New 19/Oct Scales

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{


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