source file: mills2.txt Date: Sat, 16 Dec 1995 11:13:02 -0800 Subject: New 19/Oct Scales From: Brian Thomson Gary Morrison, among others, may remember me talking about modulating standard equal-temperament scales with a numeric function such as Sine. If not, I probably didn't mention it on the list anyway. In any case. these are a couple of 19/Oct Sine-Modulated Equal-Temperament (SM-19ET) scales that I worked out using a spreadsheet (MS Excel). The idea was to try out many different combinations of sine frequency and amplitude on the interval numbers (1, 2, 3, etc.), and use statistical analysis techniques to evaluate how well the results match up with the theoretically pure mathematical intervals (e.g. 3:2 for a fifth). Standard 19/Oct ET is shown for comparison. The first SM-19ET scale is arrived at by modulating the interval number with Freq=8 and Amp=0.122889; the second uses Freq=12 and Amp=-0.195294179. Could someone with the equipment (and the time!) try these out and let me know how they sound? So far, they exist purely as numbers, and I'm dying to know how they translate to Reality(TM). If they're worth anything, please accept them as public domain and use them freely, with my best wishes (although an album sleeve credit would be nice...) Interval Std 19/Oct SineMod #1 SineMod #2 1 63.158 71.369 51.862 2 63.158 58.978 83.528 3 63.158 52.895 58.088 4 63.158 62.299 46.861 5 63.158 72.999 81.321 6 63.158 68.849 64.863 7 63.158 56.111 43.625 8 63.158 54.007 77.145 9 63.158 65.712 71.454 10 63.158 73.563 42.506 11 63.158 65.712 71.454 12 63.158 54.007 77.145 13 63.158 56.111 43.625 14 63.158 68.849 64.863 15 63.158 72.999 81.321 16 63.158 62.299 46.861 17 63.158 52.895 58.088 18 63.158 58.978 83.528 19 63.158 71.369 51.862 Total / Oct 1200 1200 1200 Merry Whatever... Brian Thomson London, UK briant@computing.emap.co.uk PS: I have a couple of spreadsheets that might be of use to "normal" keyboard or stringed instrument players. You type a key (e.g C#) into one cell, a chord or scale type (e.g. MIN7) into another, and the spreadsheet calculates and displays the scale / chord on a keyboard or tunable & customisable "fretboard", depending on the version. A few guys on the Chapman Stick list have tried one version out, and the feedback has been quite positive. I use them myself for 5-string bass and keyboards. I can mail it to anybody in Excel or MS Works formats, possibly 1-2-3 v4+ as well. PPS: You can tell I enjoy playing with spreadsheets, can't you? Sad, eh... 8{ Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Sun, 17 Dec 1995 17:16 +0100 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id IAA22700; Sun, 17 Dec 1995 08:16:40 -0800 Date: Sun, 17 Dec 1995 08:16:40 -0800 Message-Id: <9512170813.aa21978@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