source file: mills2.txt Date: Sun, 9 Mar 1997 04:14:53 -0800 Subject: Harmony and Rhythm From: rtomes@kcbbs.gen.nz (Ray Tomes) G'day all One day I was thinking about low notes and made the connection between rhythm and frequency. If we are in C and suppose C=256 Hz to make it easy on the calculations, then we have more Cs at 128, 64, 32, 16, 8 etc except that this is too low for hearing. However 8, 4, 2, 1 Hz are equivalent to tempos of 480, 240, 120 and 60 bpm. So if a piece is played in C at a tempo of 120 bpm then we can say that the tempo/rhythm is IN TUNE with the key. Because I have this idea that after every few octaves a fifth should be thrown in, I consider that the frequency of the key note should be either 2^n or 3*2^n times the tempo (when converted from bpm to Hz). In either of these cases I would say that the composer got it right. I had a look at a number of classical composers to see whether they did this or not and found that the good composers generally did. Some of the not so good ones didn't. Of course sometimes we are stuck with a tempo in words and don't know the exact rate. I had a look at a few modern composers. I like Billy Joel and he writes definite things like 124 bpm and leaves you with no doubt. Well I checked his pieces and they are in tune but there is a 2% to 2.5% difference which would be removed if A=440 was changed to A=450. So does anyone know whether he tunes his instruments to 450? That would explain things. If not then I think that he is picking up the natural earth frequencies and that A=450 is the natural rate. If it can be accepted that having the tempo and key matching is a sign of good music then it is also true that transpositions are not a good practice. If you transpose a piece up by a third then to keep the balance you would need to play it 25% faster and it would sound like the chipmunks! Any chance of conveying (the right) emotions would be gone. OK, so all shoot me down in flames again! There is an article on WWW (link on my pages) about a similar idea. That is, that chords slowed down become rhythm and that certain common chords make common drum beats etc. For example, a fifth becomes: Low note x x x x x High note * * * * * * * Result # * x * # * x * # More complicated chords become more interesting beats. -- Ray Tomes -- rtomes@kcbbs.gen.nz -- Harmonics Theory -- http://www.kcbbs.gen.nz/users/rtomes/rt-home.htm Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Sun, 9 Mar 1997 16:49 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA10262; Sun, 9 Mar 1997 16:49:50 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA10252 Received: from by ella.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) id HAA27150; Sun, 9 Mar 1997 07:47:34 -0800 Date: Sun, 9 Mar 1997 07:47:34 -0800 Message-Id: <199703091045_MC2-124F-AF65@compuserve.com> Errors-To: madole@mills.edu Reply-To: tuning@ella.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@ella.mills.edu