source file: mills2.txt Date: Sat, 8 Feb 1997 04:09:22 -0800 Subject: millioctaves From: gbreed@cix.compulink.co.uk (Graham Breed) Great idea! I've been using these for years, since before I discovered the rest of the world used cents. Silly things, surprised they caught on. It would certainly make things easier for me if everyone else came round to my way of thinking, although this does run into problems with reality. As to the notation, I suggest "moct" so that you can switch to "oct" when the intervals get big enough. 2.735 oct makes a lot more sense to me than 3282 cents. I prefer mET to MET: the latter would imply megaoctaves! Microoctaves also have their uses: the MIDI Tuning Standard works to 5 mu-oct, doesn't it? Apart from removing the 12TET bias, octaves are easier to calculate : p log2(f/f_0); f0*2^p. Step sizes of equal temperaments can be worked out really easily -- sometimes in your head. I've also been using octaves to denote absolute pitches, with f_0z. Once you know that middle C corresponds to about 8.04 oct, you know that 10.128 oct must be somewhere above the treble clef. What does 1119 Hz mean? Setting f_0Hz may be better, equivalent to subtracting 4 oct, and around the threshold of hearing. The fractional part can also be replaced with a note name: 8.04 oct becomes 8C, 8.78 oct becomes 8A. This can be generalised for any tuning system you like. Well, that's the way I see it, anyway. Graham Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Sat, 8 Feb 1997 13:15 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA29705; Sat, 8 Feb 1997 13:15:25 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA29734 Received: from by ella.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) id EAA08040; Sat, 8 Feb 1997 04:13:08 -0800 Date: Sat, 8 Feb 1997 04:13:08 -0800 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@ella.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@ella.mills.edu