This article will attempt to explain my beliefs on how every piece of music, every sound, every picture and every animation can be rated and scored on its own merits outside of human opinion.

I'm not exactly sure of the general consensus, but I have often heard the opinion that with music for example: "There can be no final, or definitive judgement" or that "One person's opinion is just as valid as another". In other words, many believe that music is only good because our minds are individually (and in different ways) - 'programmed' to enjoy it. This is of course true up to a point, but on top of this, I also think that even if we didn't exist, music has a degree of quality to it (whether good or bad), which would make it stand up in its own right. In the same way, all graphics and artwork can be given a definitive aesthetic evaluation - and that even if no-one knows for sure how good it /really/ is - that doesn't mean to say this 'score' doesn't exist.

For the sake of argument, I'm going to focus on music with a mini-section on what makes the best graphics/pictures near the end of this article.

"Surely it's too simple to give a piece of music one score?"

Yup, it's misleading to give just one score to a piece of music, so perhaps more appropriately, 3-5 scores judging the: melody/harmony, melodic/harmonic structure, intricacy, structure/rhythm and timbre (the lowest 'level' of sound/music) would be ideal. All these aspects of music are very much interwoven which is why it gets so confusing, but I believe they can all be rated - with the very best music containing high scores for all of these attributes.

One important point is that one tune can still be better than another, but with the /overall/ worse tune containing something the better one hasn't got - thus it isn't a worthless piece of music compared to the 'better' one. This applies especially to the chords or melody of a piece (as opposed to the orchestration/structure).

"But if music could be given a definitive rating/s, surely there would also be a mathematical/programmable formula to make the best music?"

Well, it's a good point, maybe there /is/ a 'formula' to create the best music; it's just that's it would be so very, very complex that it'll be millennia before we can attempt to find it. Also, maybe the best music is so, so complex that an increasingly complex formula is required for increasingly better and better music. (See later for how complex a possible formula might be.)

"Is there such thing as a perfect..... melody or chord combination?"

Maybe. Or maybe there are a dimension of perfect melodies. I only know that for every good melody/harmony that could exist, there are thousands/millions of potentially bad melodies.

"Why does someone think that tune X is better than tune Y, and someone else think the reverse?"

The answer is that one of them has better taste in music - at least over this comparison. Obviously, it doesn't necessarily mean that this person has better taste in music /overall/ - just for these two tunes.

"So what's the best style of music?"

Most 'Styles' (if done well) can contain the all important aspects of what makes music good - melody and structure. Obviously, some 'styles' are biased against melody/harmony and other styles are biased against rhythmic variety, so those styles aren't so good (....the best music combines both).

Music is only pigeonholed into genres in the first place because of reasons such as:
a: The cultural habit to imitate what already has been done.
b: The limitations and advantages of certain instruments (e.g. orchestral) and techniques.
c: The biases of different music creation software to make music in a certain way (which obviously isn't necessarily the best)
d: Simple luck that a particular set of instruments ended up with a bias towards certain chord or rhythmic progressions in the initial stage. This piece or set of pieces might then be stylistically imitated by other people (see a)

All of these combine to form a collection of recognisable 'quirks' in a piece of music - thus enabling us to see which style it is.
But because music is effectively just a combination of motifs, patterns and harmonies put together, a more thorough break-down is desired. For example, music in the style of 'rag-time' is better described by saying how the end of each 'section' (of which there are usually many) usually ends on the 'tonic' chord (C major if the key of the piece is in C major) and how the bass-line alternates between a single note and a 3 or 4 note chord). These are simple mathematical patterns/traits of which /every/ piece of music has a certain degree of.

If music has to be given 'styles' (or categorised by genre), I think the proper way to do it would be to give them 'style tags' seperately for the chord flavour/s, rhythm flavour/s, structural flavour/s, speed tempo/s and average intricacy of a piece. Ideally, it would also have a 'quality evaluation' tag too, but that's not exactly going to happen with the large discrepancy of tastes in this world... =(

"How can you be so sure that one piece of music is better than another?"

For the very simple reason that if one chord could be better than another chord, then the same applies to a whole string of chords. As with any problem, the best thing to do is break it down, so I'm going to stick to the subject of a single solitary static chord. This is complex enough...

There are obviously clashing chords which /do/ have their place in music like C, F, F#, and B which could be (say...) appropriate for a scary movie, but... try these out on your music keyboard a sec.. ;-)

C#, F, C, Eb F# Bb
...or this beauty ;-)
D, F#, B, Eb, F, C.

Too many notes? ok then, here's 5.
E, Ab, C#, F and Bb
It's very hard to make a bad chord with just 4 notes because most of them could fit in /somehow/ to a tune (i.e. resolve somehow), but I've tried:
F, A, C#, Bb. ......or maybe..... C, Eb, A, C#
hmm, that was harder than coming up with a /good/ chord ;)
All these above chords don't just simply clash, they also manage to be extremely dull, ambiguous and generally crud :)
OK, now take this stunner: C#, F#, C, Eb, G, Bb... awful huh? But just lower the C and G so that C becomes B and G becomes F#. A bit better dontcha think? :)

So the question is (and I know this will only explain what's good about a /static/ chord), why is: C#, F#, C, Eb, G, Bb much, much worse than C#, F#, B, Eb, F#, Bb ?

....with the overall point being - if maths can explain what's good and bad about the 2 simple static chords as shown above (which btw, people have tried to do, and to some point have succeeded a little - there are whole books on it!), then it could also explain /a sequence/ of chords, eventually going on to explain a melody, and how this melody interacts with the accompanying chords and how /this/ interacts with rhythm etc. etc.
And how /all these/ aspects interact with the 'sub-atomic' world of micro-second music (i.e. the timbre/pitch of the instruments/sounds etc.)

To ease the pain of those ear-aching earlier chords, here are two of my fave chords using six notes: C and deep C in the bass followed by Bb C D F G and A
or:
C and deep C in the bass followed by Bb C# E G and A

"If a formula did exist for creating the best music, how complex would it be?"

Take chess. One could get a computer to analyse a particular position for the best possible move/s. There isn't any 'easy' formula - it has to laboriously go through every single possible move branch to see which is the best possible continuation, so it's effectively doing what a human does, but faster.
Now music, is a million times more complex than this - because each new section that is 'calculated' (if such a thing could be done) would have to be cross-checked with every part of the tune that has just gone by. Assuming the best sounds, chord sequences, and rhythms could also be calculated (other variables/dimensions adding to the confusion), these would also have to be cross-checked with the tunes' history - because unlike a chess game (where the previous moves/positions don't matter any more), every part of a piece of music is inextricably linked with every other part. The mind (sub)consciously picks this up and it's part of what makes music so amazing.
So basically, I think that even if a formula was found, not even the fastest super computers would compose a decent melody for ages and ages and ages...

Are intricate/complex tunes better than simple ones?

Difficult question. First off, I'm defining 'simple' as a tune which is unadventurous in its use of chords and/or rhythms.

The short answer is yes. The long answer is tricky because there could be many simple tunes that are 'perfect' to a limited extent. To put it another way, a perfectly formed 'simple' tune still has something the perfect 'complex' tune doesn't have, but with the complex tune obviously being better overall (naturally, if the complex tune has too many flaws, this might be enough to make it inferior to the simple tune anyway).

The best analogy I can think of is comparing the simplicity of a sphere to the complexity of a beautifully intricate design (made up of many shapes). The intricate design is better overall, but it still lacks something that the simple sphere has got.
And then if this intricate design were to be distorted so that randomness and illogical shape crept in, this might well be enough to make the simple sphere better in both senses.
One other point to bear in mind is that the more complex one tries to make a tune, the more likely errors (either in the melody or orchestration) are going to creep in.

"What of graphics, pictures, artwork and moving pictures?"

In the same way music can be empirically rated on its various aspects, pictures can also be given a definitive value or values. In my experience, the best pictures contain wide use of the full palette of colours in the spectrum (including the brightest hues). Also, just like the best music, pictures which have repeating and evolving patterns (rather than solitary or non-evolving) should be held in higher regard. Goodness knows what defines a 'good pattern', but the best pictures contain a lot of them :)
Other aspects I have found which make good pictures (and the same could be applied to music) are:

a: fractal like qualities b: gradual contours of patterns c: many varieties of pattern d: colour graduation e: luminous, translucent and subtle colours. f: high detail g: '3D' scenario, so that there's a combination of big and 'small' objects.

This last one is interesting. It assumes that the best pictures contain simple (foreground) and complex (background) designs (...of course, the 'simple' foreground could still be subtly complex by the way). In fact, it's closely related to the 'fractal' aspect.
You'll also why I have trouble with the opinion that "all pictures are subjectively good" - when you see this picture at: [to be finished - come back later]

If a static picture wasn't complex enough to determine its quality - how about an animation?
Wow, I think I'd best stop there ;-)

I believe music and art are so complex and wonderful that we'll never find a 'magic formula' for creating the best of either, but maybe we'll edge closer. This doesn't mean an (undiscovered) formula doesn't exist which couldn't do this of course. And no doubt, I believe there's a whole range of 'best tunes' or 'best pictures' that are utterly different from each other, all of which are unique and amazing, and where the 'magic formula' possibly explains them all.

I hope you have enjoyed reading this article as much as I have enjoyed writing it. Please email your thoughts on this text - I'd love to hear from you!