The equal temperament commonly used in Western music divides an octave evenly into 12 semitones. No matter where you start on the piano keyboard, the ratio of the frequency from one note to its right neighbor (e.g., C to C#) is $2^{1/12}$. With the semitone as a unit, we can think of the distance between notes as a simple number relationship.


On this page, we will consider intervals between notes by focusing on number relationships rather than general music theory. Reading this probably won’t make you better at playing instruments or writing good music too much, but it may change the way you look at instruments and scores a little.


<aside> 💡 ここから先、音の名前の表記にはアルファベットを用います。Cがド、Dがレ…Gがソ、Aがラ、Bがシとなります。イロハニホヘトがABCDEFGに対応すると考えてもOKです。ハ長調はCメジャースケール、イ短調はAマイナースケールです。


Let’s begin with the C major scale, with only the white keys of the piano played in order from C. This scale has a number sequence of semitones between notes: 2, 2, 1, 2, 2, 2, 1. To make it easier to see that the notes are evenly spaced and circle back to the same note an octave above, we will visualize them in a circle.

まずはCメジャースケール、ピアノの白鍵だけをCから順番に弾いた音階から始めます。この音階は音と音との間の半音の数が2, 2, 1, 2, 2, 2, 1という数列になっています。音が均等な幅で並んでいて、一周するとオクターブ上の同じ音に戻ってくることが分かりやすいように、円の上に視覚化してみます。

Diatonic Chords ダイアトニックコード

For each note from the C Major Scale as a starting note(root), add a note two steps away on the scale, then one at another two steps. The resulting chords are called diatonic chords of the C Major Scale.


If you look closely, there are only three combinations of the number of semitones: (4, 3), (3, 4), and (3, 3). Each of these is called a major chord, a minor chord, or a diminished (minor ♭5) chord.

よく見ると半音の数の組み合わせは (4, 3)、(3, 4)、(3, 3) の3パターンしかないことに気がつきます。それぞれをメジャーコード、マイナーコード、ディミニッシュ(マイナー♭5)コードと呼びます。