[Harp-L] Semitones Cents and what not.

[Arthur Jennings]

> On Feb 10, 2019, at 1:22 PM, Aongus Mac Cana <amaccana at xxxxx> wrote:
> 
> 
> What is a semitone?
A semitone is the smallest musical interval commonly used in Western tonal music. It is defined as the interval between two adjacent notes in a 12-tone scale. For example, C is adjacent to C♯; the interval between them is a semitone.

> Is a musical scale a geometric progression where each
> step represents a percentage increase or decrease on the frequency in Hz of
> the note you start with?
Yes.

> I have been told that the octave of every note is
> twice the frequency of the note in question. Consequently if A4 is 440Hz A5
> must be 880Hz A6 1760Hz and so on ad infinitum.
That is correct.

> What bothers me is that a semitone cannot therefore be expressed as a simple
> frequency difference. The higher you go up on the harmonica or a keyboard
> the bigger the frequency difference between one note and the next.
It's a ratio, not a "simple frequency difference". The frequencies between notes increase or decrease logarithmically, not arithmetically.

In equal temperament the ratio difference between notes a semitone apart is the twelfth root of two, approximately 1.05946.

> Then what
> about these Cents that the "experts" throw about with such abandon? As in:
> "I tune all reeds a few cents high to allow for the fact that they will go a
> bit flat when actually played".
A cent is 1/100th of a semitone. In ET that is a ratio of the 1200th root of 2.

> Can Cents be expressed in Hz higher or Hz
> lower?
No, just like semitones, they are a logarithmic increase.