Z-relation, or rather, "that certain pitch-class collections share the same 'interval vector' even though they are neither transpositionally nor inversionally equivalent was first pointed out by Howard Hanson in Harmonic Materials of Modern Music (New York: Appleton-Century-Crofts, 1960), p. 22, and by David Lewin in "Re: The Intervallic Content of a Collection of Notes," Journal of Music Theory 4:1 (1960). For a general criticism of Forte's concepts of pitch-class set equivalence see Perle, "Pitch-Class Set Analysis: An Evaluation," Journal of Musicology 8:2 (1990).
George PerleRelated topics
analysis certain collection content criticism equivalence equivalent evaluation general harmonic interval journal modern music nor see set share theory vector musicology howard david hanson notesRelated quotes
The new trade theory picture of the world looks something like this: Each country has, at any given time, a set of broad resources-land, skilled labor, capital, climate, general technological competence. These resources define up to a point the industries in which the country can hope to be competitive on world markets. [...] But a country's resources do not fully determine what it produces, because the detailed pattern of advantage reflects the self-reinforcing virtuous circles, set in motion by the vagaries of history.
Paul Krugman
Subsequent hearings have presented to the public a vapid and hollow charade, in which repetition of platitudes has replaced discussion of viewpoints and personal anecdotes have supplanted legal analysis. Such hearings serve little educative function, except perhaps to reinforce lessons of cynicism that citizens often glean from government. Neither can such hearings contribute toward an evaluation of the Court and a determination whether the nominee would make it a better or worse institution. A process so empty may seem ever so tidy - muted, polite, and restrained - but all that good order comes at great cost.
Elena Kagan
By these things my Mind was now so turned that it lay like a Horse-leech at the Vein, still crying out, Give give, yea, it was so fixed on Eternity, and on the things about the Kingdom of Heaven (that is, so far as I knew, though as yet... I knew but little); that neither Pleasures, nor Profits, nor Persuasions, nor Threats, could loosen it, or make it let go his Hold. ...it is in very deed a certain Truth, it would then have been as difficult for me to have taken my mind from Heaven to Earth, as I have found it often since to get it again from Earth to Heaven.
John Bunyan
How ironic. In order to avoid the "nutty" theory of inversion, Gaskell invented the even odder notion of stomachs turning into brains with new guts forming below. No wonder then, that later biologists cast a plague on both speculative houses and opted instead for the obvious alternative: arthropods and vertebrates do not share the same anatomical plan at all, but rather represent two separate evolutionary developments of similar complexity from a much simpler common ancestor that grew neither a discrete gut nor a central nerve cord.
Stephen Jay Gould
Suppose that the organism is given the problem of determining the analysis of a stimulus at a certain level of representation - e.g., the problem of determining which sequence of words a given utterance encodes. Since, in the general case, transducer outputs underdetermine perceptual analyses, we can think of the solution of such problems as involving processes of nondemonstrative inference. In particular, we can think of each input system as a computational mechanism which projects and confirms a certain class of hyputheses on the basis of a certain body of data.
Jerry Fodor
