How I Made Sense of Music

Posted 2015-02-23
Written by Matt Frost

Music and Math

How I made sense of music

I've always loved music, as long as I can remember some of my fondest memories as a child and young adult revolved around music. I've always had a strong desire to play music, to be able to play it well and to really understand how it all works together. Part of that is the artistic side of my brain that wants to leap out, despite a lack of confidence. The other side of my brain is the logical side, this is the side that makes me good at my job as a programmer. I've never taken a music theory class in my life, in fact, I've never so much as taken a a guitar or drum lesson in my entire life. Not one. I've played both instruments in front of people and not been laughed out of the room.

I'm going to focus on guitar, because that's a bit more musically relevent in terms of dealing with notes, chords, scales etc. I learned that the major scale was made up of 7 notes (8 notes when resolving on the octave of the scale root), but more importantly I realized that there was a pattern to the major scale. The pattern included a series of whole steps and half steps, when visualized on the guitar, a whole step would be moving 2 frets and a half step would be moving 1 fret. I learned the pattern, but if you asked me what notes I was playing, I'd have to think for a bit to be able to name them. I'm generally pretty good at memorization, but memorizing the 7 notes in the 12 Major scales didn't seem like a whole lot of fun. Plus, once you do that, you have scale modes to deal with and trying to memorize the 7 notes in the Dorian, Phyrgian or Mixolydian modes...just no.

I wanted a fast way to come up with these notes that only required that I know the pattern. The pattern will remain the same for every Major scale. So if I could take that pattern and some how figure out a way to "calculate" the notes quickly, that would be more up my alley. So I think I set this up enough, I'm gonna talk about what I did. Also I should point out, I'm not necessarily claiming to have invented this system...I've never studied anything like this before, so this might be a thing that exists and I just stumbled across the idea on my own.

First, I'm going to go from A to G#/Ab and assign each note a number. It's a positional number, it's important the notes be in the correct tonal order.

  1. A
  2. A#/Bb
  3. B
  4. C
  5. C#/Db
  6. D
  7. D#/Eb
  8. E
  9. F
  10. F#/Gb
  11. G
  12. G#/Ab

I give preference to naming the notes sharp (#) as opposed to flat (b), that's my preference but you should know F# and Gb are the same exact note. I don't even really bother to memorize the whole list, I just keep in mind that C is at 4 and F is at 9. I can decipher every other note from those points, those 2 notes do not have flat notes. A half step down from C is B and a half step down from F is E. So that helps me find all the notes I need.

Major Scale

So I know the pattern of the Major Scale, I know how it corresponds to strings and frets on the guitar and I know the intervals that separate each position of the scale. So, if we remember a whole step is 2 frets and a half step is 1 fret we can take a look at the Major Scale Pattern:

Root -> Whole -> Whole -> Half -> Whole -> Whole -> Whole -> Half

By taking the knowledge of whole steps and half steps and the note/number chart above, we can find any position in any scale like this. We'll use D as an example here.

D E F# G A B C# D R +2 +2 +1 +2 +2 +2 +1 6 8 10 11 13 15 17 18

So our root note is D, which is number 6 and by adding the steps we get numbers that mostly correspond to the notes in our list. We do notice a point where the numbers are larger than 12, for those, since there are only 12 notes, we subtract 12 from those numbers. 13 becomes 1, 15 becomes 3, 17 becomes 5 and 18 becomes 6, or A, B, C# and our octave D. So no matter what note, or number we start on, we can easily figure out the notes in the pattern.

Major Chords

Major chords are made up of the notes at the first, third and fifth positions of the major scale. The first position is the root note, the note for which the chord is named. The third position is 2 whole steps from the root and the fifth position is a 1 1/2 steps from the third position and 3 1/2 steps from the root note. So starting from a root note we can add 4 to find the 3rd position note and we can add 3 to the third position note to find the 5th position. For example, let's take a look at a C Major chord. The C Major scale is by far the easiest to memorize and its' C D E F G A B C from root to octave. The C Major chord would consist of the notes C, E and G. Piece of cake with an easy scale like C Major.

What if it's not C Major, what if it's a D# Major? Well you have to extrapolate the scale out and find the 3rd and 5th position. Or you could realize that D# is 7, then add 4 to get 11, which is a G, then add 3 to get 14 which is A# (after subtracting 12). So, your D# Major chord would have the notes D#, G, A#.


So this is pretty much an introduction to this concept, I could probably write more blog posts that deal with things like scale modes and chord construction and things like that, I'm not an expert by any means. If anyone knows anything about this, and it already exists, please let me know I'd love to see how much more this is actually built out than I have come up with on my own. I feel pretty certain this has to exist already. Another note, this is a really handy method for finding notes on the neck of the guitar. In standard tuning, your strings are E A D G B E or 8 1 6 11 3 8. So by adding the frets to the initial number, you can find the note. For example E String 3rd fret is simply 8 + 3 = 11 or G. A string 9th fret, 1 + 9 = 10 or F#/Gb.

I've found for me this is the easiest way to learn the notes up and down the fretboard and quickly construct scales and chords. I realize not every mind works this way, so if you have a method that works for you, that's awesome. I'm not a trained musician, so I have to find ways to make sense of this without years of memorization. I'd be curious to know your thoughts.


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