source file: mills2.txt Date: Thu, 2 Nov 1995 07:28:43 -0800 Subject: Scale generators and ASR/OTTO tuning resolution From: Steve Curtin >Marion tells us: >There are matrix methods, which multiply sets of frequency >ratios, and there are cycle methods which multiply a single ratio >iteratively. All of them quickly generate a lot of scales, but >they are, for the greater part, scales that can not be accurately >reproduced on contemporary instruments. Also, these methods are >mostly indifferent to the consonance of the scales they produce. Sad but true. The especially odd part is that oscillator chips have pretty good resolution but making them represent ET scales cuts this down significantly. For instance, The OTTO chip in the ASR-10 has an 11-bit fractional phase accumulator. This means that a sample from unity up to an octave can resolve 2048 different intervals. An octave above that this number doubles for each octave, and each octave below this is halved. The tuning tables are represented as 7 bits between semitones, which is 1524 steps or .78 cents. However, the exponential table used to convert linear frequency isn't long enough, which is why you really only get 768 steps or the 1.5 cent resolution measured by Carter Scholz a number of years ago. (Thanks to Bill Mauchly for this info) What's needed is some kind of 'ratio mode' which calculates this directly and sets up integer ratios between different voices. Don't look for this in any sort of product from us any time soon, though. If you have a Soundscape card it is possible to hit the OTTO chip directly from the PC and put in your own ratios. Writing some Forth code to do this and implement Marion's variable loop length tuning method has been on my project stack for a while. The only big problem is that the Soundscape waveforms are in ROM, but you could possibly find different waveforms of different lengths and match them up. regards, Steve Curtin Ensoniq Corp Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Thu, 2 Nov 1995 18:38 +0100 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id IAA28879; Thu, 2 Nov 1995 08:38:00 -0800 Date: Thu, 2 Nov 1995 08:38:00 -0800 Message-Id: <9511020837.aa10239@cyber.cyber.net> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu