Beats vs cycles vs cents

[Don A. Gilmore]

Music is based on ratios between frequencies, not differences between
frequencies (as with beats).  If you think that cents are some sort of
finite size and are used strictly for academic argument, I am very
disappointed in you.  Cents express a *ratio* which is what you hear in
music.

The musical interval of an ET minor third is 300 cents.  It's always 300
cents.  It's 300 cents whether you start on middle-C, or on A0, or on Gb7.
Your ears hear an interval as an ET minor third when two notes--any two
notes--are 300 cents apart.  Yes you can hear cents!  And yes they describe
actual, perceived musical pitch regardless of frequency!  You can tell a
minor third can't you?

Don A. Gilmore
Mechanical Engineer
Kansas City

----- Original Message ----- 
From: "Richard Brekne" <Richard.Brekne@grieg.uib.no>
To: "Pianotech" <pianotech@ptg.org>
Sent: Tuesday, March 16, 2004 2:32 PM
Subject: Re: Beats vs cycles vs cents


> 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
> >  > _______________________________________________
> >  > pianotech list info: https://www.moypiano.com/resources/#archives
> >  >
>
> _______________________________________________
> pianotech list info: https://www.moypiano.com/resources/#archives