calculating beats

Hi, just a quick question. I figure someone on here will know the
answer.
Is there a formula to use for calculating how many beats per second
will be heard when tuning two given frequencies?
Given two pitches of say 352 and 443 how many beats will a person
tuning this interval hear?

thanks John

--- In tuning@y..., "johnsteven51" <johnsteven51@y...> wrote:
> Hi, just a quick question. I figure someone on here will know
the
> answer.
> Is there a formula to use for calculating how many beats per
second
> will be heard when tuning two given frequencies?
> Given two pitches of say 352 and 443 how many beats will a
person
> tuning this interval hear?
>
> thanks John

let's assume you mean a harmonic timbre, such as bowed
string, brass, wind, or human voice.

the first thing you need to know is the *ratio* that this
approximates.

there are actually *several* beat frequencies always present, but
the *relevant* one to listen to when tuning depends on the ratio.

so, let's assume that you *mean* a 5:4 ratio here.

then simply multiply the lower note by 5, and the higher note by 4
(giving you the frequencies of the harmonics that are near to
each other) and take the difference.

so 352*5 = 1760, and 443*4 = 1752. 1760-1752 = 8.

therefore, the interval will beat 8 times per second.

make sense?

--- In tuning@y..., "johnsteven51" <johnsteven51@y...> wrote:
> Hi, just a quick question. I figure someone on here will know the
> answer.
> Is there a formula to use for calculating how many beats per second
> will be heard when tuning two given frequencies?
> Given two pitches of say 352 and 443 how many beats will a person
> tuning this interval hear?
>
> thanks John

Are you tuning a piano? an organ? a harpsichord? A computer? Helmholtz
defined beats as combination tones which cause interference. For simple
tones he restricted use of the term "beats" to fundamentals differing by
about 30 Hz or less. Without knowing the timbre there is no way to calculate
beats other than those produced between fundamentals, which amounts to a
first order difference tone f1-f2.

The example of 443-352 simple tones gives nothing called "beats" by the
Helmholtzian definition, because the difference is 91 which is greater than
the cutoff of around 30 for "simple tones." It's more complicated than that
because "simple tones" don't generally exist.

A good way to learn about beats with a computer is to pick some interesting
timbres and just start listening intently for beats in sustained random
intervals < 2/1. Some intervals will seem to have fewer beats with one
timbre but will have more beats with another (though relationship between the
two should be evident.) With complex timbres, for the majority of intervals
you will hear layers upon layers of beats which change according to the
timbre you use. If you try calculating beats according to combination tones
occuring between prominent harmonics of some of the timbres for intervals
which have a beating patterns that you like, you will begin to understand the
great mysteries of the beats.

Aaron