source file: mills3.txt Date: Thu, 11 Dec 1997 04:57:59 +0100 Subject: 19-tone equal divagations From: Gregg Gibson I am pleased that my postings have elicited so many responses, some of them quite thoughtful. It is pointless to reply to those who have convinced themselves that extremely minute intervals (narrower than a quarter-tone) can acquire true melodic independance. Many years of hopeful experiment in this direction have led me to conclude decidedly otherwise. Even 24-tone equal, despite decades of determined exposition by divers revolutionaries, remains utterly irrelevant to the main course of musical evolution. While the starry-eyed among us attempt to distinguish what is not distinguishable, the 12-tone equal continues to effect its ravages on our ears. Indeed this miserable temperament has never been so universal as it is today. And so the pretended best becomes the enemy of what is actually usable (19-tone equal), and the ally of the worst. Turning now to some of the comments that have been made in response to some of my ideas. To suggest that the use of the 12-tone equal has induced subjects to fix on the 50-cent quarter tone as the limen of melodic perception is superficially plausible, but fails when it is recalled that the musically naive tend to be less, not more sensitive to the narrower intervals. See for example Szasz. This also assumes that it is possible to internalize the 12-tone equal to such an extent that it can replace the just intervals as the criterion of intervallic hearing, than which nothing is less certain. Bill Alves (quoted by Paul Ehrlich) made a very interesting comment to the effect that the four chromatic modal genera (scales) comprising 28 modes, that I have discovered and posted: C D E F G A B C C D E F G Ab B C C D E F G Ab Bb C C Db E F Gb A Bb C can be played in the 12-tone equal. But before I comment on this I would like to observe that the three most usual forms of the modern (post-Baroque) minor scale are present among these 28 chromatic modes. John Chalmers, in a private communication, has commented on this to me (I hope I do not misrepresent him), and it is certainly a very intriguing circumstance that I have long since noticed. But to return to the matter of playing these in 12-tone equal. Yes, this is of course possible, but the resulting modes conflate a number of aurally distinct modes into single, neutral modes, and lack much of the distinct melodic character of the 19-tone versions. For an example of what I mean, take the most common form of the minor scale (on C for convenience): C D Eb F G Ab B C This can be played in 12-tone equal, but loses much of its piquancy thereby. This is partly because the highly characteristic augmented tone Ab-B is confounded with the minor third. Historically, the 'minor scale' derived much of its attractiveness from the use of the mesotonic, which preserves the augmented tone close to the just values (there are several). I have elsewhere referred to the fact that this is one of the few respects in which 31-tone equal is melodically quite distinct from 12-tone equal. But 19-tone equal is still more distinct. Again, to give a better idea of exactly why one cannot adequately play chromatic modes in 12-tone equal, let me offer up Yasser's old (but very good) analogy between 12-tone equal and 7-tone equal. One can reproduce the seven diatonic modes in 7-tone equal, but they are merged into a single, neutral mode, for 7-tone equal has no semitones. This is very much what occurs when a chromatic mode such as C D Eb F G Ab B C is played in 12-tone equal - it is largely sterilized of its unique modal flavor, because the two species of semitones are confounded. Indeed, even the _diatonic_ modes are severely enfeebled in 12-tone equal, both because this temperament has such poor consonances, and because its dissonances are not intense enough to provide the requisite tension between consonance and dissonance, which is (within a suitably tempered, coherent, closed system) what propels music forward both melodically and harmonically. Paul Ehrlich asserts that 22-tone equal is the only path to escape diatonicism. Not so. His categorical attitude is refreshing, but 22-tone equal is not a temperament at all, but a mere tuning artefact that reproduces the worst defects of just intonation. Not that I wish to question the validity of the just ratios as standards for musical thought. The two principles that constitute genuine alternatives to diatonicism are: 1) The chromatic genus, where harmony is required. I have defined the four modal genera comprising 28 modes that have enough consonant chords on enough degrees (4 of 7) to be harmonically usable in chromaticism. Here is as good a place as any to remark that there are two additional chromatic genera that possess consonant chords on 4 of the 7 degrees (none have consonant chords on 5 or 7 of the degrees, and only the diatonic has such chords on 6 of the degrees): C _Db_ E F G A B C C Db Eb F G Ab _B_ C These however each contain a degree (underlined) that is a member of no consonant chord within the modal genus, and therefore the modes of these modal genera (scales) could never be established in harmony. 2)the enharmonic genus, where harmony is not an important element. This involves the use of 1/3 tones, which are never written in our music, but which fill the living rock melos of our people. No theorist should ever presume to discount the importance of what the musically untutored produce from their own melodic inspiration. They stand in need of our guidance, but we also of theirs. The 19-tone equal temperament _alone_ can give access to either of these two genera, just as it alone gives adequate access to the diatonic genus. This follows from the principle of the melodic limen, and from the incredibly close harmonic congruence between just intonation and the 19-tone equal. I have not leisure here to treat this in the depth that it deserves, but would like to observe something that I do not believe has ever been clearly noticed before. If the consonances of the senario are each taken as new tonics, we arrive at 19 just intervals within the octave: 1:1 25:24 16:15 10:9 9:8 16:15 5:4 32:25 4:3 25:18 36:25 3:2 25:16 8:5 5:3 16:9 9:5 15:8 48:25 2:1 These are the intervals that singers can actually sound accurately singing pure consonances, although there is some debate concerning the ability to reliably distinguish between the commatically separated species of tones. Of these, the 19-tone equal merges the minor and major tones, and also the two species of minor seventh, and intercalates the augmented tone/diminished third and the augmented sixth/diminished seventh. Thus this temperament directly corresponds to the most fundamental intervals of just intonation. No other temperament enjoys such a direct correspondence, although the 31- and 50-tone (_not_ the 17- 22- 43- or 53-tone) equal are next in the sequence. Finally, on a lighter note, Carl Lumma was somewhat incoherent in his remarks. Perhaps he would care to extend on them. Does he have a tuning system that he thinks is not ridiculous and not 'un-good'? SMTPOriginator: tuning@eartha.mills.edu From: Aline Surman Subject: various PostedDate: 11-12-97 07:17:47 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: 11-12-97 07:15:56-11-12-97 07:15:57,11-12-97 07:15:42-11-12-97 07:15:42 DeliveredDate: 11-12-97 07:15:42 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 C125656A.00226761; Thu, 11 Dec 1997 07:17:43 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA12373; Thu, 11 Dec 1997 07:17:47 +0100 Date: Thu, 11 Dec 1997 07:17:47 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA12369 Received: (qmail 12693 invoked from network); 10 Dec 1997 22:17:43 -0800 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 10 Dec 1997 22:17:43 -0800 Message-Id: <348F8EA8.24C9@dnvr.uswest.net> Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu