Scientific Notation of Pitch in Music

Music started off with a simple set of notes that sounded good when played together, or in any order. As music progressed, there appeared in a need to define each and every tone as unique; to assign a name to every musically significant frequency. It would allow the scientific standardization off all instruments and peg them all to an acceptable standard, such as a standard human voice. A system was proposed by the Acoustical Society of America (ASA) in 1939, where C0 was defined to be in the region of the lowest possible audible frequency (about 16.35 Hz). This was taken to be the junction of two octaves. All other notes were calculated by dividing the higher (or lower) octaves logarithmically into 12 notes. Thus the nomenclature system consisted of:

• the name of the note - viz. A, B, C....G
• the accidental character of the note - sharp, flat or natural
• the location of the note in an octave of the ASA scale with respect to the C0.

Hence the scientific notes are written as C4, D#5, A4, etc. The fact that C1, C2, C3, C4... are harmonics of C0 are maintained (they sound similar to the ear), and likewise for other notes too.



Important notes used in music are:

C0 – 16.35 Hz – hit by an organ;
C4 – 261.62 Hz (a.k.a. "Middle C");
A4 – 440 Hz, standard pitch for instrument tuning;
Eb0 – nearly 19.5 Hz, the lowest limit of human hearing;
A0 – Lowest note on a piano,
E2 – Sixth string of Guitar in standard tuning played open;
E4 – First string of Guitar in standard tuning played open; etc.

Important ranges used in music analysis are:

Singing Voices: (max. ranges C2 to C6)

1. Treble / Boy Soprano: C4 to A5, young male children (choirboys)
2. Soprano: F6 to A6, highest feminine voice
3. Mezzo-soprano: C6 to G3, feminine voice
4. Contra-alto: F5 to E3, heaviest feminine voice
5. Countertenor: D3 to F6, highest male voice
6. Tenor: C3 to A4, male voice
7. Baritone: G2 to F4, deep male voice
8. Bass: F2 to E4, deepest male voice

Instruments:

1. Piano: A0 to C8
2. Guitar: E2 to A6 or E6 when in standard tuning
   
3. Bass Guitar / Contrabass: E3 to E1
4. Violin: G3 to C8
5. Organ: C0 to C8 (one of the largest)

Also read: Middle C on Guitar - F above and G above middle C on a Guitar
http://basicmusictheory.blogspot.com/2009/08/scientific-notation-of-pitch-in-music.html

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Scientific Notation of Pitch in Music