source file: mills2.txt Date: Wed, 9 Oct 1996 09:27:41 -0700 Subject: Reply to Daniel Wolf From: PAULE I think the disagreement/agreement between the fundamental bass and the actual bass is a very important source of tension/resolution in music by any of the composers you mentioned. >2) In that only pairs of tones will share harmonic series in a subharmonic >chord, the masking will be at a lower amplitude than for a harmonic chord >where all tones share a single series. Then you must be talking about a type of masking different from that which is only a function of pitch proximity. I thought you weren't, which is why I pointed out that subharmonic series will, ceteris paribus, lead to more masking, due to the ubiquitous combination tones. However, you must be talking about a phenomenon related to the virtual pitch phenomenon, wherein partials in a harmonic relationship are subsumed into a single perception, making the components difficult to hear. This phenomenon is quite easy to demonstrate, it is what distinguishes harmonic series harmonies of sine waves, and what makes harmonic-series chords easier for the brain to understand than subharmonic series chords. >3) A division of a string into aliquot parts (subharmonic) is finite. >Successive harmonic divisions are not. Example: the division of the string >into four equal parts yields four pitches of the subharmonic sequence 1/1, >4/3, 2/1, 4/1 and no more. This is because you have defined the string as the lowest possible pitch. Clearly a series that proceeds downwards will reach a limit when you have this constraint in place, while a series proceeding upwards will not. But you can always get a longer string to see what 5/4 or 55/4 of the original string length sounds like. However, you will eventually reach impossibly microscopic string lengths with a harmonic division. This argument is going nowhere. >4) The period (for example, one second) is a function of our notation. And what isn't? Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Wed, 9 Oct 1996 18:28 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA01802; Wed, 9 Oct 1996 18:29:36 +0200 Received: from eartha.mills.edu by ns (smtpxd); id XA01795 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id JAA10071; Wed, 9 Oct 1996 09:29:28 -0700 Date: Wed, 9 Oct 1996 09:29:28 -0700 Message-Id: <31961009161113/0005695065PK3EM@MCIMAIL.COM> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu