Re: Re: [Harp-L] harp tuning

["Tim Moyer" <wmharps@xxxxxxxxxxxxxxxxxxxx>]

James Sterett wrote:
> In regard to the cents, would you explain a bit further... how is 
> a cent calculated in the A4XX tuning scheme?  Meaning, if A442 = 
> +08, what does +02 equal? etc.  Also, does A440 always = +00?

The number of hertz between notes varies as you move up and down the 
scale.  The number of cents never does.  Cents is more like an 
expression of a difference in pitch by percentage: 100% (100 cents) 
equals a semitone.  The number of hertz between two semitones will 
vary with where they lie on the scale.  

Here's a quick example: A3 to A4 is 1200 cents (100 cents x 12 
semitones), and is 220 hertz (A220 to A440, one octave).  A4 to A5 
is 1200 cents (100 cents x 12 semitones), and is 440 hertz (A440 to 
A880, one octave).  A5 to A6 is 1200 cents (100 cents x 12 
semitones), ans is 880 hertz (A880 to A1760).  In each case an 
octave is 1200 cents, but the number of hertz doubles.  You can see 
that any particular number of cents will equal a different number of 
hertz at different points on the scale.  

As for A440 equaling +/-0 cents, this depends on what we use for a 
reference pitch.  Most modern instruments and tuners use A=440 as a 
standard reference, but in the case of harmonicas it's usually 
higher, like A=442 or A=443 because some flattening of pitch occurs 
as we play harder.  I prefer to offset my reference in cents, 
because it makes it easier to add the offsets.  I use A=440 +10 
cents as a standard reference pitch, and normalize the offsets to 
that.  I could also choose A=442 (approximately +8 cents) or A=443 
(approximately +12 cents) and use all the offsets relative to zero.

I hope this makes some sense.

-tim

Tim Moyer
Working Man's Harps
http://www.workingmansharps.com/