source file: mills2.txt Date: Fri, 4 Oct 1996 01:59:12 -0700 Subject: TUNING digest 854: further response to Paul From: Daniel Wolf <106232.3266@compuserve.com> (1) I think that my musical examples are sufficient to demonstrate that unless the harmonic situation is static (which is indeed the case for some repertoires, but I sense that your algorithm is geared to more traditional western materials) your description will not be musically useful, and within a static scenario, is is probably meaningless, as any values set by your algorithm are only in comparison to sonorities external to the music at hand. "Rootedness" I find to be extremely problematic musically, in the same way that the Fuxian bass line is simply more convincing musically than the Rameau basse generale (why is it that all of those dead, white male composers read Fux and ignored Rameau?). The idea of hearing a single chord outside of its contrapuntal (voice-leading) context is strikingly _unmusical_. (2) I assume that combination tones will have significantly lower amplitudes than the instrumental tones played. (By the way, I would be interested in learning how one can calculate the amplitudes of combination tones if anyone knows). Thus, only pitch complexes constructed from (lower) harmonic series members will be significantly affected by masking, such that difficulties in discerning individual tones from the entire complex occur. (Anyone who has ever tried to dictate ensemble musics has experienced the masking problem). (3) I assume that pitch information is mentally processed as frequency rather than wave length (the ear functioning like a AD transformer): I may of course be entirely wrong about this, but it is a reasonable assumption. (An intutionist approach will takes temporal perception over spatial as the basis of the initial construction (cf Brouwer _Cambridge Lectures_); the spatial interpretations only follow.) The classical harmonics approach does not contradict this, as the first visual observation was of different strings (of different tension or thickness) moving faster and slower and yielding different pitches (this is immediately observable in gut or wire strings throughout the frequency ranges presumably used in ancient music), and then the compared lengths of a single string were then used to quantify this observation. Oscillatory periods and wave lengths are not observable as such without special apparati (this is not completely true, but the perception of wave lengths as physical distances depends on instrumentation and conditions generally outside of contemporary concert music and well outside of the ancient setting). (3a) This is a weak argument, but I give it anyways: why is it that microtonal music theorist structure their discourse almost universally in terms of frequency ratios and not stringlengths, wavelengths, or periods? Either this is just a convention (which I doubt because each individual theorist seems to like building from first principles), or there is indeed an intuitive quality to frequency ratios not shared by _alternative_ descriptions. (4) Indeed, classical harmonics had no definitive _musical_ preference for subharmonic or harmonic divisions, and their results gave stringlength measurements for scales constructed in both ways (with preference for the least cumbersome numerically, and possibly using the physical _boundary_ problem of not being able in practice to divide the string into many parts as a determinant of their preference), the issue being the prefered intonation of those (melodic) scales, not their analysis as harmonic complexes. _Mathematically_, however, the arithmetic divisions (subhamonic) were recognized as closed segments of the harmonic division; each individual arithmetic division yielded a finite number of pitches and was exhausted, while the harmonic division was continuable indefinitely. In this sense (a kind of set theory), the subharmonic divisions were considered inferior to the harmonic. The issues we are dealing with - comparing different pitch complexes - are outside of the narrow framework of classical harmonics, but I see no contradiction between mine and the classical approach. (5) I haven4t a degree in physics but I do recognize that the region between the smallest particle (10^-33 or so) and the vacuum (null) is not precisely mirrored by its inversion. Daniel Wolf Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Fri, 4 Oct 1996 11:37 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA01908; Fri, 4 Oct 1996 10:38:32 +0100 Received: from sun4nl.NL.net by ns (smtpxd); id XA01906 Received: from eartha.mills.edu by sun4nl.NL.net (5.65b/NLnet-3.4) id AA18943; Fri, 4 Oct 1996 09:55:44 +0200 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id AAA21355; Fri, 4 Oct 1996 00:54:22 -0700 Date: Fri, 4 Oct 1996 00:54:22 -0700 Message-Id: <9610040753.AA08057@arthaud.saclay.cea.fr> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu