source file: m1496.txt Date: Thu, 6 Aug 1998 17:07:28 -0400 Subject: Re: Numbers and a new tuning From: "Paul H. Erlich" Johnny Reinhard wrote, >I've been working on a new piece in a new tuning. It is for soprano, >violin, viola, and cello and scheduled for performance at De Ysbreker on >October 13th in Amsterdam. It is largely tuned to Harmonic-17 Good luck with this piece and I hope to hear it someday. Are you planning a second "Music of Johnny Reinhard" recording? >However, when every >single note is a 17-perspective, might the "-ness" resulting merely be a >manifestaion of the music's "17-ness"? Not sure exactly what this means, but remember that individual notes can have a numerical relationship only with other notes, and not standing on their own. Certainly if a 1/1 is played as a drone, and other notes form ratios of 17 with the drone, and the remaining notes are typically used simultaneously with notes they form ratios of 17 with, then 17 will define the harmonic norm of the piece and it can be said to project 17-ness, if such a thing is discernible at all. If there is no 1/1 in the music, the 17s in the ratios for the other notes may fail to create any actual ratios of 17 in the music, so projecting a sense of "17-ness" in the sense it has been discussed would be difficult. On the other hand, there are probably many simpler intervals in this tuning which occur between notes which are all defined with 17 in the numerator, or all with 17 in the denominator, and these intervals can easily come to define the harmonic norm of the piece. Recall our earlier discussion about Mayumi's Harmonic-13 piece -- Adam Silverman and I thought we heard just 3/2 intervals in it, but you denied that the tuning had any. When the details of the tuning finally became available, there were several 3/2s to be found in it. A lattice representation is more useful that a simple listing of ratios relative to a single tonic for determining the harmonic resources of a tuning. However, a 13-limit tuning may require at least 5 dimensions, and a 17-limit tuning at least 6, so in many cases a single graphical depiction of such tunings may not be able to clarify all its relationships. However, I suspect that in the case of Harmonic-13 and Harmonic-17, there may be simplifying features that could make a graphical representation feasible. Care to provide us with the details?