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Playing the piano taught me math (2016)

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Re: Playing the piano taught me math (2016)

#31

Post by elliekelly »

scop wrote: post #28

This reminds me of how I became a better guitar player by learning piano. I had been playing guitar (classical & metal mostly) for about 15 years before learning piano. Upon learning some basic piano, I found the guitar fretboard came alive in entirely new ways. I believe this to be a result of the piano keyboard having a visually clear and uniform organization of notes, enabling me to "see" how music theory operated…

Learning philosophy and then logic and then computer programming taught me math. Or at least taught me how to understand math in a way I’d never been able to in all my many years of education. It makes me wonder how many kids are missing out because we’re focused on teaching math one specific way even though it’s quite clear the way we’re teaching it just doesn’t “click” for a lot of students.

Re: Playing the piano taught me math (2016)

#32

Post by necheffa »

msravi wrote: 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 graduated highschool in the U.S. in 2009.

Was forced to memorize times tables, long division, random formulas. Rarely was proof based instruction provided.

Some teachers encouraged creative thought, others would mark a correct answer wrong because you didn't use the specific method they taught in class.

Ironically, having graduated college with a minor in mathematics - I still don't have my times tables memorized.

Re: Playing the piano taught me math (2016)

#33

Post by edejong »

jvvw wrote: post #12
edejong wrote: 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…

W.r.t. combinatorics: I was thinking of tuning systems and scales. I have always thought about the theory, but never written it down. Some other people actually did a much better job than me: http://andrewduncan.net/cmt/

W.r.t. linear algebra: mostly in relation to sound synthesis, but also in relation to music composition, theory of overtones, piano tunings... You ask, I'll explain.

Re: Playing the piano taught me math (2016)

#34

Post by dekhn »

C19is20 wrote: post #14
msravi wrote: 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.

it's just 12 notes, ignore the letters. I wrote this program to help me understand scales and modes better.

  #define TRUE 1
  #define FALSE !TRUE

  void print_key();
  void show_scale();
  double power();

  char notes[13][3]={"A ","A#","B ","C ","C#","D ","D#","E ","F ","F#","G ","G#","A "};
  char scale_name[8][12]={"Ion(M)","Dor","Phryg","Lyd","Mixolyd","Aeol(m)","Locr"};
  int scale[16]={2,2,1,2,2,2,1,2,2,1,2,2,2,1};

  int main()
  {
  int key=3,i,its;

  printf("\nWelcome to Scale Printer.\n\n");

  do
  {
          print_key(key); printf("\n");
          for(i=0;i

Re: Playing the piano taught me math (2016)

#36

Post by jedimastert »

scop wrote: post #28

This reminds me of how I became a better guitar player by learning piano. I had been playing guitar (classical & metal mostly) for about 15 years before learning piano. Upon learning some basic piano, I found the guitar fretboard came alive in entirely new ways. I believe this to be a result of the piano keyboard having a visually clear and uniform organization of notes, enabling me to "see" how music theory operated…

This is generally why all music college students take piano lessons as a form of "gen-ed". It gives a base every teacher can start from

Re: Playing the piano taught me math (2016)

#37

Post by kian »

edejong wrote: post #33
jvvw wrote: post #12

Earlier quoted context omitted.

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…

W.r.t. combinatorics: I was thinking of tuning systems and scales. I have always thought about the theory, but never written it down. Some other people actually did a much better job than me: http://andrewduncan.net/cmt/ W.r.t. linear algebra: mostly in relation to sound synthesis, but also in relation to music composition, theory of overtones, piano tunings... You ask, I'll explain.

I'd love to hear your explanations re linear algebra on all of the above, but most especially with respect to music composition.

Re: Playing the piano taught me math (2016)

#38

Post by schwich »

elliekelly wrote: post #31
scop wrote: post #28

This reminds me of how I became a better guitar player by learning piano. I had been playing guitar (classical & metal mostly) for about 15 years before learning piano. Upon learning some basic piano, I found the guitar fretboard came alive in entirely new ways. I believe this to be a result of the piano keyboard having a visually clear and uniform organization of notes, enabling me to "see" how music theory operated…

Learning philosophy and then logic and then computer programming taught me math. Or at least taught me how to understand math in a way I’d never been able to in all my many years of education. It makes me wonder how many kids are missing out because we’re focused on teaching math one specific way even though it’s quite clear the way we’re teaching it just doesn’t “click” for a lot of students.

Would you mind expanding on this? What philosophy did you learn? What logic? I'm interested in this approach to learning math.

Re: Playing the piano taught me math (2016)

#39

Post by j7ake »

C19is20 wrote: post #14
msravi wrote: 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.

You’re loose with your definition of a third. If you play C to E and E to G you will notice they are not the same distance.

Re: Playing the piano taught me math (2016)

#40

Post by edejong »

kian wrote: post #37
edejong wrote: post #33

Earlier quoted context omitted.

W.r.t. combinatorics: I was thinking of tuning systems and scales. I have always thought about the theory, but never written it down. Some other people actually did a much better job than me: http://andrewduncan.net/cmt/ W.r.t. linear algebra: mostly in relation to sound synthesis, but also in relation to music composition, theory of overtones, piano tunings... You ask, I'll explain.

I'd love to hear your explanations re linear algebra on all of the above, but most especially with respect to music composition.

Sound synthesis: mostly when I was playing with PD (Pure Data). Linear algebra comes up all the time in sampling theory.

Music composition: this is a bit more far fetched, but I always thought of composition as a combination of vectors which can vary semi-independently. We want to pick some plane through that vector space and move within the plane. For example, we can vary in harmonic complexity, melodic complexity, rhythmic complexity, dynamics, tempo. But it wouldn't make sense to do all at the same time. So we pick one plane, say harmonic complexity and dynamics, and move within that plane. This allows the listener to get used to the 'space' that is opened by the composition. We can then slowly add more vectors, to keep the interest.

A very visual representation of this is the trackpads that you can see on certain modular synthesizers. Often there is a complex setup, but the variables of the setup are reduced to two dimensions, which allows the composers to vary within this projected plane.

Piano tunings: well, basically you have a vector of 230 piano strings of which the overtones are all slightly out of tune. To tune a piano 'correctly', you need to minimise set of equations of strings and overtones (matrix).

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