The System
Beneath the Song
A first lesson, rebuilt for someone who already thinks in systems and ratios.
Three Operating Rules
Before any of the mechanics, three things to internalize. They sound like advice. They function like operating constraints — break them and the rest gets harder than it needs to be.
Most players spend 20 years learning songs phonetically — note-for-note, no underlying model. The shortcut isn't talent. It's a small system, mastered cold, then permuted. The next eight modules are that system. Roughly two pages of substance; everything else is repetition.
Why Frets Aren't Evenly Spaced
A small amount of math, used once, removes most of the mystery from a fretboard. If you understand this section, the rest of the system collapses into something obvious.
Pitch is frequency. A note is just a sound wave oscillating at some number of cycles per second (Hz). The standard reference: A above middle C is 440 Hz.
An octave is an exact doubling of frequency. That's the entire definition. The A one octave up from 440 Hz is 880 Hz. One more octave up: 1760 Hz. It's a multiplicative scale, not an additive one.
Western music divides each octave into 12 equal steps, called semitones. "Equal" here means equal as ratios, not equal as differences. Each semitone is the same multiplicative jump:
Twelve of those steps stacked: (21/12)12 = 2. The octave closes exactly. This is called equal temperament — the compromise that lets you play in any key on a fixed-pitch instrument.
Now look at a fretboard. Each fret raises pitch by one semitone. Since pitch ratios are multiplicative but string length is linear, the frets must get closer together as you go up. The math:
where L is scale length and n is the fret number. Plug in n=12: d = L × (1 − 1/2) = L/2. The 12th fret sits at exactly half the string length. Half the length = double the frequency = one octave up. The geometry encodes the physics directly.
You don't need to think about this when you're playing. But knowing it once means you'll never be confused by the layout of the neck again. The frets aren't arbitrary — they're the visible solution to an exponential equation.
E A D G B E
Six open strings, numbered counter-intuitively. String 1 is the thinnest. String 6 is the thickest. Pitch rises as strings get thinner — same reason a thinner cable on the same tension oscillates faster.
| String | Note | Frequency | Relative to 6th | Notes |
|---|---|---|---|---|
| 6 (thickest) | E2 | 82.41 Hz | ×1.000 | Low E |
| 5 | A2 | 110.00 Hz | ×1.335 | Up a perfect 4th (5 semitones) |
| 4 | D3 | 146.83 Hz | ×1.782 | Up a perfect 4th |
| 3 | G3 | 196.00 Hz | ×2.378 | Up a perfect 4th |
| 2 | B3 | 246.94 Hz | ×2.997 | Up a major 3rd (4 semitones) — the only irregular jump |
| 1 (thinnest) | E4 | 329.63 Hz | ×4.000 | High E. Exactly 2 octaves above low E. |
Note the relative column: the 1st string is exactly 4× the frequency of the 6th. Two octaves, two doublings — the math from Module 02 made concrete.
Five of six string intervals are perfect 4ths (5 semitones). The G-to-B gap is a major 3rd (4 semitones). The reason is ergonomic, not theoretical: this tuning lets you play standard chord shapes with one hand without finger gymnastics. You'll get used to it. Every guitarist resents it occasionally.
The rule: tune before every session. A clip-on tuner reads the frequency and tells you which string and how far off. Use one. Trusting your ear comes later.
Reading the Chart
Tab is a position-only notation. It tells you where to put your fingers, not when or how long. Less information than sheet music, faster to read, sufficient for most of what you'll do.
| Symbol | Meaning |
|---|---|
| Six horizontal lines | The six strings. Top line = string 1 (thinnest). Read like you're looking down at your own guitar. |
| Number on a line | The fret to press on that string. |
| 0 | Play the string open (no fret pressed). |
| Blank space | Don't play that string at all. |
| Numbers stacked vertically | Play those notes simultaneously. A chord. |
| Numbers in sequence left-to-right | Play in that order. Time flows rightward. |
What tab leaves out: rhythm, duration, dynamics. You have to know the song to play tab properly. It tells you where, not when. For now that's enough.
C Major as an Algorithm
A scale isn't a sound — it's a pattern. Pick a starting note, apply a fixed sequence of intervals, get a scale. Change the starting note, same sequence, different key. This is the whole game.
The major scale pattern, expressed in semitones:
(2, 2, 1, 2, 2, 2, 1) semitones
W = whole step = 2 semitones. H = half step = 1 semitone. Sum: 2+2+1+2+2+2+1 = 12. The pattern exactly fills one octave. Apply it from C and you get: C, D, E, F, G, A, B, C. No sharps, no flats — which is why C is the standard entry point.
Click any note below to highlight it on the fretboard. The frequency column is the math of Module 02 in action — each step multiplies by 2n/12.
Practice protocol: ascend the scale slowly, every note clean, every finger in the right place. Then descend. Then both directions in sequence. Use a metronome — start at 60 BPM, one note per click. Speed comes later. Cleanliness comes first.
When this feels automatic, the same pattern applied at the 5th fret gives you G major. At the 7th fret, A major. Same shape, shifted. That's the entire payoff of equal temperament.
Five Shapes, Whole Fretboard
Once the scale is in your hands, you need a way to navigate chords. CAGED is the framework. It works because it solves a geometry problem.
The system: there are five basic open-position chord shapes — C, A, G, D, E. Slide any one of those shapes up the neck (using your index finger as a movable nut, called barring), and you get the same chord in a new position. Five shapes × twelve fret positions = full coverage of every chord, everywhere.
A chord built from a 7-note scale needs 3 notes (root, 3rd, 5th). The guitar has 6 strings. The number of distinct ways to voice that chord across 6 strings, given the EADGBE tuning, resolves to exactly 5 patterns that interlock — each one's high note becomes the next one's low note. They tile the neck without gaps. Think of them as 5 basis positions; any chord on the neck is one of these shapes, shifted.
You don't learn all five at once. You'll learn one per lesson for the next five lessons, starting with C-shape (already implicit in the C major scale work) and adding A-shape in Lesson 03. By Lesson 06 you'll be able to play a C chord in five places on the neck without thinking about it.
Ten Questions
Pattern recognition test. Do this once with no notes. The score isn't the point — the missed questions are.
Thirty Minutes a Day
Motor skills decay exponentially without rehearsal. Daily reps at modest volume compound; intermittent long sessions don't. The constraint isn't time per session — it's consistency.
Session structure — same order, every time. Predictability builds automaticity:
| Block | Duration | Activity |
|---|---|---|
| 01 | 5 min | Tune. Pluck each string. Adjust until the tuner reads dead-center. |
| 02 | 10 min | C major scale, ascending. Slow. Clean. Every finger in position. |
| 03 | 10 min | Descending, then both directions back-to-back. Metronome at 60 BPM. |
| 04 | 5 min | Free play. Hit notes in random order. Try to find them by ear. |
When the timer ends, you're done. Close the lid. Walk away. Tomorrow you do it again. The accumulation is the system.
Lesson 02 — Monday 25 May
Memorial Day. I'm on. Same Zoom link.
Bring to lesson: tuned guitar, the C major scale playable both directions without looking, any questions that came up during practice.