I just thought of a music theorem yet to be rigorously proven.

"For each melodic phrase or section in a given piece of music, another melodic line can be found, that would sound at least as good or better than the original, while baring a ressemblance in scale, rythm, and overall feeling, but without changing the instrumentation beneath in any way. Better is to be understood as better to the ears of a music expert and an average person all the same."


Is this true?


This theorem implies you could rewrite existing pieces of music, including hits and milestones in the history of music, improving them substantially.

I thought about this theorem while listenning to great music melodies that we all love, and wondering how it could possibly get any better..

I'm conscious that a melody is only so good when taking into account the rest of a piece of music, because of how it can get developped or subject to variations! But this theorem might still apply to a big amount of modern or repetitive music, or apply to the main themes themselves!


What do you all think? Entering the music philosophy field here!

i think it's impossible to truly define "better" in such a subjective field. any melody can be good in its own right, but whether one is "better" than the other would completely vary from person to person, so there isn't really an "average person" standpoint. i think there's always room for improvement within yourself, but i don't think this applies at all consistently from an outside perspective

You can't keep on 'improving' a melody forever since there are only finite notes you can change while still keeping the same rhythm. You'd probably just eventually end up oscillating between two melodies because one is better to some people and the other is better to other people. So therefore, there is always an 'ideal' melody that will be the best possible one to 50% of the audience. And then you also have to worry about defining 'better' as Sinc-X said. More emotional? Happier? Is a piece of music that entertains you, better than a piece of music that makes you think? Different melodies are good for different purposes.

Making an endless cycle of variations is certainly possible, yet after 'n' variations of something, be it an "improvement" or a "deterioration" (what Sinc-x mentioned), it is impossible for them to always be distinctively better or worse or even be very much different than other variations

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haha fukkin nerds XDXXXDDXDD

Thanks for your great answers! Funny to see your different standpoints.

I wish I had time to answer every single one of you

This is very easily disproved mathematically as you are effectively saying there is an infinite space of the progression of improvements trying to map onto the finite space of pitch and time. Time being finite because for any sufficiently fine granulation of rhythm your ears can't tell the difference. I.e. you can't tell if the one quarter note played a 192nd note sooner.

The interesting consequence of this is the resulting corollary: there exists a melody which cannot be improved upon.

What's even more worrying, in practice this means there is a finite number of possible melodies, and while it's surely a hugeass one (especially given the fact that most pieces of music are complex combinations of multiple melodies, since many instrument parts), the probablility that a particular one has been used before will be (linearly?) increasing over time.
O no, this means the mankind is inevitably going to hit a point in time when no original music can be made anymore AAAAAAAAAAaaaaaaa
/me dies

damn, copyright will rekt musicians by then D: