Mozart/Beethoven's Comp.Techniques were simple

[gongchime]

Check out this article on their compositional approaches. http://members.aol.com/chang8828/grouptheory.htm

[ggalen]

Greg,I just started reading the piece. It is extremely enlightening. But it prompts me to ask: "If there is a formula, and when I use it I very easily create melodies that are hailed as genius by other who don't know the trick...then it really would take all the fun out of composing!"Kind of like a puzzle that no one can solve, and then your are told the "trick", and it becomes effortless.But then I read this in the piece: "the formula is followed so strictly that it can be used to identify Mozart’s compositions. However, elements of this formula were well known among composers. Thus Mozart is not the inventor of this formula and similar formulas were used widely by composers of his time. ""Some of Salieri’s compositions follow a very similar formula; perhaps this was an attempt by Salieri so emulate Mozart. Thus you will need to know details of Mozart’s specific formula in order to use it to identify his compositions. In fact a large fraction of all compositions is based on repetitions." "The beginning of Beethoven’s 5th symphony, discussed below is a good example, and the familiar “chopsticks” tune uses “Mozart’s formula” exactly as Mozart would have used it. Therefore, Mozart simply exploited a fairly universal property of music. "

[mazz]

This is very useful for a film composer who must write 45+ minutes of music in a very short period of time. To have access to a small amount of musical material and to be able to transform and evolve it quickly into a larger form is a very handy trick to have available! I've been doing this to some degree already in my current project but I'll have to read the article again to see if I can pick up some more info. A worthwhile read, even for a non-math savvy person like me!Thanks for posting, Greg!!Mazz

[gongchime]

Thanks Mazz. That means a lot coming from you. I've been trying to sell people on my ideas about inversions, retrogrades and such but most people aren't having it kuz they feel it's too intellectual or not intuitive enough. To my mind, the coming up with the simplest rule is the most intuitive thing you could ever do. Of course songs are a completely other monster, but still, when your juices aren't flowing, there's somewhere to turn as long as we don't reject good ideas out of hand.Besides all the usual transformations I just had some insight into rhythm permutations. Random permutations are not musically meaningful the same way random note permutations end up sounding meaningless, hence the need for some structure such as inversions and retrogrades provide. I remembered that, in Africa, master drummers cycle through rhythms. So, if you've got the one played all over Africa 2+2+1+2+2+2+1, when you want to play something different but related to this, you can play through one of it's rhythmic modes. For example starting on the second rhythm event and using that as the beginning aka 2+1+2+2+2+1+2. This is musically meaningful/useful permutations of the rhythm. Notice also that the first one I gave mirrors the intervals in a major scale M2 M2 m2 M2 M2 M2 m2. Because of this we can say it is the Ionian rhythmic mode. Another interesting thing about this is that the other two most prominant rhythmic modes in Africa are part of the cycle of this one. It shouldn't perhaps be surprising then that they are in fact the Lydian and Mixolydian modes. I, IV and V. Creepy, I know. Another more abstract but still musically meaningful permutation is to sort notes in ascending and/or descending order of length or perhaps rhythmic cells sorted in ascending order of probability, just like in my chart on my http://www.myspace.com/gongchime page in the Music Comps folder under pics.

[mazz]

Greg,If you haven't yet checked out my teacher's materials, I think it's right up your alley. He's written a pretty amazing book called "Harmonic Experience" which deals with reconciling "natural" tunings and temperament (to put it very simply). If I've already recommended it, forgive the repetition! http://en.wikipedia.org/wiki/W._A._MathieuHis diagrams of the harmonic series put in to musical notation are pretty amazing to look at. His book also contains a very thorough compendium of harmonic resolutions, progressions and patterns in tonal music. Well worth the investment, highly recommended! Thanks for the mental stimulus.Mazz

[gongchime]

I haven't seen Harmonic Experience before although I have seen something similar put out by Grove and something else that was at my library but all in German with just tons of diagrams showing relationships between pitches, rhythms, intervals, etc...I was looking at the chart in the other post about Probability and was thinking about how that data is similar to a zip file and that every melody used to create it is still stored in the data and we just need to unpack it. That lead me to think about a phenomenon called Automorphs. Maybe you've heard of them. You can take any kind of series melodic or rhythmic and then just continue to expand or contract it so, for example, if you move up an interval of a m2 then the next time you can move up the interval of a M2 and after that a m3 etc... Rhythmically, it might go a sixteenth followed by an eighth followed by a sixteenth morphed using rhythmic augmentation into an eighth followed by a quarter followed by an eighth and morphed again the same way into a quarter note followed by a half note followed by a quarter. Then played back to back. You can also alternate such as moving UP a m2 DOWN a M2 UP a m3 etc... I wanted to mention that not every culture thinks about things the same way we do and what they're thinking about can be very surprising to us. Specifically I'm thinking about the first comment in the article made about Mozart that said he used just a short list of melodic patterns that he composed from. I suspect this may have come from his father Leopold encountered somehow by way of Middle Eastern musicians. Before explaining, it should probably be pointed out that when Europe was wallowing in the dark ages, all of the mathemtical and scientific advancements were coming out of the Middle East of those regions at that time.When improvising, many musicians coming from Middle Eastern countries don't just go up and down the scale or hop around the way we might. They have been taught by a teacher to join fairly short melodic patterns together. There are three kinds for ease of memorization; upper tetra-chord, lower-tetrachord and one's that bridge the tetrachods. You can start on any pattern that you learned at any position, it doesn't have to be the first pitch and you can end on any position, then if you want to continue a melodic line you have to either superimpose the last note you played onto another of the basic patterns at the place where it has that pitch or to an adjacent pitch aka conjunct or disjunct respectively. This seems to be similar to what Mozart had done.Their teacher's teacher's teacher going back thousands of years had already worked out the most common solutions and taught improv using this method. And this has become the basis for much of the Middle Eastern tradition. Using my handy dandy chart recently acquired, I've made a list of the common solutions through the pitch series that are the most effective in the Western tradition. I'd like someone to tell me how to put an image into this thread so people don't have to go to the trouble of registering on myspace, logging in and searching through my page to find them.

[gongchime]

These would be similar to what Mozart would have used. They are written above, on and below the staff. They all start on pitch "C". They're all only 7 pitches in length for ease of memorization. Think of them like phone numbers. The first one is 154-3512.

[gongchime]

The above paths through the search space were based on these probabilities;The fourth one is a tentative rhythm probability chart which assumes melodic rhythms cluster around the eighth note. It may be doubled or halved for slower or faster melodic rhythms.

[ggalen]

Wow.That's cool, Greg. Lots of work!

[gongchime]

I forgot that you get better results if you take into account two or more adjacent pitches instead of only one like second order Markov chains. That would perhaps produce slightly different results but would be significantly more complex to handle by hand.