User talk:Lucius Chiaraviglio

Functional Harmony

Hello! I've just checked out your user page, and I'm starting to wonder if you might be interested in my ideas for microtonal functional harmony. I bring this up because I myself like to try and apply my own theory to the creation of new classical music. --Aura (talk) 14:42, 8 July 2024 (UTC)

While I'm thinking about it, I should mention that I tend to want to use both Pythagorean intervals- some of which would be considered as Xenharmonic- as well as both 5-limit and 11-prime-based intervals, so those have factored into my work considerably. --Aura (talk) 14:46, 8 July 2024 (UTC)

Sorry it took me so long to get back to you. I haven't had a chance to read the contents of the link you posted yet (but I just checked to make sure that it is possible for me to do so). Let me get back to you after the CrowdStrike mess is cleaned up at work. Lucius Chiaraviglio (talk) 02:42, 22 July 2024 (UTC)

Actually got a chance to read it after all before I go back to work tomorrow (this DOESN'T mean that I am done with the CrowdStrike fiasco). The names are confusing and hard to remember, but when you have numbers (including increments of EDOs), it starts to make sense. Note that it would help A LOT to move the graph of intervals up so that readers see that around the time you start naming scale degrees, as opposed to long afterwards. As for Pythagorean intervals, I have recently been thinking that it would be good to extend the table of Pythagorean intervals (of which a semi-extended version is currently found under 3-limit) up to 53 notes, also including higher-limit intervals and the differences between these and the Pythagorean intervals. Probably should go into a different article from 3-limit, though -- would like to see Xenharmonic Wiki get an Extended Pythagorean Tuning article. Lucius Chiaraviglio (talk) 04:17, 22 July 2024 (UTC)

Okay, I have to admit that I think of names a bit more than numbers most of the time, and I tried to make sure the names fit the functions as best as I could- if I need to provide etymologies for the names to help you understand them, as well as devices to help remember them, I can do so, provided we discuss how to go about doing this. The original graph there is outdated, and is there for historical context, so I'll probably have to make a new one. --Aura (talk) 16:15, 22 July 2024 (UTC)

Alright, I've added a new graph of intervals in the location that you suggested- one that's should hopefully make more sense of the article. If I need to explain the names of functions a bit more, I'm happy to. --Aura (talk) 22:07, 26 July 2024 (UTC)

That is a better place for it, although the extremely small size of the font requires me to magnify multiple times before I can read it. Also, shouldn't the descending intervals appear as the reciprocals of the corresponding ascending intervals (like starting with 99/100 and going down to 1/2)? Lucius Chiaraviglio (talk) 06:18, 30 July 2024 (UTC)

Well, there are a lot of functions, and some of the function ranges are quite narrow, so that's the biggest reason for the small text. As for the interval listings, the reason I'm not listing the reciprocals of the ascending intervals is so I can keep track of intervallic distance from the 1/1. Does that make any sense? --Aura (talk) 06:24, 30 July 2024 (UTC)

Sort of, but it is kind of confusing to have that part of the graph be labeled as descending from the tonic, but then have it notated with ascending intervals. Lucius Chiaraviglio (talk) 06:31, 30 July 2024 (UTC)

Unfortunately, I'm not near a computer right now, so I can't change it. Still, the confusion is noted, and I'll see what I can do. In the meantime, do the functions themselves now make sense? --Aura (talk) 06:39, 30 July 2024 (UTC)

I haven't had time to go back through to read with the graph side by side, but I expect that it will help as long as I can magnify it enough to read the graph. Lucius Chiaraviglio (talk) 06:41, 30 July 2024 (UTC)

Got another chance to look at it, although admittedly not in as much detail as it needs. Has an awful lot of stuff to wrap my head around, especially the names that only correspond to numbers by going back and looking at the graph (although at least seeing it early does help). I did notice that even though the graph has 7/6, it doesn't have its fifth inversion 9/7 (but it does have 11/9).

The later section Beyond Diatonic and Chromatic Functional Harmony is actually easier to understand due to having a more easily understood numeric basis (although my having read about the various types of quartertones first probably helped here).

The part about tonic having a tolerance of around ±4 cents roughly corresponds to my own reaction to music written in tuning systems that have sharper or flatter fifths -- on the flat side, 43EDO fifths still sound reasonable if maybe a bit edgy, while 50EDO and 19EDO (and 7EDO) fifths sound different enough to pass as definitely different, but 31EDO and quarter-comma meantone fifths seem to be in the worst place in between -- too flat for 3/2 or a Kirnberger fifth, but too sharp for 112/75 or 52/35; on the sharp side, the 17EDO (and 34EDO) fifth sounds okay, and the 5EDO fifth sounds different enough to pass as definitely different, but the 22EDO fifth is again in an uncomfortable in between zone -- too sharp for 3/2 or a gentle/minthmic fifth, but too flat for 50/33. This doesn't mean that I can't find music that sounds good in these tuning systems (I have in both cases), but it's a headwind that the composer has to work against.

For the last section, about changes to triads between major and minor, these sound reversed from what they should be -- what am I missing?

Lucius Chiaraviglio (talk) 07:42, 14 October 2024 (UTC)

Regarding the lack of 9/7 and 14/9 on the chart, that is because those intervals are rather close to 32/25 and 25/16 respectively, though to be a bit more helpful in this respect, 9/7 is actually on the sharp side of 32/25, while 14/9 is correspondingly on the flat side of 25/16. I should also mention that 7/6 and 8/7 are paired together in this chart as forth inversions of each other, since the 7-limit seems to want to work as a division of either the fourth or the tritave rather than as a normal division of the fifth.

For me, the 22edo fifth definitely passes as different to my ears- specifically, it registers as something akin to 128/85.

Regarding the last section, the motions indicated are not meant to reflect the direction of resolution, rather they simply indicate possible changes, and I have yet to add all of the possible transformations. --Aura (talk) 17:03, 14 October 2024 (UTC)

Just intonation 7/6 and 8/7 definitely sound like different classes of interval to me, although some temperaments (notably 19EDO, and Negri more generally) conflate them.

I just realized I didn't say very clearly what I meant about different fifths -- what I meant is that while the 31EDO and quarter-comma meantone fifths (on the flat side) and 22EDO fifth (on the sharp side) sound different from 3/2, they sound like mistuned versions of it to me, as opposed to sounding like something that is supposed to be different.

Maybe I got confused about what you meant in the last section.

Lucius Chiaraviglio (talk) 21:22, 14 October 2024 (UTC)

I know you meant that 22edo's fifth sounds like a mistuned 3/2 to you, but to me, it legitimately sounds more like 128/85. --Aura (talk) 00:10, 15 October 2024 (UTC)

I'll try to latch onto that next time I listen to 22EDO, but that prime limit is getting up there. (Although 12EDO attaches importance to primes 17 and 19, even though not for the fifth, so maybe I can pull it off.) Lucius Chiaraviglio (talk) 07:24, 15 October 2024 (UTC)

Yeah, the prime limit is getting pretty high, but 17 is a prime that I think helps immensely in simplifying some of the 2.3.11 gestures that I use, while 5 is another prime that does the same sort of stuff. I should know, considering I use 159edo frequently, and that system is consistent to the 17-odd-limit. Not only that, but, as you might imagine, 94\159 makes for a pretty good 128/85 while 93\159 makes a superb 3/2. --Aura (talk) 07:34, 15 October 2024 (UTC)

I will have to train for it. Also, Rameau's Tempérament Ordinaire has its 2 sharp fifths almost equal to the fifth of 22EDO (just a bit under 3 cents sharp of it, if I did my arithmetic right). Lucius Chiaraviglio (talk) 10:46, 15 October 2024 (UTC)

The Accuracy Fever Dream

This morning I had this weird fever dream about an increasingly futile effort to achieve perfect 5-limit and 7-limit accuracy by way of representation of pitches using DNA fragments (which I sometimes have to manipulate in my day job, although not for the purpose of representing pitches — that's a new one on me). DNA fragments representing the syntonic comma, the schisma, the septimal comma, and the garischisma were in little tubes of DNA, but as the commas got divided up in the ever more frantic quest for accuracy, the tubes of increasingly chopped-up DNA fragments representing increasingly smaller comma fractions got all mixed up into little pieces parts that nobody could any longer keep track of, and eventually I had to give up and pick some no-longer-identified DNA fragment representing (maybe) a random syntonic comma fragment and make a post with it concluding that we had reached saturation to the point of just-noticeable difference in the quest for accuracy, and that parts is parts. Lucius Chiaraviglio (talk) 20:18, 17 November 2024 (UTC)