source file: mills3.txt Date: Mon, 8 Dec 1997 05:34:51 +0100 Subject: Discrimination of Intervals in Melody From: Gregg Gibson > Perhaps that's too elementary of a distinguishing task though. But even > among some more subtle tasks, like noticing 19TET's flat M3 and P5, and > comparing that to 31's right-on M3 and slightly flat P5, or to 12TET's > way-sharp M3 and almost exact P5, I have found that there are many musical > settings where those factors are audible. > > I certainly do agree that there are many musical settings where the > notes are just simply wizzing by too fast to hear those aspects of a tuning > as such. If that's the sort of distinction exercise you're talking about, > then I'd agree with your conclusion up to a point anyway. > I did not of course intend to question the ear's ability to distinguish quite minute intervallic differences in harmony or in tones considered not in respect to their melodic category, but rather in respect to their absolute height or hauteur. In melody however, which is the primary means by which harmony is produced (at least ideally) the critical limen of intervallic perception is on the order of 55-60 cents. If a given melody has one of its members altered by less than this limen, the melody may well be heard as vaguely different, but there will be _no_ fundamental change in melody. Were differences of 30 or 40 cents melodically significant, assuredly there would be no such thing as a reproducible melody at all, for singers very commonly diverge from one anothers' performances by at least these intervals, when rendering the 'same' melody! Granted that the limen is on the order of 55-60 cents, it follows that that temperament is melodically richest whose tuning degree is just wider than 60 cents. Indeed, such a temperament is melodically far, far richer and more varied than all other musical tuning systems combined, be they just or tempered. Simple probability theory suggests that 19-tone equal has about 70 times more distinct melodies than 12-tone equal, for example. Hence my interest in the 19-tone equal. This temperament also has permitted me to study all the various modes which are melodically distinct to the ear. Of the heptatonic modes, the familiar seven of the diatonic genus have consonant chords on six of the seven degrees, as is universally known. More subtly, every one of these degrees is part of at least one consonant chord (actually, of at least two) within the untransposed diatonic order. No other heptatonic modal genus has above four of its seven degrees which are the roots of consonant chords within the genus, all of whose degrees are included within at least one consonant chord. These genera are four in number, including 28 modes. On C these are: C D E F G Ab B C C D E F G Ab Bb C C Db E F Gb A Bb C C D E F G# A B C The so-called 'minor' mode of the Baroque is to be found on A within the last of these four, so it is evident that here we have quite a new field for melodic and harmonic experiment. I hope to publish some articles on this, when I can find the time. In harmony I agree that quite small intervallic variations can of course have a remarkable effect. I agree also that the fifths major thirds of 31-tone equal are slightly but noticeably smoother and more pleasing than those of the 19-tone equal. However, if the 19-tone octave is stretched by 2-3 cents, its fifths become quite as good as those of the 31-tone. Further, because the fourth is less sensitive to mistuning than the fifth, merely to make these intervals equally deteriorated one should stretch the octave. On my DX-7IIs and my Proteus/Mac setup I use a tuning degree of 63.3 cents with an octave of 1202.7 cents, and I find this noticeably more brilliant than the 19-tone equal without an octave stretch; I even prefer its harmonies to those of the 31-tone equal. I remember when I first became interested in more than 12 tones in the octave, I liked the _idea_ of as many tones within the octave as possible, and tended to consider 31 as the absolute minimum. But experience has taught me that the only viable alternative to the 12-tone equal is the 19 system. The 22-tone equal system is rather a tuning artefact than a temperament. Like that other much-over-rated system the 53-tone equal, it merely reproduces one of the primary flaws of just intonation, viz. the presence of two varieties of tone, with the consequent failure to close the cycle of fifths. These systems are therefore certainly no more musically viable than just intonation itself. SMTPOriginator: tuning@eartha.mills.edu From: Aline Surman Subject: Gregg Gibson's comments PostedDate: 08-12-97 06:11:35 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: 08-12-97 06:09:47-08-12-97 06:09:47,08-12-97 06:09:35-08-12-97 06:09:36 DeliveredDate: 08-12-97 06:09:36 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 C1256567.001C5930; Mon, 8 Dec 1997 06:09:38 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA09173; Mon, 8 Dec 1997 06:11:35 +0100 Date: Mon, 8 Dec 1997 06:11:35 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA09163 Received: (qmail 17195 invoked from network); 7 Dec 1997 21:11:31 -0800 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 7 Dec 1997 21:11:31 -0800 Message-Id: <348B8AFC.3DB2@dnvr.uswest.net> Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu