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Everything posted by Monarcheon

  1. This isn't really music anymore. It's just math that you'd learn in school. The minor third ratio is from E to G, or the second and third places in the ratio. That's 10:12. 10:12 dividing both sides by 2 gets you 5:6 which is the proper ratio for the minor third.
  2. That's how ratios work. They divide and reduce like fractions do. It's just basic math. 8:12 divide both sides by 4, you get 2:3, perfect fifth. 10:15 divide both sides by 5 you get 2:3, perfect fifth. The fact that they're off by a factor of 4 or 5 doesn't mean anything as far as the ratios are concerned. It's just a bigger form of 2:3. They need to be that big so that the other intervals also work with it.
  3. @Quinn It's a vector because it displays varying magnitudes (in this case, intervals in a set) on a singular matrix structure. You have to realize: music theory, effectively, is a way for musicians to be lazy. We don't have time to count individual pitches that sound good. Having a system in place to describe them easily helps. There's a second point in music theory, where it becomes mostly analytical, while still attempting to create systems. Composers often leave this behind (though some don't, like Carter and Babbit), but that's why it's a field unto itself. You can use the concepts for composition, but they're a means of understanding something beyond performance practice or orchestration. Simply speaking, it's great you have what you need to know and like many people stop when it no longer becomes compositionally functional, but there are people who take it further as means of further insight into existing works. Both viewpoints are valid.
  4. They are represented. They're just multiplied by a certain factor to preserve the relationship between the two. 2:3, the perfect fifth is equal to 8:12 and 10:15. No. They're all individual and considered together at the same time.
  5. By the way, I encourage anyone who's seeing this weigh in if they want. I think it's interesting discussing the differences in compositional and analytical mindsets. It would definitely help to an extent. I think Forte has a good way of classifying related pitches, but just goes too far with it. Similarly, Schenkerian terms like "prolongation" have already seeped into our musical consciousness already and his concepts of unfolding, etc. are pretty relevant. He also, in my opinion, tries too hard to make some things work in his favor though.
  6. Not necessarily. Have you explored Schenkerian analysis at all? It can be quite detailed, but it necessarily removes particular elements of tonal music that would be audibly interpreted as important. PC set class and vector analysis, while surface, can be super in depth with a lot of information, but reduces music almost exclusively to pitch class. All analysis does this, even the form analyses you were talking about, but to me the question is can it be used in a way that explains rather than projects.
  7. and @Tónskáld I don't think anyone's really used to writing anything like this, even me, so judges are definitely gonna be more lenient with things regarding form! You're right: it is not a theme in variations. Gustav, you're in the right headspace; your example would definitely be a good example of what we're going for.
  8. I mean, I get it. The music of Schoenberg, Webern, Berg, Boulez, Babbit, Coltrane, etc. can't be easily formed into what we'd used to analyze music up to that point. So we came up with a another system; Bach certainly didn't think about chord symbols/roman numerals when he wrote his music. But when you look at the screenshots I've posted below (what I'm studying right now), does anyone really think they're describing the music they're hearing anymore? Like I said before, analysis is necessarily reductive, but my Schenkerian teachers always told me that relationships that are reduced need to be heard for them to be legitimate graphing points. We're studying contour relationships in atonal music now and while not all the theories are obviously heard, it's more audible than constant segmentation of PC sets.
  9. Sorry, nebulous was an adjective, WT0 is the whole tone scale starting on C. Whole tone makes a pretty leadless sound, so I thought that's where it was going.
  10. I don't know about that. My point was whenever a chord is played all of the ratios found in it (much like finding an interval vector) are heard and applied to your ear, the consonance and dissonance don't much matter. Same goes with inverted, chords– the ratios would just be different, but you'd still hear all of them.
  11. @Seery, it's both. Let's take a look at the ∆7 chord. 8:10:12:15 = C E G B All of the intervals related to C make sense. 10:8 = 5:4 which is a major third. That checks out because C to E is a major third. 12:8 = 3:2 which is a perfect fifth. That checks out because C to G is a perfect fifth. 15:8 = 15:8 which is a major seventh. That checks out because C to B is a major seventh. HOWEVER: All of the inner intervals also make sense. 12:10 = 6:5, which is a minor third. That makes sense because E to G is a minor third. 15:10 = 3:2, which is a perfect fifth. That makes sense because E to B is a perfect fifth. 15:12 = 5:4, which is a major third. That makes sense because G to B is a major third. So when you play a chord (C∆7, specifically), you hear ALL of those relationships at the same time. It is both all notes relative to the root and a note-to-note basis at the same time.
  12. Basically. It's a little more nuanced, but in this case it works. [0123], which is C, C#, D, D# and (0123) are slightly different. Cents are even more weird to think about it. In pitch class space only, just think about intervals between notes, ratios for simple relationships, if you must. Makes it simpler unless you're utilizing the harmonic series for compositional effect. What? I'm saying the major seventh chord's ratios are 8:10:12:15. In any given ratio between two of those numbers you get the correct ratio for that interval specifically. i.e. 10:15 reduces to 3:2 as does 12:8. They're both perfect 5ths, which makes sense, because both E to be and C to G are perfect fifths. That's not two processes, it's just one concise ratio, despite having multiple internal relationships.
  13. No, you didn't. Those three intervals are not the most dissonant if you wanted to make the most dissonant tetrachord. It would be Forte: 4-1, (0123). I just don't see why you, in your premise, think that (0137) is going to be more dissonant, especially considering it has an even interval class vector, while (0123) has a more left-heavy vector. In other words, I don't agree with your premise that the most dissonant tetrachord is one that has multiple different types of dissonances in it. You'll notice that (0137) is just the major triad (037) with an added minor second (1), so of course it isn't going to be the most dissonant, even when all bunched up. This whole ratio business gets really useless if you're considering all of this in equal temperament. In equal temperament, the perfect fifth is not 3:2. That's what I'm saying. I don't see why in your initial argument you claimed you had found the most dissonant chord which is why I was calling you out for stopping at 4 notes.
  14. Why did you stop at three? D is the inversion of A# when working in equal-tempered pitch classes. In other words, both notes are a whole step away from C. It depends on the type of music you're writing. In jazz, you'd base things on the primary or secondary roots. In early atonal music, it could be either. In Renaissance music, both matter. Both, technically. When you play a major triad (C E G) the ratio is 4:5:6. Major third ratio is 5:4 and minor third ratio is 6:5. 6:4 is a perfect fifth. Major seventh chord (C E G B), you get 8:10:12:15. 8:10 = 4:5. 10:12 = 5:6. 12:15 = 4:5. The major seventh interval from bottom to top is 8:15. All of the ratios matter, that's what makes them ratios.
  15. This is sort of an extension of the conversation @Ken320 and I were having on the chat. I was basically saying that, in my experiences reading/discussing Allen Forte: 1. Forte wanting to have it both ways (saying that it doesn't matter what the composer did, since we can never fully know anyway, and also claiming that Schoenberg/Webern/etc. strongly cared about PC sets in his music), essentially begging the question 2. There is no evidence of Schoenberg using PC sets in his music, despite us having ample evidence that he thought very deeply about how to formulate tone rows 3. the interlocutor theorists being unable to hear any of the relationships that Forte describes with PC sets 4. claiming Forte is attempting to take over the composer's authority with Forte's own as a theorist. I can definitely see where they come from, especially with No. 3. Quick rundown on PC sets: 1. convert pitch classes to numbers [C G A] -> [0 7 9] 2. transpose to 0 [0 7 9] 3. find the shortest distance between any consecutive ascending form of the set [7 9 0] 4. transpose to 0 (025). The set class is (025). Any transposition of (025), forwards or backwards is part of set (025). Forte would use these set classes in millions of ways; inverting them, finding every instance of it and its 12-tone aggregate complement in any atonal piece (segmentation), finding interval class vectors, using those vectors to construct genera of potential subsets and supersets, the list goes on. Many Forte followers have introduced many additional concepts to his theories like set multiplication, maximally related sets, etc. These arguments don't stop with atonal analysis; Schenkerian analysis for tonal music gets a lot of heat for being so reductionist that the music isn't really even being analyzed anymore. Some people even think the way we analyze chords with Roman numerals is reductionist. Even though I think analysis is inherently reductionist, I'm curious as to what anyone thinks about this kind of stuff and would be willing to go through any strange concepts (though I'm not an expert in any way). I feel like as composers we have a different take on this kind of thing.
  16. Are you looking for like "rules" feedback on contrapuntal writing, or dramatic feedback? So far, I'm just not sure why you drop the rhythmic intensity and go to a section of just whole notes near the end of the excerpt...
  17. I like how you switched the vocal texture at the end from the beginning. The result of the relatively ternary form is nice. m. 58 is my favorite chord of the work. If I had one thing to say, it might be that the close voicing of the tenor is sometimes a little too much for me: see, m. 14, m. 37. But overall, lovely work.
  18. It is certainly more dissonant, but not enough to disfigure it (at least to me; there are plenty of anthem purists who would disagree). I think the chromatic voice leading stuff is quite lovely, actually.
  19. Early three composers break a lot of their general rules. Brahms does need more counterpoint, yes. Debussy sounds extremely tonal. Shostakovich didn't sound like him to me. Didn't sound as calculated as him. I also like your variation the most. The jazz was the most confusing. It started to go in that direction, but missed a lot of character. Pretty abrupt finale.
  20. So, I got a little tired of the process is it kept going. It was cool hearing a Csus/Bb at the beginning and the occasional instrumental licks are nice, but even if I was watching a film, I think I'd be a little antsy by the 2 minute mark. Maybe some more rhythmic drivers would be nice, since your smallest rhythmic unit is split only once without an alteration of much contour.
  21. It does built tension quite nicely. The III∆7 chords in third inversion didn't feel as satisfying as a passing chord like that normally would. I think that it might be trying to have it both ways sometimes, since in the bigger end section it's over a dominant.
  22. Nice little thing here, that flows into itself rather well, despite being sectioned by standard form. The stops didn't get to me so much as Eb9 with a focus on the 9th did. I know it's part of your main progression but it always felt a little odd to me for some reason; perhaps it's the predominant function being accented as though it had dominant function, but I'm not sure.
  23. Yes, that 29 modulation is a little strange... I was excited at first because I heard the first bar as an augmented triad and I thought you were going to nebulous (WT0) with it, but the result was a little underwhelming. Also, to me most of this sounds as though it should be in 3/4. I know Ravel did something similar in his piano concerto, but it's not as ambiguous sounding to me. Though, the piece is nice in and of itself.
  24. m. 47 - The double E# in a row will take a very steady hand to not emphasize both and sound awkward. I would pick one to emphasize, but that's just me. m. 81 - the way you have the arpeggio written is a little strange, since the notational contour is one-directional but there's a note that goes down. Overall, I think this is a lovely piece. Great mixed sonorities reminiscent of Debussy's good ol' underwater cathedral. If I had one formal complaint it would be that the beginning kinda takes a while to get going. Establishing themes is great and in a sort of hymn style it makes some sort of sense, purely as a listener and not a theorist I found it a little start-stoppy. As soon as you start going, however, everything flows beautifully.
  25. I'm not really sure what you mean, but in counterpoint, voices always resolve themselves. I think it's still a rules issue, especially since the lower voice stays on the same pitch as the higher voice, before it jumps down. Whether or not you follow that rule is up to you, but it's good to know it's there.
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