User talk:Aura

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Getting Started

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 and interval naming... 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)
Wow that was a long read! I'd just like to remind, with 159edo you can think of pitch categories and you don't have to pick fixed pitches for each category, unlike 12edo where you don't have much choice. For example, the 3rd note can vary from 5/4 to 9/7 in different occasions. AFAIK Jacob does his stuff mostly in terms of JI, so I'd think this way too in this case. As for where to draw the edo stopping line, my answer would be 6 cents for human audience (cuz there's an edo around that size that's become my latest favorite :)). FloraC (talk) 06:02, 2 September 2020 (UTC)
Sorry about that! I had a lot to say, and I still have a lot to say. For the record, I define a pitch class as consisting of a given pitch plus all multiples and divisions of that pitch by powers of two, so in 159edo, that's 159 different pitch classes available to work with. Also, I'd greatly prefer to keep the number of pitch classes limited for sections of my songs that remain in a particular key so that I don't have to do as much work in tuning them, not to mention that I've grown to like the idea of chords with different diatonic functions having different tunings- something that inevitably results from limiting your pitch class selection, for better or for worse. It is true that I'll change things up for purposes of modulation and when otherwise using accidentals, but nevertheless, while working in any one particular key, I'll generally keep using the same set of fixed pitches. --Aura (talk) 10:08, 2 September 2020 (UTC)
Just to throw this out there, I classify prime-limits based on their function relative to the tonic in tonal music. The 2-limit is the "Pitch Class Prime"- tying into my aforementioned definition of "Pitch Class". The 3-limit and 5-limit are classified as the "Diatonic Primes" because of their key functions in diatonic and just chromatic music. The 7-limit, 11-limit and 13-limit are classified as "Paradiatonic Primes" due to their relative ease (and, in the case of the 7-limit, frequency) of use as accidentals in otherwise diatonic keys, and, due to the fact that these relatively low primes can create intervals that can be readily used as substitutions for diatonic intervals- again tying into comments I made before about the interval 77/64 in particular. The 17-limit and 19-limit are classified as "Quasidiatonic Primes" owing to the most basic intervals in these families having striking similarities to diatonic intervals, but with greater complexity. Finally, the 23-limit, 29-limit, and 31-limit are classified as "Quasiparadiatonic Primes", a mouthful of a name that I've given them on account of these primes either having striking similarities to paradiatonic intervals, or being able to create intervals that can find use as substitutions for paradiatonic intervals, albeit with greater complexity. I also have a distinct classification for primes between 37 and 1021, and another for primes beyond 1021, but the names of these classes ties into a whole different topic. --Aura (talk) 18:52, 2 September 2020 (UTC)
Okay, so in accordance with Sam's suggestion, I'm renaming the 23-limit, 29-limit, and 31-limit the "Pseudodiatonic Primes", since these primes are not diatonic by any stretch, yet they can still serve as substitutes for the paradiatonic primes in a pinch. Any further thoughts? --Aura (talk) 22:26, 3 September 2020 (UTC)

links again

You should try [[File:Anticipation.mp3]] in the wiki text which appears as:

BTW: interesting piece!

Best regards --Xenwolf (talk) 16:06, 4 September 2020 (UTC)

I'm glad you like what I've done on the piece... --Aura (talk) 22:05, 4 September 2020 (UTC)

Quartismic Temperament

Howdy there, Aura! I decided to try and leave this for you to check out while you have the idea of a quartismic temperament in mind.

11-limit Mapping:

        1  1 2  2  2
        0 13 7 18 33
          -9?

MOS Scale: https://sevish.com/scaleworkshop/?name=Rank%202%20scale%20(53.37418112074753%2C%202%2F1)%2C%2013%7C9&data=53.374181%0A106.748362%0A160.122543%0A213.496724%0A266.870906%0A320.245087%0A373.619268%0A426.993449%0A480.367630%0A533.741811%0A587.115992%0A640.490173%0A693.864355%0A719.632370%0A773.006551%0A826.380732%0A879.754913%0A933.129094%0A986.503276%0A1039.877457%0A1093.251638%0A1146.625819%0A1200.000000&freq=440&midi=69&vert=5&horiz=1&colors=&waveform=triangle&ampenv=organ

The temperament finder gives me different (very complex) mappings, so I'm not going to worry about that. Also something interesting to note is that there's two types of fifths, as shown in the scale above. Anyways, have fun! --CritDeathX (talk) 13:44, 8 September 2020 (UTC)

Oh, I just noticed that you had a page for quartismic temperaments. Hopefully this temperament's interesting enough to list on there! --CritDeathX (talk) 14:01, 8 September 2020 (UTC)

I found another temperament! 2.3.5.9.19 Mapping:

        1  0  1  2 2
        0 -16 15 2 14

MOS Scale: https://sevish.com/scaleworkshop/?name=Rank%202%20scale%20(106.71461627796054%2C%201200.0)%2C%205%7C5&data=106.714616%0A213.429233%0A320.143849%0A426.858465%0A533.573081%0A666.426919%0A773.141535%0A879.856151%0A986.570767%0A1093.285384%0A1200.000000&freq=440&midi=69&vert=9&horiz=1&colors=&waveform=triangle&ampenv=organ

Scale Tree Diagram: http://www.microtonalsoftware.com/scale-tree.html?left=12&right=11&rr=1200&ioi=106.71461627796054

I should mention there is an 11 in this, but its way high up. Have fun with this too! --CritDeathX (talk) 15:08, 8 September 2020 (UTC)

Okay, I have to admit that I don't quite know what I'm looking at for any of the links you've sent, or even how to read the mappings that you've posted. It is true that I can play the scales on the keyboard, however, a number of the other facets of what you've shown are flying over my head at the moment- not that I don't want to actually get this data linked to the page on quartismic temperaments, as I'm absolutely sure this data is valuable. --Aura (talk) 15:19, 8 September 2020 (UTC)
The mappings show how many generators & octaves take to get to a certain interval. For example, in the first temperament I found, our 5/4 can be found after going 7 generators up, and then to get to 5/1, we go two octaves up. The scale tree diagram shows related generators based on certain EDOs. In case you're confused more, the generators I've used are in the titles of the scales in Scale Workshop. --CritDeathX (talk) 15:38, 8 September 2020 (UTC)

Preview feature if the wiki

Hi Aura,
I just want to draw your attention to the fact that there is a preview function when editing pages. Using it regularly will save you from having to make some small changes unnecessarily. It's the [Show preview] button right to the [Save changes] button below the edit memo.
Best regards --Xenwolf (talk) 05:49, 9 September 2020 (UTC)

Thanks. Unfortunately, I seem to be quite prone to missing words or punctuation marks only to see the need for corrections later... --Aura (talk) 05:50, 9 September 2020 (UTC)
I should also point out that if you go through the records of my edits, you'll find I'm prone to second-guessing myself in terms of how I try to express stuff... --Aura (talk) 06:14, 9 September 2020 (UTC)
Never mind. I know exactly what you're talking about. 🙂
I also see (sorry only now) that you are using the visual editor, so the preview is already incorporated in editing. I personally like the wikitext editor which separates editing and preview (like here on talk pages). Lots of minor updates make it harder to keep track even of a work in progress (especially for discussions, where others may be already starting to answer) or take longer time for organizers of this wiki to patrol the recent changes page (for example as to detect vandalism attempts).
Another thought: since this is a wiki it's not necessary to immediately fix every tiny error you make all the time. Improving your edits could as well be a good starting point for your fellow users here in the wiki. 🙂
Best regards --Xenwolf (talk) 11:57, 9 September 2020 (UTC)

Great idea

I'm very interested in learning about your Ideas of Consonance. Maybe this can help me figure out my own ideas about Consonance/Dissonance. --Xenwolf (talk) 19:36, 11 September 2020 (UTC)

undecimal subminor second, undecimal supermajor seventh

May I invite you to discuss the topic(s) under Talk:33/32#undecimal subminor second? --13:09, 18 September 2020 (UTC)

Feature request to Diatonic Function Map

I think an important improvement to File:New Diatonic Function Map.png would be to add a cents scale somewhere. I just tried to do it myself but it turned out as too hard. I hope it's not a big issue to you... --Xenwolf (talk) 22:02, 21 September 2020 (UTC)

Would be great, but I'm not sure how to do that... I mean, it's already a little less than one cent per pixel as is in terms of its overall size- it wouldn't be feasible to add markers for all 1200 cents... --Aura (talk) 02:12, 22 September 2020 (UTC)
I think 50-cent steps would absolutely suffice, maybe even 100-cent steps. It's for the reason that you don't have to look up intervals or calculate from ratio. And furthermore you can see at a glance that it is a logarithmic diagram. This scale could as well have bigger and smaller ticks and maybe only some numbers like 0, 300, 600, 900, 1200 (if numbers at all). I'm currently not able to decide what would look best... --Xenwolf (talk) 05:00, 22 September 2020 (UTC)
Alright, here's the latest version with the cents markers added...

Diatonic Function Map (Version 3).png

What do you think? --Aura (talk) 15:14, 22 September 2020 (UTC)
I think it's more useful now. I still have to figure out what all it may tell me...
I'm also surprised how large the 50-cent steps appear. Sadly we have no image map feature active in this wiki. I also plan to add a graph for the interval categories. --Xenwolf (talk) 17:23, 22 September 2020 (UTC)
I reckon you might want to make pages for all of the listed intervals on the chart if they don't exist already, and gather their sizes in cents. Once that's done, you can go through the Gallery of Just Intervals page manually and catalog the interval categories you see as well as calculate where they fall on this chart. Don't forget to also check the SHEFKHED interval names page, as it could also be of help for classifying intervals that are not listed on the chart. --Aura (talk) 17:46, 22 September 2020 (UTC)
Thanks for this enlightening reading (the SHEFKHED page). Now the meaning of these "confusing" labels P, M, m, A, d gets so obvious! It's really hard to see it if you are not an English native speaker (and even harder to recognize what you don't see); in German for example they would read R, G, k, Ü, v (R: rein, G: groß, k: klein, Ü: übermäßig, v: vermindert). --Xenwolf (talk) 18:11, 22 September 2020 (UTC)
You're welcome! Oh, and one other thing, Augmented intervals, Diminished intervals and the like are likely to be the main group of exceptions as to what type of interval is found in which region on my chart... --Aura (talk) 18:16, 22 September 2020 (UTC)
Just to make things easier, I can tell you that aside from this chart and the resources I've created, everything else here on this Wiki assumes Bass-Up tonality, so you should only focus on where intervals fall relative to the upper half of the chart for now. My predictions for the results of going through the aforementioned process is that in the Superdietic region, you should find lots of primes and seconds interspersed with one another whereas this is less common in the adjacent regions, likewise, the Subdietic region should host a similar interspersing of sevenths and octaves. In the Contravaricant region, you should expect to find seconds and thirds interspersed with one another, with a corresponding interspersing of sixth and sevenths in the Varicant region. In the Varicoserviant region, you should expect to find thirds and fourths interspersed with one another, with a corresponding interspersing of fifths and sixths in the Varicodominant region. Finally in the Antitonic region, there's a mixture of fourths and fifths. Aside from these specific regions, most of the other intervals are pretty straightforward in terms of what to expect- for example, primes in the Supercommatic region, seconds in the Reverse Lead, Reverse Semilead and Supertonic regions, thirds in the Mediant region, fourths in the Serviant and Semiserviant regions, Fifths in the Semidominant and Dominant regions, Sixths in the Contramediant region, Sevenths in the Subtonic, Semilead, and Lead regions, and octaves in the Subcommatic region. While I do expect there to be outliers, they should be relatively few in number. --Aura (talk) 18:03, 22 September 2020 (UTC)

tri vs. tre

The English one, two, three is uno, due, tre in Italian. Because classic music language is mostly (derived from) Italian, both is right. --Xenwolf (talk) 12:45, 22 September 2020 (UTC)

Ah... Still, I assume "tridecimal" is the form we ought to use- for consistency's sake. --Aura (talk) 14:26, 22 September 2020 (UTC)

programming language of choice

What programming language do you usually use (if you use one at all)? I ask because I plan to enrich the cent page with some snippets. --Xenwolf (talk) 09:50, 19 October 2020 (UTC)

Truth be told I don't really know how to program, so I guess the answer is "none of them"... --Aura (talk) 12:14, 19 October 2020 (UTC)