source file: mills2.txt Date: Wed, 26 Feb 1997 19:22:26 -0800 Subject: Re: Reply to Matt Nathan From: Manuel.Op.de.Coul@ezh.nl (Manuel Op de Coul) From: PAULE >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. Yes, this bears repeating because I really believe it is true: Pieces in minor tended to end with a Picardy (major tonic) chord in the days when the minor triad was tuned 10:12:15. When the tuning became much closer to 16:19:24, it became ok to end on a minor triad. I claim, because I hear this (maybe it's just difference tones, maybe not) that this is due to that fact the the fundamental of 16:19:24 is octave-equivalent to the root, establishing a more stable sonority. The distinction between the two chords is enough to give them a different nature, both useful, while the distinction between a just and an equal-tempered major triad is merely that the former is smoother than the latter. So JI composers might have little use for two versions of the major triad (4:5:6 vs. 1/24:1/19:1/16), while relishing the distinctions between 10:12:15, 16:19:24, and also 6:7:9. >> 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. let me add "of melodies that exceed a perfect fourth in range" to the above. Also, I said important, I didn't mean necessary, I meant helpful. >> 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? In the West, these modes (which I love using and talking about; don't forget the harmonic major scale) arose in the era of triadic harmony. The melody has deferred to the harmony. I guess that just proves your point, doesn't it? Well, I still think there is room for an "unaccompanied melody" aesthetic in harmonic music. More on this later. Modes like these and even more complex ones arose in the Middle East and India, though. However, the modes which do exhibit some tetrachordal similarity are considered more basic in these cultures. They use altered modes as a means of achieving the musical depth and variety for which the West relies on harmony. Sometimes I really prefer the purely melodic approach, and find classical modulatory contrivances boring. Other times there is nothing more breathtaking or subtlely beautiful that a well-conceived modulation. >[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, A severe violation of Occam's razor! >or at least a different >7 pitches than say I-IV-I, Well, I don't see a single pitch that would have to be different, but if you meant I-V-I, yes, you're correct. >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. So you're saying that even if the melody really stands up on its own, different harmonizations may produce different pitch inflections in the melody. That may be so in slow tempi, but it must be recognized that if the melody is the basis of the composition, these inflections do not represent different pitch classes but just acoustically favorable dispositions of some pitch classes. The melody should have a description, in terms of slighlty mutable pitch classes, that reflects the fact that it is the same melody regardless of harmonization. If you treat the different JI dispositions of a given pitch class as different pitch classes, your analysis of thematic development in common-practice works would end up reaching ridiculous conclusions, since a downward drift is so common in JI realizations of the repertoire. The home key is the home key, not a key seven commas flat. This is why I love meantone tuning. It is almost as pure as JI, and you don't have to worry about any of this! Unfortunately, dominant sevenths are rather ugly in meantone, so it's better for Monteverdi than for barbershop. Augmented sixth chords in meantone are great barbershop sevenths, though! >> >(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. Recent data I have seen on barbershop singing points to major thirds of around 397 cents (string players average around 405 cents), but plenty of flattened minor sevenths. It appears musicians are unwilling to lessen the degree to which tendency tones "lean" to their target from the equal-tempered standard, but are quite willing to increase this leaning when the results are acoustically favorable. In any case, understanding the fact that the Helmholtz, as Ellis attests, was more interested in proving his theories than making objective measurements. He was a genius of natural physics, but music is not a natural phenomenon. Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Thu, 27 Feb 1997 04:44 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA16882; Thu, 27 Feb 1997 04:44:41 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA16915 Received: from by ella.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) id TAA00607; Wed, 26 Feb 1997 19:43:10 -0800 Date: Wed, 26 Feb 1997 19:43:10 -0800 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@ella.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@ella.mills.edu