source file: mills3.txt Date: Thu, 8 Jan 1998 22:34:50 +0100 Subject: RE: Special Way From: "Paul H. Erlich" I thank Carl for the review, and I will try to respond to some of his contentions. > >}What is this Special Way? Krumhansl, quoted by Mr. Erlich, seems to be >}touching on it: "If chord construction is determined in some principled way >}by scale structure, then this further serves to maintain the tonal >}framework for encoding pitch information." > >"Special Way?" You are a Yes fan, you must be a Genesis fan too :) > >}Most western classical music happens to work in this Special Way, and the >}thing it uses to do it is the diatonic scale. Mr. Erlich's goal, if I'm >}not mistaken, is to find a new scale suitable for use in this Special Way. > >}To recap so far, I am using "Special Way" to mean a way of explaining >}beauty in music from how melody and harmony are related, a construct >}heretobefore unknown to music theory, at least at the level Mr. Erlich >}takes it. > >Wow, I strongly disagree. Virtually every music theorist who does not care >about tuning issues understands harmony in terms of the diatonic scale and >tonal functions. "Functional harmony" -- ring a bell? Unfortunately, >virtually every alternative-tuning theorist does not so understand harmony. >This is unfortunate. It seems that "music theory" is divided into two >schools, and Carl is perhaps only familiar with the alternative-tuning >school. There is much of value in the other school, Carl. > >} In his paper, it is called "Generalizing diatonicity". I >}suggest this is an unfortunate term, as it implies the diatonic scale, >}which is exactly what he wants to replace, kind of how "octave" isn't a >}good way to say "2/1", since it implies 12-tone... > >Actually, octave implies a heptatonic scale, not necessarily in 12-tone. But >I don't think I invented the term "diatonicity." > }He then defines a set of scales as candidates for representing the 7-limit. }These scales are assumed to be root of 2 equal-step tunings, with only one }pitch per 7-limit approximation. > >}The one pitch per approximation thing is necessary for the Special Way to >}work, as far as I can tell. I can't quite tell you how, but I have a gut >}feeling it is, and since the Special Way is what we're after, I won't argue >}it. Besides, it keeps the size of the pitch set manageable. > >I couldn't very well consider every possible tuning system in the paper. >Keeping the pitch set manageable is an important goal. Modulation flexibility >is as well; although I don't mention it in the paper, I assume readers are >familiar with this feature of ETs. However, I leave it to you to prove to >yourself that your gut feeling is correct, or if it is not, and there is a >non-equal-step tuning that satisfies all the properties I list, then we >should know about it! > >}The root of 2 part is understandable, considering that we need strong low >}identies for our 7's to work. This seems contradictory to the rule that >}the higher identities are more sensitive to mistuning, since there are more >}low-numbered fractions near them. > >I don't see any contradiction. > >}Indeed it is, and perhaps it is a >}counterbalance to this principle. The paper offers only that "octave >}equivalence seems pervasive" and that it is "universally perceived, even by >}some animals". > >That's the key. I did not have room in the paper to consider tempering the >octave, but as you know, I have no objections to doing so. > >}The matter of mistuning is far from clear, even touching back on our old >}bone about unknowingly passing low-numbered ratios when measuring cent >}detuning of an interval. Paul's paper addresses this by making the >}standard deviation in log-frequency detuning inversely proportional to the >}limit of the interval. > >That is not correct. I do offer this as an alternative model, but the first >model, in which the standard deviation is constant for all intervals, is the >one which yield the candidate tunings: > >}So the list of scales comes down to 22, 26, 27, and 31 tone equal >temperament. > >Can you suggest a way to make the paper less confusing on this point? > >}..in what would be letter "d", Mr. Erlich makes use of a term I do not >}understand: "characteristic dissonance". He defines it to be any dissonant >}interval that shares the same number of scale steps as a consonant >}interval. Shadings of dissonance aside, what kind of scale steps we >}talkin'? The example of the diminished 5th is given, but why it should be >}considered a type of 5th, or why the P5 should not be considered a 7th is >}not made clear. > >Are you serious? Count scale steps. Anyone in a traditional theory class >could answer this blinfolded; perhaps I presumed too much of the traditional >theory background when writing this paper. > >By the way, all the numbering and lettering in my paper is screwed up, thanks >to Microsoft. > >}So has the paper provided a good definition of the Special Way? Yes. Has >}it succeeded in convincing me that the Special Way is still good, and that >}the 22TET decatonic scale is a fresh vehicle for it? Without a doubt. >}What it hasn't provided is a name for the Special Way. Maybe "tonality" is >}best, but I didn't use it because it has so many other meanings. > >In alternate-tuning land, yes. In traditional theory land, it has a very >specific meaning. Traditional theorists usually think that extending >consonance to the 7-limit means throwing out tonality. I make a case that a >7-limit system of tonality exists. > >}Serialism is certainly devoid of the Special Way -- and no doubt there is >}good serialism to be done -- but it is also lacks consonance. > >Hmmm. Serialism, and much 12-tone theory, _does_ make a big deal about using >the same pitch sets for melody and harmony. I think 11TET would work much >better for dissonant serialism than 12TET, since 11TET is the most effective >tuning for random dissonance, and 11TET is a subset of 22TET. > >}Far out avant garde music is certainly lacking of Special Way, if not other >}things. > >And I do love far-out avant garde music like Henry Cow, when I'm in the mood >for it. I love Phish when they go far out, and I think 22TET can take you a >lot farther out than 12TET. But sometimes you just want to listen to >something that "takes you home". > >}Indian chamber music and Bagpipe music are good examples, but they stay >}inside one tonality, the fundamental of which is played on a drone. I love >}them both, and they are extremely consonant, but this is not going to >}satisfy hardcore Special Way fans. > >I will admit that the closer you are to JI, as long as major and minor whole >tones are not too different, the better for these styles. > >You did not address the rest of my paper, such as my demonstration that 22TET >is virtually the best tuning for the decatonic scales. It may seem circular >since I found the scales in 22TET, but one might have hoped for a better way >of tuning them, which (perhaps unfortunately) does not exist. > >Modulatory effects only possible in JI -- can you give a specific example? SMTPOriginator: tuning@eartha.mills.edu From: John Starrett Subject: new microtonal freeware PostedDate: 09-01-98 00:28:35 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: 09-01-98 00:28:09-09-01-98 00:28:11,09-01-98 00:28:05-09-01-98 00:28:05 DeliveredDate: 09-01-98 00:28:05 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 C1256586.0080E8DB; Fri, 9 Jan 1998 00:28:31 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA31737; Fri, 9 Jan 1998 00:28:35 +0100 Date: Fri, 9 Jan 1998 00:28:35 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA31685 Received: (qmail 16842 invoked from network); 8 Jan 1998 15:28:32 -0800 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 8 Jan 1998 15:28:32 -0800 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu