you must be anosmic?

http://www.youtube.com/watch?v=hTWKbfoikeg

hehe
spirit is smelly
-I gotta sleep, my house is all out of imbibables

No, at least not for some intervals (like the major third) - providing one has a good ear of course.
ET major thirds are about one seventh of a semitone (about 13.7 cents) wider than acoustically pure major thirds (5:4), but we are so accustomed to them that we can no-longer hear how "bad" they actually are.

Nowadays, in the West, we are conditioned to think that equal temperament sounds "in-tune" and everything else sounds "out-of-tune", but that has little basis in mathematics, it is a cultural thing.

Of course there are still some cultures (and some kinds of music) which do not use equal temperament (just of course as there are many cultures and styles which do not use western tonality).

dont forget the role that cute girls play.

much of music is composed solely to impress cute girls and contains material meant to be "catchy".

Really? I just know that a major third in ET is 1.259921 rather than 1.25 of just intonation, so I figured our brains saw it as pretty close. Like you said, I guess we're just used to it. I suppose the 12 note equal temperament tuning was really a convenience that hit the main ratios that we like (such as the fourth and fifth extremely close) and came somewhat close to the other ratios of just intonation. I'd be curious actually to see what it's like to play a keyboard that was tuned to just intonation rather than equal temperament. In the world tunable soft synths, it should be pretty easy, but I can't say I've ever tried (to my knowledge).

An ET M3 is 13.69¢ sharper, really, and I can hear it every time.
I have no idea what your numbers are supposed to mean. Looks dodgy.

it's a compromise owing to the desirability of making more than one key consistent by temperament. Once you've taken the results of just ratios based on 'C' and transposed them to a new 'home' or tonic note, the relationships are gone.

The just ratios typically were built from the ground of the 'perfect fifth', a 3:2, 2:3 correspondence in vibration. Geometrically, 2:1, the octave, and 3:2 will never agree. So temperament was born. In the form of "Commas" by Pythagoras, et al.

Equal temperaments were calculated in antiquity, for instance in China, close enough for rock and roll anyway. For what purpose I don't know. But in the west, it was about new keys. It didn't happen overnight.

a great book on this is 'How Equal Temperament Ruined Harmony (and why you should care)'.

that's absurd.

fixed pitch is strictly from convention. the physical laws of sound do not accord with, let alone rely on such conventions. The cart doesn't pull the horse.

The conventions in place you have a passing familiarity with are not a bit like univeral laws of physics. They are entirely artificial and serve a style area owing to a particular culture. Other cultures have other rules, some of which don't fix pitch necessarily, or demand A=440 or any other vibration as A. Persian musicians find that a corruptor for a musician, *fixed pitch*.

If you require to work inside a convention, you follow that convention. That should be self-evident.

Western European musicians have sought such a hegemony over the world they have tried to argue the natural law-fulness of their ways. Cf. Furtwangler. It's just not true, it's completely unreasonable blather.

Ratios expressed as decimals are dodgy? Yikes. Just a simple fraction turned into decimal. A pure major third is 5:4, or 5/4, which is 1.25. A major third in ET is about 5.04:4, or 5.04/4. I just wrote the whole thing as a decimal rather than mixing decimal numbers with fractions. Wikipedia has a decent comparison to just intonation here:
http://en.wikipedia.org/wiki/Equal_temperament#Comparison_to _just_intonation
It's just a matter of talking in ratios/fractions rather than cents, because cents are part of the system we were attempting to describe.

So I would say that our brains still perceive 5.04 to 4 as at least relatively similar to 5:4, even though you can tell the difference. In terms of cents, yes significant. In terms of ratios, less so, but noticable.

The real offender is the minor seventh. 1.78 rather than 1.75! (31.17 cents sharp)! Death to the ET minor 7th!!

On another note, what do you guys think about the claim that tuning to A=444hz puts everything in the natural harmony of the universe blah blah.... ? Apparently A440 is to mess us up.

I've tried that and there is still disharmony in the universe.

damn. I was so hopeful.

duplicate post
Last edited by jancivil on Wed Jun 20, 2012 3:29 pm; edited 1 time in total

That post made 14¢ look neglible to me. My fault, if I was sharper I will have noticed 1.25 indidates 5:4. The approach seemsed dodgy, as if you had gainsaid the point.

'our brain' does? speak for your brain please. I hear it and in some cases must temper it. depending on context. It's enough of a problem I think of it as a special dissonance and would maybe exploit that. I did a cover of a Satie piece and his close voicing and insistent bass emphasis got me to a definite concern in the EQing of that piano [as the harmonic was just that dissonant with the ET thirds]. The timbre I wound up with was a def. factor in orchestration.

I find M3 the worst particular outcome of the compromise of ET, by ear.
Last edited by jancivil on Wed Jun 20, 2012 3:42 pm; edited 1 time in total

I think it's silly. there is a better argument for 432 if you go for that kind of thing. There are some hilarious outcomes of that if you want to follow it down the rabbit hole.

I have noticed it going up over the years rather like loudness wars in quality of intention.