hypertext by association

>My suggestion is maybe a directory of web pages proactively hyperlinked by
>all who come here. So that we can visit each others life & each others work
>in this particular (read peculiar) dimensional virtuality.

This may not be what you're talking about, but there are several pages of
links to sites concerned with tuning.

>>>

sorry I dont have the proper quoting doolies:

Im personally interested anything & everything in this space that lends
itself to more interactive participation of all posters, lurkers, specialists
etc. What I had in mind with my suggestion was more of a actually link page
of web sites, ftp sites, newsgroups, other mailinglists, of all who come here
regularly, EVEN IF IT DOESNT SPECIFICALLY REFER TO ALTERNATIVE TUNING.

MIEKAL

reread my post from yesterday & the spelling errors make it sound like my
keyboard is gummed up with old coffee spills & fingernail clippings. sorry
about that, any future submissions will be more closely edited. I was
obviously on a jag...

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>> Paul H.,
>>
>> I believe your original definition leads to consistency for level
>> N>1.5. For 1intervals
>> will be consistent with one another.

>Yes, I noted that in my "erratum" followup message. However, the
>algorithm I just posted in response to John Chalmers is correct.

Your new algorithm is not correct either -- at least it does not reproduce
my definition of consistency. In particular, no tuning can fail to be level
1 consistent according to your algorithm, and some tunings would be level 2
consistent according to this algorithm that wouldn't be according to your
original definition. I will give the correct consistency algorithm if you
wish. John C., you are correct that "fractional consistency" is kind of
meaningless; I was using it in the sense of Paul H.'s original definition
with respect to the maximum error size.


>> I don't think the concept of consistency has much to do with
whether a
>> particular JI interval is approximated well enough to be used as a
harmonic
>> consonance.

>I don't think that's exactly what I meant, or even what I said.

I was responding to your assertion that common-practice harmony did not find
7-tET sufficient. Clearly, 7-tET would not provide the desired harmonic
effect when used for common-practice harmony. I believe the reasons lie not
with higher-level consistency but with accuracy.

But the actual historical reasons for not adopting 7-tET lie not with
5-limit, but even earlier with 3-limit harmony, as practiced in Medieval
music. Although 7-tET may have a high level of consistency within the
3-limit, its accuracy in approximating 3-limit consonances is questionable.
Medieval musicians tuned fifths and fourths with enough accuracy that is was
clearly seen that the eighth note in a circle of fifths was different from
the first. Thus the process of chromatic alteration began that ultimately
led to 12-tET. In China, fifths and fourth were also the main harmonic
consonances, and China developed 12-tET before the West did. In Thailand,
however, the accuracy of the fifths and fourths was less important, since
their role was more melodic than harmonic and because most Thai instruments
do not have harmonic partials. Thus it is not surprising that Thailand did
develop 7-tET.

[bigsnip]
>> What consistency offers is a supplement to considerations of how
good
>> the approximations to JI are. Essentially, composing with a consistent
>> tuning will be no more difficult than composing in JI, while in
inconsistent
>> tunings, complications may arise if one attempts to always use the best
>> approximations to JI intervals.


>Here's where we part company, I'm afraid. I find level 1 consistency to
>be far too low a standard. Very weird things can happen in level 1
>consistent tunings. A simple example: 5TET is consistent at the
>5-limit. A 16/15, represented as a 4/3 less a 5/4, becomes 2-2=0 steps,
>or a unison. However, a 25/24, represented as a 5/4 less a 6/5, becomes
>2-1=1 step. In other words, a larger interval becomes a unison while a
>smaller interval does not. Maybe this doesn't bother you, but for me it
>causes cognitive dissonance.

Well, the idea of using 5-tET for 5-limit harmony bothers me. Didn't you
read my post? I explained why, even though 7-tET is consistent at the
5-limit, it is not a good tuning for 5-limit harmony. The same goes for
5-tET. If a tuning is both consistent and has good approximations to JI
however, then I will admit it, even if the second-order intervals do not
behave as in JI. I think 22-tET is marginally good enough for 9-limit
harmony, if the texture doen't get too thin, but observe: 64/63, an 8/7
less a 9/8, is 4-4=0 steps, while 81/80, a 9/8 less a 10/9, is 4-3=1 step.
"In other words, a larger interval becomes a unison while a smaller interval
does not." This doesn't bother me in the slightest -- in fact I like it.

The ear does not have a pre-defined map of JI; it does, however, perceive
consonance, dissonance, and scale structures. Sometimes the most effective
scale structures for consonance differ significantly from JI, but I think
these differences can be just fine, even necessary, unless they violate
simple consistency.


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On Fri, 20 Sep 1996, PAULE wrote:
> Your new algorithm is not correct either -- at least it does not reproduce
> my definition of consistency. In particular, no tuning can fail to be level
> 1 consistent according to your algorithm, and some tunings would be level 2
> consistent according to this algorithm that wouldn't be according to your
> original definition.

Er, pardon me but it _is_ correct; at least, it is cribbed directly from
the code that generated the table at
, and I haven't
discovered any errors in that table yet. (And that table _doesn't_
claim that all tunings are level 1 consistent. Code it up and run it
yourself if you don't believe me.) Don't be misled by the natural
language paraphrase that I followed it with--the paraphrase is not
exact, but I couldn't think of a concise and non-technical way to say it
precisely.

[another bigsnip of stuff I have no disagreement with]

> > Very weird things can happen in level 1
> >consistent tunings. A simple example: 5TET is consistent at the
> >5-limit. A 16/15, represented as a 4/3 less a 5/4, becomes 2-2=0 steps,
> >or a unison. However, a 25/24, represented as a 5/4 less a 6/5, becomes
> >2-1=1 step. In other words, a larger interval becomes a unison while a
> >smaller interval does not. Maybe this doesn't bother you, but for me it
> >causes cognitive dissonance.
>
> Well, the idea of using 5-tET for 5-limit harmony bothers me. Didn't you
> read my post? I explained why, even though 7-tET is consistent at the
> 5-limit, it is not a good tuning for 5-limit harmony. The same goes for
> 5-tET. [snip]

Holy cow, it was just an example. The point is that such discrepancies
will occur in any tuning that is level 1 but not level 2 consistent, as
you demonstrated with 22TET.

> "In other words, a larger interval becomes a unison while a smaller interval
> does not." This doesn't bother me in the slightest -- in fact I like it.

That's absolutely fine with me. More than fine, it's great. Odd
structural artifacts like this in low-consistency tunings are features
of, for example, several of Easley Blackwood's 12 Microtonal Etudes, and
massively cool pieces I think they are. It's just a different path than
that which I am attempting to follow.

Please understand that I am not trying to talk you out of composing in
22TET or whatever tuning you please; I am simple trying to explain that
my preference for higher consistency is _not_ "arbitrary", but justified
given certain assumptions which you may not share. I respect your
compositional choices; please do me the same courtesy.

--pH (manynote@library.wustl.edu or http://library.wustl.edu/~manynote)
O
/\ "Foul? What the hell for?"
-\-\-- o "Because you are chalking your cue with the 3-ball."

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