Talk:Z-relation
imperceptible" is better than "imperceivable"[edit]
Why? Did I construct a fake word? Hyacinth 00:27, 15 Dec 2004 (UTC)
Just a drive-by comment on history[edit]
Z-relations were first formally defined in print (I believe) by David Lewin in JMT in 1959... perhaps early 1960. Of course, he did not use that term. The idea of Z-relation was considered much earlier, however... I believe first by Bacon in 1917. Many of the ideas of set theory in music predate their supposed origin in the 1950s and 60s -- between Schoenberg and Forte we had Ziehn, Bacon, Hauer, Haba, Schillinger, Slonimsky, Perle, etc., each of them working on ideas of collections of pitches in different ways. I've seen the bias to move back to Hanson in some of the Wiki articles... but Hanson's book was/is little known (as opposed to Perle and later Forte), and many of the ideas in that book were around earlier (even if the authors are forgotten today).
Misleading Statement[edit]
"Similarly the more familiar major triad {0,4,7} and minor triad {0,3,7} have the same interval vector (<0,0,1,1,1,0>)." This statement is true, but the two sets are not in a Z-relation. Rather, they are inversionally related and therefore reduce to the same [037] prime form. No Z-relations hold for sets of cardinality three. —The preceding unsigned comment was added by 69.93.182.178 (talk • contribs).