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Music is a language where all concepts and thoughts are abstract, where semantics can be re-formulated in each work and statements are made, (using an external device, aka "musical instrument"), embedded in an imaginary grid of Time. This environment of non predefine words or meanings, makes the communication of clear ideas a tricky endeavor, and at the same time gives music the power to express emotions like no other language.
How do we justify the presence of an element in a musical phrase? Why is the ending of a certain phrase the logical conclusion to its antecedent? In other words:
What makes a musical statement valid?

There is no simple answer to this question. ...maybe there is no answer. In the end this is all very subjective. Nevertheless music must follow certain universal rules since it's meant to be interpreted and understood by us: humans and ergo by our brains (or should we say: our minds). Music must talk to us in a way that our embedded language system can understand and process.

One of the key rules music must obey is, what we could call, a "pattern-predictability" rule.
Our minds are always looking for patterns, always trying to predict outcomes, to anticipate what's next. When we listen, we use time as a grid to discern between chaos and patterns.

A metronome at 60 will click every second and, after listening to it just a couple of times, we are able to predict when the next click will come. We interpret that as a beat, probably the most simple pattern there is. Now... Is that music? Probably not. The lack of variation is what makes it not musical. If, at least, the timbre of the click would have changed over time, or some of the beats went missing at a set amount of clicks; then we would have been closer to some kind of musical statement.

That balance between repetition and variation (new information) is what turns sound into music. Too much repetition is too predictable, too monotonous, it is just sound that comes at regular intervals. Too much new information (variation) is chaos. When composing or improvising, we must always remember that's the game we're playing.

A great musician is a master of balance, of equilibrium, he/she knows when to add something new, when to create tension, and when to give us the predictable and let us feel at home.

But that's not the end of it. There's an almost unsolvable problem in all this argument: us. The Audience. The Listener. Who is 'us'? There's one more variable we need to take into account:
Culture, because, unfortunately, what's repetition to me it is not always repetition to someone else, in fact it might be chaos. And then comes the famous quote: "That's not music! It is just noise"

So we must add that parameter to our equation:
Music = Balance (Repetition vs. Variation, Culture)

While writing about this, I've been listening to Mozart, The Beatles, John Coltrane, Keith Jarret (and many more...) and I must add something to my previous statement:

A great musician is a master of balance, of equilibrium, he/she knows when to add something new, when to create tension, and when to give us the predictable and let us feel at home. A master musician is one that makes Culture minimal in the equation of Music.



mDecks

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"A master musician is one that makes Culture minimal in the equation of Music"

This sounds as a paradox. On the one hand, we would like to consider music as a universal language, independent of a specific culture, so the Culture element in your equation is minimised. On the other hand, music generally appeals to our culture-specific notions: romantic, religious, heroic, fairy tales etc (impressionism is probably an exception here, as it is related to nature more than to culture). People with low Culture generally do not understand a deep music. Specific Culture elements, however, have universal subconscious images, which sometimes cannot be formulated verbally or visually, but can be expressed musically. I would reformulate your latest phrase as follows:

A master musician is one that knows how to appeal to universal subconscious images, related to important values of various Cultures.
"at the same time gives music the power to express emotions like no other language."

In my view, emotions are catalyzed in listeners, but they're in no sense literally transferred from music to listeners. The emotions that music causes to arise in each listener (for whom emotions arise) can be very different because of this.

I even believe that natural languages work that way, but that's another issue that would be off-topic.

"How do we justify the presence of an element in a musical phrase? Why is the ending of a certain phrase the logical conclusion to its antecedent? In other words:What makes a musical statement valid?"

Nothing, in my opinion. I see that as a category error. It's trying to graft concepts onto domains where the concepts do not fit.

"Nevertheless music must follow certain universal rules"

That's not at all the case, and it clearly hasn't been the case for many years now--there are examples of just about every kind of recorded sound imaginable--just about everything you could think of doing--in the past 60 years, where all of them have been cherished as music by various listeners.

"since it's meant to be interpreted and understood by us"

Again, I do not even buy interpretational transparency for natural languages. That's just not how language works in my view. Admittedly, I have a pretty radical view on this stuff, even for postmodernist hermeneutics "standards", but I believe that my view accurately reflects the facts about what languages are, how they work, etc. (of course--who would have a view that they believe is inaccurate? lol)

"Music must talk to us in a way that our embedded language system can understand and process."

To me, that only suggests that it was a bad idea to use "language" for music, since folks are going to conflate natural language semantics with the metaphorical usage.

"One of the key rules music must obey is, what we could call, a 'pattern-predictability' rule."

While the vast majority of music uses patterns, there is music that does not--like many of John Cage's strictly aleatoric pieces, and it's still recognized and enjoyed as music by many people.

"Our minds are always looking for patterns, always trying to predict outcomes, to anticipate what's next."

I agree that we tend to look for patterns, at least.

"Now... Is that music?"

Music, in my view, is any sound that an individual mentally frames in an aesthetic way. It's only music to the individuals who do that. So if someone mentally frames that (the metronome's clicking) that way, then it's music to them.

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