3 ms·

Ironically, the situation is very similar to math. It's relatively easy to read music theory notation, so that the Gibberish and Goobeltygookus make sense, sim

by diN0bot 15y ago

Ironically, the situation is very similar to math. It's relatively easy to read music theory notation, so that the Gibberish and Goobeltygookus make sense, similar to learning mathematical notation. (I personally believe this is easier than learning the alphabet, but that's a different story) However, understanding what the abstractions mean is difficult. The difference between memorizing formulas and intuiting patterns. Maybe this is no harder than understanding the abstractions behinds words. Like most "hard" things, the largest reason for difficulty is one of obtaining persistent practice. If it were common to sing piano music using theory words rather than a single "lalala", for example, or if our language made use of specific tonal changes (up a second v down a major third), or if everyone learned the theory at the age where we now learn the alphabet, the gibberish goobeltygook would seem "easy".

kabdib 15y ago
The problem I always had with math (when it came to integrals, anyway) was the whole 'dx' notation, where you apparently just had to "go with the flow" and understand what was being expressed. It ain't "d times x", it's this other thing that's syntactically similar to saying "ab" which means "a times b". Someone on HN is going to hammer me. I just muddled through the ambiguity. Then again, what I used to think was the real solution (an exensible grammar -- say, s-expressions -- which would remove the ambiguity) would result in really ugly-looking math. [Don't get me started on denotational semantics. I tried, I really tried to understand the foundation of Standard ML through some DS-based books on the subject, but in the end I just got sick of yet another system of poorly defined heiroglyphics. Maybe I'm just allergic.]
- juiceandjuice 15y ago
  One thing you learn in math/physics is all the different ways you can denote a derivative. It makes a lot more sense when you get into Lagrangian mechanics, ODEs/PDEs, QM, complex variables, your first analysis class, etc... classes where you learn why they denote operators and variables in certain ways because other ways don't make much sense given the context.
- agumonkey 15y ago
  About that, one author of SICP build a new physics class based around functions for every physical operator, no more syntactic craze, just functions ( higher order though ). Check SICM on google.
  - WildUtah 15y ago
    This is exactly what I was going to reply when I saw the GP. SICM is a brilliant book I've only started that revolves around putting concrete understanding ahead of notation. Unlike most books of that type, this one is a seriously advanced math/physics work. At world class universities, upper division undergrads in Physics can study Lagrangian Mechanics in their third year if their calculus is good enough. One note from the excellent introduction focused how to learn math (q.v.): "In his book on mathematical pedagogy [15], Hans Freudenthal argues that the reliance on ambiguous, unstated notational conventions in such expressions as f(x) and df(x)/dx makes mathematics, and especially introductory calcu- lus, extremely confusing for beginning students; and he enjoins mathematics educators to use more formal modern notation." Plus, Lisp!
nandemo 15y ago
I disagree. Mathematicians care much more about notation than do musicians. Mathematical notation should be precise, concise and consistent. The hard parts of maths are the abstraction and the formalization of stuff we take for granted. In contrast, the essence of music theory is fairly easy (if you have a math background, you could learn it in a few hours!). But music notation a strange mix of time-tested, concise notations with cruft that remains due to backwards compatibility. So we write "𝆮" to mean pedal down, but "𝆯" to mean pedal up. We write C7, Cmaj7 and Cmin7 but the modifiers "maj" and "min" modify different parts of the chord. And so on. And sometimes the notation is there, but people simply don't use it consistently. For instance, the usage of 6th and 13th interchangeably without proper justification (e.g. the post in question).

by diN0bot 15y ago

kabdib 15y ago

The problem I always had with math (when it came to integrals, anyway) was the whole 'dx' notation, where you apparently just had to "go with the flow" and understand what was being expressed. It ain't "d times x", it's this other thing that's syntactically similar to saying "ab" which means "a times b". Someone on HN is going to hammer me. I just muddled through the ambiguity. Then again, what I used to think was the real solution (an exensible grammar -- say, s-expressions -- which would remove the ambiguity) would result in really ugly-looking math. [Don't get me started on denotational semantics. I tried, I really tried to understand the foundation of Standard ML through some DS-based books on the subject, but in the end I just got sick of yet another system of poorly defined heiroglyphics. Maybe I'm just allergic.]

juiceandjuice 15y ago
One thing you learn in math/physics is all the different ways you can denote a derivative. It makes a lot more sense when you get into Lagrangian mechanics, ODEs/PDEs, QM, complex variables, your first analysis class, etc... classes where you learn why they denote operators and variables in certain ways because other ways don't make much sense given the context.
agumonkey 15y ago
About that, one author of SICP build a new physics class based around functions for every physical operator, no more syntactic craze, just functions ( higher order though ). Check SICM on google.
- WildUtah 15y ago
  This is exactly what I was going to reply when I saw the GP. SICM is a brilliant book I've only started that revolves around putting concrete understanding ahead of notation. Unlike most books of that type, this one is a seriously advanced math/physics work. At world class universities, upper division undergrads in Physics can study Lagrangian Mechanics in their third year if their calculus is good enough. One note from the excellent introduction focused how to learn math (q.v.): "In his book on mathematical pedagogy [15], Hans Freudenthal argues that the reliance on ambiguous, unstated notational conventions in such expressions as f(x) and df(x)/dx makes mathematics, and especially introductory calcu- lus, extremely confusing for beginning students; and he enjoins mathematics educators to use more formal modern notation." Plus, Lisp!

nandemo 15y ago

I disagree. Mathematicians care much more about notation than do musicians. Mathematical notation should be precise, concise and consistent. The hard parts of maths are the abstraction and the formalization of stuff we take for granted. In contrast, the essence of music theory is fairly easy (if you have a math background, you could learn it in a few hours!). But music notation a strange mix of time-tested, concise notations with cruft that remains due to backwards compatibility. So we write "𝆮" to mean pedal down, but "𝆯" to mean pedal up. We write C7, Cmaj7 and Cmin7 but the modifiers "maj" and "min" modify different parts of the chord. And so on. And sometimes the notation is there, but people simply don't use it consistently. For instance, the usage of 6th and 13th interchangeably without proper justification (e.g. the post in question).