source file: mills2.txt Date: Sun, 1 Jun 1997 20:01:20 +0200 Subject: Re: millenium From: Daniel Wolf Gary: The problem is that we count passing time in two ways. One way is for birthdays - we count years completed as discreet units (except as children when we enthusiastically noted the half year completed as well). The other way of counting applies to calendars. Days, months, and years are identified in terms of periods of time, and any moment within each of these periods recieves that identification. By your birthday-style counting, today would be 31 May 1996 (as I write it is 1 June 1997) because these are the last full day, month, and year completed. Would you even go further and call this the first millenium - because we have not yet completed the second? Your interval-counting example is a good one. The common pitch class notation with numbers does use 0, however, as the value for unisons, so that intervals in the system can be added without subtracting 1. 0 in this case is exactly like that moment when years 1 BC and AD met - it has no magnitude. The value 0 is not always meaningful for musical purposes, however. Consider a harmonic series over the fundamental n. The series goes: (1n, 2n, 3n ...). In terms of frequency, 0n (Zero n) is undefined. Unfortunately, one notation frequently used by practicing musicians considers 2n to be the ''first flageolet'' - in effect, your birthday notation - which leads to real confusion in reading scores where the actual pitch is not notated. Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Sun, 1 Jun 1997 20:17 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA06094; Sun, 1 Jun 1997 20:17:11 +0200 Date: Sun, 1 Jun 1997 20:17:11 +0200 Received: from ella.mills.edu by ns (smtpxd); id XA06099 Received: (qmail 18443 invoked from network); 1 Jun 1997 18:17:03 -0000 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 1 Jun 1997 18:17:03 -0000 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu