Know-it-all 101 🎓 ➡️ ~ The Invention of Music Theory

 Have you ever wondered why music has exactly 12 notes? Why not 13 or some completely different number? As strange as it sounds, the answer goes all the way back to a name you’ve definitely heard before; Pythagoras. Yep, the triangle guy. But he didn’t just obsess over triangles, he basically invented music theory, too.

It all started when Pythagoras noticed something odd while listening to a blacksmith at work. As the hammer struck the anvil, it produced a musical note. He realized that using a hammer half the size produced the same note, but in a higher octave. That was his first big insight; octaves aren’t spaced out arithmetically they’re spaced geometrically. In simpler terms, the frequency of a note and its octave follows a 1:2 ratio.

Personally, I find it easier to think in solfa notation, so I’ll stick with that for this explanation.

Pythagoras kept experimenting. When he used a hammer one-third the size of the original, the new note sounded like a fifth of the higher octave, like jumping from ‘do’ to ‘sol¹’. He then halved the frequency to bring it back into the same octave as the original ‘do’. This gave him a 3:2 frequency ratio between ‘do’ and ‘sol’. Boom, he had discovered fifths. He found other musical intervals, too; ‘mi’ – 5:4, ‘ri’ (between ‘do’ and ‘re’) – 6:5, ‘re’ – 9:8, ‘di’ (also between ‘do’ and ‘re’) – 16:15

From here, he tried filling up the octave by stacking perfect fifths (multiplying by 3/2) and bringing the resulting notes back into the same octave (by dividing by 2). After 12 steps, he had generated 12 distinct notes, forming the foundation of the modern 12-note scale.

But there was a problem. His system assumed that 12 stacked fifths would land perfectly on the 7th octave. Mathematically, that would mean (3/2)¹² = 2⁷. But that’s not true. In reality, (3/2)¹² ÷ 2⁷ ≠ 1. It equals 531441/524288, or about 1.0136. This tiny discrepancy is called the Pythagorean comma. While small, it causes big problems in music, especially when you play across multiple octaves. The result? Awkward, dissonant intervals like 262144/177147, known as the Wolf Interval, which supposedly sounds pretty terrible to the ear.

Pythagoras tried to fix it by using other neat ratios like 6/5 and 9/8, but he kept hitting the same wall: you can’t multiply a fraction a set number of times and expect it to equal a clean power of 2. So early musicians had to make do. They literally avoided playing certain notes together depending on the key they were in. Imagine G♯ sounding slightly different every time you played in a different key and instruments having to be tuned for just one key at a time. It must’ve been a nightmare.😵‍💫

Then came the game-changer: irrational numbers.

Musicians adopted the Equal Temperament Scale, which divides the octave into 12 equal parts using powers of the 12th root of 2 (¹²√2). So instead of ‘do’ to ‘sol’ being exactly 3/2, it’s approximately (¹²√2)^7, which is close enough to sound harmonious. And now, G♯ is always G♯, no matter the key. Problem solved. Phew!😪

Thanks to equal temperament, keyboard instruments like the piano were invented, and they exploded in popularity. Soon came other keyboard instruments: the harpsichord, the massive pipe organs in cathedrals, and even the modern electronic keyboard. They all work more or less the same way. And today, we’ve even got futuristic ones like the Seaboard, the newest and most expressive evolution in the keyboard family.

And there you have it, how music was invented. Wild, right?