source file: mills2.txt Date: Tue, 24 Sep 1996 00:45:07 -0700 Subject: More on spacing From: Daniel Wolf <106232.3266@compuserve.com> Responding to Paulīs comments: (1) Your modification of my timbre restriction to "generic harmonic timbres played at a reasonably loud volume" is fine. My own practical work has been with sine waves, however, (Rayna synthesizer) and I probably should have identified the subharmonic by lowest (theoretical) summation tone. (Your phrase has the virtue of sparing me a summation tone controversy; but the use of (theoretical) summation tones has been useful to me in the past in describing aspects of a significant repertoire of real music (Wagner, Debussy, Varese, Partch, Young, among others). (2) I am interested in evaluating as many algorithms as possible. I am especially interested in the possibility of a sequential processing of intervals, from most simple to most complex, allowing for re-evaluation of the complex with the addition of each new interval. (3) I have deliberately avoided the issue of temperaments which contain _puns_ of just intervals (being hearable as approximations of two or more distinctive rational intervals), because that is an issue best determined by diachronic context. (I must add my disagreement to your statement that an interpretation of a pitch complex as 10/12/15 or 16/19/32 (and, I may add, 54/64/81) makes "no musical difference". In terms of diachronic relationships, these difference are profound. Consider, for example, a progression from a tonic minor triad to the Major triad on the flat sixth degree (i to bVI, or c minor to Ab Major): each of the above interpretations of the minor triad suggests an alternative tuning for the second chord, and each progression is part of a very different scalar environment (resp. triadic just, extended just or harmonic, and pythagorean), each of which implies very different possibilities for going on further (try it for yourself: continue the progression by descending fifths to _return_ to the _tonic_.)) (4) From this pitch spacing perspective, the "optimal frequency range" may be more relevantly identified with the perceived fundamental of a complex when mapped onto a harmonic series. The most profound musical conditions seem to be determined by the lower limit to _pitch_ perception. When a fundamental falls below this boundary, perception is made more difficult (although work with standing waves played for very long durations suggests that it is not impossible when additional _listening_ techniques (the sense of touch, for example) are called into play), (5) My comment on emotional effect should not be taken too literally. I am aware of research on "happiness" and low electrical activity in the brain; the calculation hypothesis is my own; ascribing quantum effects to the infintessimal is not without controversy. Daniel Wolf Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Wed, 25 Sep 1996 10:55 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA19875; Mon, 23 Sep 1996 19:37:13 +0200 Received: from eartha.mills.edu by ns (smtpxd); id XA22816 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id KAA11301; Mon, 23 Sep 1996 10:36:08 -0700 Date: Mon, 23 Sep 1996 10:36:08 -0700 Message-Id: <94960923173349/0005695065PK2EM@MCIMAIL.COM> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu