tag:blogger.com,1999:blog-6980672.post109960376272907372..comments2023-10-08T08:38:09.714-04:00Comments on Musical Perceptions: Journal Club: Math and Ozzy OsbourneScotthttp://www.blogger.com/profile/01286095156825716887noreply@blogger.comBlogger6125tag:blogger.com,1999:blog-6980672.post-74149137068927549322007-07-26T16:02:00.000-04:002007-07-26T16:02:00.000-04:00Sorry so long in responding!To answer anonymous's ...Sorry so long in responding!<BR/><BR/>To answer anonymous's question, Thom Yorke of Radiohead consciously uses NROs in his songwriting, though he does not refer to them by name. He alludes to them in a discussion of common-tone chord progressions in an interview with Alex Ross (New Yorker, August 20 & 27, 2001).<BR/><BR/>To answer Scott's question about the perceptual difference between "synonyms" such as PLR and RLP (both of which map C major onto F minor), Richard Cohn (JMT, 1997) cites this as an open research question. It depends on how much ontological weight you want to place on the Tonnetz moves. Does the C major to F minor move have three distinct stages, each of which deserves audibility, or is it one move that happens to pass through three locations on the Tonnetz?<BR/><BR/>As for Scott's question about enharmonic equivalence, most theorists state that enharmonic equivalence is what makes the wraparound Tonnetz possible, which in turn makes the elegant mathematical group structure of NROs possible. You could construct a Tonnetz that lacks enharmonic equivalence--it's just going to be "messy" from a mathematical point of view.Sonia and Guy's Bloghttps://www.blogger.com/profile/03237268048765257215noreply@blogger.comtag:blogger.com,1999:blog-6980672.post-47830893054815715052007-07-24T11:50:00.000-04:002007-07-24T11:50:00.000-04:00Hey Guy, while I have you on the phone, how do you...Hey Guy, while I have you on the phone, how do you feel about having to rely upon enharmonic equivalence for these operations to work? Is there any way to make a closed system without using enharmonic equivalence? And does it make any difference, especially as applied to music that is clearly performed in just or Pythagorean tuning (orchestral music, non-piano chamber music, and a cappella choral music, especially)?Scotthttps://www.blogger.com/profile/01286095156825716887noreply@blogger.comtag:blogger.com,1999:blog-6980672.post-56146033746680675442007-07-24T11:45:00.000-04:002007-07-24T11:45:00.000-04:00Anonymous, I won't speak for Guy but I place these...Anonymous, I won't speak for Guy but I place these techniques as analysis, not compositional strategy. However, I have seen attempts to use similar operations as a method to teach improvisation. I don't see this method as successful.Scotthttps://www.blogger.com/profile/01286095156825716887noreply@blogger.comtag:blogger.com,1999:blog-6980672.post-40641040299979036412007-07-24T11:43:00.000-04:002007-07-24T11:43:00.000-04:00Guy, thanks for the clarification on the transform...Guy, thanks for the clarification on the transformations from triads to seventh chords. I was trying to state that another operation, besides L P and R, is needed when dealing with both triads and seventh chords. How do you feel about my statement that the inclusion operation doesn't add much to the perceived complexity of a model?<BR/><BR/>As for the flexibility, you have a point. However, one can make a perceptual distinction between V7/IV and Ib7, as well as a logical/systematic distinction. The V7/IV places that chord lower in the tonal hierarchy, relying upon the following IV chord (and eventual V and I) to give it identity. Ib7 does not rely upon the following IV chord, as it is the first statement of the top dog tonic chord, albeit chromatically altered. Thus these different descriptions of the chord have different perceptual meanings. What is the difference in perception between RR', R'L', and PP'PR?Scotthttps://www.blogger.com/profile/01286095156825716887noreply@blogger.comtag:blogger.com,1999:blog-6980672.post-51488496019573476752007-07-21T17:33:00.000-04:002007-07-21T17:33:00.000-04:00Just out of wild curiosity... Would you say that t...Just out of wild curiosity... Would you say that these techniques are more useful for after-the-fact analysis, or are these used in actual composition?Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-6980672.post-56070546879163724722007-07-21T15:01:00.000-04:002007-07-21T15:01:00.000-04:00Thanks for your interest in my article, Scott. I w...Thanks for your interest in my article, Scott. I will respond to two points you made. <BR/><BR/>First, it's not always the case that a transformation from a triad to a seventh chord (or vice versa)requires an "extra" operation. For example, the transformation between G major and G dominant seventh is / (using / to designate the inclusion sign). Likewise, the transformation between G minor and E half-diminished seventh is /. The "extra" operation creeps in depending on the roots of the chords, not the cardinalities. For instance, the transformation from G major to E half-diminished seventh is P/ (first do P, then do /). <BR/><BR/>Second, I find the ability of Neo-Riemannian operations to model a move between two chords in numerous ways to be a boon, not a bane. Similar things happen in common-practice harmony. For instance, the opening chord of Beethoven's First Symphony is V7/IV if you're Walter Piston and Ib7 if you're Heinrich Schenker. I understand your concern that Neo-Riemannian theory has the potential to spin out of control, heedlessly labeling every triadic transformatin in its path, but it's the analyst's responsibility to prevent that, not the system's. <BR/><BR/>Let's keep the dialog going! Great minds don't think alike.<BR/><BR/>Cheers,<BR/><BR/>GuySonia and Guy's Bloghttps://www.blogger.com/profile/03237268048765257215noreply@blogger.com