# Is there the exact same frequency-multiple between any-2 successive keys in any keyboard-instrument?

The pattern of key arrangement in harmonium/keyboard/piano is like this:

, where I can see 2-types of condition between 2 successive keys.

1: black to white (or white to black) (say their freq. (Hz) is X-times different)

2: white to white (say their frequency is y-times different)

(3: There is no 2 black side by side)

Now is x = y ? i.e the frequency-multiplier between any-2 successive keys are same?

I can't conclude this by judging it through ear; because just like each x sounds the same to each y; from this pattern, if I play only the white-keys; still I sense there difference as the same (i. e m=n); and if I play only the black-keys, I sense (hear) their difference as same, too (i.e. u=v).

(what a bizarre illusion!!! hats of to who designed the scale)

Now any 1 of them is correct. which one?

P.S. As well I'm not a musical person and never learnt music. so please elaborate/hyperlink about terminologies.

• Isn't this where 12edo (12et) comes in? But not the same frequency difference but ratio. Frequency difference just can't work.
– Tim
Commented Oct 1, 2016 at 17:18
• That would be more in line with what you're trying to establish.
– Tim
Commented Oct 1, 2016 at 18:48
• The downvotes are likely coming from the fact that you'd invented an idea and then asked about that idea, rather than asking directly about the underlying relationship between notes. It is also quite hard to follow since your graphic and wording seems to be related to the physical distance between keys on the keyboard -- which is both varied and meaningless from a theoretical standpoint -- instead of with regard to actual notes.
– user28
Commented Oct 2, 2016 at 3:40
• There is also zero innate different between white notes and black notes; it's purely to aid playing, which is why other instruments played differently do not have such an obvious distinction between adjacent semitones. There are even keyboards where every key is physically identical. TL;DR: Make fewer assumptions, and start your questions from a more basic level while you learn!
– user28
Commented Oct 2, 2016 at 3:41
• As for the ratio of 2: A note and its octave differ by a factor of two. In your diagram, the white key furthest to the left has a frequency that is 1/2 of the white key 3rd from the right, etc.
– user28
Commented Oct 2, 2016 at 3:44

In almost all cases the tuning standard for modern keyboards is 12-tone equal temeperament. This has the feature that the frequency ratio between two successive (chromatic) notes is `2^(1/12)` approximately 1.05946309435. Our ears, to a good approximation, hear pitch as the logarithm of the frequency, so each black-to-white (or white-to-black, or between two adjacent white keys w/o a black between them) seems like the same step size.

Due to the characteristics of their strings, in practice the tuning of pianos does not exactly conform to 12-TET, in order that the pianos actually sound good.

Most synthesized sounds more accurately conform to the standard.

• Whilst this answer relates well to modern 12edo tuned instruments, it's actually not a complete answer. More to come, I expect. Even pianos are not tuned to agree with this!
– Tim
Commented Oct 1, 2016 at 17:34

Another thing to consider about pianos is that most of the notes have multiple strings. I believe each string is also tuned slightly differently to make the notes fit better in relation to different key signatures.

• Check your information source. I think eac of the 2 or 3 strings on a particular note need to be the same pitch, otherwise there will be some beating occurring, which is not necessarily a good sound for a piano note.
– Tim
Commented Oct 2, 2016 at 9:30