This is kind of rambling and idiosyncratic, but it turned into a decent discussion of temperment and tuning systems, and the associated design compromises.
Startup Task XXX : The western 12 tone music scale is limited and out of tune. Many of the reasons for it being useful (instrument construction, notational complexity) are no longer show stoppers. Anyone who can create software that makes it practical and intuitive to create good-sounding music using natural 'just' intervals or/and alternative scales could shake up the entire world of music. 'Scala' is a nice tool but it doesn't count. Bonus points for being able to automatically convert existing 12-tone music to just intervals in a way that makes it sound better.
It's so hard to understand this topic when I just can't hear it. I've tried to understand equal temperament, but I just don't hear the difference.
I'm not tone deaf as far as I know (I can tell the difference between different tones), and I enjoy music, but I can't hear when something is out of tune.
Or that 12 tone commercial that someone posted - the comments say it's funny - but what's funny about it? Presumably I'm missing something massive, but what?
You might be able to pick up the difference in tuning. As for being able to hear when something is "out of tune," everyone has a different ability to pick up on subtleties like that. In some cases, I'd guess you hear a pitch when it's wrong, it just doesn't bother you enough to make a judgment on it so you don't remember hearing it.
I had a post prepared saying basically the same thing (Chazelle's algorithm work is awesome), but then I realized that bdr is, strictly speaking, correct: the number of combinations of notes you can play is a factorial of the number of notes, and factorials grow faster than exponential functions.
Of course, when you're writing an essay on the relationship of music and very simple math, I think it's forgivable to use "exponential" to mean "growing at or faster than an exponential rate". Using a more specific term like "factorial", "combinatorial", or "super-exponential" sounds pedantic and out-of-place.
I don't understand. If you have 300 notes, and 12 tones, the number of different melodies you can play is 12^300 (12 choices at each step). Why is it 300 factorial? You don't have 300 distinct entities to permute.
It was in the context of drawing the diagonals on the polygon, so I thought of quadratic growth. I guess everyone interpreted it differently, and the author is justified in using 'exponential' in an informal way.
Huh, I watch that and chuckle at how dated it is, and totally missing the point. Should we all point and laugh at how "Why So Serious?" from The Dark Knight soundtrack isn't something you can sing in the shower?
And 12-tone music isn't the result of an especially "mathematical approach" to music. It's the result of the attempt to break the boundaries of the traditional tonal systems using the musical language that existed at the time. It's the primary endgame of atonality within equal temperament system. Traditional western music is all tonal. It's all in "keys." 12-tone music is an attempt to create meaningful, coherent music that avoids relying on tonality. It's an attempt to create music that can't be identified as being in "C Major" or any other key.
1. The particular popular, "catchy" sense that was fashionable when the parody was created. If that's a "point" then sure. To me it's like calling a stone fortress on not being a tent.
2. Anything can be called 'stylistically uniform' if you ignore enough details, and music is all about details.
3. This "point" is applied carelessly, merely pairing up random recordings with video seemingly at random and with no taste. Furthermore, attempt to dismiss something as suitable as "incidental music" for movie scenes is hilarious in itself, given the importance music currently plays in movies.
WTF? Is this the thread where everyone completely misunderstands everything? Did I say "bad"? Did the video say "bad"? Is Brittney Spears the comparable here?, or perhaps should we pit the entire 12 tone catalog against one movement of anything written by Beethoven and see how it stands up? It's just a joke. There are two classes of people who cannot tolerate humor:
Humor is the most subjective of all entertainment. I don't find that particular video funny (in the manner it was intended) because the ignorance and apparent dating is too distracting.
Have you considered that there might be 12-tone music that is funny for people who know how to listen to it?
Also, you said The mathematical approach to music has one endgame, and it isn't pretty. If that's been misunderstood somehow please feel free to clarify.
You're talking about a mathematical approach to the choice of notes in a piece, while the article is talking about a mathematical approach to the choice of frequencies for the notes... which, as the article points out, relates directly to how the ear senses sound. Rather than leading to twelve-tone music, the article gives a physical reason why people might dislike twelve-tone music: it doesn't favor any particular frequency ratios.
However, nearly all music with "scales" is mathemagical to a large extent. Anyone who is interested in this sort of thing should check out the 2-volume book "Musimathics" by Gareth Loy.
