Yahoo Tuning Groups Ultimate Backup mills-tuning-list RE: Special Way

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
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RE: Special Way

🔗"Paul H. Erlich" <PErlich@...>

🔗"Fred Kohler" <Fred_Kohler@...>