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Where is the Middle C (Sunday, 10 May, 2025)


According to the MIDI 1.0 (and 2.0) standard, the middle C on a piano keyboard is MIDI Note Number 60. However, the MIDI standard does not define the corresponding octave, which can be C2, C3, C4, or C5.

The following equation gives the frequency (Hz) of the n^{th} key on a standard piano with the 49th key tuned to A_4 at 440 Hz:

    \[ \boxed{ \!\begin{aligned} f(n) &= \left( \sqrt[\leftroot{-2}\uproot{2}12]{2} \right)^{n-49} \times 440Hz \\ &= 2^\frac{n-49}{12} \times 440Hz \end{aligned} } \]

On the 88-key piano keyboard the middle C (designated as C_4 in Helmholtz pitch notation) would start the fourth octave (key number 40, corresponding to MIDI note number 60. The C_4 is approximately 261 Hz). However, someone playing a flute with a narrower and higher range may denote C_5 (523 Hz) as middle C. Therefore, some have argued to standardize C_4 as the middle C.

Image. An 88-key piano, with the octaves numbered and Middle C (cyan) and A440 (yellow) highlighted. Copied from Wikipedia.

 

Table 1. Middle C defined as C3

MIDI Note Number  Note name
127 G8
120 C8
60 C3 (middle C)
24 C0
0 C-2

 

Table 2. Middle C defined as C4

MIDI Note Number  Note name
127 G9
120 C9
60 C4 (middle C)
12 C0
0 C-1
Published On: May 10th, 2025Last Updated: May 10th, 2025Categories: Musical DiaryTags: ,