source file: mills3.txt Date: Sat, 13 Dec 1997 02:53:12 +0100 Subject: Worthy & Worthless From: Gregg Gibson My qualification of some temperaments as 'worthless' seems to have caused much offense to a few. By 'worthless' I do not mean 'morally reprehensible' or 'indicating criminal insanity in those who use them'. I mean that certain temperaments grossly reduce the number of expressible, distinct melodies as compared with other temperaments _or_ deprive us of even so much consonant harmony as is found in the senario. (I find septimal intervals quite valuable as dissonances, but happen to believe the senario includes all consonance... that is another subject though.) Actually, every one of the worthless temperaments that have some following (17- 22- 29- 34- 41- & 53-tone equal) impoverish _both_ melody and harmony. This is too complex to even begin to prove here. This will have to wait for its own post. Some assume that every system has at least a few interesting features, and therefore, I presume, that music should use an infinity of different temperaments, with perhaps the best (if they can bring themselves to make any judgements at all) enjoying slightly greater use. This is the opposite error to that made by previous generations of theorists, who with the enormous resources of the 19-tone equal staring them in the face, looked at its flat fifth for a second or two, dismissed this temperament without taking five minutes to inquire if this could be remedied, and went on to lose themselves in the serpentine coils of 53 tones in the octave. I am thinking of Ellis in particular, but thousands more made the same mistake. Every generation seems to delight in making the opposite mistakes from those made by its predecessors. This universal, unconditional tolerance betrays an astounding naivet? about human nature, and also about musical reality. For those who haven't noticed, 12-tone equal rules our musical life perhaps more than any musical system has ever tyrannized over a culture. One is reminded of the Chinese with their sacred bamboo pipes and later, their edicts against wicked temperers of the pythagorean scale. Those who expect instrument-makers to provide us with thirty different fundamentally different kinds of guitar or keyboard or oboe, and who imagine music teachers will be found to instruct pupils on them, inhabit the happy realm of Faerie, where all things are possible. Happily however, anyone who dispassionately investigates the subject of temperament with the view to expanding our musical resources will at once (I mean, after 10 years or so) find one temperament - and one only - that _dramatically_ expands the melodic and harmonic resources of the 12-tone equal... and of just intonation as well! This is 19-tone equal. I would like to now begin to explore why this is so, at least in outline. Here we have a temperament that opens up to us an immense world of enharmonic melody, to begin with. This, as the great theorist Francisco Salinas long ago noted, is the _only_ system that does so, for it alone provides us with an interval, the 1/3 tone, that is wide enough to always effect a change in melody when a given melodic member is altered thereby, but narrow enough never to be confused with the diatonic semitone. To give some idea of just how immense this universe is - and remember these are _real_, usable resources, not purely theoretical, aurally imperceptible variations - compare the number of modes (I here use the term loosely merely to indicate a collection of seven notes used in a melody) consisting of 12 notes taken 7 at a time: nCr where n = 12 & r = 7 = 792 with the number of modes consisting of 19 notes taken 7 at a time: nCr where n = 19 & r = 7 = 50,388 Most of the difference consists of 19-tone enharmonic modes. Later, if there is an interest, I will provide some summaries of some of my studies of chromatic modes (those modes that are neither enharmonic nor diatonic) which should make it clear that in that respect as well, the 19-tone equal is far, far richer melodically than the 12-tone equal. The harmonic contrast between 12- & 19-tone equal is no less dramatic. It is not merely that 19-tone gives much more consonant chords. It also gives much more powerfully, wrenchingly _dissonant_ chords. These are not whining, commatically mistuned consonances such as one finds in 53-tone equal, but outright dissonances that possess full _melodic_ independence from any consonance. This power of the 19-tone dissonances is obvious when one recalls that the augmented primes, augmented & diminished fifths, and augmented & diminished octaves of the 19-tone equal are roughly 1/3 tone from the just consonances, instead of about 1/2 tone as in the case of the 12-tone dissonances, and consequently much more dissonant. These 19-tone dissonances happen to fall in precisely the most dissonant regions that surround these most powerful consonances. One proof of this is Helmholtz' famous graph of the smoothness of violin tone; when the 19-tone dissonances are superimposed thereon it will be found as I have observed above. 12-tone equal has weakly consonant, rather simpering chords and weakly dissonant chords; the contrast between the two classes is feeble, and the overall effect leaves the heart stone-cold. It is scarcely surprising that under the leaden weight of such a temperament, harmony has fallen into disrepute. 19-tone equal has, especially if its octave is stretched by two or three cents to equalize the roughness of its fifths and fourths, extremely smooth consonances. The fourth is scarcely more sensitive to mistuning than the third, for reasons having to do with beating partials present in the fourth. Consequently one can mistune the fourth much more than the fifth without noticeably impairing its consonance. The consonances of the 19-tone equal are just mistuned enough to be brilliant, but of course not quite so smooth or quiet as those of just intonation. Hence, 19-tone equal gives rise to a powerful contrast between consonance and dissonance, both melodically and harmonically speaking. The effect is to give music a kind of elastic, forward impetus quite unknown in the 12-tone equal, which has a more static, uncertain esthetic. This contrast between consonance and dissonance affects the emotions very poignantly. Composers with a reputation for formalism or mannerism such as Gesualdo, Haydn and Mozart seem bursting with suppressed vitality in the 19-tone equal. Gesualdo in particular is virtually a different - and a far better - composer in the 19-tone equal, lending credence to the story that he owned a 19-tone clavier (not necessarily, but quite possibly more or less equally tempered.) No other temperament, and certainly not the 31-tone equal with its continual problems of interval confusion in melody, can remotely compare to the 19-tone equal for sheer tension and force. In a famous passage, Fokker has spoken of 31-tone equal having two faces, one turned to the past, one to the future. This is far, far more profoundly true of the 19-tone equal. For the 19-tone equal, at the same time that it renders the ancestral music of our own culture more present to the imagination and the emotions, also opens up to us the unsuspected melodic riches both of rock music and of non-Western cultures, of which the former however is of more vital concern to our own people than the latter. For any song that can be sung and reliably reproduced by singers, can be notated and played in 19-tone equal. This is a consequence of the fact that, providentially, the human melodic limen (55-60 cents) is just narrower than the tuning degree of 19-tone equal (~63 cents). This may not, by the way, be _entirely_ providential. Our species may have evolved as a 19-tone-equal and 5-limit interpreter of musical experience. I merely suggest this by the way... obviously this is very speculative. All this means that, for the first time, this temperament permits us to notate all musical traditions - especially our own living, popular, rock tradition - with as much precision as singers (and listeners) can reliably reproduce (and esthetically understand) their own native melodies. All this is very exciting, and at least merits determined popularization. I make no doubt that popular, Renaissance, and classical musicians alike have very much to gain from the commercial development of 19-tone instruments. The academic 12-tone equal abortions of our century are of no concern. Undoubtedly the museums could preserve a few 12-tone instruments so that the odd musicologue could study these compositions, if he has nothing better to do. Instead of embracing the 19-tone equal temperament however, we seem, mostly through ignorance (the subject of temperament is at once very difficult, and poorly remunerated, and so progress has been slow) but partly from less excusable motives, more concerned to endlessly prove how better we are at hearing than the poor, stupid masses. Thank God we are all so wise. But among those masses are popular musicians, some of whom have more creativity in their little fingers than many a whole conservatory. Certain of the most creatively sterile academic composers are the most eager, either to perpetuate the 12-tone equal as some kind of apostolic chrism, or else to have us adopt some utterly lifeless, dissonant, emotionally neutral temperament, whose only claim to recognition is the certainty that no paying, demanding audience would ever sit still to hear such aimless, random impudence for five minutes. In other words, they seem to adopt temperaments other than 12-tone equal only as a means to out-Schoenberging Schoenberg. I would like to emphasize however that our 12-tone equal mandarins are far more malevolent (as will as far more powerful) than our most inconsequent microtonal devotees. Absurdities that everyone politely ignores are harmless, and beneath the civilized to condemn; it is absurdities enshrined in dogma that stunt and maim. SMTPOriginator: tuning@eartha.mills.edu From: "Bob Lee" Subject: Singing small intervals PostedDate: 13-12-97 08:35:43 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: 13-12-97 08:33:45-13-12-97 08:33:45,13-12-97 08:33:28-13-12-97 08:33:28 DeliveredDate: 13-12-97 08:33:28 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 C125656C.00298987; Sat, 13 Dec 1997 08:35:38 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA14408; Sat, 13 Dec 1997 08:35:43 +0100 Date: Sat, 13 Dec 1997 08:35:43 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA14411 Received: (qmail 20965 invoked from network); 12 Dec 1997 23:35:40 -0800 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 12 Dec 1997 23:35:40 -0800 Message-Id: <01bd0799$17c948e0$1f379bce@default> Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu