Re: On the Hindoo division of the octave
- It's the structure of the interval system as a whole, and the way this structure is accessed/implemented (ie, modality) that matter most.
Specific close approximations to rational intervals don't have magical powers, and may even be irritating factors in context.
What's good about the "regular temperament paradigm" is that it runs backwards from what seems to be the usual contemporary conception. With 12-tET so ubiquitous, it is understandable that people assume that an equal division of the octave is some kind of "natural" starting point, which of course it is not.
Rather than starting with a grid (an equal division of an octave) and searching for rational intervals and structures within, the "regular temperament paradigm" names the desired intervals by constructive ingredient (primes) and constructs, not a tuning, but a deliberate and purposeful system of interals which can be tuned to varying degrees of accuracy.
This is radically, utterly, different from seeking approximations to rational intervals within equal divisions of the octave.
Without a system of intervals in mind, and specific musical standards, approximation cutoffs are indeed arbitrary. If our desired pure fifth is "beatless for all practical purposes", 7 cents is an absurd cutoff. With a fifth defined as "beatless", that's not even the same interval. Whereas if our fifth is defined as "moveable Sol", we can be even more generous in error tolerance, no problem (QED, just look at how out of tune diatonic melodies can be and still be completely recognizable and even aesthetically pleasing).
--- In email@example.com, Mike Battaglia <battaglia01@...> wrote:
> On Thu, Mar 31, 2011 at 11:58 PM, Jake Freivald <jdfreivald@...> wrote:
> > John,
> > Someone (Mike? Michael?) recently talked about people tolerating sharp
> > tones better than flat ones. Being the empirical sort of guy that you
> > are, you might consider looking into that: +7.2 cents might be
> > tolerable, but -7.2 might not.
> I don't ever remember saying anything like that. I'm also really tired
> of these arbitrary +7 -7 whatever cent cutoffs.
> 12-tet's 300 cent minor third is 16 cents flat, but is very tolerable.
> 12-tet's 400 cent major third is 14 cents sharp, but is also
> Furthermore, mistuning tolerance is clearly subject to some sort of
> individual variation - you have people like Igs who don't mind
> father-tempered fifths that are in the 730 cents range, and then you
> have folks like Gene on the other extreme who don't like 17-tet for
> the 13-limit.
> > Also, when you're putting chords together, have you considered the
> > overall tolerances of the various intervals? In other words, if your
> > major third is 380 cents and your fifth is 708 cents, each is within the
> > tolerance, but the minor third between the 3 and the 5 is 708-380 = 328
> > cents, a full 13 cents sharp. Throw in a seventh or ninth and things get
> > more complicated.
> Paul Erlich would have you flogged for doing anything less.
Me>> "But I'm unconvinced, for example, that this fact means all theories in the future must match the closest expert theory."
MikeB>"All theories in the future should match the results of listening tests. If they don't, then they don't accurately represent how music works with human beings."
The new theories must match some sort of listening tests, but NOT past theories: that's my point. Past theories that are listening tested is not equal to the process of running listening tests on new theories and a new theory can agree with a new listening test without being the same as an old theory that was listening tested.
>> For example, what pattern in the HE curve explains how MiddleEastern music (which uses several intervals NOT at HE minima) works?
>"Uh, it means that discordant intervals can have a use in music?If you slap a sticker saying what's not low-limit JI must be discordant and don't question if certain higher-limit intervals can be concordant. I see a nice share of Middle Eastern music theory as a great example, in many cases, of higher limit concordance that Westerners often have simply proven ignorant of and unwilling to, ahem, listening test on fair grounds. Cameron, myself, Igs, and several others have noticed countless times where things like 11/9 and 11/6 can be quite concordant. And don't even get me started on Igs's "Map of the Internal Landscape", an album which threw even my fairly liberal attitude toward many high-limit intervals in a loop.
>"John's theory is not listening tested from scratch."Listen again, I said " My take: if an "expert theory" does NOT cover the ground of a certain type of music, this opens the door for new theories, "even" unrelated to older ones, to cover it...and for those new theories to be listening tested from scratch."
This implies we should open theories like John's FOR TESTING...I never said such theories were tested but, rather, am saying they deserve a fair chance TO be listening tested (and that they should be tested, specifically because they have not been).
>"Go ahead, and please post the results."Cool...I already have a basic 13-or-so-interval survey on the Mechanical Turk (mainly debatable areas like neutral thirds, the area between 7/5 and 8/5, and different types of sevenths) and am just looking for a place to post the sound sample files (all samples done with the same guitar sample...NOT sine waves).
Does anyone have an ftp directory that translates to a website URL they are willing to open up for this?
>"I suggested that he improve the 6.776 cent cutoff because IT IS RIDICULOUS. Almost the entire world uses a tuning system that is out of the 6.776 centcutoff and loves every minute of it."
True about "the entire world uses..."...and people regularly ALSO accept 18/17-ish semitones when they clearly violate the testing results of P&L's "scientifically derived" curve and "love every minute of it".
However, typically, I agree with John that around 7 cents or less or error is a "guarantee of safety" for virtually ANY type of interval you are trying to approximate while 14 cents, for example, only seems to work safely for very simple intervals IE 5/4.
John's limit clearly seems to aim for "what can always be considered safe for any interval" rather than "what's the greatest error that can EVER possibly work...even if it fails with more 'unsafe' intervals". You are obviously trying to solve a different problem than John...no wonder you disagree with his answer.
>"The goal is not, at the end of the day, for everyone to have their ownproprietary theories. The goal is to figure out how music works."
No kidding. So, instead of repeatedly suggesting people change their goals to fit existing theories, or so it seems, why not merely help in the cause of getting together some listening tests? I'm doing one for my theory...why not suggest ideas for doing one for John's instead of griping how you 'know his theory is wrong'?
>"Your criticism that my suggestions "are too similar to the existing theory" is tantamount to saying that my suggestions are in line with the best information that we currently have on how the perception of consonance works."If we knew how consonance works...we surely wouldn't have leading musical ambassador's like Igs and Chris finding gaping exceptions in 'leading' theories and surely would have found microtonal scales that work for the average listener and are "anything but just a personal opinion"...eh? But we haven't....and, rather than sitting around and pretending everything is fine and the theories we have already are near-perfect...IMVHO we should go out and seek new grounds, At least until we do break through. No, this does not mean outright crazy popularity (think "Nickelback"...ugh)...but rather for microtonal music to be as seriously accepted as a household art as any other type of music. We have a lot of work left to do (especially with listening tests on the general public) and little bragging rights with music (we may with math...but mathematicians aren't necessarily good musicians)...