source file: mills3.txt Date: Fri, 9 Jan 1998 20:55:02 +0100 Subject: RE: 22TET From: "Paul H. Erlich" >}There are apparently two ideas at work here... > >}A) That higher limit intervals are more sensistive to mis-tuning "since >}they are more apt to be confused with other intervals". > >}B) What I call Tonality, and what Partch calls "Observation One". An >}effect created by the harmonic series, such that the number of pitches a >}given pitch will harmonize with is inversely proportional to the odd limit >}of the given pitch. > >WHAT!?? That makes no sense! First of all, Observation One is (A). Secondly, >(B) is false, or so wrong it's not even false. there is no such thing as the >odd limit of a pitch -- all intervals can be constructed above and below any >pitch. What do you really mean? > >}Idea "A" seems to suggest that we temper the octave the most, the fifth the >}next most, and so on up. But we can't do this without wrecking tonality, >}since the low identities provide that, as explained in idea "B". > >}Both A and B are really one idea, in that they're both caused by the way >}superparticular fractions get closer to eachother, so there's no >}"contradiction", true. But when tempering, it presents a trade-off >}situation, one which can't be well-addressed by just making the de-tuning >}inversely proportional to limit. > >None of the above makes any sense to me. Perhaps you have something in mind >that you'd like to clarify, but insofar as you're relying on (B), I honestly >can't figure it out. Moreover, I don't see anything special about >superparticulars. > >}>>}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: > >}I don't have the charts! But it says that the candidate tunings are the >}same, except that 22 & 26 are no longer better than 12 at the 5-limit. >}Nowhere do you say your candidates must be better than 12 at the 5-limit. > >The other list (22, 26, 27, and 31) comes from exactly this criterion (better >at the 7-limit than 12 is at the 5-limit), using a standard deviation of 1% >for all intervals. The alternative model uses 1% as the std. dev. for ratios >of 5, and 22 & 26 fail to approximate the ratios of 7 well relative to a st. >dev. of 5/7%. > >}>>}So the list of scales comes down to 22, 26, 27, and 31 tone equal >}>>temperament. > >How did you think I arrived at this list, if not by insisting that the >candidates must be better in the 7-limit than 12 at the 5-limit? > >}>> >}>>Can you suggest a way to make the paper less confusing on this point? > >}On the point of what scales are in the candidate list? > >Yes. > >}>>}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. > >}1) Conventional theory is full of holes. The tritone is spelled as an >}augmented forth in certain contexts, and as a diminished fifth in others, >}but it's the same pitch. > >First of all, it's an interval, not a pitch. Secondly, the augmented fourth >and diminished fifth _sound_ different in context, and one must resolve >outwards while the other must resolve inwards. > >}All the enharmonics should be thrown out in 12. >}But that's just my opinion. Why you consider it a type of fifth in your >}example was, in any case, not clear to me. > >Because you have to count 5 scale steps to get from the lower note to the >upper note, inclusive. > >}2) The smallest step in 12 is the semitone. Counting semitones, the >}tritone and P5 do not share the same number of steps. Thus, the tritone is >}not a characteristic dissonance of the 5th in semitones. So what kind of >}step did you mean? I would expect a definition of "step" that would be >}good for all the temperaments the paper was looking at. > >I did provide such a definition -- "step" means a step in the scale, not a >step in the tuning. Without a basic, "generalized diatonic" scale, the >concept is meaningless. My experience with pentatonic scales is what >convinced me that generic step sizes were a function of scalar context, and >not the result of some inborn affinity to 7TET or any such thing. > >}Funny enough, I actually understand what you were trying to do with these >}characteristic dissonances in your criteria, but the lack of a robust >}definition from the beginning really hurt me. > >Wow, I thought my definition was fine. It certainly seems robust to me. How >would you suggest I improve it? Perhaps by spelling out every single interval >occuring in each of the "generalized diatonic" scales? > >}>>By the way, all the numbering and lettering in my paper is screwed up, >thanks >}>>to Microsoft. > >}I noticed that. But why is it Microsoft's fault? Did you used some >}automatic numbering scheme? I hate that trend in software nowadays! It's >}not already so easy that you can't do it yourself? > >I couldn't figure out how to turn off the auto-numbering in Word 97. > >}>>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... > >}I actually had written that there's a time and a place for far out stuff, >}but I deleted it for style considerations. Do you mean Henry Cowell? I >}got a great Cd with Set of Five, Four Combinations for Three Instruments, >}Hymn and Fuguing Tune #9, and Trio in Nine Short Movements. Great stuff. >}And Junta! > >Henry Cow was a British group whose music was very composed, a bit Zappa-like >but much deeper emotionally (I feel). Have you seen or heard Phish live? >There's no comparison. > >}>>Modulatory effects only possible in JI -- can you give a specific example? > >}I'm not the best person to ask, since the only JI I've done is on the >}Cosmolyra (everything in root position) and on an conventional organ tuned >}justly (only one key). It just stands to reason that there are all kinds >}of effects, probably most of them un-discovered, based on the "anomalies" >}of JI. > >Actually, my composition in 22TET on the tape swap tape has nothing to do >with my paper; it has to do with the fact that various intervals, including >the syntonic comma "anomaly," are represented by the same interval in 22TET. >JI is only one of an infinite number of tunings with "anomalies." > >}The Ben Johnston thing does come to mind, this quote of his appearing in >}one of your ancient posts... > >[snip] > >}I've not heard the results of his efforts. > >The same thing would happen in 53TET. In 34TET, the drift would be greater. >In a schismatic temperament, about the same as JI. Nothing special about JI. > >}Probably the greatest expert on modulation in JI who ever lived was Partch, >}and I'm sure I've heard effects not possible in temperament in Rotate the >}Body and Delusion. > >I'm sure you can transcribe all Partch music in 72TET and not lose anything >in the modulatory effects. > >}Please Note: How the intervals are heard depends on context!!! I'm just >}throwing in my analysis here because sometimes a particular context seems >}to be assumed when giving rational approximations for the 22TET intervals... > >what context are you assuming??? SMTPOriginator: tuning@eartha.mills.edu From: alves@orion.ac.hmc.edu (Bill Alves) Subject: Re: 22TET PostedDate: 09-01-98 21:31:29 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 21:30:58-09-01-98 21:31:00,09-01-98 21:30:52-09-01-98 21:30:52 DeliveredDate: 09-01-98 21:30:52 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 C1256587.0070B18B; Fri, 9 Jan 1998 21:31:23 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA18602; Fri, 9 Jan 1998 21:31:29 +0100 Date: Fri, 9 Jan 1998 21:31:29 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA18295 Received: (qmail 18675 invoked from network); 9 Jan 1998 12:31:26 -0800 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 9 Jan 1998 12:31:26 -0800 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu