source file: mills3.txt Date: Sat, 20 Dec 1997 02:24:48 +0100 Subject: More of Septimals From: Gregg Gibson Gregg Gibson said: > > There do exist a few septimal triads that seem to escape this argument, > > e.g. 5:6:7, 4:5:7, 4:6:7. But a few triads do not begin to compare with > > the richness and variety of the harmonies of the senario. Graham Breed said: > Exactly what are you trying to say, Gregg? You come up with an > "undeniable" argument, and then deny it! Or, am I > misunderstanding? To my ears, these chords are certainly more > concordant than their constituent dyads. Three examples are quite > enough to disprove that little theory. I mean, for example, if you add a fourth note to the triad 4:6:7, e.g. 4:6:7:8 or 4:6:7:12 you very often get an undoubtedly dissonant chord. 4:6:7:8 is dissonant because of 8:7, 4:6:7:12 is dissonant because of 12:7. This is what I mean when I say the senario (i.e. the consonant chords of the senario, the least consonant of which are more consonant than the least disssonant septimal chords) are consistent with themselves, while the septimal chords give rise to dissonance when a fourth tone is added. For what it is worth, I find the septimal triads 4:6:7 and 4:5:7 more 'major' in effect than 'minor', but definitely dissonant. I have heard them in many different temperaments, but of course the just versions are the standard. There are excellent acoustical reasons for supposing the septimals dissonant. Musical dissonance and consonance are not absolutely relative, but must remain to the physical constraints of nature if they are to have any artistic meaning. A translation of Mersenne has been done, although maybe not the relevant part. You are very well-informed about the modern habits of thought, but the older writers also repay study. The '5-limit' and '7-limit' habit of thought can be very dangerous if it is not carefully borne in mind that each include very different intervals and chords, with different effects. I have heard people wrap themselves in knots trying to 'hear' 9:7 as consonant because they got it into their muddled heads (I was one of them, boy have I had some strange notions) that it somehow had something to do with the 'consonant 7-limit'. SMTPOriginator: tuning@eartha.mills.edu From: "kris peck" Subject: aliens who actually like worthless lemons! PostedDate: 20-12-97 03:22:47 SendTo: CN=coul1358/OU=AT/O=EZH ReplyTo: tuning@eartha.mills.edu $MessageStorage: 0 $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: 20-12-97 03:20:37-20-12-97 03:20:38,20-12-97 03:20:13-20-12-97 03:20:13 DeliveredDate: 20-12-97 03:20:13 Categories: $Revisions: Received: from ns.ezh.nl ([137.174.112.59]) by notesrv2.ezh.nl (Lotus SMTP MTA SMTP v4.6 (462.2 9-3-1997)) with SMTP id C1256573.000CDEB0; Sat, 20 Dec 1997 03:22:30 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA22422; Sat, 20 Dec 1997 03:22:47 +0100 Date: Sat, 20 Dec 1997 03:22:47 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA22384 Received: (qmail 6527 invoked from network); 19 Dec 1997 18:22:44 -0800 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 19 Dec 1997 18:22:44 -0800 Message-Id: <199712200219.UAA10051@riptide.wavetech.net> Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu