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Playing the piano taught me math (2016)

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Re: Playing the piano taught me math (2016)

#11
Music and piano playing taught me things about (math related):

- Exponentials and logarithms

- Harmonic series

- Combinatorics

- Chaos theory

- Some calculus

- Resonance

- Linear algebra

It also taught me about physics, cognitive psychology, learning theory, history and even some sociology.

Re: Playing the piano taught me math (2016)

#12
post #11

Music and piano playing taught me things about (math related): - Exponentials and logarithms - Harmonic series - Combinatorics - Chaos theory - Some calculus - Resonance - Linear algebra It also taught me about physics, cognitive psychology, learning theory, history and even some sociology.

Coming from the opposite direction, I'm quite curious as to where the linear algebra and combinatorics fit in. As a former mathematician (switched to computing after one post-doc) who has been trying to learn about music and to play the piano, I'm trying to make sense of how music and mathematics relate.

There's some stuff with group actions going on - I think you can think of a dihedral group acting on sets of triads or something along those lines and there are some articles out there about that, but I feel like I don't have a good mapping in my head as to the relationship between music and mathematics.

Re: Playing the piano taught me math (2016)

#13
post #10

> When all my first-grade classmates were memorizing math facts like “2 + 3 = 5” > I was called out during class when my teacher saw me fiddling with my fingers during a classroom exercise From their LinkedIn profile, it appears that the author went to school in the US. I'm not from the US, but my impression of US schools is the complete opposite of one where students are taught to "memorize math facts" or one where…

I think there's significant variance, but I don't think this is necessarily the norm. Everyone must memorize some basic tables as well as standard algorithms, but I wouldn't say it ever struck me as a problem.

The only exception to this for me was pre-calc, in which they taught us trigonometry rules without explaining it's basic relationships to the unit circle. Our calculus teacher was dumbfounded the next year when we had no intuitive understanding for these things. It took an hour to correct. No big loss. Shrug.

Re: Playing the piano taught me math (2016)

#14
post #10

> When all my first-grade classmates were memorizing math facts like “2 + 3 = 5” > I was called out during class when my teacher saw me fiddling with my fingers during a classroom exercise From their LinkedIn profile, it appears that the author went to school in the US. I'm not from the US, but my impression of US schools is the complete opposite of one where students are taught to "memorize math facts" or one where…

Music...where 3 + 3 = 5. Ie c to e is a third, and e to g is a third, but c to g is a fifth.

Re: Playing the piano taught me math (2016)

#15
post #10

> When all my first-grade classmates were memorizing math facts like “2 + 3 = 5” > I was called out during class when my teacher saw me fiddling with my fingers during a classroom exercise From their LinkedIn profile, it appears that the author went to school in the US. I'm not from the US, but my impression of US schools is the complete opposite of one where students are taught to "memorize math facts" or one where…

I'm not from the US, but my impression of US schools is

You can't generalize US schools. There are a lot of them, and they generally answer to different authorities, local school districts, state school districts, religious (Catholic) schools do their own thing, etc.

Re: Playing the piano taught me math (2016)

#16
post #5

I've been looking at music over the last year or so, bits of basic music theory. As a child I had no idea how linked to maths it was, and how much easier music is once you realise that it's just applied mathematics and touch typing

My music theory teacher used to say that that music is the only art that's also a science. I think this headline should not be surprising to anyone who reads music.

Re: Playing the piano taught me math (2016)

#17
post #14
post #10

> When all my first-grade classmates were memorizing math facts like “2 + 3 = 5” > I was called out during class when my teacher saw me fiddling with my fingers during a classroom exercise From their LinkedIn profile, it appears that the author went to school in the US. I'm not from the US, but my impression of US schools is the complete opposite of one where students are taught to "memorize math facts" or one where…

Music...where 3 + 3 = 5. Ie c to e is a third, and e to g is a third, but c to g is a fifth.

Nothing like some good ol' off by one errors.

Re: Playing the piano taught me math (2016)

#18
post #10

> When all my first-grade classmates were memorizing math facts like “2 + 3 = 5” > I was called out during class when my teacher saw me fiddling with my fingers during a classroom exercise From their LinkedIn profile, it appears that the author went to school in the US. I'm not from the US, but my impression of US schools is the complete opposite of one where students are taught to "memorize math facts" or one where…

The algorithmic flexibility is part of ‘common core’ which is in most US schools now. However the method teaching algorithmic flexibility is often forcing the kids to use each of the several algorithms and marking their answers wrong if they didn’t use the technique requested by a specific question.

Re: Playing the piano taught me math (2016)

#19
post #14
post #10

> When all my first-grade classmates were memorizing math facts like “2 + 3 = 5” > I was called out during class when my teacher saw me fiddling with my fingers during a classroom exercise From their LinkedIn profile, it appears that the author went to school in the US. I'm not from the US, but my impression of US schools is the complete opposite of one where students are taught to "memorize math facts" or one where…

Music...where 3 + 3 = 5. Ie c to e is a third, and e to g is a third, but c to g is a fifth.

Not really. C to E is a major third (4 semitones), E to G is a minor third (3 semitones), and C to G is a fifth (7 semitones).

4 + 3 = 7

Re: Playing the piano taught me math (2016)

#20
post #12
post #11

Music and piano playing taught me things about (math related): - Exponentials and logarithms - Harmonic series - Combinatorics - Chaos theory - Some calculus - Resonance - Linear algebra It also taught me about physics, cognitive psychology, learning theory, history and even some sociology.

Coming from the opposite direction, I'm quite curious as to where the linear algebra and combinatorics fit in. As a former mathematician (switched to computing after one post-doc) who has been trying to learn about music and to play the piano, I'm trying to make sense of how music and mathematics relate. There's some stuff with group actions going on - I think you can think of a dihedral group acting on sets of triad…

I can see combinatorics relating in the sense that exploring the space of potential compositions can be approached as a ‘combination of’ type problem for different elements.. chords as combinations of notes, chord progressions as combinations/orderings of chords, likewise for the order of notes in an arpeggio.. rhythms/grooves can be thought of as like combinations of emphasised beats (emphasis on 2 & the and of 3 vs. emphasis on 1 & the and of 3 for example) at different levels of beat-subdivision.. then the sounds each emphasised beat can take come from a discrete set (kick, snare etc.) so can be thought of as another combination-of type problem. many possibilities.

Perhaps this is not what the GP meant though, I’m curious about however it applies. No idea about where linear algebra could fit in, I have yet to see those parallels myself yet but interesting to think how it could relate

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