# how do all the notes of the same name relate? [duplicate]

I suppose that frequencies were randomly assigned letter names

here we have A4 = 440Hz

http://www.phy.mtu.edu/~suits/notefreqs.html

C3 here = 130.81Hz

C4 here = 261.63Hz

C5 here = 523.25Hz

How is C3, C4 and C5 related? How are they all "C"?

• music.stackexchange.com/questions/44783/… may be of interest. – topo Reinstate Monica Aug 30 '16 at 7:51
• There is no fixed assignment of names to frequencies, but a concert pitch convention. A4=440 is somewhat official, but typical orchestra tune somewhat higher (441/442), period instrument ensembles possibly considerably lower (415 or even 391 Hz). – guidot Aug 30 '16 at 8:20
• Look closer at those frequencies... – el.pescado Aug 30 '16 at 8:57

They are in different octaves. They sound the same to the human brain, because it's wired this way and I have no idea why. It's a phenomenon called the Octave Illusion. Also, every upper octave is twice the frequency of the lower, as @KirkA meant, citing the powers of two.

This illusion, combined with our tendency to "like" multiples of a base frequency, brought us to define all the tones in all the musical scales. They initally all related to the base, called "tonic", frequency by a factor, then things became more complicated... because of a number of reasons. A long number of reasons.

• Might be an unnecessary answer, but I felt the need to hilight the octave illusion. – ZJR Aug 30 '16 at 1:00
• They probably sound the same because of overtones/harmonics. Which makes it make sense. – Tim Aug 30 '16 at 5:17
• @Tim, overtones do indeed enhance the so called illusion, but the phenomenon exists even with a pure sine wave. I gather most people, musicians in particular, would recognize two sine waves with one frequency twice the other as the "same" note. It is not universal, though, as this question and the number of +1 is has seem to show, so it may be a learned trait rather than a universal neuro-phsysiological phenomenon. – José David Aug 30 '16 at 9:11
• Minor correction - the base frequency is the tonic, not the dominant. – alex_d Aug 30 '16 at 9:20
• I think the proper term here is 'octave equivalency' – Michael Curtis Feb 14 at 13:38

They are all different octaves. And octave are related by frequency in the powers of two. For instance, C5 is twice the frequency of C4 -- that is, C5 = C4 x 2. And C4 = C3 x 2, and so on.

To expand on Kirk's answer, in equal temperament (the most commonly used, to my understanding), each successive note is tuned 2^1/12 Hz above the previous. Since there are 12 named notes, this means that each repeated note is twice the frequency of the previous note of the same name.

Also, in a resonance column open at both ends or a string fixed at both ends, the octave is the first overtone of the fundamental frequency. This may go some way to explain why we hear octaves as "special".

All these answers are great but I think it's helpful to remember that between C3 and C4 you always have 11 notes. Same thing between C4 and C5. You can do that forever and it will always be 11 notes between the start of one octave and the beginning of the next.