User talk:CritDeathX

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categories

Hi Sam,
I saw that you - seemingly - tried to add categories to the see-also section within the wiki page (on 19/11 and 22/19). This is not possible this way. It is possible to add links to categories by prefix the word category by a colon (for example, [[:category:Interseptimal]] gives category:Interseptimal), but most category pages are not really informative ...
Best regards --Xenwolf (talk) 17:44, 18 April 2020 (UTC)

I don't remember adding anything to the see-also section? The only things I remember doing on those pages are adding the colour name for 19/11 and adding a hyperlink to the Godzilla page on 22/19. If I had done that and I don't remember, then I'm sorry and I'll make sure to remember that. || --CritDeathX (talk) 21:39, 18 April 2020 (UTC) ||

You are welcome. Here is one of the changes "you" made. To me it seems likely being an issue in the visual editor. --Xenwolf (talk) 07:37, 27 May 2020 (UTC)

Message ID

How did you find the message here? I tried the same yesterday for another article with no success. I was wondering if the original message IDs were present in the archive data and could be automatically provided through the view? --Xenwolf (talk) 06:35, 29 May 2020 (UTC)

PS: and of course, a big thanks for this kind of work. 😊 --Xenwolf (talk) 06:36, 29 May 2020 (UTC)

As I saw, the original message IDs are available. In the case I mentioned, you obviously did some archeology to correct the original references which seem indeed incorrect. --Xenwolf (talk) 11:58, 29 May 2020 (UTC)
Thanks for the appreciation! I believe that the original IDs seem to not correlate to the archive's IDs, which makes it a slight pain in the butt. I might ask the person who made the archive to add a search function to make finding past messages easier. --CritDeathX (talk) 08:04, 31 May 2020 (UTC)
You might be interested in the zip Archive available on archive.org. I did some local searches on my lasktop (if you are on Windows, Notepad++ and Grepwin are great helpers). --Xenwolf (talk) 10:29, 31 May 2020 (UTC)
I forgot (at least) on thing: Special:LinkSearch is one more great tool for wiki gardening it lists pages with external links that match a given pattern. --Xenwolf (talk) 10:55, 31 May 2020 (UTC)
Ah, thank you for directing me to that ZIP file there. I had kinda stumbled on that a bit ago, but I didn't think it would actually be useful. I'll try downloading it and see if searching for messages are easier that way. --CritDeathX (talk) 15:00, 31 May 2020 (UTC)
Update; thank you so much for showing me this. I actually love this soooooo much. I can't wait to find messages easier using this. --CritDeathX (talk) 15:36, 31 May 2020 (UTC)
Glad I could help. 😊 --Xenwolf (talk) 15:45, 31 May 2020 (UTC)

Notation terminology

Hi CritDeathX,
Some time ago, I made template:monzo for preventing people from typing <nowiki>|</nowiki>0 0 -1 1&gt; over and over again and to better show the intent. Now I remember that there is also the (seemingly) opposite notation <12 19 28 34| that could benefit from some support. But to make such a template, we I need the name of this notation. Do you know it?
Thanks in advance for your help.
--Xenwolf (talk) 07:00, 29 May 2020 (UTC)

Correct me if I'm wrong, but are you speaking of template:val? Its the only thing I could think of looking like an opposite of a monzo. --CritDeathX (talk) 08:04, 31 May 2020 (UTC)
Yeah, it has been created (even for me surprisingly) meanwhile by User:Cmloegcmluin --Xenwolf (talk) 10:37, 31 May 2020 (UTC)
I didn't even see that there! Guess I was late to the party by ~2 days. --CritDeathX (talk) 15:00, 31 May 2020 (UTC)
If you mean this: the Revision history of "Template:Val" - Xenharmonic Wiki is shown antichronological, so the starting point is at the end. 😉 --Xenwolf (talk) 10:08, 1 June 2020 (UTC)
PS: Now it seems to me that you didn't mean that at all. Well, anyway... --Xenwolf (talk) 10:11, 1 June 2020 (UTC)

How to indicate that contents is (or started as) a quote?

Hi CritDeathX,
I find that a horizontal line for separation (either as ------- or as <hr>) is perhaps not the best option. We could also use typography to separate the source from the rest of the text, maybe (also) a subtle indentation? Here are the three options so far:

  1. Magic22 as srutis
  2. 79MOS 159edo
  3. A shruti list

What so you think?
--Xenwolf (talk) 10:33, 1 June 2020 (UTC)

Thanks for telling me about this; I'm not entirely too familiar with how MediaWiki works (or other people, really), as I've never really edited for a wiki in general, so I apologize about my formatting. I think that option 3 might be a better option for this situation. --CritDeathX (talk) 11:56, 1 June 2020 (UTC)
No need to apologize, we all learn and *still* make mistakes! :-) --Xenwolf (talk) 13:17, 1 June 2020 (UTC)

The magic of internal links

Hi CritDeathX,
I hope not to bother: I saw on User:CritDeathX/Sam's Musings (no I didn't actually read it but this is now also on my todo list) that you used external link syntax for internal pages or files. I'd remember to change this when you find the time to unlock the What links here feature (access key j, in Firefox under Windows this is the hotkey [Alt]+[Shift]+[j]) on pages you linked. This is maybe not so important for "14edo#Titanium[9]" but for "File:Christopher(9) resolution.wav" because the file looks orphan to the wiki software (see Special:UnusedFiles and Special:LonelyPages) - BTW: I forgot to mention that I find all your contributions very valuable, thank you for taking all the time. Through your cooperation I am always discovering interesting content in these over 7000 pages. 🙂
Beat regards --Xenwolf (talk) 11:16, 1 June 2020 (UTC)

Thank you for making me aware of this! I didn't think that it wouldn't work using hyperlinks, so I'll make sure to change it immediately.
Also, you're welcome! --CritDeathX (talk) 12:13, 1 June 2020 (UTC)
Okay, uh, quick question; how do I tell the system that the file links back to my page? --CritDeathX (talk) 12:23, 1 June 2020 (UTC)
File usage is done by embedding a file (by typing [[File:Christopher(9) resolution.wav]] without the colon (:) after the opening double-bracket), whereas the What links here function is still aware of the backlink. --Xenwolf (talk) 13:13, 1 June 2020 (UTC)
Alright, I actually fixed it now. Takes a while to learn how things work, don't it? --CritDeathX (talk) 13:24, 1 June 2020 (UTC)
Well, but it's better to learn as we go... --Xenwolf (talk) 14:30, 1 June 2020 (UTC)

the dead link

Hi Sam,
great to see this and thanks! I already forgot about it: yesterday the whole site was [:wikipedia:HTTP 403]. So I was wondering if it could mean something really terrible. Fortunately, I was wrong. 🙂
--Xenwolf (talk) 13:29, 13 June 2020 (UTC)

No problemo! --CritDeathX (talk) 19:47, 14 June 2020 (UTC)

built-in subpage function

It may be interesting to you that you can get sub pages of a given page automatically, for example {{Special:Prefixindex|prefix=User:CritDeathX/|hideredirects=1|stripprefix=1}} produces

As to get sub pages of a page on that page, you can use {{Special:Prefixindex|prefix={{FULLPAGENAME}}/|hideredirects=1|stripprefix=1}} instead. The switches hideredirects and stripprefix can be omitted in case they are not set.

Best regards --Xenwolf (talk) 21:11, 14 July 2020 (UTC)
PS: I'm keen to get an audible impression of your 17-note-temperament.

Ah, thank you for telling me about that! I'd assume that it would look nicer than what I have so far. --CritDeathX (talk) 21:40, 14 July 2020 (UTC)
ps: id be happy to try and either retune a piece or make a piece to demonstrate that temperament if you would like

Retuned piece

Hi CritDeathX,
It is quite intereating to hear File:Thirteen Preludes No. 1, tuned to sam's 17-tone temperament.wav, I'm not able to check the quality of the retuning but am impressed by the speed at which you can deliver this kind of stuff. Let me share a few thoughts about retuning of existing (classical, mostly 12-EDO) pieces in general: I doubt that this process can give us a really valid demonstration of the potential of a given tuning/temperament for two reasons: 1) The timbre will be unaffected and 2) the composition (kind of) "lives" in the 12-EDO world. As for the actual piece, I must admit that it's too fast for me as to value the tuning/temperament.
I hope my comments will not discourage you but instead help you in further exploring your 17-note Well Temperament.
Best regards --Xenwolf (talk) 05:03, 15 July 2020 (UTC)

Yeah, that's some fair points. I'll see if maybe an original work can do justice for this tuning. Thank you for your thoughts. --CritDeathX (talk) 16:51, 15 July 2020 (UTC)

Closed Up

Congratulations! Closed Up is an interesting composition (and hopefully just an opening!), it makes me curious for more. Reminds me of The Book of Sounds by Hans Otte (see also Hans Otte - Wikipedia). --Xenwolf (talk) 21:54, 15 July 2020 (UTC)

Thank you a bunch! Admittedly, I didn't think of this as an opening, but rather more of a soundworld, if that makes sense. I will consider making more pieces in this tuning (and more well temperaments too!). --CritDeathX (talk) 23:23, 15 July 2020 (UTC)

I agree too this one sounds neat! Thank you for making it. --Arseniiv (talk) 22:21, 27 September 2020 (UTC)

internal links ...

... get the capitalization of the first letter for free. So (provided the titles are well-chosen) it's possible to link without any extra effort for instance cent (here in the text written with lowercase c, but at the target capitalized). Hope that helps a bit in everyday editing. --Xenwolf (talk) 06:53, 27 July 2020 (UTC)

Ideas and Impressions

Hello, I'm curious as to whether or not you have any further thoughts on the ideas I've posted on my own talk page. I would also like to know how you made your list of edo impressions... I admit I don't have many edo impressions to share myself, just impressions of 1edo, 2edo, 3edo, 4edo, 5edo, 6edo, 12edo, 24edo, 53edo, 94edo, and 159edo, but I think it would make sense for me to get started with those. --Aura (talk) 20:55, 2 September 2020 (UTC)

Howdy here, fellow pard (my gender neutral term for pardner, since i dont know your pronouns yet)! I don't have too many thoughts on your ideas at the moment; it sounds pretty promising, especially with your prime-limit categories! Speaking of which, have you thought of thinking of another name for the quasiparadiatonic limits? I'd suggest microdiatonic, though I imagine that would probably not work too well with your ideas.
On how to make a list of EDO impressions, I'd recommend making a subset of your userpage by writing User:(USERNAME)/(PAGE TITLE) into the wiki's searchbar. This will lead you to an empty page that'll ask if you want to add anything to the page, and of course you should try to add stuff to your page!
Hope that helps! --CritDeathX (talk) 15:50, 3 September 2020 (UTC)
For the record, I'm a male- which means I'm a "he". Anyhow, I'm glad you find the idea of prime-limit categories promising. Still, I have to admit that I find the 23-limit, 29-limit, and 31-limit very hard to use. I know that the paradiatonic primes can give rise to "parachromatic" intervals such as 55/54... Oh! What about renaming the "quasiparadiatonic" primes the "pseudodiatonic" primes? After all, these primes are not diatonic by any stretch, but they still seem to be good substitutes for the paradiatonic primes in a pinch... --Aura (talk) 16:45, 3 September 2020 (UTC)
That sounds like a good idea! It helps with not having to say a mouthful, I'll say that much. --CritDeathX (talk) 16:56, 3 September 2020 (UTC)
Thanks for letting me know how to create an EDO impressions page! If you go to my user page, you should be able to find the link to it at the bottom of the page. However, my links in general need work... --Aura (talk) 00:49, 4 September 2020 (UTC)
The links on Aura's user page are fixed meanwhile. --Xenwolf (talk) 09:53, 4 September 2020 (UTC)
Indeed... --Aura (talk) 15:01, 4 September 2020 (UTC)
Alrighty, added the impressions to the Big List. Welcome to the party! --CritDeathX (talk) 00:45, 5 September 2020 (UTC)
Thanks! --Aura (talk) 02:58, 5 September 2020 (UTC)
I'm curious... have you heard the piece that I recently wrote? --Aura (talk) 02:58, 5 September 2020 (UTC)

The table is gonna explode if everybody adds their impressions nonstop. It doesn't seem like a final solution in the future. Maybe we split them into individual edo subpages? FloraC (talk) 05:01, 5 September 2020 (UTC)

Yeah, that's a good thing to bring up. I could try to put them into subpages for the respective EDOs if another person throws in their impressions. --CritDeathX (talk) 14:55, 5 September 2020 (UTC)

Unnoticeable Commas

Okay, one thing I do in my list of intervals in 159edo is to try and keep the list trimmed down to 23-limit intervals, odd limits less than 1024, and intervals which are less than 3.5 cents away from the steps of the EDO. It's a complicated system, but so far, it seems to be working. One particular quirk I've noticed while working on this is that in 159edo, the difference between five 33/32 quartertones and a 7/6 subminor third is tempered out so that five tempered 33/32 equals one tempered 7/6. I worked out the difference between five 33/32 quartertones and a 7/6 subminor third to be 117440512/117406179- a comma only slightly more than half a cent in size. I also see that this comma has only been mentioned once on this wiki- specifically on the page for 3125edo. Is there already a name for this comma? If not, I want to give it a name... --Aura (talk) 05:51, 6 September 2020 (UTC)

I don't believe this was given a name yet. Go and name it, I guess. I wonder what temperaments this can bring, though. --CritDeathX (talk) 15:01, 6 September 2020 (UTC)
Would you look at that... This same comma- 117440512/117406179- is also the amount by which six 33/32 quartertones fall short of a 77/64 subminor third... Since this comma involves quartertones- how about I call it the "Quartisma"? --Aura (talk) 22:03, 6 September 2020 (UTC)
If the idea of calling this comma the "Quartisma" makes sense to you, then when this comma is tempered out, can we can call the resulting temperaments "Quartismatic"? --Aura (talk) 22:13, 6 September 2020 (UTC)
We usually use -sma, -smic. IlL (talk) 22:29, 6 September 2020 (UTC)
Maybe, but "Quartisma" comes from "Quarter" and "Schisma" on account of this comma both involving stacks of quartertones and being extremely small itself, and, the name for temperaments that temper out the Schisma is "Schismatic". --Aura (talk) 22:34, 6 September 2020 (UTC)
If "Quartismic" is a better name for temperaments that temper out the "Quartisma", then I'll go with "Quartismic". However, I'd like to hear more opinions on this first... --Aura (talk) 22:40, 6 September 2020 (UTC)
Let me give examples: kleismic family, keemic family, and pages listing chords of a temperament are titled X-smic chords (Category:11-limit and Category:13-limit has some of them). It seems "schisma" is the only exception among comma names that end in -ma. IlL (talk) 00:12, 7 September 2020 (UTC)
(Even for diaschisma "diaschismic" is more common than "diaschismatic".) IlL (talk)
Okay then. "Quartismic" makes sense for the temperament name then. I'll go with it. --Aura (talk) 00:33, 7 September 2020 (UTC)

Sorry about blowing up your talk page Sam... --Aura (talk) 04:35, 7 September 2020 (UTC)

No worries, its not like you're bursting into my house and sleeping in my walls. --CritDeathX (talk) 13:12, 8 September 2020 (UTC)

Temperament Mappings

Hey there, I see the temperaments you've found, and while I can play the notes on the keyboard, there are a number of senses in which I don't know what I'm looking at, as when it comes to music, I'm steeped in a combiniation of traditional music notation, mainstream quartertone accidentals, and other accidentals of the sort found in MuseScore. However, I do very much believe that the data you've found is worth linking to the page on quartismic temperaments. I've said something partially to this same effect on my own user talk page, but I figured I might as well leave a message here as well for good measure. --Aura (talk) 15:29, 8 September 2020 (UTC)

Sam, would you mind helping me out a bit? I'm trying to go through and sort out various options for 5-limit commas as a means of extending to the full 11-limit among quartismic temperaments, and I want to separate different types of 5-limit extensions by giving them different names- after all not every possible 5-limit extension for a quartismic temperament results in something related to meantone. Personally, I like the name "Altierran" for non-meantone quartismic temperaments that temper out the schisma... --Aura (talk) 20:28, 10 September 2020 (UTC)

Looking at some of the common commas, I can suggest a couple of these names:
3125/3072 - magician (quarter magic)
15625/15552 - skirtismic (combination of schi- and -rtismic)
20000/19683 - doublefour (the comma belongs to tetracot and our temperament is quartismic)
81/80 - meanfour (meantone but the tone is replaced with four, cause quartismic)
--CritDeathX (talk) 13:51, 11 September 2020 (UTC)
Okay, out of all the ones you've suggested here, I really like "doublefour" as a way of refering to combinations of the quartisma and the tetracot comma. I like both "meanfour" and "meanquarter", but "meanfour" sounds like it could also refer to combinations of meantone and tetracot, so perhaps "meanquarter" is a better descriptor for the specific combination of the quartisma and meantone. I'm not a fan of "skirtismic", because the combination in question is actually a combination of the 5-limit kleisma with the quartisma- how about "kleirtismic" instead? As for combinations of the quartisma and the magic comma- well, this one's trickier, the name you proposed sounds unoriginal, so we need to think of something better. --Aura (talk) 14:16, 11 September 2020 (UTC)
Meanquarter & kleirtsmic are better, yes, though I have no idea how to say kleirtsmic. On magician, I guess it is a bit bland. Maybe coin temperament? IDK, my brain sucks at thinking. --CritDeathX (talk) 14:20, 11 September 2020 (UTC)
For "kleirtismic", just remember that "kleir-" is pronounced like "Clair". I definitely like the idea of call combinations of quartismic and magic temperaments "coin" temperaments. --Aura (talk) 15:07, 11 September 2020 (UTC)

Ideas of Consonance

Hello Sam, I just posted my own ideas of consonance. I'd like to hear what you think of these. Perhaps our ideas of consonance are mutually compatible. Also, I think we need to examine Harmonic Entropy in a new light- take the individual sections of the minimum Rényi entropy that correspond to different octaves and combine successive octave sections into a single curve. I predict that intervals that have a high degree of connectivity- of the sort explain on my page- will become more pronounced, while those that don't will be weakened. --Aura (talk) 05:49, 12 September 2020 (UTC)

Hello, Aura! I read through your page, and it looks like a really promising theory. Although I'm not in a place where I can try to make an image of averaging out the points on the entropy graph, I can try to look at a couple of triads & intervals and see if your theory works with mine (note that a lot of the chords follow either (a+c)/2 or (2ac)/(a+c)).
8:9:12 (3-limit) - 3 linear tones
4:5:6 (5-limit) - 4 linear tones
10:12:15 - 3 linear tones
6:7:9 (7-limit) - 4 linear tones
9:11:13 (11-limit) - 4 linear tones
13:15:17 (13-limit) - 4 linear tones
17:20:24 (17-limit) - 2 linear tones
16:19:24 (19-limit) - 2 linear tones
20:23:25 (23-limit) - 1 linear tone
58:76:87 (29-limit) - 1 linear tone
24:31:36 (31-limit) - 2 linear tones
3/2 - 3+2=5 (5/2), 3-2=1 (1/2)
8/5 - 8+5=13 (13/5), 8-5=3 (3/5)
5/3 - 5-3=2 (2/3), 5+3=8 (8/3)
11/8 - 11-8=3 (3/8), 11+8=19 (19/8)
17/12 - 17-12=5 (5/12), 17+12=29 (29/12)
Hope this starts something in your thinker! --CritDeathX (talk) 18:05, 12 September 2020 (UTC)
Thanks! I did have to rethink the transformation of the harmonic entropy curve upon the successful overlay of different sections- now I'm thinking that what is required is not averaging the sections together but adding them together. If I'm thinking this through correctly, the addition results in the values for more-connected harmonic entropy minima adding up slowly, while the values for other, less-connected intervals basically add up quite fast. --Aura (talk) 18:21, 12 September 2020 (UTC)
Yeah, that makes sense. I'd like to mention that comparing the intervals here to how you've described them, it seems that ones that hold more tonal opportunity are ones where the linear tones aren't powers of 2; it explains why 8/5 has a better "effect of fostering a stronger sense of tonality," as you've said, than 5/3, where its linear tones are only powers of 2. --CritDeathX (talk) 18:31, 12 September 2020 (UTC)
Hmm... let's try other intervals, such as 2/1 (perfect consonance), 6/5 (imperfect consonance), 5/4 (perfect consonance), 4/3 (perfect consonance), 16/11 (imperfect dissonance), 24/17 (perfect dissonance), 15/8 (imperfect dissonance), and 16/15 (imperfect dissonance)... --Aura (talk) 18:41, 12 September 2020 (UTC)
Alrightios, lets see how that checks out:
2/1 - 2-1=1 (1/1), 2+1=3 (3/1)
6/5 - 6-5=1 (1/5), 6+5=11 (11/5)
5/4 - 5-4=1 (1/5), 5+4=9 (9/5)
4/3 - 4-3=1 (1/3), 4+3=7 (7/3)
16/11 - 16-11=5 (5/11), 16+11=27 (27/11)
24/17 - 24-17=7 (7/17), 24+17=41 (41/17)
15/8 - 15-8=7 (7/8), 15+8=23 (23/8)
16/15 - 16-15=1 (1/15), 16+15=31 (31/15)
Should we count n/(2^x) when it comes to figuring out dyad consonance? --CritDeathX (talk) 18:49, 12 September 2020 (UTC)
First, is there a mistype in your results for 5/4? Second, it's obvious that 2/1 and 3/2 are perfect consonances while 4/3 counts as a perfect consonance because it's effectively the utonal counterpart of 3/2... Hmm... it looks like otonal and utonal intervals play by different rules... --Aura (talk) 18:58, 12 September 2020 (UTC)
With that in mind, 3/2- with the result following the formula of n/(2^x)- should be counted. However, in the case of 5/3, the powers of two are in the numerator, so they don't count. --Aura (talk) 19:01, 12 September 2020 (UTC)
Yes, there is an error with 5/4! Lemme fix that and we'll be good.
On the topic of n/(2^x), that seems like a decent way of treating 2^x in this system. If you do find any exceptions to the rule, do tell me.
On the topic of otonal & utonal intervals, its possible that they need different ways of figuring out sonance, although its unclear to me how different we should treat them. --CritDeathX (talk) 19:10, 12 September 2020 (UTC)
Hmm... because the otonal and the utonal pitches are equivalent in terms of their consonance, and because otonal and utonal pitches are octave complements of one another, it seems that for this, intervals must be judged in pairs. Thus, since 5/3 and 6/5 are the octave complements of one another, and 5/3 has powers of two in the numerator, that means both 6/5 and 5/3 are disqualified. (preceeding unsigned comment by Aura (talk))
I should point out that if the numerator is "1", that doesn't count as a power of 2 for this rule due to the fact that anything to the 0 power is 1. --Aura (talk) 19:17, 12 September 2020 (UTC)
Well, then 6/5 should be saved since 6-5=1 (1/5) and 6+5=11 (11/5). I would suggest that a utonal interval's tonality will be opposite of the otonal version's tonality, though there's a couple exceptions to that rule as well. --CritDeathX (talk) 19:23, 12 September 2020 (UTC)
Okay, I just found a major problem- 7/6 and 12/7 are both disconnected intervals, leading to a lack of potential above the Tonic. However, their results are as follows:
7/6 - 7-6 = 1 (1/6), 7+6 = 13 (13/6)
12/7 - 12-7 = 5 (5/7), 12+7 = 19 (19/7)
As for what you're saying... The reason I say that otonal intervals and utonal intervals ultimately have the same type of tonality has everything to do with the fact that the overtone series and the undertone series are mirror images of one another. --Aura (talk) 19:32, 12 September 2020 (UTC)
Hmm... it seems that sum and difference tones have different properties relative to whether or not the resulting interval is otonal or utonal... (preceeding unsigned comment by Aura (talk))
If so, that means there's a sense in which we're comparing apples and oranges... --Aura (talk) 19:40, 12 September 2020 (UTC)
So that means we need to figure out a separate method for otonal & utonal notes. Interesting. --CritDeathX (talk) 19:55, 12 September 2020 (UTC)
Wait, I noticed that you typed 12/5 instead of 5/7. --CritDeathX (talk) 19:59, 12 September 2020 (UTC)
Good catch! Still, we need to figure out our separate methods for otonal and utonal intervals... Perhaps once we get Treble-down tonality sorted out, we'll have more space to work with... --Aura (talk) 20:17, 12 September 2020 (UTC)
One thing I know right off the bat in this realm is that the harmonic properties of a 10:12:15 Minor chord are a match for the subharmonic properties of a 4:5:6 Major chord. This is because a 10:12:15 minor chord has the same configuration as a 1/4:1/5:1/6 Antimajor chord- Antimajor being the treble-down counterpart to Major. (preceeding unsigned comment by Aura (talk))
In light of this, we need to first find the treble-down counterparts to the sum and difference tones, then work out how they are related to the main tones in a utonal dyad or chord. --Aura (talk) 20:23, 12 September 2020 (UTC)
I can try to see what happens with 9:11:13, which has 4 linear tones:
9x11x13=1287
1287/9=143
1287/11=117
1287/13=99
And 99:117:143 has 1 linear tone. --CritDeathX (talk) 20:31, 12 September 2020 (UTC)
Hmm... I think I have a simpler way to find the countersum and counterdifference tones (my makeshift terms for the treble-down counterparts of the sum and difference tones). For example, let's take a 5/3 Major Sixth. We already know that both the sum tone and the difference tone will be of the same pitch class courtesy of what we see in the numerators of your calculations: 5-3=2 (2/3), 5+3=8 (8/3). From there, we can construct a chord using the base interval plus the sum and difference tones surrounding it, this chord coming to 2:3:5:8. From there, we simply have to swap the numerators and denominators of each number in the chord, thus resulting in 1/2:1/3:1/5:1/8. Given that the middle two values correspond to the initial 5/3 interval, it is the two outer numbers that express the countersum and counterdifference tones. --Aura (talk) 20:43, 12 September 2020 (UTC)
I can already tell that the linear tones from bass-up operations correspond to a strikingly different sort of operation for their treble-down counterparts. --Aura (talk) 20:50, 12 September 2020 (UTC)
Okay, I've tested out twelve-tempered versions chord on the piano, and it sounds every bit as consonant as the twelve-tempered version of the original 2:3:5:8 chord once all known relational factors between bass-up tonality and treble-down tonality are accounted for, and this is despite the rather obvious lack of linearity. Something is afoot here... we just need to find out what... --Aura (talk) 21:04, 12 September 2020 (UTC)
How would you find the counterlinear tones? I'm not too experienced with understanding things, so its possible that I don't know what you're talking about. --CritDeathX (talk) 21:06, 12 September 2020 (UTC)
I should probably specify that I'm wanting to know how to turn the fractions of 1/2 and 1/8 into something I can understand.
I'm looking for the more direct operation for finding the contralinear tones myself. As for how to turn the fractions into something you can understand, let's take a look at more familiar ratios- in the ratio of 4:5:6, there's a hidden denominator to each number, and if this denominator is made explicit, the result for this chord is 4/1:5/1:6/1. The "1" at the bottom signifies the fundamental pitch- or else, the pitch that acts as a virtual fundamental. Therefore, "4/1" means that you're dealing with a pitch that's four times the frequency of the fundamental, "5/1" means that you're dealing with a pitch that's five times the frequency of the fundamental, and "6/1" means that you're dealing with a pitch that's six times the frequency of the fundamental. If you flip these fractions, you get 1/4:1/5:1/6- a ratio in which the fundamental is four times the frequency of the first pitch, five times the frequency of the second pitch, and six times the frequency of the third pitch. Does this make sense so far? --Aura (talk) 21:29, 12 September 2020 (UTC)
Basically, whereas whole numbers such as "2", "3", and "4" that show up in these ratios correspond to harmonics, fractions such as "1/2", "1/3" and "1/4" correspond to subharmonics. Does this help? --Aura (talk) 21:41, 12 September 2020 (UTC)
Just to show that I'm not making this stuff up out of whole cloth- see this article on the undertone series. (preceeding unsigned comment by Aura (talk))
Alright, yeah, that makes sense so far. Do you think that its possible that we can combine linear & contralinear tones to get a better sense of the consonance of a chord/interval, or is it really just two separate things? --CritDeathX (talk) 22:12, 12 September 2020 (UTC)
I think we can do this, but this field we're working with is basically linear-contralinear consonance- a different type of consonance than connectivity. --Aura (talk) 22:19, 12 September 2020 (UTC)
That said, it would be interesting to make a chart and see how connectivity-type consonance relates to linear-contralinear consonance, and see which intervals meet both criteria. --Aura (talk) 22:24, 12 September 2020 (UTC)
I'd be happy to try and make it if you haven't already. --CritDeathX (talk) 22:27, 12 September 2020 (UTC)
We need our data first- and yes, you'd likely have to make the chart... One thing that has become readily apparent is that we need to superimpose the linear and contralinear tones for any one single interval or chord and see if the intervals between the difference and contrasum tones, and between the sum and contradifference tones, demonstrate high harmonic entropy or not. I can already tell you that for for 5/3, I'm seeing high-entropy results. --Aura (talk) 22:37, 12 September 2020 (UTC)
For the starting interval 2/1, I can tell you that the intervals between the difference and contrasum tones, and between the sum and contradifference tones is a 3/2 perfect fifth in each case, and because this interval demonstrates low harmonic entropy, we can then go on to check the linear and contralinear tones of these intervals, if the results are again a low-entropy interval, we can keep on going, but once we hit a high-entropy interval, we have to stop. The number of iterations of this process before hitting a high-entropy interval is the rank of the base interval in terms of linear-contralinear consonance. --Aura (talk) 22:51, 12 September 2020 (UTC)
Oh, and if your starting interval has high harmonic entropy, that means that interval is rank 0 in terms of linear-contralinear consonance. This is because you don't even get to perform the operation even once before arriving at a discordant interval. --Aura (talk) 23:01, 12 September 2020 (UTC)
I can't believe I forgot to mention this, but if the intervals between the difference and contrasum tones, and between the sum and contradifference tones, are greater than an octave- well, octave reduction is a must. Sorry about all the comments! --Aura (talk) 23:09, 12 September 2020 (UTC)

Temperament Names

Okay, I'm looking for names for both quartismic temperaments that also temper out the escapade comma, and quartismic temperaments that also temper out the the diaschisma. Do you have any ideas? --Aura (talk) 21:50, 13 September 2020 (UTC)

Diartsmic and escapismic? --CritDeathX (talk) 14:03, 14 September 2020 (UTC)
I like "escapismic". However, "diartismic" I'm not a fan of. Oh! How about the name "Quartismatic" for the no-fives version of the Quartismic temperament? I mean, the main no-fives version is just like the original, except there's no mapping for five... --Aura (talk) 19:56, 14 September 2020 (UTC)
Quartismatic might be good, yes. On diartismic, we could also do dismatic. --CritDeathX (talk) 03:53, 15 September 2020 (UTC)

My Take on the Diatonic Scales

Hey Sam! Have you ever checked out my take on the seven Diatonic Scales? I don't know about you, but I think that dissonance is actually valuable as a propulsive force in music- even the grave fifth can be useful in this regard if it's well placed within a scale... --Aura (talk) 03:10, 15 September 2020 (UTC)

I haven't read through the actual descriptions of each scale, though I do enjoy the examples that you've provided for each. --CritDeathX (talk) 03:54, 15 September 2020 (UTC)

159-based retemperings for other EDOs

Hey, Sam. I'm using an approximation of 159edo as a way of making retemperings other EDOs for an extensive song that covers retemperings of 12edo, 14edo, 17edo, 19edo, 22edo, 24edo, 27edo, 31edo, 35edo and 41edo, with a stretch in an approximation of 53edo before using the full 159edo approximation. I want to know if you can think of any good chord progressions for any of these EDOs... If they're good, I can use them in the song. --Aura (talk) 03:32, 19 September 2020 (UTC)

12EDO - I-bII-V-iv
14EDO - bIII-bvii-VI-I
17EDO - I-v-IV-iv
19EDO - I-V-ii-III
22EDO - vIII-i-V7-II7
24EDO - I-^ii-IV-^V
27EDO - ^I-^V-^ii-^vidim
31EDO - bIII-bvii-VI-I
35EDO - IV-bVII-i-bIII
41EDO - I-III7-II7-V7
Not the best, but these are ones that just popped in my head! --CritDeathX (talk) 13:13, 19 September 2020 (UTC)
Hmm... which EDO steps comprise these chords, and what do they sound like? Also, are their any other really good ones you can think of? --Aura (talk) 21:20, 19 September 2020 (UTC)
The steps of a major chord in order are 0-4-7, 0-4-8, 0-6-10, 0-6-11, 0-8-13, 0-8-14, 0-9-16, 0-10-18, 0-11-20, 0-13-24.
The steps of a minor chord in order are 0-3-7, 0-3-8, 0-4-10, 0-5-11, 0-5-13, 0-6-14, 0-7-16, 0-8-18, 0-9-20, 0-11-24.
As for how they sound, I'll try to make some later today! --CritDeathX (talk) 23:28, 19 September 2020 (UTC)
Okay Sam, are are you making the sounds? Also, can you think of other cool chords for the EDOs we listed? I've recently finished the 14edo section, and it turns out that since the tritone is the only shared interval between 12edo and 14edo aside from the octave itself, and other types of tritone are also very frequently shared amongst the retempered versions of other EDOs, I'm having to build the majority of my chords around a bVM-Im type progression. --Aura (talk) 19:18, 20 September 2020 (UTC)
Here's a clip showing all the progressions, twice for each EDO! https://clyp.it/yaojbf2d
On extra chords, I guess maybe try any kind of subminor or supermajor chords (or anything with neo-gothic intervals, those are extra cool). Can't wait to hear your piece! --CritDeathX (talk) 00:07, 21 September 2020 (UTC)

Notation system for 159edo

Hey Sam, I'm trying to figure out what to do in light of the fact that 33/32 is the simplest quartertone we have and thus the best JI candidate for the interval of "demisharp" or "demiflat", yet, when the rastma is not tempered out, a stack of two of them falls short of the apotome- the traditional interval used to indicate a Pythagorean chromatic semitone. Is it me or is the 5-limit case of a stack of 25/24 chormatic semitones falling short of a 9/8 whole tone actually a good parallel? For the record, 159edo is one of those EDOs where the rastma is not tempered out... --Aura (talk) 23:31, 7 October 2020 (UTC)

I guess that'd be good for a parallel, yeah. --CritDeathX (talk) 12:41, 8 October 2020 (UTC)
Hmm... Okay, so, as per the title of this section, I'm trying to develop a notation system for 159edo, and according to Kite, the fact that two 33/32 fall short of an apotome makes the idea of using mainstream quartertone accidentals for 33/32 counterintuitive, and yet, 33/32 is the simplest quartertone we have and thus the best JI candidate for the interval of "demisharp" or "demiflat", as I mentioned. I'm trying to find a way to make things work... I can't pretend the rastma will be tempered out if it isn't... so, how do I make things more intuitive? --Aura (talk) 13:57, 8 October 2020 (UTC)
You could have where a line strikes through the flat & have the lines layer for every 33/32 thing. --CritDeathX (talk) 01:58, 10 October 2020 (UTC)
I have to admit that one of my concerns is that if I don't use some variation of the mainstream quartertone accidentals for 33/32, then the 159-notation system won't be as accessible to microtonalists who got their start with 24edo like me. Hmm... what if I set the two broad cross strokes of the demisharp accidental closer together than those of the sharp accidental while keeping the same traditional "demiflat" accidental? Of course, I'd have to do the same thing with the "sesquisharp" accidental and the "sesquiflat" accidental as those modify the base tone by an interval consisting of an apotome and a 33/32 quartertone... Does that sound like a good idea? --Aura (talk) 05:02, 10 October 2020 (UTC)
As a complement to this, I could also make a second set of quartertone accidentals based on the original quartertone accidentals as well, and the second "demisharp" and "sesquisharp" accidentals could have the two broad cross strokes set further apart than those of the sharp accidental, while the corresponding "demiflat" and "sesquiflat" accidentals see a stroke on their stems. The two "demisharp" accidentals and the two "sesquisharp" accidentals could thus be distinguished as "narrow" versus "wide" if the design is done right, with the "wide demisharp" and "wide sesquisharp" accidentals modify the base tone by an interval consisting of a 33/32 quartertone and a rastma... Is this also a good idea? --Aura (talk) 05:14, 10 October 2020 (UTC)
Yeah, that sounds like a good idea so far. I'm probably going to have to make a piece with 159EDO once the notation gets finalized... --CritDeathX (talk) 15:06, 10 October 2020 (UTC)
Well, we need Xenwolf's help redesigning the glyphs though, so let's carry this conversation to the relevant thread on the 159edo Notation talk page. Oh, and what program do you use to make microtonal music? --Aura (talk) 18:58, 10 October 2020 (UTC)
I mainly use Musescore, but I also have Mus2 for more microtonal stuff. --CritDeathX (talk) 20:11, 10 October 2020 (UTC)
Nice! I actually have MuseScore, MuseScore 2, and MuseScore 3, and I have Audacity to tie things together if I have to use multiple programs. Anyway, let's move this conversation over to the 159edo Notation talk page, shall we? --Aura (talk) 21:09, 10 October 2020 (UTC)

Another Comma

Hey Sam, I already asked Xenwolf about this, but I figure it would be a good idea to get another opinion on this. Basically, I've found this unnoticeable comma- 1771561/1769472- that marks the difference between three 128/121 semitones and one 32/27 minor third, and I want to name it. Since the 3-limit and the 11-limit are both major navigational primes, and tempering out 1771561/1769472 leads to the joining of these primes limits, and, since "nexus" means "a connection or series of connections linking two or more things", which describes exactly what happens when 1771561/1769472 is tempered out, I figured that 1771561/1769472 could be call the "nexusma" or even the "nexus comma"... Is this a good name or do I need a better name? --Aura (talk) 17:15, 14 October 2020 (UTC)

You can try calling it a nexusima or a nexuma, as a couple of options. --CritDeathX (talk) 18:03, 16 October 2020 (UTC)
Okay, the article has been written. What do you think? --Aura (talk) 19:10, 16 October 2020 (UTC)
Looks good! --CritDeathX (talk) 19:38, 16 October 2020 (UTC)
Thanks! My main concern at this point is the link to my own corner of the wiki in which I demonstrate the 11-limit's significance. I don't want that link to remain if the theory on that particular portion of the linked page doesn't make musical sense... --Aura (talk) 19:45, 16 October 2020 (UTC)

The Foundations for My Music System

Hey Sam, remember how we talked a little bit about my ideas for stuff on my main talk page when I first came here? Well, I'm starting to pull the various pieces of my music theory together, and I'd like to know what you think of what I have so far... --Aura (talk) 05:39, 18 October 2020 (UTC)