[jeofken]

Thank you. I too was a guitar player of chords memorised for a long time, but took a gap year to study music. I’ll share how to level up so you don’t have to take a year off :).

When I said the tones are divisions by 12 it was a small simplification. On your guitar you can see a physical representation of the difference in frequencies between tones - the first fret is very wide, but they narrow as you traverse the neck. Tell me, how much shorter is the 12th fret compared to the 1st? And after reading this whole reply, tell me how much shorter is the fret of the major 5th compared to the fret of its tonic? It’s fraction magick...

A shorthand for remembering scales my teacher taught me is this. When building a scale we call the first one the tonic, and given the frequency of the tonic and knowing what scale (major, minor, lydian, etc), we can find the rest, like a simple algebra problem.

To find a major scale, the shorthand is “2.5, 3.5”. That means first 2 whole steps, then a half step, then 3 whole steps, then a half step.

A whole step is 2 frets on the guitar. A half step is one fret. That’s how you filter out 8 of the 12 frets to play a major scale on your guitar neck.

So go to your guitar and let’s say we ‘let tonic = loose D string’.

From there on, do a whole step, pluck, and one more time, then a half step, then whole+pluck, whole+pluck, whole+pluck, then half+pluck. You’ve just found the major D scale!

The 4th tone in the major scale of E is A. The 4th of A major is D. Do you now see the pattern of why you tune the next string to fret 5 (I.e 2.5 whole steps)? The guitar is tuned in these 4ths, except for one string which is the B string which is a 3rd of its precious IIRC. Haven’t played guitar for ages.. From now on tune like a pro - start with a A of 440Hz and tune the other strings from there. Just temperament rocks equal temperament sucks ;p. By tuning like a pro and plucking two loose strings and tuning until you recognise “as, it’s a 4th!”, you learn to remember how that interval sounds. You can check by putting your finger on the previous strings 5th fret, but tune only one string (A) after an electronic tuner.

Now you know how to from any tonic find its major scale with the shorthand 2.5,3.5. If you look up a minor scale, what would its shorthand be? Now you can find a minor scale always. What would the shorthand of the pentatonic (meaning 5-note scale) blues scale be? Now you don’t need sunglasses indoors to be cool anymore.

Sadly much music theory online shy away from the math beauty and systematicness of music, because most people have trauma from government school maths class and say “I’m not good with maths”, but the truth is music is simple, fractional, and beautiful.

Let’s learn how to construct chords now. You know how to find a major scale. Let’s say you wanna play a C major chord, something you may have memorised. On the A string, you put a finger on the 3rd fret. Wow! That’s also the tonic of the C major scale! On the next string you hit fret 2. After D comes D#, then E. wait, that’s the 3rd in C major scale!! Holy smokes. Then comes a G right? In C major scale, G is the heavenly, awe-inspiring, 1.5 frequency multiplying, major 5th! And so on. To make a chord, select the 1st (I.e tonic) of a scale, the 3rd, and the 5th.

To make a 7th chord, add the 7th to the mix (for C major that’d be B in English I.e H in Germanic countries where I’m writing from).

I’d love to have (or maybe to have written) a book “music for programmers”. My instrument tutor was a retired physics teacher, that was great...

Ok one more practical tip: start a new instrument. You don’t have to buy but can rent for maybe $30-$40/month. For me it was such a habit to have the guitar and strum some cool chords, that switching to a new instrument where I was a beginner, and there were no websites of “1000 chord diagrams to make you a rock star” freed me to learn the basics. I suggest finding a tutor to meet once a week in a basement, pay $40 cash, and learn with sheet music and all. Homework is your friend here! Instruments I recommend are fiddle/cello (awesomely fun and really gets you thinking about frequencies and fractions as you don’t have the crutch of frets) or flute or clarinet, because they sing so beautifully. My biased choice is to start with the fiddle, and play European classical but also folk (American and European folk both use a lot of fiddle). American folk is so much fun. Good luck and feel free to reply with any question.

[petervm]

Thank you so much for this. You may have derailed my Sunday :)

A physics teacher would probably make for a great music teacher indeed. Understanding things from first principles is so powerful. Compressed knowledge. I always try to move towards that but it has eluded me so far when it comes to music. Granted, I haven't put much effort in. I would totally buy that book of yours.

Or anything "for programmers" really :) Not that we're especially dumb that we need our own custom teaching materials but I do think we are more qualified than most to identify systems, decompose them, and explain the relations between their parts. And do it in a gradual way with progressive disclosure, until we're satisfied with our new lego pieces.

[palimpsests]

my goodness. I appreciate your personalized take on music theory for its iconoclasm but would never in a million years subject any of my students to learning this beautiful topic in this way. Unless they were perhaps computer scientists / programmers who were having trouble with this material using more conventional, time-tested approaches. But I have yet to see that.

for anyone else reading this just know that music theory in study and application can be approached in a much more intuitive, less “algebraic” manner.

(nothing wrong with algebra...)

[jeofken]

Sorry if it’s not for you. I am rather frustrated by music teachers often even not knowing or being interested in the first principle of what they’re teaching, and think I was lucky to have a retired physics teacher teach me music. It is all about fractions, so why shy away from it? Many teachers can tell me about intervals and scales, but not answer why those sounds fit together - like how a 5th is 1.5x the frequency of the tonic. That’s no better than just memorising chords on a piano. I want to see the beauty in its essence!

Good thing this world can accommodate more than one style of learning! Take care

[palimpsests]

Thanks for your reply, no apologies necessary, and I am glad you found a teacher that you resonate with!

I have degrees in physics and music. I understand all of this from first principles.

Speaking as someone who has spent tens of thousands of hours in music, with other musicians at many different stages of learning - for probably the majority of music students, this is (initially) essentially useless and potentially even obfuscatory and unhelpful. It can be interesting to learn about later if someone wants to. Does nothing to help people get better at playing their instrument, which is what most people seem to want. Having an interest in acoustics and the physics of music can be helpful in driving someone to play and practice if it simply gets someone to spend more time with their instrument.

In your reply I wonder if past music teachers have emphasized memorizing theory without application - in what I have seen, this is not the norm. The emphasis is on practice and application, developing an internalized somatic memory (e.g. muscle memory & ear training), and technique in order to avoid hurting yourself.

Internalized somatic memory is not the same thing as memorizing concepts with your mind :)

Let me ask you this - it sounds like you are coming from a classical / folk perspective? I’m coming from a jazz foundational perspective, that’s the “form” of music theory education I am referring to. Which is quite common in the U.S. Do you have much practical experience playing / learning jazz or related genres on an instrument? (is this a genre that even interests you?)