Don A. Gilmore wrote: > Whether you like to believe it or not, music is mathematical. No... music is not math. That math can describe many musical relationships is a completely different matter. > The best > sounding intervals are based on simple fractions. An octave is 2:1, a > perfect fifth is 3:2, a perfect fourth is 4:3, etc. When two tones are > played together with these ratios of frequency they sound pleasant--not > because I say so, because they just do. Thats exactly my point Don... they sound good because humans are pleased by them... not because of any mathematics. The fact that these intervals correspond rougly to simple ratios is an interesting study in itself... but there is nothing in that fact that suggests that music is math. Music is what it is.... and we use math models to describe much of it. Thats as far as it goes. The very fact that people were playing music long before they had even rudimentary knowledges of math should be indicator enough to see and admit this distinction. Math is simply a descriptor of things.... as a thing in itself math is something entirely different. As for the rest of what you write.... most of us have this under our belts 20 years or more back. We all know this stuff Don. But infering that music IS math because we can use math convientiently to describe some of what music is about... is... well wrong.., IMB I repeat... none of this discounts in anyway the usefullness of cents in applications where it is appropriate. Cheers RicB > They also sound similar. So as > long as one frequency is twice the other, we hear an octave, no matter what > frequencies they are. This is simply a fact of nature; who knows why? > > To get the ratio of a fifth (3:2) you can multiply any frequency by 1.500 > and get a beautiful interval. To get another fifth above that, you can > multiply the higher value by 1.500 and get another perfectly consonant > fifth. When you do this you are performing an exponential function because > you keep multiplying. That's why the formulas are exponential, not because > of some theory foisted upon you by the scientific community. This is high > school math here, not rocket science. The formulas may seem complex to you, > but they are due simply to the fact that intervals are ratios, because your > brain *likes* simple ratios, not because of some ethereal scientific theory. > The exponential nature of music is a consequence of these fractions. > > Perhaps you are confusing this with the concept of equal temperament. From > the tonic to the dominant (do to sol) is not the only "fifth" in a key. It > should also be a fifth from re to la, mi to si, fa to do, sol to re and la > to mi. But there just is no set of fractions that can make them all come > out to the perfect 3:2 ratio (try it sometime). Equal temperament evens the > intervals out so that all of those fifths (as well as all other intervals) > that I mentioned are the same. This means that they must be at a ratio of > 1.498 instead of 1.500, but at least they are all the same now. > > The mathematical relationship between notes has nothing to do with the > historical introduction of equal temperament, or the concept of cents. It's > because we hear in ratios. Music was *always* exponential since the dawn of > man. > > And so we return to the question of how to specify how far out of tune a > note is. And cents work universally, every time. The piano is not the only > instrument tuned to ET. Nearly all instruments are. The holes in a > saxophone are sized and located to ET. If it were possible to detune a > single note on the sax by, say, 20 cents, it would sound sour. If a singer > sang a note off by 20 cents, it would sound sour. And no matter what the > note is and in what octave, 20 cents sounds exactly as sour in either case. > And in neither of these cases would you hear a single beat. > > Don > > >>Nonsense. Music is based on the total net effect two or more differing >>tones create when played together. With out a wholistic perspective to >>put tones in, a scale, or any other secquence of notes would quickly >>become meaningless and totally uninteresting... and music would never >>have become a part of our beings. >> >>Cents are a human construct that came into being looooooonnnnnggg after >>mankind began to pound his pickles. >> >> >> >>>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. > >>Welll ok... you tune your next piano so that absolutely every minor >>third is exactly 300 cents... first off you will have to choose which >>coincident pair you will space thusly... sacfricing all others to being >>something other then 300 cents, and creating a piano that will sound no >>doubt very interesting indeed... >> >>Regardless... a ET minor third ... even in the ideal.. even if you could >>get absolutely all minor thirds at exactly 300 cents is still an >>interval arrived at primarilly by listening to intervals and finding >>arrangements that humans found pleasing. The math modeling and analysis >>came later... much later. >> >> >> >>>Your ears hear an interval as an ET minor third when two notes--any two >>>notes--are 300 cents apart. >> >>That is purely coincedental... :).... you hear a minor third because it >>is what it is... it is 300 (roughly) cents apart only because we have >>contrived a scale with which to reference frequencies on such. The >>chicken came first... not the egg..... at least in this case :) >> >>Yes you can hear cents! >> >>Sure you can... along with pennies and quarters.... but not the kind you >> are refering too. A cent is a concept you can no more hear a cent then >>you can a herz. You <<hear>> soundwaves... and there interplay with >>each other. >> >> >> >>>And yes they describe >>>actual, perceived musical pitch regardless of frequency! >> >>They do describe pitch... thats what cents were contrived to do. The >>percieved musical part is not relvant to that task. >> >> >>>You can tell a >>>minor third can't you? >> >>Why yes.... I can... depending on where it is... which octave.... it is >>exactly ..... <<so tense>>. You could just as easily describe in a >>ratios just what <<so tense>> is using beats... as in how many per >>second as some function of the the frequency of the lowest note in the >>pair... or you could contrive a thousand ways of describing it.... but a >>description remains only a description .... not the thing itself. >> >>>Don A. Gilmore >>>Mechanical Engineer >>>Kansas City >>> >> >>Sometimes people get too hung up in numbers to see reality in front of >>their noses. Cents are a valuable construct, very handy in our work... >>but they do not determine our perception of musical pitch. They are >>simply numbers on a scale and nothing more. >> >>Sorry Don. I'm not buying this at all. But who says we have to be in >>agreement eh ?? >> >>Cheers >>RicB >> >>_______________________________________________ >>pianotech list info: https://www.moypiano.com/resources/#archives > > > _______________________________________________ > pianotech list info: https://www.moypiano.com/resources/#archives >
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