Octave, the Perfect Fifth and the Perfect Fourth with an odd limit of 243 or less should gain the explicit label of "Diatonic"- this lends itself to names such as "Diatonic Major Sixth" for 27/16. Following along this same line of thinking for 5-limit intervals, we can similarly build off of the SHEFKHED interval naming system and explicitly label both 5/4 and 8/5, as well as intervals connected to them by a chain of Perfect Fifths "Diatonic"- assuming the odd limit for said interval is 45 or less. Among the end results of this are that 5/3 is labeled the "Classic Diatonic Major Sixth". I'm currently thinking that certain other 5-limit intervals should also gain the label "Classic" such as 25/16 or even 25/24... --Aura (talk) 06:58, 1 September 2020 (UTC)
Hello and thx for contributing your ideas! This topic is of my interest and I actually opened a conversation on our FB group on how we may call most 5-limit intervals. To summarize, some would use "pental" for 5-limit intervals, some others would default to simplest ratios in the group and add definitives when needed, but the solution most convincing to me is to call any Pythagorean intervals "Pythagorean" and any 5-limit intervals "classic" (sometimes "grave/acute" for high-odd-limit intervals), though to distinguish 25/24 from 135/128 this needs further disambiguation. I'd also refrain from a meantone-centrist view, where "aug" and "dim" are sometimes abused e.g. "aug sixth" for 7/4, which is only true in meantone. FloraC (talk) 08:24, 1 September 2020 (UTC)
For the record, I'm doing this with 159edo in mind, and this is not a meantone temperament as the syntonic comma is not tempered out. I'm not keen on using too many numeric descriptors like "pental" or "septimal" or even "undecimal" for this particular idea, as at the end of the day, my goal is to build off of the SHEFKHED interval naming system for EDOs up to 160edo. I should also point out that not all Pythagorean intervals are Diatonic intervals- only those with an odd limit of 243 or less, therefore, I'm thinking that "Diatonic" is the label that ought to be privileged over "Pythagorean". On a semi-related note, my preferred major scale consists of the intervals 1/1, 9/8, 5/4, 4/3, 3/2, 27/16, 15/8, and 2/1, and I do in fact build directly off of this scale for my diatonic chords- yes, the grave fifth occurs between the sixth and the third, and for me, this serves to amplify the diatonic functions of the VIm chord, as this kind of tuning says "we're not done yet", especially in deceptive cadences. --Aura (talk) 15:39, 1 September 2020 (UTC)
While I'm on this whole topic of Diatonic intervals, I should mention that I prefer the notes of all my scales to connect directly to the tonic by means of the intervals between the tonic and the other notes in the scale having a power of two in the numerator and or the denominator- that said, I still recognize that 6/5 doesn't meet this criteria when this interval occurs between the I and the IIIm scale degrees, and thus, my preferred minor scale consists of the intervals 1/1, 9/8, 77/64, 4/3, 3/2, 8/5, 16/9, and 2/1. It is for this reason- along with the fact that the 7-limit finds frequent use among barbershop quartets and the like as accidentals in otherwise diatonic keys- that I would classify 11/8, 16/11, 7/4, and 8/7 as "Paradiatonic" intervals. --Aura (talk) 16:09, 1 September 2020 (UTC)
Now, back to this discussion of notation, some will undoubtedly ask where this process of coming up with labels for scale steps of differing edos should stop, and I have an answer for that as well. There is a step-size limit at play in which the step size should be greater than 7 cents. This is because at a step size of 7 cents, the distance halfway between steps is 3.5 cents, which, from what I'm gathering, is below the average just noticeable difference between pitches. At step sizes of 7 cents and smaller, the steps will begin to bleed into one another and become indistinguishable from one another to even the best trained ears. Thus, any edo with a step size of 7 cents or less is ineligible for this kind of extensive process of labeling different step sizes. --Aura (talk) 16:51, 1 September 2020 (UTC)
I can anticipate that some may object that I should draw the line for defining edo steps at something more substantial like 13.5 cents, but I while concur that an edo step size between 7.5 and 13.5 cents is not viable in the traditional musical sense as a step between consecutive notes, I do notice that it does have a usage as a comma pump, and therefore, it has musical value as an edo step size for purposes of modulation, especially for modulating Jacob-Collier-style between keys. --Aura (talk) 17:49, 1 September 2020 (UTC)
One of the problems I have with notation that doesn't take these kinds of kleismatic differences into account is that without such distinctions, it's hard to determine which notes should have which tunings in order to accomplish a seamless modulation between keys on different circles of fifths, and I've honestly found that to be a significant problem with transcriptions of Jacob Collier's rendition of In the Bleak Midwinter in particular. --Aura (talk) 18:33, 1 September 2020 (UTC)