source file: mills2.txt Date: Thu, 6 Feb 1997 16:52:43 -0800 Subject: to PAULE, Major 6 9, subharmonics From: Matt Nathan [belated reply to Jan 14 message] PAULE wrote: > >[Matt Nathan] > >The "problem" here may be in trying to transfer what in 12tet is considered > >a > >consonant chord--a Major 6 9 chord--into JI and trying to make it serve the > >same purpose. > > Well, many JI advocates try to do this sort of thing all the time, equating > "purpose" with ratios. In fact, it sounds like that's just what you're doing > here: > > >My question would be, "why try to use a structure which doesn't suggest > >itself > >musically?". > > where by "musically" you mean nothing but "in terms of ratios." You're putting words in my mouth. Let me paraphrase, first "purpose", then "suggest itself musically". What I mean by purpose is the association "a pleasant chord". In 12tet, a Major 6 9 chord has taken on this association over time just as diminished chords have taken on the association of "danger". This can happen because in 12tet a Major 6 9 chord is relatively consonant compared to other possible structures, even though if you listen closely, it's actually dissonant. This sort of thing can take place in any limited pitch set, where there are only so many possible structures, so that there are no competing "better" choices for producing an effect, and so a particular stucture will win out. In unlimited JI, being an infinite pitch set (infinite yet not containing all intervals of course), relative dissonance or consonance is based directly on the tuning so this ability to "choose the lesser of two evils" in creating associations doesn't exist in the same way. In JI there are many many more-consonant and more-pleasant structures than the various approximations of a 12tet Major 6 9 chord. When people put up examples like this to show me that there's a problem in JI because, say, a Major 6 9 chord is dissonant in JI, I note that the problem is in trying to transfer a structure that means something in another tuning system into JI and expecting JI's various approximations of this structure to mean the same thing (have the same association, especially as compared to other structures available in the system). What I meant by "suggest itself musically" is to play around with the resources in JI (improvise, if you will, on paper or in real time) to find out what's there, and see what kinds of consonance-dissonance relations can be found, and what kinds of associations spring up, and to use these musically--rather than improvise in 12tet and then try to translate it into JI. To me, a Major 6 9 chord doesn't "suggest itself musically" in JI, the way it does in 12tet. Other structures do "suggest themselves musically". > >1/1 9/8 5/4 4/3 3/2 5/3 [...] starts to support its own dissonance in a > really nice way since > >each little otonal 8:9:10 subset resonates on its own even with the 40/27's > >and stuff going on between them, at least to my ear. > > Yeah, but try the utonal version of this chord -- blech! I can't hear it in my head, but I'll bet you're right. I tend n ot to "believe in" utonal structures at this point in my exploring. I mean, I can use them and hear them, just as I can hear and use stacks of various arbitrary intervals, but utonality doesn't seem to have the same self-organizing "pull" that otonality has even though the math would suggest it. I reserve the right to alter my position. > Polytonality is > much easier to establish with otonal than with utonal units, as every early > 20th century composer knew. This is probably because otonality is easier to establish period! The difference tones in otonality tend to support the same otonality. The difference tones in utonality tend to disrupt the utonality by producing difference tones which would support an otonality instead. Summation tones would tend to support utonality, but I lean towards the camp that holds that these are rarely heard and are practically unimportant in the natural hearing process. I've even read that difference tones may be generated internally, as part of the hearing process itself, so that even listening to two sine waves in head phones at low levels, we do some "otonal"-style internal processing. After once reading mail from Marshal Tuttle on the Fidonet Comp 101 echo (BTW, does anyone know how to access Fidonet via internet?) who said that string players tend to tune major thirds as pythagorean (81/64) and minor chords 12tet (300 cents), I wanted to see what JI interval a 12tet minor third is close to. It turns out to be a close match with 19/16 at 297.5 cents; roughly the same error as a 3/2 receives in 12tet. Compare this to the generally accepted standard JI minor third 6/5 at 315.6 cents. The first-order difference tones for 16:19:24 are 3:5:8, making it possible that these string players are intuitively aiming for an otonal, not utonal, minor chord! > Or you can see this chord as a > 24:27:30:32:36:40, whose first-order difference tones form a > 2:3:4:5:6:8:9:10:12:13 chord . . . Neat. It would probably work well in the high register, to bring this out. Matt Nathan Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Fri, 7 Feb 1997 05:03 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA14256; Fri, 7 Feb 1997 05:02:59 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA28594 Received: from by ella.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) id UAA24653; Thu, 6 Feb 1997 20:01:19 -0800 Date: Thu, 6 Feb 1997 20:01:19 -0800 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@ella.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@ella.mills.edu