A math guy looks at scales

[swink]

You will soon be ready for Math rock

 

[thetragichero]

You must be thinking of a different "common core" math than what's being made fun of.

- John

watched a video on i think common core multiplication and was amazed at how it teaches a process that is adaptable beyond base 10 instead of just memorizing multiplication tables. for those of us above the age of roughly 25 our brains tend to be averse to change so the general consensus is that this is "bad." as someone who was a college math major until his career as an alcoholic took off, this stuff excites me because we're training the youts to be smarter and more analytic than we are

 

[Robscott]

More scales

View attachment 3605854

Is that a short scale Bass?

 

[IamGroot]

Is that a short scale Bass?

Gonna be a no scale bass.

Unlike my fretless, where the scales are optional.

 

[Ric5]

Is that a short scale Bass?

diminished

 

[dalkowski]

My son took AP Theory in high school a couple years back (incredibly tough course!). Ever since, when we talk about music I get all like:

My last bass teacher hammered me with theory (in a good way). But when he told me "it's really all math" I knew I was sunk.

 

[Steve Freides]

But when he told me "it's really all math" I knew I was sunk.

It is and it isn't - it's rightly called "music math" IMHO. Being good at math helps, but if you can't play your instrument and in particular, if you can't play scales fluently on your instrument, all the math in the world isn't going to help you.

Let's take this is in what I think is a similar direction, but with chords instead of scales. Someone could certainly graph these things, too:

Am6 and F#m7 are the same four notes.

The top 3 notes of a G7 chord are a B dim triad. The top 4 notes of a G9 chord are a B dim 7 chord. The top 4 notes of a G maj9 chord are a B min7 chord. The top 3 notes of a C min7 chord are an Eb major triad. The top 3 notes of a C min7b5 chord are an Eb min triad.

C+ and E+ and Ab+ triads are all the same-sounding note, each one with one of the three notes spelled as its enharmonic equivalent (C-E-G#, E-G#-B#, Ab-C-E) because the octave is divided into 3 equal parts.

Have fun with dim7 chords: C dim7, Eb/D# dim7, F#/Gb dim7, and A dim7 are all the same notes, save for enharmonic spellings, because the octave is divided into 4 equal parts.

-S-

 

[avocado]

When he's digested all that, he can move on to this: Musical temperament

Did you read How equal temperament ruined harmony (and why you should care) by Ross W. Duffin? Interesting book, and accessible for someone with even just a little theory like me.

 

[IamGroot]

Every scale system can be played counterclockwise, and you will get a new system unless its a symmetrical scale like a diminished scale.

I think.
Need coffee to confirm.

My guess was wrong.

 

[Vinny_G]

Did you read How equal temperament ruined harmony (and why you should care) by Ross W. Duffin? Interesting book, and accessible for someone with even just a little theory like me.

No, but I am particularly interested in this subject. Thanks for that.

 

[IamGroot]

It is and it isn't - it's rightly called "music math" IMHO. Being good at math helps, but if you can't play your instrument and in particular, if you can't play scales fluently on your instrument, all the math in the world isn't going to help you.

Let's take this is in what I think is a similar direction, but with chords instead of scales. Someone could certainly graph these things, too:

Am6 and F#m7 are the same four notes.

The top 3 notes of a G7 chord are a B dim triad. The top 4 notes of a G9 chord are a B dim 7 chord. The top 4 notes of a G maj9 chord are a B min7 chord. The top 3 notes of a C min7 chord are an Eb major triad. The top 3 notes of a C min7b5 chord are an Eb min triad.

C+ and E+ and Ab+ triads are all the same-sounding note, each one with one of the three notes spelled as its enharmonic equivalent (C-E-G#, E-G#-B#, Ab-C-E) because the octave is divided into 3 equal parts.

Have fun with dim7 chords: C dim7, Eb/D# dim7, F#/Gb dim7, and A dim7 are all the same notes, save for enharmonic spellings, because the octave is divided into 4 equal parts.

-S-

Arpeggios can be shown as well, as you implied.

 

[SteveCS]

My instinct is to be highly suspicious of any representation or analysis of music that does not, indeed cannot, provide for marking the passage of time. How is one to distinguish chord from arpeggio, scale from melody, note from rest, or downbeat from upbeat?

 

[IamGroot]

Can we do ‘a math guy looks at the Groove’ next?

 

[okcrum]

re: common core and snark, I once read an article lambasting common core math, and realized while reading it that the math they were so offended by is exactly how you make change as a cashier without a calculator (back in the day...) By adding rather than subtracting, counting back up to the value of the currency the customer gave you. You'll almost never make an error that way, and will be able to do it almost instantly.

In other words, common core can be very old school, and functional. Most middle-aged + people who never had to make to change would miss that, and protest against the very same technique their contemporaries used. (maybe, just maybe, we should leave teaching math to the math teachers....kick out the government, and kick out the non-teacher opinion mob as well)

Seeing patterns visually from numbers is quite interesting, and it's illuminating to see a pattern that was under your nose the whole time, and you never saw!

Actually, what it does is teach everyone a single way of making change. And a terribly inefficient one, at that. To compound the fail, any other way of solving the problem correctly is considered wrong.

Yeah, I've made change. In binary, octal, and hexadecimal too.

Calling something stupid when it's stupid isn't snark.

 

[IamGroot]

My instinct is to be highly suspicious of any representation or analysis of music that does not, indeed cannot, provide for marking the passage of time. How is one to distinguish chord from arpeggio, scale from melody, note from rest, or downbeat from upbeat?

I feel the same way about Laplace transforms manipulating the time domain. There a cheap trick too.

 

[okcrum]

I feel the same way about Laplace transforms manipulating the time domain. There a cheap trick too.

Part of that is because (at least in my EE courses) they made you solve the first problems the hard way. Then they whip out Laplace Transforms and say "Yeah, but this way's much easier" and you think to yourself "If I'm gonna build filters and stuff, why didn't they just show me this in the first place?". Plus, they're easier to code.

It was the same with anything that wasn't laminar to do with fluid mechanics until chaos theory came along.

 

[IamGroot]

Part of that is because (at least in my EE courses) they made you solve the first problems the hard way. Then they whip out Laplace Transforms and say "Yeah, but this way's much easier" and you think to yourself "If I'm gonna build filters and stuff, why didn't they just show me this in the first place?".

It was the same with anything to do with fluid mechanics until chaos theory came along.

I felt the same way. Wait, you mean i can do ODE with algebra! I am not a EE .. who are the guys that really use this stuff proficiently. I used it in heat and flow simulation with step inputs. I understand the math purists fought LTs for decades, as the proofs lagged the results and Heaviside didnt care.

 

[IamGroot]

Harmonic Minor, Harmonic Major, Double Harmonic Major

 

[La Faro]

Should be able to put them all in order off brightness and see the evolution

 

[Steve Freides]

My instinct is to be highly suspicious of any representation or analysis of music that does not, indeed cannot, provide for marking the passage of time. How is one to distinguish chord from arpeggio, scale from melody, note from rest, or downbeat from upbeat?

It's not a representation of music, just of one aspect of the theory of one aspect of music. It's not suspicious.

Consider Schenkerian analysis of music - it doesn't contain any representation of the rhythm of music in a direct or literal sense, but that doesn't mean that rhythm isn't included in what it's trying to represent. Many people do consider Schenkerian analysis suspect; I was fortunate to study it in depth and found it taught me more about certain, very important aspects of music than I was able to learn by any other means. It forced me to really think about what makes a piece of music, each piece that we studied, work.

-S-