Friends, I'm sure that you feel the insecurity of casting of the limits, whether they be the pure octave or the tempered fifth. Where will it end? And, even more important, what is the ideal toward which we are moving? Is it good sounding triple octaves? There is another standard which could become our ideal. That is harmony. I have been using a temperament approach which uses triads as tests. The combination of major triads, first position and third position, form an excellent harmony test. My plan works toward making the harmonies as perfect as possible, then the harmonies dictate the octave size. I find that my double and triple octaves sound quite good, also. However, there is a lot to think about when we start looking for new parameters. My conclusions are probably premature but I'm thinking, anyway. Ken Burton, "Doctor Piano" Calgary Alberta
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