The Numbers of Music
First off, let's get some things straight. This is not a blog about how music and math are mysteriously linked, or that Bach's music is mathematically organized, or that sound is frequencies and frequencies are the number of vibrations in a given time (also a number) or any number of other number relationships.
Music is an art. Math is a science. Arts values the unique: science values the reproducible. And a mathematical formula never moved anyone to tears. Okay, so forget that last example.
And, while music may express itself in numbers, they don't add up. A 3rd plus a 3rd is a 5th, and an interval and its inversion add up to 9 but spans an octave.
Actually, numbers are only incidental to this blog. It's real title should be something about perfection, as in music is the only human activity where we expect perfection. At the weekend's symphony performance, if there is a mistake it becomes the subject of the next day's review. If there's a mistake in a recording after a while all you can do is wait for the mistake.
Now, here's where the numbers come in.
Let's look at the numbers associated with that symphony performance.
Let's say there are 100 musicians in your orchestra. Orchestras may range from 80-ish to over well over 100 members, but let's work with round numbers.
And let's say that a concert lasts 100 minutes. Most are 90, some over 2 hours long. 100 is a good round number.
And let's say the music is written in a tempo of 100 beats per minute. Actually, tempi range from the low 40's to well over 200 beats per minute and each beat might have as many as 8 subdivisions, but who's counting? (By the way, that's a musician joke.)
100 players x 100 minutes x 100 beats per minute = 1,000,000 notes. Per concert. Each week of the season.
These guys may be human, but they're only musicians, after all (or is that the other way around?) They're bound to make some mistakes. But how many mistakes are acceptable? Schools use letter grades to rank how many mistakes are acceptable. Let's us that approach. Let's see if they deserve an A.
94% would be a good grade on a test. It's a low A, maybe even an A- but it makes a good example. 6% of one million is 60,000 or 60 mistakes a minute or one mistake every second of every one of the 100 minutes of music played by 100 musicians (see how I keep working numbers into this blog?)
That's a lot of mistakes. I've had students who couldn't count up to 60 in a minute, let alone make 60 mistakes in a minute.
And there's more to it than simply playing the notes. There's tempo, dynamics, timbre, various types of attacks and special techniques like legato, staccato, spiccato, pizza cato (a special string technique), and zamboni (a special technique for.. oh, you figure it out).
Let's not split hairs about this. Sure maybe someone would have made a mistake but instead he just doesn't play. Is that a mistake? If a tree doesn't fall in the forest and doesn't make a sound, is it a mistake? Is it even a tree?
Is a mistake every second still music? Who knows: you would have stopped listening PDQ. (And let's leave him out of this.)
First off, let's get some things straight. This is not a blog about how music and math are mysteriously linked, or that Bach's music is mathematically organized, or that sound is frequencies and frequencies are the number of vibrations in a given time (also a number) or any number of other number relationships.
Music is an art. Math is a science. Arts values the unique: science values the reproducible. And a mathematical formula never moved anyone to tears. Okay, so forget that last example.
And, while music may express itself in numbers, they don't add up. A 3rd plus a 3rd is a 5th, and an interval and its inversion add up to 9 but spans an octave.
Actually, numbers are only incidental to this blog. It's real title should be something about perfection, as in music is the only human activity where we expect perfection. At the weekend's symphony performance, if there is a mistake it becomes the subject of the next day's review. If there's a mistake in a recording after a while all you can do is wait for the mistake.
Now, here's where the numbers come in.
Let's look at the numbers associated with that symphony performance.
Let's say there are 100 musicians in your orchestra. Orchestras may range from 80-ish to over well over 100 members, but let's work with round numbers.
And let's say that a concert lasts 100 minutes. Most are 90, some over 2 hours long. 100 is a good round number.
And let's say the music is written in a tempo of 100 beats per minute. Actually, tempi range from the low 40's to well over 200 beats per minute and each beat might have as many as 8 subdivisions, but who's counting? (By the way, that's a musician joke.)
100 players x 100 minutes x 100 beats per minute = 1,000,000 notes. Per concert. Each week of the season.
These guys may be human, but they're only musicians, after all (or is that the other way around?) They're bound to make some mistakes. But how many mistakes are acceptable? Schools use letter grades to rank how many mistakes are acceptable. Let's us that approach. Let's see if they deserve an A.
94% would be a good grade on a test. It's a low A, maybe even an A- but it makes a good example. 6% of one million is 60,000 or 60 mistakes a minute or one mistake every second of every one of the 100 minutes of music played by 100 musicians (see how I keep working numbers into this blog?)
That's a lot of mistakes. I've had students who couldn't count up to 60 in a minute, let alone make 60 mistakes in a minute.
And there's more to it than simply playing the notes. There's tempo, dynamics, timbre, various types of attacks and special techniques like legato, staccato, spiccato, pizza cato (a special string technique), and zamboni (a special technique for.. oh, you figure it out).
Let's not split hairs about this. Sure maybe someone would have made a mistake but instead he just doesn't play. Is that a mistake? If a tree doesn't fall in the forest and doesn't make a sound, is it a mistake? Is it even a tree?
Is a mistake every second still music? Who knows: you would have stopped listening PDQ. (And let's leave him out of this.)
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