I’m sure this has been asked before, but I couldn’t find anything online. Are there notes in-between the piano keys? And if so, why are they never used? Do they sound terrible? I’d love it if someone could clear it up. Thanks!
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I wrote some of this for a friend a few months ago. It explains the mathematical relationships between some of the notes.
This page is a table of the frequencies of the notes as a piano is laid out.
http://pages.mtu.edu/~suits/notefreqs.html
The note A4 (440 Hz) is the standard, kind of like 0° F or 0° C is a standard. It’s convenient to count from somewhere, and A4 (440Hz) is where musicians count from.
Here’s the interesting thing:
If you double 440 you get 880.
A4 is 440Hz. Double that is A5 (880), which is the same pitch, but one octave higher.
A5:A4::2:1
(does that make sense? A5 is to A4 as 2 is to 1?)
If you picture a line from point Y to point Z, you could represent A4 as a single hill, and you could represent A5 as a hill that goes exactly halfway from Y to Z, and a mirror-image valley that goes the rest of the way from Y to Z. A full sine wave. The A5 hill is exactly half the length of the A4 hill. The A5 hill is a 1/2 ratio to the A4 hill.
**Here’s the next interesting thing:**
Simple adjacent ratios produce other pleasing note combinations.
Here are the first few simple adjacent ratios:
2:1
3:2
4:3
5:4
6:5
These ratios form the basis of music theory.
2:1 is called an octave. A5:A4, for example. 880:440
3:2 is called a perfect fifth. E5:A4. 660:440
4:3 is called a perfect fourth. D5:A4. 586.66:440
5:4 is a major third. C#5:A4. 550:440
and 6:5 is a minor third. C5:A4. 528:440
https://en.wikipedia.org/wiki/Interval_(music)
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