> "riddle," and it is insoluble.. > How true...this helps keep life interesting! And us, employed! Three contiguous Mj3rd can be used to balance the octave..is there a better way aurally to set two precise markers inside the octave? As far as using M3rds in the temperment, sure, P5ths and other intervals need to be used..,.but... Nine contiguous Mj3rds can be used in setting a 13 note temperment.... I think the point of coloration, historically, and now, is more likely to be focused on the M3rd as the primary interval of contention, for the listener. Dan Reed Dallas, Tx On Mar 8, 2009, at 2:44 PM, Fred Sturm wrote: > On Mar 8, 2009, at 1:13 PM, Dan Reed wrote: > >> My vote is, that comparing the P5 to the M3rd, the M3rd was (and >> still is), the target interval to adjust......the interval that most >> dramatically stands out, from beatless. > > Yes, the M3 is the target interval to adjust. But how do you adjust > it? You can't just do it directly, and come up with a complete, > balanced temperament. The actual temperament procedure requires using > 5ths. > You can adjust M3s directly within an octave: CE, EG#, G#C. But that > doesn't get you 12 notes. You have to use another interval to come up > with a circular system, where you produce all 12 notes. The 5th > (together with its inversion, the 4th) is the practical alternate > interval. > And you have to keep in mind that whatever you do to "improve" one > thing, it requires you to make something else worse. That is the basic > temperament "riddle," and it is insoluble. All one can do is come up > with a compromise. > Regards, > Fred Sturm > University of New Mexico > fssturm at unm.edu > > > -------------- next part -------------- A non-text attachment was scrubbed... Name: not available Type: text/enriched Size: 1774 bytes Desc: not available URL: <http://ptg.org/pipermail/caut_ptg.org/attachments/20090308/92d41c5e/attachment.bin>
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