I will admit that it is not the only possible system but it is not entirely arbitrary. Pairs of tones whose frequencies are in low-order fractional ratios (like 2/3, 3/4, etc.) tend to sound pleasing to the ear because of the beat notes they produce. If you decide to produce a scale where all of the intervals are ratios of powers of 2^(1/N), you'll find that N=3D12 is a nice choice because it's not too small (can't do too much with a scale of only 2 notes) and reproduces many of these low-order fractions almost exactly. The next closest choice would be N=3D25 if I recall correctly, whi= ch is then too many notes to choose from. On Tue, Aug 19, 2014 at 3:28 AM, David C Brown wrote: > The division of a bicade - as I shall now call it - into twelve intervals > grouped into seven notes of two different sizes is the method favoured by > European musicians of the last three centuries. It is not the only > system, and, indeed, many other systems are/were used by other cultures a= nd > at other times. > So, apart from being illogical, the word octave is very politically > incorrect favouring, as it does, the world's dominant culture. Hence my > use of the word bicade which, like decade, is a scientifically derived > word. > > > > __________________________________________ > David C Brown > 43 Bings Road > Whaley Bridge > High Peak Phone: 01663 733236 > Derbyshire eMail: dcb.home@gmail.com > SK23 7ND web: www.bings-knowle.co.uk/dcb > > -- > http://www.piclist.com/techref/piclist PIC/SX FAQ & list archive > View/change your membership options at > http://mailman.mit.edu/mailman/listinfo/piclist > --=20 http://www.piclist.com/techref/piclist PIC/SX FAQ & list archive View/change your membership options at http://mailman.mit.edu/mailman/listinfo/piclist .