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And have they all been used?
Because a melody depends on pitch and rhythm. Although there are a limited number of relationships that can occur between notes, rhythm, in theory, could be infinite. You could have a melody pattern that only repeats after several hours....or years for that matter.
there's a finite number of chord sequences, but not of melodies. That's why you can sue someone for stealing your tune, but loads of songs share bits that sound similar.
but the number would be so large its unlikely it could ever be reached. there'd be 12! (1x2x3x..x11x12) ways of arranging the 12 notes in western music, which you'd then have to multiply by a ridiculously huge number to account for all the different ways in which you could hold particular notes and pause between others. even discounting all the "non musical" permutations of the 12 note scale (though schoenberg might disagree) you'd have a ridiculously huge number. and that's only accounting for using each note once before returning to it. there's also microtonal notes and non western tunings to account for. may well be possible to work out a finite number, but it would be so huge you may as well say infinite
definitely not all been used for the second question.
or infinite ones. If there's a limit on length then we're looking at finite sequences of numbers base 12, which can be thought of as an infinite subset of the rational numbers, and so is countable infinite. If we remove the limit on length then we're looking at infinite sequences of numbers base 12, which is the very definition of the real numbers, so we're talking uncountably many different variations.
I suppose if it had a pattern that became more complicated but retained a pattern, like the number sequence
123112311223112233111223311122233111222333111122233311112222333111122223333 etc it could probably be considered an infinite melody, or an infinite series of melodies though.
but probably relatively few that sound like a melody, and lots of them would be the same relationships just with a different starting point note so would be the same even though they strictly aren't, so no and yes. But im quite interested in other tuning systems since I saw this schools program on channel 4 about music, the western scale is relatively new and impure, it is just an octave split into 12 notes and means that it you cant have a note and its fifth (the 2nd most harmonious relationsip after an octave of a note) just an approximation of it (but for some reason this means you can shift keys without retuning), there are other musical systems, I think the indian system has 17 notes, arabic 24, so there is plenty to play around with but still the most pleasing relationships are probably similar in each system and well explored by now
the timbres of different instruments, rhythmic noise, all can change the feel. It is like drawing, im sure every geometric shape has been drawn but there are still infinite paintings to be made
...the question should be then, "have we exhausted all the most emotive melodies - the ones that seem to connect with human beings? I'd like to see what more learned members have to say about that? I think the question is going to depend on whether you think that reaction is purely subjective, or whether there is indeed some objective fact which accounts for why certain melodies are going to be more affecting than others.
I'd like to read what people think about this.
not only do melodies sound different when placed with different chord progressions, but a large part of a melody's emotive impact are the words (if there are any) that go with it. there are a huge number of words that can go to a huge number of melodies over a huge number of chord progressions.
music is miles away from peaking, it's just arguably in a bit of a cultural rut at the moment. perhaps the reason that popular music is borrowing so heavily from the past right now is that the music industry wants to emulate the successes of that era on a new generation of uneducated ears. it's not really a time where anyone wants to take risks.
you can never run out of good music, everyone relates to the world through music in a different way and from a different perspective and so there'll always be fresh outlooks.
Has what you're looking for - in fact the concluding chapter uses the findings of the mathematical analysis of music to more or less prove his thesis.
Which is... (and this is from Amazon's description of the expanded version of this work, published 2005)
"Our love of art, writes John Barrow, is the end product of millions of years of evolution. How we react to a beautiful painting or symphony draws upon instincts laid down long before humans existed. Now, in this enhanced edition of the highly popular The Artful Universe, Barrow further explores the close ties between our aesthetic appreciation and the basic nature of the Universe. Barrow argues that the laws of the Universe have imprinted themselves upon our thoughts and actions in subtle and unexpected ways. Why do we like certain types of art or music? What games and puzzles do we find challenging? Why do so many myths and legends have common elements? In this eclectic and entertaining survey, Barrow answers these questions and more as he explains how the landscape of the Universe has influenced the development of philosophy and mythology, and how millions of years of evolutionary history have fashioned our attraction to certain patterns of sound and color. Barrow casts the story of human creativity and thought in a fascinating light, considering such diverse topics as our instinct for language, the origins and uses of color in nature, why we divide time into intervals as we do, the sources of our appreciation of landscape painting, and whether computer-generated fractal art is really art. Drawing on a wide variety of examples, from the theological questions raised by St. Augustine and C.S. Lewis to the relationship between the pure math of Pythagoras and the music of the Beatles, The Artful Universe Expanded covers new ground and enters a wide-ranging debate about the meaning and significance of the links between art and science."
It's a brilliant book, highly recommended
Eine Kleine Nachte Musik
This thread has helped me get some ideas together to research for my essay :)
because there can't be a truly infinite number of ways to combine notes, pitch, tone, rhythm etc
it might be a very large finite number but mathematically eventually it will reach it's limit
so, essentially infinite
But it's a big enough number that it might as well be.
so there are a finite number of potential melodies
for instance you could say (as I have above) that the 'size' of time/space is the limiting factor and then you can say that the number of melodies is finite because the universe is finite
but how can we be sure that the universe is finite?
and even if we could, string theory predicts the multiverse which is itself a possibly infinite number of parallel or alternate universes
but it is certain that there are enough melodic permutations to last until the end of time and so, essentially there are an infinite - or eternal if you prefer - number of potential melodies
thats just cheating
it's just a reference point (in this example) for defining cosmic finity
All of the other variables are finite, so their product must be finite (albeit very big).
I'm not sure you are correct. If you extend the gap between the notes enough I think it stops being a melody and becomes a series of isolated notes. I would accept that it's hard to define when you reach that point, but I instinctively feel that if, say, there was an hour between the notes the human brain wouldn't perceive it as a melody.
if you accept that the space between two notes can be infinite, then there must be an infinite number of melodies.
if you place a restriction on the amount of time between notes then there would be a finite amount and so a finite amount of combinations (even though it would be a huge number)
same thing with pitch (although I don't know if there is a natural maximum limitation on this number already).
if each component of melody has a finite number of permutations, then the total number of combinations must also be finite.
and not just spaces between notes but note lengths, pitch swoops etc
Debatable. You would have to impose some kind of limits on what constitutes a different melody. i.e. something that was 10 tones long would be made up of a series of combinations of 'melodies' that you would already have accounted for when calculating the number of 4,5,6... tone melodies.
The question isn't well defined enough to be answerable (mathematically) is what I'm saying.
and there's no other melody that seems to work that well but the Eels one
I reckon although technically infinite someone could come up with a ballpark figure if they used a few assumptions based on what most people understand melody as, there is a lot of tiny variation and flourishes but for most it is the main pattern behind that. Although technically it could be infinitely long, really it has to be short enough for short term memory, I reckon anything longer than 4 measures could be chunked as part of a series of melodies rather than a single one, so set that as the max and it will contain shorter ones within it. Then there is the issue of the infinite number of notes that can be played in a measure, I think really anything quicker than 16th notes would no longer be recongnised as melody it would either blend into one sustained note if they are the same note, or be dismissed as tiny variation to the main pattern if different notes, people will just pickout the main notes. So say 16 notes x 4 measures, at 4/4 would be 64 slots in a melody. So if there are 12 notes, plus one extra for silence, that is 13 possible notes for each slot. I have no idea how to work out number of combinations, would it be 13 notes to the power of 64 slots? If it is divide that by 12 to get rid of duplicate melodies in different keys (not sure if that would work?), repeat for a number of different time signatures, I guess there would be 16 if limiting to no notes quicker than 16ths (but not sure) and lots of overlap between them, ones with fractions in I reckon would just be percieved as close enough to one of the other ones. I guess there is still the problem of there really being more than 12 notes, but I assume it is possible to know the resolution of human hearing and know within what range people perceive pitches as different, and run the whole thing again based on that number. But then there is also the issue that the same note in different octaves will feel different, so you would have to multiply the number of notes by the number of octaves people can hear. If someone went through all that, I reckon it would cover the vast majority of possible melodies. I dont really know what I am talking about though, should probably abadon reply