Talk:Identity (music)

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[edit] Disambig

First, the disambig at Identity is completely mistaken that "identity" is a musical term coined or exclusively used by George Perle. Secondly, I hardly think we need stub articles for terms which are nearly if not identical to the meanings of the mathematical terms from which they were borrowed. See: Musical set theory, please. Hyacinth 23:39, 5 Aug 2004 (UTC)

[edit] Incomprehensible

I know something about music theory and something about universal algebra, but I find the article basically incomprehensible. The examples given seem not to be identities but fixed points of certain transformations. Lambiam 13:59, 18 February 2006 (UTC)

What is incomprehensible? Hyacinth 08:57, 19 February 2006 (UTC)

First off, there is no notion of "identity" in universal algebra; there is a notion of identity in specific algebras, such as monoid algebras. It is not clear how that would apply here. The second sentence mentions identity function, which is a well-known notion in general mathematics. However, a function is an identity function (and the identity function on A) precisely when for all elements x in A we have f(x) = x. In words, this function does "nothing"; it just passes on its input without change. This does not fit the description at all.

Second, the article never states what an identity in music is. The disambiguation page at least states that it is "a transformation of pitches". So apparently in the article the reader is assumed to identify "identity" in the caption and first sentence with "identity function" in the second sentence. That is not at all an obvious thing to expect a reader to do.

Third, is it any pitch transformation? Is transposing all pitches upwards by a minor third an identity (function)? Speaking mathematically, it transforms the class of all pitches into itself. Presumably it is not a coincidence that all examples given are fixed points, as noted above. So is an identity a fixed point of a transformation? (In that case everything is an identity, since everything is a fixed point of the identity function.) Or is it a transformation together with a fixed point? It is all not quite clear to me.

Fourth, if the retrograde operation "transforms a pitch class", then why not the operation of replacing any sequence of tones by 0123... (which, when applied to 0123..., produces the same thing!)? Then it would appear that any process of "melody in – melody out" fits the description.

Finally, in the last part, I don't know what is meant by "interval-4 family" (tones that are a major third apart?), by "sum-2" family, or (in this context) "axes of symmetry" and "family of symmetrically related dyads". I see that the next two lines show chromatic ascending and descending scales starting from D, but what they have to do with anything discussed before or after escapes me. I cannot discern a relationship with any of the surmised notions of identity given above. Lambiam 19:23, 19 February 2006 (UTC)