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 > > > > _______________________________________________ > > > > pianotech list info: https://www.moypiano.com/resources/#archives > > > > > > > > _______________________________________________ > > pianotech list info: https://www.moypiano.com/resources/#archives > > _______________________________________________ > pianotech list info: https://www.moypiano.com/resources/#archives
This PTG archive page provided courtesy of Moy Piano Service, LLC