User talk:CritDeathX: Difference between revisions

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Congratulations! [[:File:Closed Up.mp3|Closed Up]] is an interesting composition (and hopefully just an opening!), it makes me curious for more. Reminds me of [https://www.youtube.com/watch?v=U5310fFktbU The Book of Sounds by Hans Otte] (see also [https://en.wikipedia.org/wiki/Hans_Otte Hans Otte - Wikipedia]). --[[User:Xenwolf|Xenwolf]] ([[User talk: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!). --[[User:CritDeathX|CritDeathX]] ([[User talk:CritDeathX|talk]]) 23:23, 15 July 2020 (UTC)

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

== internal links ... ==

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::: We usually use -sma, -smic. [[User:IlL|IlL]] ([[User talk:IlL|talk]]) 22:29, 6 September 2020 (UTC)

:::: Maybe, but "Quartisma" comes from "~~quarter~~" ~~plus~~ "schisma", and the name for temperaments that temper out the schisma is "~~schismatic~~". --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 22:34, 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". --[[User:Aura|Aura]] ([[User talk: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... --[[User:Aura|Aura]] ([[User talk: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. [[User:IlL|IlL]] ([[User talk:IlL|talk]]) 00:12, 7 September 2020 (UTC)

::::: (Even for diaschisma "diaschismic" is more common than "diaschismatic".) [[User:IlL|IlL]] ([[User talk:IlL|talk]])

:::::: Okay then. "Quartismic" makes sense for the temperament name then. I'll go with it. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 00:33, 7 September 2020 (UTC)

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

: No worries, its not like you're bursting into my house and sleeping in my walls. --[[User:CritDeathX|CritDeathX]] ([[User talk: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. --[[User:Aura|Aura]] ([[User talk: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... --[[User:Aura|Aura]] ([[User talk: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 ''tetra''cot and our temperament is ''quart''ismic)

: 81/80 - meanfour (meantone but the tone is replaced with four, cause ''quart''ismic)

: --[[User:CritDeathX|CritDeathX]] ([[User talk: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. --[[User:Aura|Aura]] ([[User talk: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. --[[User:CritDeathX|CritDeathX]] ([[User talk: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. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 15:07, 11 September 2020 (UTC)

== Ideas of Consonance ==

Hello Sam, I just posted [[User:Aura/Aura's Ideas of Consonance|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 [[Harmonic_Entropy#a.3D.E2.88.9E:_Harmonic_Min-Entropy|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. --[[User:Aura|Aura]] ([[User talk: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! --[[User:CritDeathX|CritDeathX]] ([[User talk: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. --[[User:Aura|Aura]] ([[User talk: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. --[[User:CritDeathX|CritDeathX]] ([[User talk: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)... --[[User:Aura|Aura]] ([[User talk: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? --[[User:CritDeathX|CritDeathX]] ([[User talk: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... --[[User:Aura|Aura]] ([[User talk: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. --[[User:Aura|Aura]] ([[User talk: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. --[[User:CritDeathX|CritDeathX]] ([[User talk: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 [[User:Aura|Aura]] ([[User talk: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. --[[User:Aura|Aura]] ([[User talk: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. --[[User:CritDeathX|CritDeathX]] ([[User talk: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. --[[User:Aura|Aura]] ([[User talk: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 [[User:Aura|Aura]] ([[User talk:Aura|talk]]))

:::::::::: If so, that means there's a sense in which we're comparing apples and oranges... --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 19:40, 12 September 2020 (UTC)

::::::::::: So that means we need to figure out a separate method for otonal & utonal notes. Interesting. --[[User:CritDeathX|CritDeathX]] ([[User talk:CritDeathX|talk]]) 19:55, 12 September 2020 (UTC)

::::::::::: Wait, I noticed that you typed 12/5 instead of 5/7. --[[User:CritDeathX|CritDeathX]] ([[User talk: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... --[[User:Aura|Aura]] ([[User talk: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 [[User:Aura|Aura]] ([[User talk: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. --[[User:Aura|Aura]] ([[User talk: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. --[[User:CritDeathX|CritDeathX]] ([[User talk: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. --[[User:Aura|Aura]] ([[User talk: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. --[[User:Aura|Aura]] ([[User talk: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... --[[User:Aura|Aura]] ([[User talk: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. --[[User:CritDeathX|CritDeathX]] ([[User talk: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? --[[User:Aura|Aura]] ([[User talk: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? --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 21:41, 12 September 2020 (UTC)

:::::::::::::::: Just to show that I'm not making this stuff up out of whole cloth- see [https://en.wikipedia.org/wiki/Undertone_series| this article on the undertone series]. (preceeding unsigned comment by [[User:Aura|Aura]] ([[User talk: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? --[[User:CritDeathX|CritDeathX]] ([[User talk: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. --[[User:Aura|Aura]] ([[User talk: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. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 22:24, 12 September 2020 (UTC)

::::::::::::::::::: I'd be happy to try and make it if you haven't already. --[[User:CritDeathX|CritDeathX]] ([[User talk: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. --[[User:Aura|Aura]] ([[User talk: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. --[[User:Aura|Aura]] ([[User talk: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. --[[User:Aura|Aura]] ([[User talk: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! --[[User:Aura|Aura]] ([[User talk: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? --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 21:50, 13 September 2020 (UTC)

: Diartsmic and escapismic? --[[User:CritDeathX|CritDeathX]] ([[User talk: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... --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 19:56, 14 September 2020 (UTC)

::: Quartismatic might be good, yes. On diartismic, we could also do dismatic. --[[User:CritDeathX|CritDeathX]] ([[User talk:CritDeathX|talk]]) 03:53, 15 September 2020 (UTC)

== My Take on the Diatonic Scales ==

Hey Sam! Have you ever checked out [[User:Aura/Aura's Diatonic Scales|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... --[[User:Aura|Aura]] ([[User talk: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. --[[User:CritDeathX|CritDeathX]] ([[User talk: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. --[[User:Aura|Aura]] ([[User talk: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! --[[User:CritDeathX|CritDeathX]] ([[User talk: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? --[[User:Aura|Aura]] ([[User talk: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! --[[User:CritDeathX|CritDeathX]] ([[User talk: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. --[[User:Aura|Aura]] ([[User talk: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! --[[User:CritDeathX|CritDeathX]] ([[User talk:CritDeathX|talk]]) 00:07, 21 September 2020 (UTC)

Hey Sam, it's been a while since we've talked. I wanted to let you know that the song I've talked about in this section is almost done now. I only have a few sections left to go, and yes, I've gotten through the sections with 159edo-based retemperings of 12edo, 14edo, 17edo, 19edo, 22edo, 24edo, 27edo, 31edo, 35edo and 41edo. I only have the 53edo section and the last full 159edo section left to do. I hope the wait for "Space Tour" will prove to be worth it. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 23:28, 30 November 2020 (UTC)

Hey, Sam, just letting you know that I've finally finished the song- "[[:File:Space_Tour.mp3|Space Tour]]", and it's now available on my user page. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 19:14, 3 December 2020 (UTC)

: Sorry for not talking for so long, but that sounds amazing! I don't know how, but you managed to make Musescore soundfonts sound cool! --[[User:CritDeathX|CritDeathX]] ([[User talk:CritDeathX|talk]]) 16:26, 5 December 2020 (UTC)

:: I just used Musescore 3. That version has better soundfonts. Tuning each note was painstaking work though... --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 23:15, 5 December 2020 (UTC)

:: Also, I'm glad you liked the song, and I understand if you didn't talk for so long because you were busy- I get it. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 23:26, 5 December 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 [[243/242|rastma]] is not tempered out, a stack of two of them falls short of the [[2187/2048|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... --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 23:31, 7 October 2020 (UTC)

: I guess that'd be good for a parallel, yeah. --[[User:CritDeathX|CritDeathX]] ([[User talk:CritDeathX|talk]]) 12:41, 8 October 2020 (UTC)

:: Hmm... Okay, so, as per the title of this section, I'm trying to develop a [[159edo_notation|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? --[[User:Aura|Aura]] ([[User talk: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. --[[User:CritDeathX|CritDeathX]] ([[User talk: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? --[[User:Aura|Aura]] ([[User talk: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? --[[User:Aura|Aura]] ([[User talk: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... --[[User:CritDeathX|CritDeathX]] ([[User talk: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 [[Talk:159edo_notation#Dart_symbol(s)|the relevant thread]] on the 159edo Notation talk page. Oh, and what program do you use to make microtonal music? --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 18:58, 10 October 2020 (UTC)

::::::: I mainly use Musescore, but I also have Mus2 for more microtonal stuff. --[[User:CritDeathX|CritDeathX]] ([[User talk: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? --[[User:Aura|Aura]] ([[User talk: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? --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 17:15, 14 October 2020 (UTC)

: You can try calling it a nexusima or a nexuma, as a couple of options. --[[User:CritDeathX|CritDeathX]] ([[User talk:CritDeathX|talk]]) 18:03, 16 October 2020 (UTC)

:: Okay, [[nexuma|the article]] has been written. What do you think? --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 19:10, 16 October 2020 (UTC)

::: Looks good! --[[User:CritDeathX|CritDeathX]] ([[User talk: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... --[[User:Aura|Aura]] ([[User talk: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 [[User:Aura/Aura's Ideas on Tonality|what I have so far]]... --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 05:39, 18 October 2020 (UTC)

== Harmonize categories of interval pages ==

Hi CritDeathX, we are interested in your opinion about [[Xenharmonic Wiki:Things to do #Categories of interval pages|Categories of interval pages]], thanks in advance for taking the time. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 21:19, 8 November 2020 (UTC)

== My First Microtonal Piece ==

Hey Sam, have you've ever heard "[[:File:Folly of a Drunk.mp3|Folly of a Drunk]]" before? This was my first microtonal piece- it got its start in 2014. Others seem to like this piece also. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 17:08, 10 December 2020 (UTC)

: Its a pretty good piece! Quick tip for sheet music: make sure to hide the staffs that you aren't using on whatever page. Musescore should have that option somewhere in the Style section. --[[User:CritDeathX|CritDeathX]] ([[User talk:CritDeathX|talk]]) 21:53, 10 December 2020 (UTC)

:: Actually, master scores like the one you're looking at don't hide staves like this- at least not the ones I've seen. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 05:09, 11 December 2020 (UTC)

::: Ah, okay, makes sense. --[[User:CritDeathX|CritDeathX]] ([[User talk:CritDeathX|talk]]) 18:08, 11 December 2020 (UTC)

@@ Line 94: / Line 94: @@
 Congratulations! [[:File:Closed Up.mp3|Closed Up]] is an interesting composition (and hopefully just an opening!), it makes me curious for more. Reminds me of [https://www.youtube.com/watch?v=U5310fFktbU The Book of Sounds by Hans Otte] (see also [https://en.wikipedia.org/wiki/Hans_Otte Hans Otte &#45; Wikipedia]). --[[User:Xenwolf|Xenwolf]] ([[User talk: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!). --[[User:CritDeathX|CritDeathX]] ([[User talk:CritDeathX|talk]]) 23:23, 15 July 2020 (UTC)
+I agree too this one sounds neat! Thank you for making it. --[[User:Arseniiv|Arseniiv]] ([[User talk:Arseniiv|talk]]) 22:21, 27 September 2020 (UTC)
 == internal links ... ==
@@ Line 133: / Line 135: @@
 ::: We usually use -sma, -smic. [[User:IlL|IlL]] ([[User talk:IlL|talk]]) 22:29, 6 September 2020 (UTC)
-:::: Maybe, but "Quartisma" comes from "quarter" plus "schisma", and the name for temperaments that temper out the schisma is "schismatic". --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 22:34, 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". --[[User:Aura|Aura]] ([[User talk: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... --[[User:Aura|Aura]] ([[User talk: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. [[User:IlL|IlL]] ([[User talk:IlL|talk]]) 00:12, 7 September 2020 (UTC)
+::::: (Even for diaschisma "diaschismic" is more common than "diaschismatic".) [[User:IlL|IlL]] ([[User talk:IlL|talk]])
+:::::: Okay then.  "Quartismic" makes sense for the temperament name then.  I'll go with it. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 00:33, 7 September 2020 (UTC)
+Sorry about blowing up your talk page Sam... --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 04:35, 7 September 2020 (UTC)
+: No worries, its not like you're bursting into my house and sleeping in my walls. --[[User:CritDeathX|CritDeathX]] ([[User talk: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. --[[User:Aura|Aura]] ([[User talk: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... --[[User:Aura|Aura]] ([[User talk: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 ''tetra''cot and our temperament is ''quart''ismic)
+: 81/80 - meanfour (meantone but the tone is replaced with four, cause ''quart''ismic)
+: --[[User:CritDeathX|CritDeathX]] ([[User talk: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. --[[User:Aura|Aura]] ([[User talk: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. --[[User:CritDeathX|CritDeathX]] ([[User talk: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. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 15:07, 11 September 2020 (UTC)
+== Ideas of Consonance ==
+Hello Sam, I just posted [[User:Aura/Aura's Ideas of Consonance|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 [[Harmonic_Entropy#a.3D.E2.88.9E:_Harmonic_Min-Entropy|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. --[[User:Aura|Aura]] ([[User talk: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! --[[User:CritDeathX|CritDeathX]] ([[User talk: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. --[[User:Aura|Aura]] ([[User talk: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. --[[User:CritDeathX|CritDeathX]] ([[User talk: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)... --[[User:Aura|Aura]] ([[User talk: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? --[[User:CritDeathX|CritDeathX]] ([[User talk: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... --[[User:Aura|Aura]] ([[User talk: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. --[[User:Aura|Aura]] ([[User talk: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. --[[User:CritDeathX|CritDeathX]] ([[User talk: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 [[User:Aura|Aura]] ([[User talk: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. --[[User:Aura|Aura]] ([[User talk: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. --[[User:CritDeathX|CritDeathX]] ([[User talk: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. --[[User:Aura|Aura]] ([[User talk: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 [[User:Aura|Aura]] ([[User talk:Aura|talk]]))
+:::::::::: If so, that means there's a sense in which we're comparing apples and oranges... --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 19:40, 12 September 2020 (UTC)
+::::::::::: So that means we need to figure out a separate method for otonal & utonal notes. Interesting. --[[User:CritDeathX|CritDeathX]] ([[User talk:CritDeathX|talk]]) 19:55, 12 September 2020 (UTC)
+::::::::::: Wait, I noticed that you typed 12/5 instead of 5/7. --[[User:CritDeathX|CritDeathX]] ([[User talk: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... --[[User:Aura|Aura]] ([[User talk: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 [[User:Aura|Aura]] ([[User talk: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. --[[User:Aura|Aura]] ([[User talk: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. --[[User:CritDeathX|CritDeathX]] ([[User talk: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. --[[User:Aura|Aura]] ([[User talk: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.  --[[User:Aura|Aura]] ([[User talk: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... --[[User:Aura|Aura]] ([[User talk: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. --[[User:CritDeathX|CritDeathX]] ([[User talk: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? --[[User:Aura|Aura]] ([[User talk: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? --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 21:41, 12 September 2020 (UTC)
+:::::::::::::::: Just to show that I'm not making this stuff up out of whole cloth- see [https://en.wikipedia.org/wiki/Undertone_series| this article on the undertone series]. (preceeding unsigned comment by [[User:Aura|Aura]] ([[User talk: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? --[[User:CritDeathX|CritDeathX]] ([[User talk: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. --[[User:Aura|Aura]] ([[User talk: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. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 22:24, 12 September 2020 (UTC)
+::::::::::::::::::: I'd be happy to try and make it if you haven't already. --[[User:CritDeathX|CritDeathX]] ([[User talk: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. --[[User:Aura|Aura]] ([[User talk: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. --[[User:Aura|Aura]] ([[User talk: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. --[[User:Aura|Aura]] ([[User talk: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! --[[User:Aura|Aura]] ([[User talk: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? --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 21:50, 13 September 2020 (UTC)
+: Diartsmic and escapismic? --[[User:CritDeathX|CritDeathX]] ([[User talk: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... --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 19:56, 14 September 2020 (UTC)
+::: Quartismatic might be good, yes. On diartismic, we could also do dismatic. --[[User:CritDeathX|CritDeathX]] ([[User talk:CritDeathX|talk]]) 03:53, 15 September 2020 (UTC)
+== My Take on the Diatonic Scales ==
+Hey Sam!  Have you ever checked out [[User:Aura/Aura's Diatonic Scales|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... --[[User:Aura|Aura]] ([[User talk: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. --[[User:CritDeathX|CritDeathX]] ([[User talk: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. --[[User:Aura|Aura]] ([[User talk: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! --[[User:CritDeathX|CritDeathX]] ([[User talk: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? --[[User:Aura|Aura]] ([[User talk: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! --[[User:CritDeathX|CritDeathX]] ([[User talk: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. --[[User:Aura|Aura]] ([[User talk: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! --[[User:CritDeathX|CritDeathX]] ([[User talk:CritDeathX|talk]]) 00:07, 21 September 2020 (UTC)
+Hey Sam, it's been a while since we've talked.  I wanted to let you know that the song I've talked about in this section is almost done now.  I only have a few sections left to go, and yes, I've gotten through the sections with 159edo-based retemperings of 12edo, 14edo, 17edo, 19edo, 22edo, 24edo, 27edo, 31edo, 35edo and 41edo.  I only have the 53edo section and the last full 159edo section left to do.  I hope the wait for "Space Tour" will prove to be worth it. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 23:28, 30 November 2020 (UTC)
+Hey, Sam, just letting you know that I've finally finished the song- "[[:File:Space_Tour.mp3|Space Tour]]", and it's now available on my user page. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 19:14, 3 December 2020 (UTC)
+: Sorry for not talking for so long, but that sounds amazing! I don't know how, but you managed to make Musescore soundfonts sound cool! --[[User:CritDeathX|CritDeathX]] ([[User talk:CritDeathX|talk]]) 16:26, 5 December 2020 (UTC)
+:: I just used Musescore 3.  That version has better soundfonts.  Tuning each note was painstaking work though... --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 23:15, 5 December 2020 (UTC)
+:: Also, I'm glad you liked the song, and I understand if you didn't talk for so long because you were busy- I get it. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 23:26, 5 December 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 [[243/242|rastma]] is not tempered out, a stack of two of them falls short of the [[2187/2048|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... --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 23:31, 7 October 2020 (UTC)
+: I guess that'd be good for a parallel, yeah. --[[User:CritDeathX|CritDeathX]] ([[User talk:CritDeathX|talk]]) 12:41, 8 October 2020 (UTC)
+:: Hmm... Okay, so, as per the title of this section, I'm trying to develop a [[159edo_notation|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? --[[User:Aura|Aura]] ([[User talk: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. --[[User:CritDeathX|CritDeathX]] ([[User talk: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? --[[User:Aura|Aura]] ([[User talk: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? --[[User:Aura|Aura]] ([[User talk: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... --[[User:CritDeathX|CritDeathX]] ([[User talk: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 [[Talk:159edo_notation#Dart_symbol(s)|the relevant thread]] on the 159edo Notation talk page.  Oh, and what program do you use to make microtonal music? --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 18:58, 10 October 2020 (UTC)
+::::::: I mainly use Musescore, but I also have Mus2 for more microtonal stuff. --[[User:CritDeathX|CritDeathX]] ([[User talk: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? --[[User:Aura|Aura]] ([[User talk: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? --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 17:15, 14 October 2020 (UTC)
+: You can try calling it a nexusima or a nexuma, as a couple of options. --[[User:CritDeathX|CritDeathX]] ([[User talk:CritDeathX|talk]]) 18:03, 16 October 2020 (UTC)
+:: Okay, [[nexuma|the article]] has been written.  What do you think? --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 19:10, 16 October 2020 (UTC)
+::: Looks good! --[[User:CritDeathX|CritDeathX]] ([[User talk: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... --[[User:Aura|Aura]] ([[User talk: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 [[User:Aura/Aura's Ideas on Tonality|what I have so far]]... --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 05:39, 18 October 2020 (UTC)
+== Harmonize categories of interval pages ==
+Hi CritDeathX, we are interested in your opinion about [[Xenharmonic Wiki:Things to do #Categories of interval pages|Categories of interval pages]], thanks in advance for taking the time. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 21:19, 8 November 2020 (UTC)
+== My First Microtonal Piece ==
+Hey Sam, have you've ever heard "[[:File:Folly of a Drunk.mp3|Folly of a Drunk]]" before?  This was my first microtonal piece- it got its start in 2014.  Others seem to like this piece also. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 17:08, 10 December 2020 (UTC)
+: Its a pretty good piece! Quick tip for sheet music: make sure to hide the staffs that you aren't using on whatever page. Musescore should have that option somewhere in the Style section. --[[User:CritDeathX|CritDeathX]] ([[User talk:CritDeathX|talk]]) 21:53, 10 December 2020 (UTC)
+:: Actually, master scores like the one you're looking at don't hide staves like this- at least not the ones I've seen. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 05:09, 11 December 2020 (UTC)
+::: Ah, okay, makes sense. --[[User:CritDeathX|CritDeathX]] ([[User talk:CritDeathX|talk]]) 18:08, 11 December 2020 (UTC)