source file: mills2.txt Date: Tue, 25 Feb 1997 09:41:48 -0800 Subject: Re: Reply to Matt Nathan From: Matt Nathan > PAULE wrote: > > I think the diatonic scale long predated the discovery of 5-limit harmony in > most cultures (India is a possible exception, though only 3-limit > consonances are mentioned in the original texts). It was constructed from > melodic considerations only, which means that ratios beyond the 3-limit are > of negligible importance. Ascribing 5-limit ratios to the diatonic scale is > in most cases, as I have said before, a historico-geographic fallacy, and a > very Eurocentric one at that. A few other list participants have responded to the historical issues, and I will defer to them, not being an historian. I do think that just as practice differs from theory today, the two have probably differed through history. Even if your 3-limit history is correct regarding practice, we live today, and 5 is important now and has been for hundreds of years. I will hopefully live tomorrow as well, and 7, 11, 13, 17, and 19 are important to me too, so my music will reflect this. My ear doesn't seem to want to do anything with 23 or above right now, in fact, it kind of ignores 13 and 17 and jumps right from 11 to 19. This may be because I keep hearing 12tET minor thirds which are within 3 cents of 19/16. [snipped interesting stuff which I don't really have a response to] > The paradigm of similar tetrachords seems to be important > for melodic comprehensibility. I don't know where you get the data for statements as general as this. All I can say is that I can find examples of comprehensible melodies without simliar tetrachords. > The diatonic scale simply takes this concept to its extreme, > as tetrachordality manifests itself in every octave species. Neither ascending melodic minor nor harmonic minor have similar tetrachords. Each of these has modes which have also been used. Maybe you wouldn't considered these diatonic? [snipped more interesting stuff which I don't really have a response to] > ...Deriving the > diatonic scale from the tonic, subdominant, and dominant triads is utterly > inaccurate, in my opinion. There are too many pieces in major that focus on > I-ii-I progressions, and pieces in minor (aeolian, to be more academic) that > focus on i-VII-i progressions, for this to be an accurate explanation, for > not even the tuning of the chords will be correctly specified by such an > explanation. Here would be cases, like I-ii-I, which I would say are implying more than 7 pitches, or at least a different 7 pitches than say I-IV-I, which is what I meant when I said that much diatonic music implies more than 7 pitch classes and will be played that way when the ear is given sway. > >(I read, I think in Helmoholtz, > >about the comparative difficulty of solfege students to > >stay in tune as a group when accompanied by the (ET) > >church organ and ease when unaccompanied and allowed > >to sing in JI.) > > If they were not harmonizing but singing in unison, I seriously > doubt that they gravitated towards a scale with unequal whole > steps, though Helmholtz was clearly biased in favor of believing > that they did! I dare say that your own bias is clearly showing here, and that Helomholtz was probably more observant than you and I combined. I suppose one could rerun the experiment now to get another opinion. > As for quantifying dissonance... Thanks for the math references. Matt Nathan Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Tue, 25 Feb 1997 20:34 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA28910; Tue, 25 Feb 1997 20:34:02 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA25394 Received: from by ella.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) id LAA21949; Tue, 25 Feb 1997 11:31:19 -0800 Date: Tue, 25 Feb 1997 11:31:19 -0800 Message-Id: <199702251929.LAA21796@ella.mills.edu> Errors-To: madole@mills.edu Reply-To: tuning@ella.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@ella.mills.edu