Beats vs cycles vs cents

[Jason Kanter]

Ric and Don, your disagreement is more semantic than real. I beg you, don't
get into these impending fisticuffs.

Jason

----- Original Message ----- 
From: "Don A. Gilmore" <eromlignod@kc.rr.com>
To: "Pianotech" <pianotech@ptg.org>
Sent: Tuesday, March 16, 2004 1:53 PM
Subject: Re: Beats vs cycles vs cents


> 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
> > >  > _______________________________________________
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> > >  >
> >
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