>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...
Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Fri, 20 Sep 1996 00:14 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA31597; Fri, 20 Sep 1996 00:16:21 +0200 Received: from eartha.mills.edu by ns (smtpxd); id XA31708 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id PAA10289; Thu, 19 Sep 1996 15:16:19 -0700 Date: Thu, 19 Sep 1996 15:16:19 -0700 Message-Id: <00960919221500/0005695065PK5EM@MCIMAIL.COM> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu
>> 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.
Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Fri, 20 Sep 1996 21:51 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA29365; Fri, 20 Sep 1996 21:53:15 +0200 Received: from eartha.mills.edu by ns (smtpxd); id XA31963 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id MAA13137; Fri, 20 Sep 1996 12:53:13 -0700 Date: Fri, 20 Sep 1996 12:53:13 -0700 Message-Id: <55960920195155/0005695065PK2EM@MCIMAIL.COM> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu
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."
Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Sat, 21 Sep 1996 03:04 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA21302; Sat, 21 Sep 1996 03:06:09 +0200 Received: from eartha.mills.edu by ns (smtpxd); id XA20209 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id SAA19747; Fri, 20 Sep 1996 18:06:07 -0700 Date: Fri, 20 Sep 1996 18:06:07 -0700 Message-Id: <960920210400_482611093@emout20.mail.aol.com> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu