Re: [tuning] Re: Phi Tonality (response to Rick)

> --I keep on going on about it to you because you keep on missing the

> point. And I have --listened to the site and already said that it sounds

> out of tune.

    We've been battling on the topic of if irrational numbers CAN be a good option for generating consonant scales. 
>>>>>>>>>>>>>
   And I've come to the conclusion that we're both right; they both can AND can't. :-D
   In short...they can be based on irrational generators but, afterward, it helps to round the irrational results to the nearest rational ones. :-)
<<<<<<<<<<<<<<<

   The result below is a melodic example of a scale made of rational numbers built to closely approximate the original irrational-number-generated PHI scale I made:

http://www.geocities.com/djtrancendance/micro/rationallytemperedPHItuning.wav

Does this STILL sound "out of tune" to you? :-)

BTW, the ratios the above scale uses are:
10/9
19/16
4/3
16/11
25/16
13/8

(all ratios either based on the x/9 or x/16 harmonic series OR 'tempered' very close to them (IE 16/11).  The idea is to use rational numbers to improve my tuning while still keeping intervals that are very close (in cents) to the irrational/PHI-based version of the
scale.
  
-Michael

--- On Sun, 3/15/09, rick_ballan <rick_ballan@...> wrote:

From: rick_ballan <rick_ballan@...>
Subject: [tuning] Re: Phi Tonality
To: tuning@yahoogroups.com
Date: Sunday, March 15, 2009, 8:47 PM

--- In tuning@yahoogroups. com, djtrancendance@ ... wrote:

>
> Funny...I've never heard you say it. Out of tune to what, exactly?

> Anyway, my point is not to sound like 12TET or harmonic-series- like intervals, but to sound consonant/relaxed. I never challenged you to prove my scale is/isn't out of tune...but, instead, to prove it is/isn't consonant. I asked you if you believed something didn't work, then which notes clash?

> But, apparently, you found it more convenient to simply change the topic to the idea of "keys", which I never mentioned...

>

> ---What does the term 'alternate' mean in this 'alternate

> tuning' site, alternative to what?

> To me, it simply means anything which can generate intelligent sounding easy to listen to musical expression. Which may or may not follow intervals from the harmonic series...

>

> --It is alternatives to the harmonic

> series,

> Saying all of micro-tonal and music in general is ONLY based on the idea of mimicking the harmonic series seems blatantly ignorant to me. Sure, most micro-tonal is "variations on the theme of the harmonic series", but people like Sethares and Schubert have messed at least somewhat successfully with the idea of scale systems and compositional styles that sound beautiful yet royally break the harmonic series.

>

> ---12 edo, meantone, in short all of those systems

> -- which

> experience has taught us to trust.

> Nothing wrong with those, but nothing really new about them either: like you said they all pretty much boil down to the same "monopolistic" thing. A very easy counter example: Sethares' use of 10TET in his song "Ten Strings" where he re-aligns the timbre of the instruments to something that looks completely unlike the harmonic series.

>

>

> ---And how can we find valid options if

> we do not understand the benefits and downfalls of ---those systems and

> take them as our starting point?

> Simple...we can realize that there is more than one pathway to consonance. Sethares found one in making "out of key" scales not based on the harmonic series and matching them with timbres that create a fair degree of consonance.

>

>

>

> --Well it is called the "harmonic" series for a reason. It is a natural

> phenomenon which ---occurs whenever we pluck a stretched string or blow

> air through a pipe. Its discovery --dates back to the very beginnings of

> science with Pythagoras (570 B.C.). Without this --spiritual aspect of

> "harmonia", which meant universal order, mathematics probably would

> --have remained a form of accounting.

> Right...and, note, Sethares use of timbre becomes IMPOSSIBLE with instruments in nature because those in nature produce overtones aligned with the harmonic series...yet his "unnatural/bent harmonic series" can also produce consonance to a fair degree. Sure, Pythagoras found something very natural and useful...but that doesn't mean it's the ONLY way the mind can easily organize sound artistically so as to smoothly communicate emotion.

>

>

> ---The difference b/w the harmonic series and the GCD is that we can play

> upper harmonics --on two different instruments and create a new

> fundamental frequency which is not played --on the original two. This

> phenomenon realises itself as the key and is called tonality.

> Meaning...two different tones point to a tone below those two with is equal to the GCD of those tones. You act like it's something I'm just learning now...but I've known that concept ever since I started studying micro-tonal music.

> And, yes, It's a good and working theory but, again, I don't think it's the only way the mind can easily organize tones. To me that's like saying imaginary numbers are useless because the square root of -1 is impossible in nature.

>

> When people sound-engineer/ program PADS with their synthesizers. ..they often use frequency modulations on overtone that deviate from the harmonic that actually increase the pleasantness of the sound...now compare that to the essentially perfect harmonic series formed by a pluck of a guitar string: the PADS, in many cases, actually sound more relaxed.

>

>

> --And no, beating is independent of the harmonic series. It is half the

> difference b/w ANY --two frequencies. It dissappears when two strings

> (say) are in tune because the beat freq --becomes an harmonic.

> If you are saying "the harmonic series resolves beating"...try playing harmonics 25,26, and 27 of any note together. Note they beat so much...that even though they point to the same harmonic they still sound un-relaxed. Even the harmonic series has its faults so far as consonance. My point is, again, there are two ways to generate "beating consonance" relatively well...one is to make the beating the same between notes IE 200hz,300hz, 400hz (IE basically, the harmonic series; the beating in this example is of course 100hz) and the other is to make all beating between tones multiples of each other IE 200hz,400hz, 600hz (multiples = 1, 2, 3), but that can also be 100hz 162hz 262hz (multiples = 1, 1.618, 1.618^2). When you think about it, the multiples method uses a generator in a >>>mean-tone< <<-like way...but it certainly doesn't have to be

> stuck with mean-tone like or near-rational. intervals

>

>

>

> --You also said that you tried 10 tet and it sounded out of tune. But

> nobody has ever --claimed (especially not Bill) that all equal

> distributions will be the same or that disproving --one will

> automatically discount all the others.

> Agreed, nobody has...before you said "this is because the distribution among notes is equal"...and now you seem to be admitting "not always"...which was my point in the first place.

>

> --Again, the 12 tet and meantone

> systems evolved out of attempting to distribute the --harmonic series

> over all keys. We find similar types of tunings in other cultures such

> as --the 7 (??) tet of Turkish music.

>

> So what? Yes, they work, but it surely is not the only way toward easily listen-able music, just the most obvious (both in nature and in the ease of calculating how to make real-world/non- electronic instruments that match it).

> Again, Sethares' timbre-matched use of 10TET already seems to hint at that: even if my attempts to twist the use of consonance sounds bad in your mind, there have still been a few people who have successfully pushed for alternatives to the "equal-speed beating" ideal of the harmonic series.

>

> The difference between the old and new...at least to me...is that now we have the advantage of technology to test things that used to be very hard to calculate quickly and thus build more scales by experimentation and more abstract patterns than 1,2,3 (1,2,3 (as multiples).. .is exactly what the harmonic series is).

>

Michael,

The GCD frequency isn't restricted to acoustic instruments. It is a fact of wave theory and Fourier analysis. It will apply whenever you generate sounds via any method whatsoever. In fact in the early 90's I worked closely with a scientist named Tony Childs who worked for the company which invented many of the programs you take for granted. My point has been that the traditional beating/consonance type approach which made popular by for eg Helmholtz deals with + and - actually misses the point of harmony, which is ratio based (division, multiplication) . As a jazz musician, I use 'dissonances' all the time and yet it is still in tune. Similarly, I find Bill's music quite beautiful and have told him so many times. And in fact Bill's idea that certain timbres (which is still based on harmonics) fit with certain tuning systems fits well with the fact that a single note already brings with it it own tuning system (for notes are also chords, the idea of a
single note besides a single sine wave being an illusion).

"Yes, they (12 tet/meantone) work, but it surely is not the only way toward easily listen-able music, just the most obvious (both in nature and in the ease of calculating how to make real-world/non- electronic instruments that match it)." But as Sherlock Holmes said, "Watson, everything is obvious upon explanation" . And in fact there is nothing obvious or easy about them, as there is nothing obvious or easy about Bill's work (which you don't understand either). eg the term "12 tet system" itself can be a bit reductionist. It includes 6, 4, 3 and 2 tets as subsets, therefore giving the only equal intervals, triads or 4 note chords. It can be seen as equal 4ths over 5 8ve's, equal 5th's over 7 8ve's, and closer to the actual practice of 12 tet music, successive minor and major thirds and vice-versa. But to describe the model exactly, we would have to describe the study of jazz/classical musical harmony which is a lifetime pursuit. In other words, it is
much, much more difficult than simply downloading scalar and reading a few articles on micro-tuning and then imagining that you are at the cutting-edge of the "neuveax open-minded" .

-Rick