The melody Theorem
BotB Academy Bulletins
Level 16 Pixelist
post #93017 :: 2017.12.11 10:49am
  themnotyou, raphaelgoulart and Sinc-X liēkd this
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!
Level 27 Chipist
post #93018 :: 2017.12.11 10:58am
  Savestate, raphaelgoulart, goluigi, Apsarah, MiDoRi and Galak Sea liēkd this
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
Level 26 Chipist
post #93033 :: 2017.12.11 12:46pm
  Flaminglog, raphaelgoulart, Jimmyoshi, goluigi and Sinc-X liēkd this
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.
Level 20 Chipist
post #93036 :: 2017.12.11 2:00pm
  Sinc-X liēkd this
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
Level 27 Chipist
post #93047 :: 2017.12.11 6:58pm
  Dimeback, Flaminglog, themnotyou, MiDoRi, Sinc-X, Galak Sea and FamicomForever liēkd this
a lot of music is just "one sequence of notes on top of a framework that doesnt care *too* much abt what is up there" so itd hold true there, but less as u get higher in quality. theres plenty of "great songs"/music in general where the intervals used in the melody (both horizontally [note-to-note intervals] and vertically [inside currently-playing harmony] r inextricable and u wldnt get the same inner relations if u changed any of it, since its already pretty optimised

nonetheless i do agree w this thread, its something a lot of high-quality music consciously takes into mind and i think abt it a lot myself, its basically "the craft of note compostion" more abstractly, couple things to keep in mind when ur thinking abt "what note to use":

UR-RULE) there r basically two kinds of intervals u shld consider when writing. these r namely harmonic (vertical) intervals and melodic (horizontal) intervals. i will go into detail on both:

1) due to acoustics, here r some good ground rules for Harmonic intervals above the root, or tonic (treat this like piece values in chess, so not Authoritative, but a good rule of thumb), from strongest to weakest:

• unison/octave
• fifth
• either third (so long as u use one at a time)
• either seventh (so long as u use one at a time)
• major ninth/second
• either fourth/eleventh (so long as u use one at a time)
• either sixth/thirteenth (so long as u use one at a time)
• minor second
• all other intervals

ok, so with harmonic intervals theres two main things to worry abt:

a) position above the root at any given moment (i.e. if ur in G minor and u play a D over a Bb chord, its position over the root (Bb) is a third)

b) position above the tonic at any given moment (i.e. if ur in G minor and u play a D over a Bb chord, its position over the tonic (G) is a fifth)

i.e. here is a good example of a song that uses both of these to good effect. undertale - spear of justice (dont get mad at me fags)
. in the opening here u can see theres a great variety of two things:

> the same notes in b) have a large variety in a) (i.e. the note G is repeated, but its an octave/unison above a G bass, a fifth above a C bass. the D is is a fifth above a G bass, a seventh above a Eb bass, a ninth above a C bass etc. u can go wild with this, )
>> the same notes in a) have a large variety in b) (i.e. the note G is played over G, the note D is played over G, the note F is played over G, the note C is played over G, etc.)

there is also nice sliding *between* these two styles, when one style gets too saturated. when there r too many notes over a single bass (as in >>), it switches over to having single notes over many basses (as in >), often using pivots. (i.e. when a lot of notes r played over a single bass, it plays those same notes again over a different bass when the bar resets. when "playing them all again" gets boring, it will play certain notes over different basses, using "D over G" as in >>, to become "D over Eb" as in >)

2) due to ease of singing, here r some good ground rules for Melodic intervals. the melodic intervals r basically the same as harmonic intervals, except instead of the interval between a note and the root/tonic, its the interval between *two notes* that are both over a root (or tonic), u can calculate which ones to use as which intervals go between the intervals shown up top. for example; a major sixth is consonant when it is going between a fifth and a third above a root, or tonic. so, idk. i.e.:

• unison/octave
• fifth (btwn unison and fifth)/fourth (btwn fifth and octave)
• third (btwn unison and third, third and fifth)/sixth (btwn fifth and third, third and octave)
• third (btwn fifth and seventh), sixth (btwn seventh and fifth), tritone/fifth (btwn third and seventh, seventh and third), seventh (btwn unison and seventh)/second (btwn seventh and unison)
• second/ninth (btwn unison and second)/seventh/second (btwn octave and second) etc etc
etc etc

now, with THESE melodic intervals there r two sets of main things to worry about:

a>) relative melodic interval over root
a>>) relative melodic interval over tonic

(for example, a fifth-third sixth, considered over the root, or the tonic)

b) absolute melodic interval (for example, ANY major sixth)

a good example of both of these, is here: the beach boys - god only knows
. the harmonic interval over the root is always changing (D is fourth over A root, F# is seventh of G# root, A is third over F# root, C# is ninth over B root), and since there's no clear tonic because it keeps modulating (altho its around F# minor) theres little hope of coherency there. instead, the coherence is in its melodic intervals, and particularly the absolute ones. for example:

• "note, second down, second up" (often both minor, changed to major for effect at last one) starts every line in the melody, and "note, second up, second up" often ends it
• melodic intervals r small in first half of phrase, large in second half of phrase
• otherwise nonsensical changes in contour (E D# E -> F# A [major sixth]), becomes E D# E -> G# C# [fifth] become justified by similar relative intervals over the changing roots. first one is a [fifth-seventh] major sixth, the next one is a [seventh-third] fifth). so they r actually quite similar

another good example is here: kazumi totaka - nantendo funcenter
. here it takes advantage of two things: that one) melodic intervals dont *have* be next to eachother to be heard (as long as they are both on strong beats), and two) the direction can be reversed and still be intelligible.

the melody opens with a [ninth-octave] second (G F over Fmin7). this then becomes a [tenth-eleventh] second (Bb C over Gmin7). as well as pleasingly using different relative intervals over each chord, the absolute interval also moves in a different direction, while still being a movement of a major second. this then happens again, only this time a new note interjects (G Eb, F rather than G F); while you still hear the second two notes across, this is significant in a lot of interesting ways; the Eb is a seventh in Fmin7, but now the F has been delayed across to the Gmin7, in which it is now also a seventh. over this Gmin7, another second, "C Bb" from the tenth-eleventh second is played, now in reverse (making it a eleventh-tenth second). before u get to hear the "Bb C" from before though, its already switched back to Fmin7, in which this C is a new interval (fifth). this then ends on the opening G (seventh over Fmin7, octave over Gmin7); that opening is generally an amazing class in quickly racking up a lot of variety while sticking to two chords and a pentatonic melody based almost entirely on seconds and fourths

if u really wanted to compress it even further you could hear it as an elaboration of two pairs of seconds in opposite directions, rhythmically displaced over the two chords: "G F \ Bb C \ G F \ Bb C"
Level 20 Pixelist
post #93054 :: 2017.12.12 2:04am
  sleeparrow, Dimeback, Xaser, mk7, Quirby64, Sinc-X, Galak Sea, Jimmyoshi, RazerBlue6 and charlotte liēkd this
Level 9 Mixist
post #93057 :: 2017.12.12 6:40am
  R3M and FamicomForever hæitd this
haha fukkin nerds XDXXXDDXDD
Level 16 Pixelist
post #93082 :: 2017.12.12 3:23pm :: edit 2017.12.12 3:23pm
Thanks for your great answers! Funny to see your different standpoints.

I wish I had time to answer every single one of you
Level 19 Criticist
post #93217 :: 2017.12.14 8:30pm :: edit 2017.12.14 8:33pm
  Baron Knoxburry, RazerBlue6, MiDoRi, Dimeback and Sinc-X liēkd this
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.
Level 20 Pixelist
post #93231 :: 2017.12.15 3:22am
  Galak Sea and RazerBlue6 liēkd this
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
Level 22 Pedagogist
post #93240 :: 2017.12.15 1:17pm
damn, copyright will rekt musicians by then D:

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