Scales – Finding Good Sounds

First, ask yourself: why does music sound “good”? Every day we are surrounded by all kinds of noises—car horns, office keyboard clicks—yet these sounds are not as “pleasant” as music. Why?



These questions lead us to the topic of “scales” in music theory. Scales are also what TV talent shows call “keys” or “modes”; they are the bedrock of music.



Recall junior-high physics: sound is produced by vibration. The faster an object vibrates, the “higher” the pitch. A bee flaps faster, the buzz sounds “higher” and harsher.



So “pitch” is essentially vibration frequency.

Human ears are naturally fond of certain frequencies. The underlying principle of music is that simple. As mentioned in the prologue, ancient people found that striking specific pitches sounded “nice”, but they only had empirical knowledge, no standards or rules. Random trial-and-error produced uneven quality and low efficiency, so people began searching for standards and patterns to create pleasant, smooth music.

Generations explored and passed down experience, discovering that if the pitches within a set obeyed certain ratio relationships, the music felt harmonious and smooth. We call such a set a “scale”.

Most people first meet the “Do-Re-Mi-Fa-Sol-La-Ti-Do” scale (numbered 1 2 3 4 5 6 7 1 in cipher notation).C4D4E4F4G4A4B4C5. Click the note blocks on the left to feel the pitches within this scale.



You may wonder what the letter C and the number 4 in C4 mean.

Besides inventing “scales”, our predecessors also created “note names”. As said, pitch is fundamentally “frequency”; higher frequency sounds sharper, lower frequency sounds deeper. We name specific frequencies for convenience—e.g., 440 Hz is called A. If two pitches’ frequencies differ by exactly double, e.g. 261 Hz C4 and 522 Hz C5, the distance between them is an “octave”. The number after C4, C5 etc. means the right note is one octave higher; they sound like the same pitch class. Click “play” below to feel the consonance of notes an octave apart:

Inside this octave we pick a note every certain interval. The first note is C4; the second note’s frequency is 1.06× the first C#4 (“#” means raise a semitone, “b” means lower), the third is 1.06× the second D4, and so on, giving 12 notes (1.06 is approximate; search “12-tone equal temperament” if curious). The distance between two pitches is called an “interval”; the smallest interval in modern music is a “semitone”; its frequency ratio is ~1.06. A “whole tone” is 1.06×1.06. No need to memorize the numbers—just grasp the idea.



Feeling dizzy? That’s normal—dizziness means knowledge is swirling in your brain. If anything is unclear, ask the AI helper at the top 🤖



Continuing the 1.06× calculation until the last note’s frequency is double the first (the “octave”) yields the 12 standard pitches of modern music: C, C#, D, D#, E, F, F#, G, G#, A, A#, B. “#” is sharp, raising a note by a semitone; E-F is already defined as a semitone (many such “rules” exist in music—no need to over-think). Listen to these 12 notes:

The highest note above is B4; adding one more semitone lands on C5, entering the next octave.



But these are all letter names ABCD; how do they relate to the 1 2 3 4 5 6 7 we started with?

Note names are fixed labels for individual pitches; 1 2 3 4 5 6 7 is a scale, a set of relationships—it’s dynamic. When you hum 1 2 3 4 5 6 7, no matter which pitch you start on, it feels “the same” because a scale is about the intervals between notes. As long as the interval pattern is identical, you’re singing the same scale; you can let 1 be C, D, or anything you like.



Natural major scale when 1 = C; the pink row shows scale degrees, dark pink marks 1:

Natural major scale when 1 = D:

Don’t they look like stair “steps”?

1 2 3 4 5 6 7 1 (major scale) is simply a set of pitches obeying this pattern:





Animation:



You should also realize that the absolute pitch of a melody doesn’t matter; what matters is the “intervals”. As long as the intervals are identical, it sounds similar. Scale degrees have specific interval relationships, proven by predecessors to be harmonious and pleasant.



But scales aren’t limited to “1 2 3 4 5 6 7”. Pleasant pitch sets are countless. The Chinese-sounding “pentatonic scale” is “1 2 3 5 6”. Try clicking these notes at will C4D4E4G4A4C5—whatever random clicks still feel “Chinese”. Different places and eras breed different scales, each with a unique flavor: the pentatonic sounds grand and open, while the Japanese pentatonic sounds dark and winding C4Db4F4G4Ab4C5. Many more scales exist—minor, Phrygian, Dorian, etc.—but the major scale “1 2 3 4 5 6 7” is the most widespread and versatile, so it’s our default.



A “scale” is only a standard and a rule, yet beyond rules lie infinite possibilities. Creating within a scale is easy, fast, and stable, but confining ourselves is never humanity’s goal. We explore new scales, fuse different ones, or insert foreign notes; such changes can yield unexpected effects. All progress follows the cycle: discover rules → break rules → discover new rules. If you find a set of pitches that sounds good, you have created your own scale.



There are infinitely many pitches, but with scales we know which ones sound good, instantly reducing the choices for composition! Next we’ll learn how to use scales to create melody➡️/post/basic/rhythm