Beats vs cycles vs cents

[Richard Brekne]

Don Gilmore wrote:

> Sure you do, Ric.  Cents are what it's all about.  Cents ARE what you 
> perceive in pitch.  Being off 100 cents takes you to the next note.  50 
> cents takes you half way there, no matter what note you're on.  Ten 
> cents out of tune sounds like ten cents out of tune, no matter what your 
> beat frequency is.  As you said, there are minor discrepancies when 
> tuning, but you are pedantically missing the point. 
>  
I beg your pardon... but I rather think its you who are missing the 
point Don. Cents are NOT what we percieve in pitch. We arent listening 
to sign waves here.  Musical sounds are comprised of many frequencies 
that only loosely correspond to any mathematicl idealizations. Even a 
<<simple>> pianostring is so complex its quite silly to speak of it in 
terms of having a cents degree or offset or value unless one qualifies 
that by relating to which partial you are talking about. When we listen 
to a piano string vibrating... we are not listening to one partial... or 
even getting a sense of a single pitch. Nor is a single note in tune or 
out of tune unless it can be related to other notes.... These 
relationships have to do with prefered amounts of tension between 
notes... not a comparison to some chart of numbers. In tune-ness is from 
the get go a subjective matter. Cents is only a convienient way of 
placing pitch on a reference scale. It has in itself nothing at all to 
do with musicality or pitch perception.  By way of simple example... 100 
cents does not take you all the way to the next note.  Not really even 
in ET because there are not real ideal strings to begin with. And that 
doesnt even address tuneings that do not space semitones rougly at 100 
cents.


> Using beats to tune a string is just a convenient crutch.  It wouldn't 
> do you much good when tuning a solo clarinet, would it?  To tune an A0 
> (27.5 Hz) to a beat frequency of one cycle per second in comparison to 
> another A0 string would require it to be at 27.5 + 1 = 28.5 Hz. 

So why would anyone do that ? the practicle tuning instruments of all 
sorts has been done in all maner of fashion through time. But in the end 
it is the interaction between two or more notes that becomes the 
determinant for what we decide is <<tuned>> in any given perspective.

> This is 
> 62 cents sharp!  That's wayyyyy off.  It's closer to Bb!  And 62 cents 
> sharp sounds just as bad for A0 as it would for C7, or A-440, or any 
> other note.  

If its waaaaayyyy off its because it sounds bad to our ears... so we 
adjust the tone so that it sounds better... and then we measure that 
pitch in relation to other measured notes and put it a number we call 
cents, or Hz, or whatever unit we choose too use for any given 
application with which to reference this with.  Its not the other way 
around.
>  
> For comparison, a beat frequency of 1 Hz for C7 only means it's less 
> than half a cent off!
>  
In relation to what ??... its all relative to begin with.

> Beats are a phenomenon related to the *difference* in frequency 
> (subtraction); cents are a phenomenon related to the *ratio* of 
> frequencies (division), which is what music itself is based on.  Sure, 
> you can hear beats, but as you can see it really has no relationship to 
> what you hear pitch-wise at all.
>  

I am well aware of what beats are... and as you can see... I totally 
dissagree with your position here.  Beats, the interaction between 
various partials of two or more notes is precisely what pitch perception 
is all about. A note is sharp if it sounds too tense in relationhip to 
certain other notes... it sounds tensse because of this phenomenon.

Sorry... I dont buy the numbers game here Don.

Cheers
RicB

> Don A. Gilmore
> Mechanical Engineer
> Kansas City 
>  
>  
>  > I really have to take issue with this. No one <<percieves>> cents at
>  > all.  Our perceptions of out of tuneness have far more to do with how
>  > "clean" any given interval relationship sounds, or how close any
>  > interval is to what we expect of it. This is exactly beat related.
>  > Cents is an idealization, a mathmatical representation or modeling of
>  > musical pitch. There is no musical way of defining <<in tuneness>> based
>  > on cents to begin with. Only close approximations.  Beats are used both
>  > individually and whollistically to create a musical effect... the very
>  > best tuners know exactly what kind of vibrational effects they want a
>  > piano to send out through the air for each interval and are very good at
>  > achieving these. Many tuners I know speak of a the overall <<tone>> of a
>  > tuning.... in kind of voicing sense. <<Voicing>> through tuning is a
>  > mulitpartial prospect to begin with, which removes it from a simple
>  > cents perspective from the get go.
>  >
>  > 100 cents is not always a half step in real piano frequencies.... it is
>  > at best only a half step for one partial at a time.  Pitch perception is
>  > a conglomerate of all partials, their relative loudness, and a good deal
>  > more.
>  >
>  > Cheers
>  > RicB
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