Hi Celestial mechanic,

<ul><hr>The 12th roots of two are irrational numbers! Rational numbers can only approximate them and likewise they can only approximate rational numbers! Ratios are what the ear expects to hear, not frequencies culled at random from the spectrum.<hr>[/list]I could equally argue that the irrational numbers are what ear expects to hear. Have you any proof that the 'rational' pitches are better? Once again, I can understand that logically speaking - rational numbers seem as though they are the best option, but there's always a chance they might not be.
To my ear at least, from root C, the pitch of 1.259921 (2^(4/12)) sounds a better major third than 1.25 (5/4) either melodically or harmonically.

<ul><hr>not all cultures even have chords (chords only date back to the 13th Century or so), consequently the quality of thirds and sixths makes no difference in their music.<hr>[/list]Well obviously the best music contains chords =P
Remember that a whole culture could (ultimately) be mistaken - there's /always/ that possibility.


<ul><hr>Evidently you have not heard anything beyond 12et.<hr>[/list]Well you guessed wrong [img]/phpBB/images/smiles/icon_smile.gif[/img] I have heard a lot of the supposedly best 19-et and realised some of it was ok, but would've sounded much better had it gone fully 12-et instead.

I think that any aspects which make say... 19-et sound ok, are things which (like I've said previously) relating to rhythm and structure (or even that many of the notes are close to 12-et anyway - in which case the closer, the better [img]/phpBB/images/smiles/icon_wink.gif[/img].

<ul><hr>One example is the diminished triad, which justly intoned should be 7:6:5 and has intervals of 12+10 microtones in 53et, 3+3 in 12et. The sound is a lot better in 53et!<hr>[/list]Just because the sound is smoother and doesn't have the 'beating' effect, it doesn't mean it's ultimately 'sweeter' than the nearest 12-tone equivalent.

<ul><hr>Beyond that, it is all culture and conventions accumulated with the passage of time.<hr>[/list]Whatever 12-note system you choose (whether its pythagoras' system of fifths, or the 'just' scale ratios, or my preferred 2^(x/12) pitches), there's no doubting the other pitches (3rds, 6ths, diminished 2nds, augmented 5ths etc. etc.).... all have universal significance.

You mentioned the Commodore C64 - I love some of the music from that [img]/phpBB/images/smiles/icon_smile.gif[/img] heard 'Monty on the Run'?

<font size=-1>[ This Message was edited by: dwhite on 2002-08-28 10:17 ]</font>

<font size=-1>[ This Message was edited by: dwhite on 2002-08-28 10:33 ]</font>

<font size=-1>[ This Message was edited by: dwhite on 2002-08-28 12:12 ]</font>

I'll respond to a few people in this message (no point in sending multiple posts):


Hi GrapesOfWrath,

<ul><hr>

<ul><hr>On webpage, dwhite wrote:
I'm wondering if there's any truth in the possibility that the 12-note system contains the perfect pitches
after all, and that they are therefore /not/ a compromise. <hr>[/list]Not a chance, seeing as how you mean the tempered scale. Just look at fretless music.

<hr>[/list]Well, music with slides and pitches that land /outside/ the 12 'golden' pitches are fine, but maybe only inbetween beats. There's still not sufficient evidence for me to believe otherwise.



Hi Silas,

<ul><hr>Finally, there's the "individual" red. What I see. And, who knows? It might be different from what you see. If we ever work out a way of projecting mental constructs for others to see, we might solve some of those riddles. (And I know some blokes I betcha could make a lot of money selling recordings of their dreams!)<hr>[/list]As regards the individual red, I admit there's a very small chance we could all be seeing something different, but I doubt this very much (whether one believed in God or not).
As for the dreams part, wow - it'd be amazing to see dreams on the TV the very next morning! Ever tried lucid dreaming?



Hi CP,

<ul><hr>The 12et system is a compromise, but it is the most practical we have for now. It has been dicussed among musicians that different keys have differing qualities, i.e. the key of G Major sounds bouncy and bright, E Major has a "darker" quality. Perhaps the perceptions relate to the relative closeness of the tones in an even-tempered key to the whole number ratios of the just tempered scale.<hr>[/list]That's interesting. I would've thought E major is no different than a G major chord or any other (B major, Eb major etc....). Perhaps it could be that certain resonances strike a chord (haha) in us for some reason. Or it could've be that subconsciously, people are relating it to an imaginary C major chord playing before.



Hi Espritch,

<ul><hr>hypothesising some musical law existing separate from our biology. If you meet an alien and he/she/it also thinks Mozart is terrific, then you might have a case.<hr>[/list]Yep, I'd guess the alien would like (the best of) say... Mozart too [img]/phpBB/images/smiles/icon_smile.gif[/img]
One of the reasons I think there's a quality or 'universal rating' to music - is because of the fact that if one chord could be better than another really awful chord (and everyone agreed on this), then the same reasoning would apply to a whole string of chords and ultimately to a whole melody/tune.

<font size=-1>[ This Message was edited by: dwhite on 2002-08-28 10:28 ]</font>

Rational intervals are better because upper partials coincide and do not beat. Pray tell, what irrational intervals does the ear "expect" to hear?
That it sounds better to you cannot be argued. But I don't think that most people would think so. I'm sure that in a properly conducted double-blind test of major thirds of different types and pitches played one after another in random sequences that most people would prefer the just third to the "equally-tampered" one. In fact, if you were one of the test subjects you might prefer the just one too.
But have you heard any 53-tone? Nineteen is not one of the continued fraction convergents (it's one of the "secondary convergents") and this is important. The 53-tone scale has better approximations for all ratios having 3 and 5 as prime factors, and approximates ratios with 7 as a prime factor fairly well. The approximations are much better than 12et.
Smoothness and lack of beats does make for sweeter tones. If roughness and beats do not disturb you, then why choose any particular pitches at all?

__________________
Microsoft is over if you want it.

The bar has been lowered for the promotion of ATM ideas; the bar for the acceptance of ATM ideas must remain high.

I'm leery of the whole idea of "key color" coming from equally-tempered instruments of roughly constant timbre over their range of pitches. Only a few rare people like Mozart are blessed with absolute pitch and could tell what tones are being sounded and hence what key is being played. Most of us would not recognize anything amiss if say, the Moonlight Sonata were transposed and played in d-minor instead of c#-minor. For all practical purposes key color disappeared on keyboard instruments with the advent of equal-temperament.

On the other hand, orchestral music is likely to have key color because of the way that string instruments are played, that generally there is some adjustment of pitch in context. Also, the quality of open strings versus stopped strings is different, so there are differences arising from the number of open strings appearing as scale degrees.

By the way, my general perception of key color has been that sharp keys are "brighter" and flat keys are "mellower", but how much of this is expectation derived from accounts of other people's perceptions? In short, your mileage may vary!

__________________
Microsoft is over if you want it.

The bar has been lowered for the promotion of ATM ideas; the bar for the acceptance of ATM ideas must remain high.

I'm pretty sure the reason for that is the same for your response below

However, I'm pretty sure that studies of musicians playing, for instance, violins, showed that they were hitting the 5/4 rather than not--when they did not have to match some tempered instrument.

So, your personal preference is probably an oddball one--not that there's anything wrong with that, but I wouldn't use that as a basis for a theory that tempered notes are natural, or better sounding in general.

This really is my field, having taught music theory for many years, and through this discussion I can see what clearly frustrates the scientists here, for "atonal" in the field of music theory, is in reality a highly inaccurate, misleading populist term, like "big bang" is for cosmology. Especially when applied to what the Big Bang Theory actually addresses.
Music is an artform that can be created in more than 12-tones and still be "tonal." (Alois Haba did it.) Schoenberg's non-12 tone music (Five Piece for Orchestra) is actually more "keyless" than his later "12-tone technique" pieces, and if you want to be more precise about what people hear, all of Schoenberg is harmonically actually "crossed key context - chromatic modality" to the ears. There is also "tonal" music that is much harsher and more dissonant than so-called "atonal" music, and visa versa. But that's not the point. The crux of it is, as with folks who get uptight about the "Big Bang" or other scientific theories, you're trying to apply a general, aesthetic term (that musicians use as a catch-all phrase) to more precise phenomenon, such as the pitches of the Western tempered scale. They actually don't connect when you analyze what the ear and mind deals with.

So your argument is that since human and other animal brains do not function like robot CPUs, that's evidence for god? Maybe for you. I see no reason evolution could not account for an appreciation of color or music.

__________________
~~ ><>><> ~~ ><,,> ><,,> ...`;=;p d;=;' /\/\^/\ ^^ ^/\/\_
Democracy Now! - The lost art of investigative news reporting.

Hormones.

Organic brains can trigger the release of hormones which determine how we "feel" about a particular stimulus. (This could have its origin in the "fight or flight" response, a survival trait.)

Electronic brains cannot.

(I like the new sig, be.)

__________________
Never attribute to malice what can be adequately explained by ignorance or stupidity.
Isaac Asimov

"Before the song
all music came like
muted, empty octaves
begging a composer's pen.
The notes cried silently
for paper staves and
kept their sound in theory only."
- Calvin Miller

__________________
"As I lay beneath the Southern Cross, the stars tell more than I could" . . . David Meece

Hi Celestial Mechanic,


<ul><hr>
<ul><hr>
I could equally argue that the irrational numbers are what ear expects to hear. Have you any proof that the 'rational' pitches are better? Once again, I can understand that logically speaking - rational numbers seem as though they are the best option, but there's always a chance they might not be.

<hr>[/list]Rational intervals are better because upper partials coincide and do not beat. Pray tell, what irrational intervals does the ear "expect" to hear?
<hr>[/list]Like, I said - maybe the 12th root of two pitches. Remember that even PI is an irrational number, but is a very important number in mathematics. The 'imperfect' beating of course is a by-product from the irrational numbers, but perhaps ultimately not one which is of any significance.


<ul><hr>
<ul><hr>
To my ear at least, from root C, the pitch of 1.259921 (2^(4/12)) sounds a better major third than 1.25 (5/4) either melodically or harmonically.<hr>[/list]That it sounds better to you cannot be argued. But I don't think that most people would think so. I'm sure that in a properly conducted double-blind test of major thirds of different types and pitches played one after another in random sequences that most people would prefer the just third to the "equally-tampered" one. In fact, if you were one of the test subjects you might prefer the just one too.

<hr>[/list]Good point, and I might agree with you, except I conducted these sort of blind tests on myself.
Amongst other comparisons, I've spent hours trying to prefer the tone of 1.25 (5/4) over 1.259 (2^(4/12)) by putting both in a rippling chord made up of exactly tuned 'saw-wave' and 'sine-wave' instruments.
I've even put tried comparing the differences by trying out both in a melody. In my opinion, the logarithmic ~1.259 (12-eT) pitch was 'sweeter' and better.
Now obviously, I could be mistaken - maybe I've wrongly got used to the 12-eT pitch. But I think there's always a chance I /could/ be right. So far, as far as I know, I'm seem to be the only one who's even considered the 12-eT scale not an imperfect compromise, so I'm perfectly willing to accept that I may be wrong [img]/phpBB/images/smiles/icon_frown.gif[/img]


<ul><hr>But have you heard any 53-tone? Nineteen is not one of the continued fraction convergents (it's one of the "secondary convergents") and this is important. The 53-tone scale has better approximations for all ratios having 3 and 5 as prime factors, and approximates ratios with 7 as a prime factor fairly well. The approximations are much better than 12et.
<hr>[/list]Well, if we were to go to the full length, 100,000 tone would be even better, since it contains notes which are very, very close to the allegedly 'perfect' ratios. My point is that 53 note scales, 289 note scales, or 567,833,781 eT note scales contain mostly 'dud' notes which I don't believe should really be used in music (apart from for pitch slides etc. between beats).
However, I would be very interested to hear your favourite 53-tones piece/s. Perhaps you'd like to point me to a url?

Also, Chip - if you're reading this, then I would be interested in hearing your favourite non-12 note piece of music. I'll really try to enjoy it - by listening to it many times, but I have a feeling that any non-12 note music would benefit from the full transition to 12-eT.

<font size=-1>[ This Message was edited by: dwhite on 2002-09-09 15:27 ]</font>

Hi GrapesOfWrath


<ul><hr>
<ul><hr>On 2002-08-28 10:08, dwhite wrote:
To my ear at least, from root C, the pitch of 1.259921 (2^(4/12)) sounds a better major third than 1.25 (5/4) either melodically or harmonically.
<hr>[/list]However, I'm pretty sure that studies of musicians playing, for instance, violins, showed that they were hitting the 5/4 rather than not--when they did not have to match some tempered instrument.

So, your personal preference is probably an oddball one--not that there's anything wrong with that, but I wouldn't use that as a basis for a theory that tempered notes are natural, or better sounding in general.

<hr>[/list]You make a very strong case, and as I have said previously, I'm still not 100% sure.
Now this is only a theory, so don't jump on this, but maybe the violins used in any experiment were wavering, and they presumed that they were playing 1.25 instead of 1.259 (perhaps by taking the trough of the wave instead of the middle or peak).
Also, it could've been that maybe the violionists were /aiming/ for chords which didn't beat rather than for what actually sounded best.
Finally, perhaps the violinists involved didn't quite hit the exact pitch that they should have done anyway.

Hi beskeptical,

<ul><hr>
<ul><hr>

On 2002-08-28 09:57, dwhite wrote:
To sum up, the best robot we could create might have eyes with the detail of 1mil x 1mil pixels and 256bit colour definition - and a 10^1,000,000 MIPS processer. This could certainly outperform our eyes, but it would never be able to 'experience' true red or even enjoy seeing pictures.
<hr>[/list]So your argument is that since human and other animal brains do not function like robot CPUs, that's evidence for god? Maybe for you. I see no reason evolution could not account for an appreciation of color or music.
<hr>[/list]I kinda agree. But it is one those things which would seem to have a /chance/ that there's something more going on than meets the eye (no pun intended [img]/phpBB/images/smiles/icon_smile.gif[/img]

dwhite:
"One of the reasons I think there's a quality or 'universal rating' to music - is because of the fact that if one chord could be better than another really awful chord (and everyone agreed on this), then the same reasoning would apply to a whole string of chords and ultimately to a whole melody/tune."

Chip:
The more one listens too music, the more it becomes obvious that there is no absolute supreme aesthetic. In other words, the same chord that sounds completely awful in one piece can be wonderfully beautiful in another. Its an artistic relativity principle. If there were an absolutely true music, (or absolutely true science) there would be no art, and no knowledge. An absolutely "true" form (of music, astronomy, basket weaving, whatever...) would be static, and have to be created the same way every time to be recognized. (It would be very ugly too.)

Music, or a scientific principle can feel "right" because you are used to it, and because it works within its parameters.

<font size=-1>[ This Message was edited by: Chip on 2002-09-10 13:14 ]</font>

Hi Chip,

Well, instead of saying 'chord', what if I said 'chord sequence'? There's no doubt that certain chord sequences are better than others. Obviously, the rest of the tune has to be taken into account if that sequence was in an actual tune (as then it would be a giant chord sequence), but generally, there are bad chord sequences, good chord sequences and everything in between.

In fact, I do think the same principle can be applied to a solitary chord, though I agree that a lot of chords can be used one way or another in any tune (up to a point), especially if that chord is made up of around 5 or less notes.

Oh by the way, by saying 'it would be very ugly', that's an objective statement which veers once again to the theory of universal aesthetic/s ;-P

My point is that there could still be a dynamic 'rating' system for all music, and that it would obviously have to be very complex - so as to take into account the tremendous variety and possibilities available in music.

But no doubt there are good tunes, and bad tunes. They might be bad or good in different ways and for different reasons, but even then, one could create a piece of music which scores highly for all the main attributes (rhythm, melody, intricacy, harmony etc.) and possibly derive an 'average' rating or enjoyment factor which takes all these factors into account.

<font size=-1>[ This Message was edited by: dwhite on 2002-09-10 14:16 ]</font>

<font size=-1>[ This Message was edited by: dwhite on 2002-09-10 14:39 ]</font>

You missed the point entirely. But no matter, I simply can't communicate it more lucidly to you, so that's that. I've tried to relate this music topic at least remotely to science and astronomy, but in my opinion, the thread has now drifted too far away from the spirit of this board, so I need not continue in it. To be blunt, the proposed rating system for "good" and "bad" music is totalitarian to me.

You'd probably be better off taking this to http://www.skepticfriends.org if you want to debate it with people. It won't fly on a serious music discussion board. Have a nice day.

<font size=-1>[ This Message was edited by: Chip on 2002-09-10 15:32 ]</font>

To quote Duke Ellington:

If it sounds good, it is good!

'nuf said.

__________________
I am a doctor, but I don't play one on TV.

Hi Chip,

Hmm... well after looking and studying your original post again, I'll try and answer your points directly and as lucidly as possible. I'll also probably make this my last post if you still think I'm 'missing the point' [img]/phpBB/images/smiles/icon_frown.gif[/img] (not to mention that like you said, it is more of sub-thread). Also, misunderstandings happen all the time. Perhaps I'm at fault for (maybe apparently) misinterpreting what you said. Or maybe you're at fault for not explaining certain points clear enough. Or maybe nobody's at fault, because there are sometimes many ways to take a particular sentence, and it would take a long time to explain it completely, but in the end... please don't mind :-/

I agree entirely. But what matters is the combination these chords are put in (and what chords are chosen). Certain combinations are more appropriate (or yes - better) than others.

This could mean one of a few things, so maybe you'd like to elaborate?
Of course, obviously a culture's taste will reflect the kind of art and music they like, but certain studies have to some extent proved that universal criteria of the aesthetics of art have emerged, and that they actually transcend individual preferences.

This could mean one of a few things, and my response was: that indeed - there are infinite possiblities in music - and that any possible formula for the best music would have to be very complex to take the enormous variety of 'styles' into account.

Thompson on 2002-06-27 22:40 ]</font>
[/quote]
Tims stuff is interesting but not open minded. Recent observatins have shown that the universe is accelerating in its expansion. This means that all matter and energy may very well already be traveling at the speed of light. it amy infact have been traveling at the speed of light ever since the big bang. That means according to Einstein that matter and energy has not aged relative to the starting point of the big bang because it is traveling at the speed of light.. Even tho relative to the earth billons of years have passed. It all depends on your frame of reference. We humans all get our time relative to the earth so we see billions of years passing but matter traveling at the speed of light relative to the starting point of the big bang sees no time passing at all because it is traveling at the speed of light relative to the starting point. So if matter and energy both came into existence with the big bang then true time and speed must be measured from the starting point of universe expansion. Not from earth as we humans came into existence in a different frame of reference and see time differently than the universe.. If energy and matter ages relative to the starting point of the big bang then it is still very young.

uralph, the accelerating universe you are talking about is really not interprable as "matter moving at the speed of light". Indeed, matter is at rest in its local frame. End of story. If you compare frames of reference you will end up with an event horizon in an accelerating universe whereby we will not see the mass that is outside the horizon. This does not mean time is "different" for them. It is the same in the local frames.

To avoid some of these problems, cosmologists do most of their calculations in comoving coordinates. This enables us to assess exactly how the universe behaves due to the initial conditions and the Freidmann Equation. When we say that the universe is "accelerating" this simply means that some of the universe is expanding more in our vicinity. This is a hard concept to visualize since it really relies on the expanding of the metric (the way we measure spacetime) in the proper coordinates.

I hope this offers some elucidation as to why your statement is a little bit off. Cheers.