Tones

Piano keys

Only a limited set of frequencies is used in music. All these frequencies (that exist in music) can be played by a piano. In other words, whenever some instrument plays some tone, there is a piano key, which plays the identical tone (of the same pitch). To describe tones that exist in music, we can describe tones that exist on a piano. There are only two rules:

  • the first key must play a tone of 27.5 Hz
  • each next key must play a tone 6% higher than the previous key

Try to play a virtual piano below! Use dots to drag it.

Observation

If we increase any number by 6% twelve times, we double it.

  • The first key plays 27.5 Hz. Move twelve keys to the right (13th key), and we have 55 Hz. Twelve more keys, and we are at 110 Hz, 220 Hz, 440 Hz, 880 Hz, and so on.
  • At any piano key, to play a 2x higher frequency, we move 12 keys to the right. To play a 2x lower frequency, move 12 keys to the left.
  • The 23rd piano key plays 98 Hz, followed by the 24th key - 103.83 Hz. You can never hear a tone of 100 Hz or 102 Hz in any music (as there are no keys between the 23rd and the 24th piano keys).

Key names

Each frequency that is used in music, i.e., each piano key, has a name. These names are a little confusing, as they have been "evolving" for centuries.

The first piano key is called "A". Keys are named in a "circular fashion": only 12 keys have names, and then, these names repeat. These names are:

A  A#  B  C  C#  D  D#  E  F  F#  G  G# (the symbol "#" is pronounced as "sharp")

You should learn these twelve names as they go, one by one. If you start at F, and move seven keys to the right, you end up on ... C (you should be able to count it in your head). If we start at E and move three keys to the left, it is the same as moving 9 keys to the right (12 - 3 = 9).

To have unique names, keys are also numbered, but the numbering starts from the first C, which is named C1!!! The first three piano keys are called A0, A#0 and B0. Let's write down full names:

A0  A#0  B0  C1  C#1  D1  D#1  E1  F1  F#1  G1  G#1  A1  A#1  B1  C2  C#2  D2, ...  A#2  B2  C3 ...

Observation

  • A name such as D refers to many keys (frequencies) D1, D2, D3 ..., but they are all "related" (one is double of another).
  • Keys with "sharp" in their name are painted black on a piano.

First Song

Let's play our first song, Happy Birthday To You! Simply press the keys on a piano (you can use a real one if you have it near you). You can start playing from the G2 as the lowest tone (G = G2, A = A3, ...).

 G  G  A  G  C  B
 G  G  A  G  D  C
 G  G  G  E  C  B  A  (you can play the third G 12 keys higher than the first two)
 F  F  E  C  D  C

You can try to play it from G3 (i.e., a double frequency of all tones), or G4, G5, and so on. Does it still sound like Happy Birthday To You?

Do you need help? Ask us at our Reddit!