source file: mills2.txt Date: Mon, 7 Oct 1996 08:26:32 -0700 Subject: Reply to Daniel Wolf From: PAULE Daniel, I'm not familiar with Fux's fundamental bass, but I know that I would disagree with Rameau where he does not allow the fundamental bass to progress by second. >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). My point about combination tones was that the masking that occurs with complexes constructed from subharmonic series members will be at least as bad as that which occurs with harmonic complexes. >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. And this quantification would have led to subharmonic relationships forming an arithmetic progression, the simplest progression to understand (and to continue to infinity). >Oscillatory periods and wave lengths are not observable >as such without special apparati True, but note the frequency is one over the ocsillatory preiod; therefore if temporal measurements are basic, as you say, oscillatory periods are logically prior to frequencies. >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. Note that only very recently is this the case; as recent and as scientifically astute a microtonal theorist as Huygens used the inverse representation (which could have referred to stringlengths, wavelengths, or periods). I'm sure you knew what my answer would be: (a) frequency ratios describe the perception of the chord by the central pitch processor, so important characteristics such as the root of the chord can be inferred from this representation; (b) the combination tones will only make this representation more relevant in terms of the implied root. The importance and special status of the harmonic series, _especially_ when used to organize sine waves, cannot be denied. It comes into play every time we hear a musical instrument and we think we know what note it's playing. >_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, What on earth do you mean? >while the harmonic division was continuable indefinitely. This seems utterly nonsensical. Clearly the harmonic divisions _had_ to be expressed in terms of the arithmetic divisions, not vice versa, in order to instruct makers of instruments where to put the frets. Your "set theoretic" distinction of one set as superior or more general than the other is likewise nonsense. >(5) I havent 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. 10^-33 what? 10^-33 meters? Are meters a unit of frequency? No, they are a unit of length. Therefore, it is at small lengths, of strings or of waves, where you would expect a "boundary problem"; i.e., high freqencies. Your argument falls flat on its face. -Paul Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Mon, 7 Oct 1996 18:00 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA03936; Mon, 7 Oct 1996 17:01:41 +0100 Received: from eartha.mills.edu by ns (smtpxd); id XA03934 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id JAA03262; Mon, 7 Oct 1996 09:01:39 -0700 Date: Mon, 7 Oct 1996 09:01:39 -0700 Message-Id: <65961007152256/0005695065PK2EM@MCIMAIL.COM> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu