RE: 22TET

>}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???


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From: alves@orion.ac.hmc.edu (Bill Alves)
Subject: Re: 22TET
PostedDate: 09-01-98 21:31:29
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