source file: mills3.txt Date: Sun, 28 Sep 1997 21:52:14 +0200 Subject: Prime neighborhood From: DFinnamore@aol.com All of us have no doubt noticed that the strangeness/poignancy/difficulty of intervals increases as higher primes are introduced into ratios, up to and including 13. After that, 17 and 19 are fairly tame/consonant sounding and relatively easy to work into the rational scale fabric, then with 23 it starts getting pretty bizarre-sounding again. Here's a related observation I find interesting. Look at the neighboring integers of prime numbers in terms of their octave-equivalent factor(s): 3, the most consonant ratio-maker lies above and below octaves of 1 5 lies above 1 and below 3 7 lies above 3 and below 1 OK. So far the neighbors are all octave-equivalents of 1 and 3. Perhaps consequently, most people easily accept 7-limit harmony but have trouble with higher numbers like: 11, which lies above 5 and below 3 13 lies above 3 but below 7 17, however, lies above 1 and below 3^2 - almost back to the simplicity of base-10 single-digit primes 19 lies between 3^2 and 5. That might seem to be as complex as 11 but notice that the order is swapped - above 3 and below 5 this time. With 23 and beyond, we're back to more complex neighbors. Does this mean anything? It seems a pretty wacky coincidence if that's all it is. David J. Finnamore Nashville, TN SMTPOriginator: tuning@eartha.mills.edu From: Fred_Kohler@bc.sympatico.ca Subject: Re: TUNING digest 1191 PostedDate: 29-09-97 17:58:18 SendTo: CN=coul1358/OU=AT/O=EZH ReplyTo: tuning@eartha.mills.edu $UpdatedBy: CN=notesrv2/OU=Server/O=EZH,CN=coul1358/OU=AT/O=EZH,CN=Manuel op de Coul/OU=AT/O=EZH RouteServers: CN=notesrv2/OU=Server/O=EZH,CN=notesrv1/OU=Server/O=EZH RouteTimes: 29-09-97 17:57:59-29-09-97 17:58:00,29-09-97 17:56:58-29-09-97 17:56:59 DeliveredDate: 29-09-97 17:56:59 Categories: $Revisions: Received: from ns.ezh.nl by notesrv2.ezh.nl (Lotus SMTP MTA v1.1 (385.6 5-6-1997)) with SMTP id C1256521.0057B0F3; Mon, 29 Sep 1997 17:57:49 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA01515; Mon, 29 Sep 1997 17:58:18 +0200 Date: Mon, 29 Sep 1997 17:58:18 +0200 Received: from ella.mills.edu by ns (smtpxd); id XA01502 Received: (qmail 22787 invoked from network); 29 Sep 1997 08:58:14 -0700 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 29 Sep 1997 08:58:14 -0700 Message-Id: <199709291555.IAA00482@zorro.bctel.ca> Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu