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 subjective opinion is just as valid as another - and that it's only a matter of personal preference"
. In other words, many believe that music is only good because our minds are individually (and in different ways) - 'programmed' or 'geared' (for whatever reasons) to enjoy it from their perspective. This is called the "Subjective or Relative Aesthetics View"
Well, no doubt people's 'taste' is biased (to varying degrees) due to a number of reasons:- what they're 'used to' hearing, 'cultural trend', simply their quality of taste in music, or even 'nostalgia' (though obviously a tune could still be nostalgic to someone and
But if as I think, music is ultimately objective - this would mean that even if we didn't exist, every infinite possibility in music has a degree of quality to it (whether good or bad), which would make it stand up in its own right. In other words, every picture or piece of music contains an inherent (mathematical?) 'goodness' intrinsic to that design. 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 'judgement score' doesn't exist.
Theoretically then, the better one's taste in music - generally - the closer one would agree with this 'Universal Aesthetic' or 'Universal Musical Evaluation' (UME).
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.
Aesthetics of music theory
"Surely it's too simple to give a piece of music one score?"
Well, it's possible, but incomplete to give just one ('average') score to a piece of music, so perhaps more appropriately, 3-5 (maybe more!) scores judging the: melody/harmony, melodic/harmonic structure, rhythm/intricacy, time duration/structure 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.
Of course, each 'whole' piece of music is greater than the 'sum of its parts', but no doubt if you were to break a tune down - every single chord, 'sub-melody' or 'bit' of that tune could be rated and evaluated on all the aforementioned attributes - too.
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. I should imagine 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 sequence?"
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.
What's amazing is how a tune's quality can be good in so many different ways - each 'style' with its own impact on the emotions. There's probably a vast multi-dimensional hierarchy to chord sequences for example. The best chord combinations are at the top - all unique, brilliant and varied.
Fruity chord fun
Here's a completely unscientific but fun way of describing the quality of all those chords =)
Note that 'chord change' can refer to a static chord, but generally refers to 2 or 3 chords (/ changes). Sometimes though, if the chord 'grows' or 'develops' over a technical 5 or even 10 'chords', with generally the same notes (but not quite) - this can be said to be part of the 'same' chord/c.change (if that makes sense =)
Orange is a 'nice' normal chord/change. ' "Deep" orange' is the same kind of 'ordinary' chord change - but well implemented.
'Shallow' orange is the same chord/change but not done so well.
You can probably guess what I'm going to say...
'Deep' and 'Pale' apply to the other 'fruit' chords:
'Strawberry' - this is more unusual than orange and more fun to listen to.
'Lemon' - A 'sour' chord/change - great for 'tense' climatic moments in tunes.
'Apple' - for the chord changes which don't need to sound good in themselves, but are necessary to blend well with the rest. Tunes generally have lots of these.
'Lime' - A cross between the 'tense' mysterious-ness of Lemon, and the cool Strawberry chord.
'Blackberry' - A bitter / sweet chord change ... ummm... similar to lemon but... erm nevermind :)
(by the way, these terms are not at all arbitrary ;-D
The best tunes utilise all these 'types' of chord changes (and perhaps use them in a hierarchical structure (i.e. mostly apple (fill in), a lot of orange, some strawberry / lime and a couple of lemon / blackcurrant twists put in for good measure ;)
(All of these would be the 'Deep' (as opposed to Shallow) versions for the best tunes by the way).
So for example, "Shallow Lemon" is a 'tense' chord change that's more of a whimper. But 'Rich' (even stronger than 'Deep'!) Strawberry is something to really look forward to!
Oh, the treasured 'Rich Kiwifruit' chord array has possibly the best chords of all! (even better than the Strawberry chords!!!)
"Why does someone think that tune X is better than tune Y, and someone else think the reverse?"
The answer could well be that one of them has better taste in music - at least over this tune's comparison. They are picking up subtleties in the melody, chord patterns and rhythm complexity that the other person either doesn't or can't recognise. Obviously, it doesn't necessarily mean that this person has better taste in music /overall/ - just for the various aspects in that tune per se
. There's also the small possibility that the reason/s they prefer the better tune isn't the reason/s that they should
prefer the better tune for - thus reducing the validity of their opinion. Yes, complex I know =)
Incidentally, throughout this text, when I refer to music that's 'better', I also mean that it's more fun, 'atmospheric', enjoyable, perhaps exciting - and ultimately more rewarding to listen to. If people don't find the best music to be enjoyable, perhaps they are 'missing out' and lack discernment (in one way or another, to varying degrees and for whatever reasons)
in melody, rhythm and certain chord patterns.
Without any 'All-Time Super Formula', possibly the best way of finding out who's right, is to apply the 'Test of Time' theory. This asserts that a piece of art is intrinsically good if held in high regard throughout the ages - rather than just 'what's in fashion' at the time. I would guess that it's certainly a more valid approach as it removes (most) cultural bias, but nevertheless - not a definitive judgement - as there are other factors in people's taste which distort what's good or bad about music.
Despite all of this, I think there's a good possibility that a quality of music - better than anything anyone's ever heard on Earth - would theoretically appeal to practically everyone! =)
"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' separately 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?"
In my opinion, there's a wealth of positive evidence, but here's one simple example; If one single chord could be better than another chord, then the same reasoning would apply to a whole string of chords - and ultimately to a whole tune. Naturally, a chord that sounds bad in one piece could fit very well into another tune, but there surely comes a point when a chord is so bad that it becomes practically impossible to fit into any tune.
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.
Could one somehow fit these chords into a decent tune appropriately? I doubt it...
Now I'll try to make a bad chord with just 5 notes...
E, Ab, C#, F and Bb
All these above chords don't just simply clash, they also manage to be extremely dull, ambiguous and generally crud ;-)
It's very hard to make a bad chord with just 4 notes, because most combinations could fit in /somehow/ to a tune (i.e. resolve), but I've tried:
F, A, C#, Bb. ......or maybe..... C, Eb, A, C#
Hmmm... that was harder than coming up with a /good/ chord ;-) Actually, it's my guess that these two chords could possibly fit into a tune by playing briefly, or as part of a more underlying chord, but I wouldn't go as far to say the 6 note chords mentioned earlier could do this.
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
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 by the way, 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.). It's very, very
complex, which is why no formula currently exists. Amazing also how despite this 'behind the scenes' complexity, how music can reach our emotions and affect us all on such a fundamental level.
To ease the pain of those ear-aching earlier chords, here are just two of my fave chords using
C and deep C in the bass followed by Bb C D F G and A
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 (more or less) 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.
Any possible program to create good music would probably be made up of many sub formulas (one dedicated to the melody, one for the harmony, rhythm etc. etc.) - each eventually combining and 'growing' music in some way to create the final piece. I believe if you start off with even a slightly different 'seed' of music, the best possible continuation would continue vastly different and unexpectedly.
Good music defined
Can beauty be defined or even measured? Yes, probably. We just don't know how. I think a thorough explanation of what makes good music would be almost as profound to know as how the universe started :) There are just too many questions. But anyway, here's my attempt to define musical beauty in general. I have tried my best to make these criteria as universal as possible, so that it applies to all music. No doubt I've overlooked a few ideas, what with the diversity of styles and possibilities in music...
Anyway, here goes. The best music seems to have the following properties (with most important at the top):
a) Music with timbre based around the harmonic series, where the best timbres tend to contain 'clusters' of harmonics, and 'evolving' harmonics. If you look at the spectroscopic analysis of a sound in say... Cool Edit Pro, you'll find the best instruments or sounds have 'nicer looking' and more 'logical' patterns. Yes, I know. This just pushes the problem further out, but it's the best I can do for now.
b) Music based around a scale of 12 equal spaced notes to the octave (for the underlying harmony and melody).
c) Chord sequences that are good. This is hard to define or pin down, but it's somehow related to the tonal 'hierarchy'. The human soul knows when a chord sounds good, and authors have written whole books on the subject, but we're still far away from explaining it all!
d) Chords and melodies approaching 'atonal' could break up some sections and chord sequences for contrast, but generally the best music will be 'more or less' tonal in my opinion. Similiarly, a good dose of musical dissonance is a good thing, as long as it's carefully balanced out with the degree of consonance.
e) In good music, a small section taken from the whole is amazing too (for example, zooming into a picture would reveal a new and 'different' picture; and that as part of the whole, it still fits in appropriately). Also, slowing a tune down with a significant amount of (fast playing) detail will often still provide a pleasurable listening experience.
f) Related to the above, fractal-like patterns to the tune are essential. A good example is the beat, where a relatively faint hi-hat will sound every beat, but more prominent percussion (such as a snare, or bass-drum) will sound every 2 or 4 beats. A nice big 'smash' could sound every 16 beats. This example is only a very limited view of the whole picture of course. Generally speaking, structures and (some) consistent patterns are vital. Also see I and L.
g) Rich and numerous layers of contrapuntal melody, but perhaps with more 'solo-esque' textures elsewhere in the tune for contrast (for example, at the beginning, so as to allow for a feeling of crescendo). Two, three, or more simultaneous melody lines (polyphony) will add tremendously if done well.
h) Melodies or chords that smoothly flow from note to note via semi or whole tones, with relatively few 'big' jumps. These would tend to fit in with the underlying or implied chord at that point in the tune. Broken chords (for example in Moonlight Sonata) might count as seperate melody lines, so that would explain the constant 'big jumps'. I know, quite vague - your mileage may vary.
i) Hooks and motifs are paramount. A hook or motif is a 'piece' of melody, perhaps a bar or two, which recurs (or 'echoes' upon itself), afterwards in the very same bar, or perhaps later in the tune. Or it might repeat later on, but in subtlely different ways (with for a example, a note higher or lower) - so as to fit into the new chord/key structure. Also see F.
j) Dynamics in the tune help to provide contrast and variety. Anything from a single bar to a whole movement could be quieter, slower, faster or louder than the rest. Or you could have every second or third note being quieter/louder than the others. Again, we're going back to fractal territory here...
k) The cadences of excellent melodies usually have 'something' about them. For example, a crescendo, richening of the chord/s, effect (such as a bass/melody slide), drum 'fill-in', melody 'embellishment', a new temporary instrument etc. etc.
l) A 'beat'. It doesn't necessarily have to be a snare/drum/hi-hat beat, but whatever it takes to keep the tempo each bar. A more general description would be a quick-changing dynamic-volume sound effect. But I have heard 'beats' (or more like 'sounds') which can last the duration of the bar and still sound effective. Also see F.
m) Lots of cool and unusual sound FX and synthesizer sounds :)
n) Tailored timbre according to each note (something virtually no music has to any significant degree).
Anyway, 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 'on the fly' when listening to music - and it's part of what makes it 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 (light sourced) 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.
For those who are interested (and even for those who aren't ;P ), you can hear my music at the Soundburst Shrine
. See if you like it! =)
Further comments, thoughts and possibilities
At the moment, only people can really create decent melodies - and I suspect it will stay that way for a long time to come. But imagine some kind of 'super-brain' or future super-computer - the music equivalent of the chess program 'Deep Blue' - only much better. One could ask it all sorts of questions such as: What's the best possible melody for a 6 note tune? ...or a 60 note tune?
......or either of these with say.... 2, 4 or 10 simultaneous melodies (contrapuntal melody or 'counterpoint'). Imagine how exciting that would be - finding the incredible results that this supreme formula would produce!
Then one could have more fun by:
...Seeing what piece/s of music would fit best to a certain rhythm - say... 6/8 time.
...Restricting the formula so that certain notes couldn't be played, or that the tune always had to be in harmony with a particular note - and see what the best tune would sound like then.
...Limiting the length of each note so that no one note lasts longer than a quarter of a second. No doubt a very intricate staccato styled tune would result.
All of these would probably make the tune 'averagely worse' in some way, but it would be of great interest to hear the interesting 'styles' and 'musical surprises' that would come from these 'filtering' techniques.
What of graphics, pictures, artwork and moving pictures?"
Is there a definition of aesthetics? 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 probably contain a lot of them :)
Other aspects I have found which make good pictures (and the same could be applied to music) are:
a: symmetry & 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/complexity
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.
How should one go about the huge task of 'rating' a picture though? What criteria would be involved and what are the 'elements' of the picture? You might want to visit my Rating Art
page. This was specially done for a web site forum I frequent, but its principles would apply universally.
One important point is that any implied meaning behind a picture is a separate aspect from the actual design (shapes/lines/contours/colours) of the picture. This isn't to say that the meaning or 'story' or 'expression' behind doesn't add something, but one could equate it to adding lyrics to music, or background music to a TV film - or even pleasant smells to a shop (i.e. effectively multimedia). Just like with music, the most intricate and ultimately beautiful artistic designs do not have to rely on apparent 'meaning' to justify their beauty.
A (mathematical) formula for graphics?
There is no strict art aesthetics definition, at least not for the foreseeable future, but who knows; one day, we might start unravelling the mathematical mysteries of good art...
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 imagine any possible 'formula' to create the best music/art would need to contain numerous concepts or sub-formulas working in conjunction. This is similar to the solving of Fermat's last theorem, where the combination of known mathematical concepts and entirely new ideas were put together to finally solve the problem.
If there is one thing that I have
found in common with the best pictures and music, it's that a small section taken from the whole is amazing too (for example, zooming into a picture would reveal a new and 'different' picture; and that as part of the whole, it still fits in appropriately).
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!
Alternatively, message your comments and stir up some debate on the Skytopia Forum
"One of the truly magical things about music and art in general, is the way it transcends language and cultural barriers and embodies universal truths."
- Claire Johnson
"The present study suggests that personal tastes about art con be in dispute; the students didn't particularly like what are, according to the experts, great works of art. Nevertheless, some universal criteria of the aesthetics of art must have emerged, those that make a painting "right," and these transcended individual preferences"
- Lindauer, 1987
Keywords for further research:
Plato, (Savile) Kant, Thomist, Thomas Reid, aestheticism, objective, subjective, relativism, cultural relativism, modernism, post-modernism, modernism, postmodernism, modernist, postmodernist, contextualism, subjectivism, beauty, aesthetic/s, test of time theory, intrinsic value, intrinsically good, pure aesthetic/s, relative aesthetics, universal aesthetic/s, absolute music, program music, definitive, absolute, aesthetic attitude, definition, quantify, quantitative, criteria, judgement, taste in music, transcendental language, music is the universal language, beauty is in the eye of the beholder, 'elitist', qualitative judgment, purely subjective, empirical evidence, music psychology, musicology, empirical musicology, quantitative musicology, universal musicology, grand unified theory of music, autonomy.
Extra incidental keywords:
symmetry, transcend, transcendental, atmosphere, haunting, best, amazing, emotion, evaluate, evaluation, mathematical, formula, perfect taste in music, timeless, rhythm, melody, melodic, intricate, complex, hierarchy, complex music, meaningful, intricacy, imagination, creative, sublime, esthetic, exhilarating, profound, orchestration, intricate melody, woven melody, counterpoint, catchy, objectivist, visionary, idealism, idealistic, analysis, analysis of, classic, classical music, Bach, Beethoven, Mozart, Chopin, charts, more than just nostalgia, video game music, multiple melodies, strawberry chord/s, dream chord/s, simultaneous melody, simultaneous melodies, zoom in, fusion, hierarchical, hierarchy, contrapuntal, full spectrum of sound, philosophy, contingent, patterns of sound, patterns in music, 70s, 80s music, eighties, 80's, old school, old skool, classical, discord, concord, building up, climax, last cadence, final cadence, 4th cadence, tension, cascade, cascade of notes, subtle, dynamic, fractal, harmony, connoisseur, standing the test of time, stands the test of time, makes a good melody.
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