Chord Progressions as Modular Arithmetic (C Major Example)

WHEN YOU ARE IN SCALE MODE ON ABLETON, IT IS NOT +7 ITS +7 WHEN YOU HAVE SACLE MODE OFF, YOU WILL HAVE TO LEARN WHAT THEY ACC ARE W/O SCALE MODE THEN PUT THEM

Great question. What you saw is basically pitch-class arithmetic (mod 12)—a mathy way to describe the same harmony rules musicians usually learn by ear or with Roman numerals. Once you connect the math to scale degrees, it becomes very clear how chords “go well together.”

I’ll walk this step-by-step using C major, and I’ll keep tying it back to the number logic you quoted.

1. Your formulas → what they really mean

We label notes as numbers mod 12:

C=0  C#=1  D=2  D#=3  E=4  F=5
F#=6 G=7  G#=8 A=9  A#=10 B=11

Intervals in your system

x + 7 → Perfect fifth
x + 4 → Major third
x + 3 → Minor third
x + 10 → Minor seventh
x + 11 → Major seventh
+12 (or +15/+16) → same note, higher octave / brighter voicing

So your formulas are just chord construction rules.

2. The C major scale (the allowed notes)

C major uses only these pitch classes:

C  D  E  F  G  A  B
0  2  4  5  7  9 11

👉 Rule:

Chords “go well together” if they are built using only notes from the scale.

That’s the key idea.

3. Building diatonic chords using your math

Now we pick x from the scale and only allow notes that stay in the scale.

I — C major

x = 0 (C)
0 + 4 = 4 (E)
0 + 7 = 7 (G)

✅ C major (C–E–G)

ii — D minor

x = 2 (D)
2 + 3 = 5 (F)
2 + 7 = 9 (A)

✅ D minor (D–F–A)

iii — E minor

x = 4 (E)
4 + 3 = 7 (G)
4 + 7 = 11 (B)

✅ E minor (E–G–B)

IV — F major

x = 5 (F)
5 + 4 = 9 (A)
5 + 7 = 0 (C)

(mod 12 wrap)
✅ F major (F–A–C)

V — G major

x = 7 (G)
7 + 4 = 11 (B)
7 + 7 = 2 (D)

✅ G major (G–B–D)

vi — A minor

x = 9 (A)
9 + 3 = 0 (C)
9 + 7 = 4 (E)

✅ A minor (A–C–E)

vii° — B diminished

x = 11 (B)
11 + 3 = 2 (D)
11 + 6 = 5 (F)

(tritone instead of perfect fifth)
✅ B diminished (B–D–F)

4. The “chords that go together” in C major

This gives the diatonic chord set:

Degree	Chord
I	C major
ii	D minor
iii	E minor
IV	F major
V	G major
vi	A minor
vii°	B diminished

These chords all work together naturally because they share the same scale.

5. Why certain progressions sound good (math + physics)

Some movements are especially strong:

Fifth relationships (x → x+7)

C → G
G → D
F → C

This is circle-of-fifths math, and it aligns with the harmonic series.

Functional pull

Tonic (rest): I, vi
Predominant (movement): ii, IV
Dominant (tension): V, vii°

So common progressions:

I – V – I
I – IV – V – I
ii – V – I
vi – IV – I – V

These aren’t arbitrary — they follow interval attraction rules baked into acoustics.

6. Adding 7ths with your system

Using your formula:

Cmaj7

0 + 4 + 7 + 11 = C E G B

Dm7

2 + 3 + 7 + 10 = D F A C

G7 (dominant)

7 + 4 + 7 + 10 = G B D F

That G7 → Cmaj7 resolution is one of the strongest forces in Western music.

7. Big idea (the “number theory” version)

You can think of harmony like this:

Pick a scale → a subset of ℤ₁₂
Build chords by adding allowed intervals
Chords work together if:
- Their notes stay in the scale
- Their roots follow low-distance interval motion (5ths, 4ths, stepwise)

So music theory = constraints + modular arithmetic + psychoacoustics

8. Want to go further?

Next logical steps (still math-friendly):

Why borrowed chords break the scale but still work
Why secondary dominants use x+7 outside the key
Voice-leading as minimizing pitch-class distance
Why modes are just rotations of the same set

CHords