MIDI & equal tempered scale -the relation & effect

When we make music, we need to define a set of tuning-frequencies. Such a set of frequencies often called a scale. Before get into the topic MIDI & equal tempered scale we will discuss on basics.

In western music, the most popular scale is the equal tempered scale which is based on starting at some reference-frequency. The equal tempered scale is relatively fixed scale used for the tuning of pianos and other instruments.

Example : (frequency) f = 440Hz

This anchor frequency has been assigned the musical pitch name for example A1, A2, A3 etc.

You can find the real example in Piano with various scale where each key has different frequecy and pitch.

An octave is the difference in pitch between two notes where one has twice the frequency of the other.

The octaves come out as A1 = 55Hz, A2 = 110Hz, A3 =220Hz, A4 = 440Hz, A5 = 880Hz ect.

MIDI & equal tempered scale relation

To subdivide the octave, the number 12 was chosen. Intervals of that subdivision interval are called semitones and a frequency which is a factor

c = ¹²√2 times

The representation of pitch in the MIDI-standard (Musical Instrument Digital Interface) is directly based on the equal tempered scale and defines 128 (numbered from 0 to 127) possible values for note-pitches.

The frequency 440Hz is represented in MIDI by the note-number 69, and each whole number codes one semitone, such that the MIDI-representation of A3 (which is an octave below A4) is 69 − 12 = 57.

In general, if we denote the pitch in terms of a MIDI note number as p and the frequency in Hz as before with f, the formulas for converting between pitch and frequency become:
p = 12 · log2(f/440) + 69