Interactive theory · Lesson 2
The Twelve Semitones: Semitones and Whole Tones
Semitones are the "ruler" of music theory. Divide an octave into 12 equal parts, and you can measure all pitch relationships.
Did you know · Last time we said: one octave = two notes where the frequency doubles (e.g., C4 and C5); Hz means "vibrations per second" (440Hz = 440 vibrations in 1 second). Today, let's clarify how this "doubling" is divided into 12 steps—and why pianos have 7 white keys + 5 black keys, and why there is no black key between Mi and Fa (and why you can't find a "semitone above Mi")?
There are 12 semitones in one octave, each step being equal distance. Adjacent keys = semitone; skipping one key = whole tone (= 2 semitones). Counting from C4 to C5 gives you a feeling of "climbing stairs":
Try it
Why 7 white + 5 black? The 12 semitones were defined mathematically first (dividing an octave into 12 equal parts); "which 7 become white keys" was a design choice made by piano makers 300 years ago—they chose the 7 notes of C Major (C D E F G A B).
↑ "C Major" = pieces that use C as Do (the most common/simplest key); these 7 notes are its "family members" (we'll discuss "keys" in detail in Lesson 7).
The distances between these 7 white keys: 5 whole tones + 2 semitones.
- 5 whole tones (C→D, D→E, F→G, G→A, A→B): Each pair has a black key "inserted" in between as a semitone
- 2 semitones (E→F, B→C): These pairs are already adjacent, with no space for a black key—their distance is itself a semitone
Key point: The distance E→F = 1 semitone (not "no semitone"—it means "the distance is a semitone, but there's no black key in between"). So Mi (E) "a semitone up" = Fa (F)—on the piano, you won't find a key named Mi#; that position is simply the Fa white key (similarly, Si (B) "a semitone up" = Do (C), so there is no key named "Si#").
Whole tones can also fall on black keys: A whole tone above Mi is Fa# (path: Mi→Fa is a semitone, Fa→Fa# is a semitone, totaling 2 semitones = whole tone)—Fa# is a black key. So "white/black key" refers to color/appearance, while "semitone/whole tone" refers to distance—two different things, regardless of whether the landing spot is white or black.
Why are white keys long and black keys short? The 5 notes are "inserted" into the gaps of the white keys—so they are made shorter and set further back (black keys); the 7 white keys lie flat at the front, so they are longer.
↑ "C Major" = pieces that use C as Do (the most common/simplest key); these 7 notes are its "family members" (we'll discuss "keys" in detail in Lesson 7).
The distances between these 7 white keys: 5 whole tones + 2 semitones.
- 5 whole tones (C→D, D→E, F→G, G→A, A→B): Each pair has a black key "inserted" in between as a semitone
- 2 semitones (E→F, B→C): These pairs are already adjacent, with no space for a black key—their distance is itself a semitone
Key point: The distance E→F = 1 semitone (not "no semitone"—it means "the distance is a semitone, but there's no black key in between"). So Mi (E) "a semitone up" = Fa (F)—on the piano, you won't find a key named Mi#; that position is simply the Fa white key (similarly, Si (B) "a semitone up" = Do (C), so there is no key named "Si#").
Whole tones can also fall on black keys: A whole tone above Mi is Fa# (path: Mi→Fa is a semitone, Fa→Fa# is a semitone, totaling 2 semitones = whole tone)—Fa# is a black key. So "white/black key" refers to color/appearance, while "semitone/whole tone" refers to distance—two different things, regardless of whether the landing spot is white or black.
Why are white keys long and black keys short? The 5 notes are "inserted" into the gaps of the white keys—so they are made shorter and set further back (black keys); the 7 white keys lie flat at the front, so they are longer.
Try it
Mi# objectively exists; it is exactly the Fa white key.
Since E and F are already adjacent (no black key in between), the position a semitone above E is the F white key—the piano calls it Fa, not Mi#. So Mi# = Fa (the same white key, two names), just like C# = Do# = Re♭.
Don't confuse them: Fa# is the black key above Fa (located between F and G)—it has nothing to do with Mi.
Reference table for 12 semitones (Note Names / Solfège within one octave):
↑ Same column = same note, just different names. Octave numbers follow: C4=Do 4 (Middle C), A4=La 4=440Hz (440 vibrations per second), C5=Do 5 (one octave higher).
The 12 semitones came from "math" first, then "instruments": The piano has 12 equally spaced keys (like an elevator); the violin has 4 strings and a fretless fingerboard (like a slide, continuous and smooth)—both can reach those 12 positions (Lesson 4 covers the violin's four strings specifically).
Want to go deeper? Lesson 8 explains "if you change the starting key, the naming changes too."
Since E and F are already adjacent (no black key in between), the position a semitone above E is the F white key—the piano calls it Fa, not Mi#. So Mi# = Fa (the same white key, two names), just like C# = Do# = Re♭.
Don't confuse them: Fa# is the black key above Fa (located between F and G)—it has nothing to do with Mi.
Reference table for 12 semitones (Note Names / Solfège within one octave):
| C | C# | D | D# | E | F | F# | G | G# | A | A# | B |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Do | Do# | Re | Re# | Mi | Fa | Fa# | Sol | Sol# | La | La# | Si |
The 12 semitones came from "math" first, then "instruments": The piano has 12 equally spaced keys (like an elevator); the violin has 4 strings and a fretless fingerboard (like a slide, continuous and smooth)—both can reach those 12 positions (Lesson 4 covers the violin's four strings specifically).
Want to go deeper? Lesson 8 explains "if you change the starting key, the naming changes too."