# Piano Key Frequency and Micro Tuning

## Equal Temperament Tuning (Standard Tuning)

on a piano, each adjacent key (color doesn't matter), from left to right, their frequencies forms a geometric sequence. The scaling factor is 2^(1/12)≈1.05946.

Here's the standard tuning:

## Micro Tuning

Micro tuning means change the pitch of each key so that the scaling is less than 2^(1/12).

here's a video of micro tuning.

## Naming of the Keys

the white keys are labeled A B C to G. Starting with C on the left most white key of the 2 black keys group.

black keys don't have a name by themselfs, but is named relative to adjacent white keys. A black key to the right of a white key (say C) is called C♯ (sharp), or D♭ (flat). Basically, ♯ is used to jump to the right.

## What is a Semitone (aka half-step), Whole Tone, Octave

- Semitone basically means adjacent keys. (color of the key doesn't matter.)
- A whole tone, is 2 semitones.
- An octave, is 12 semitones. in standard turing, it means the pitch frequency doubles or halves.

## The Middle C Key and Concert A Key

move hand to somewhere in the middle and find the closest C key, that key is called **Middle C**, and find the A key above it.
That A, is called **Concert A**.
By standard tuning, that A key, has a frequency of 440Hz.

now, the western music scale is such that, every 12 intervals, the frequency doubles. So, when you find the middle A key (which has frequency 440Hz), the next A to the right, has frequency 880Hz.

since Bach's The Well-Tempered Clavier (1722), we have “equal temperament”
tuning.
Adjacent keys frequency differ by a constant multiplicative factor.
e.g.
Key A has frequency 440Hz.
The key right of it has frequency `440*c`

, where `c`

is a constant.
then, next to it is
`440*c*c `

,
then, next to it is
`440*c*c*c`

,
etc
, till 12 keys after it we have
`440*c^12`

, and should be 880Hz.
`440*c^12==880`

.
So
`c = 2^(1/12)`

## Why the Black Keys?

on a piano, you might wonder why the black keys? why not all just white keys? well, lots history, but basically, the function of the current irregular shape (the 2/3 groups of black keys jutting out) is so that it's easier for fingers to find keys by touch.

on a piano, since key's frequencies is regular by a factor, why are they named irregularly C C# D D# E F F# G G# A A# B C. (those with # are black) Why not A to L? again, history. Like programing language syntax and math notations, most are result of hundreds years of habit, convention, from gradual evolution.