Modified 10-TET-type scale sounds much more natural than 10-TET

Simple stretched 10-tone scale:

    If you use the ratio 2.06 as a stretched octave and split it into 10 equal steps (IE 1.00, 1.07, 1.15, 1.24, 1.34, 1.44, 1.54, 1.65, 1.78, 1.91, 2.06.) ....it appears to produce a very natural sounding scale, at least with a sine wave, featuring a full ten notes of tonal freedom. 
Its creation is based on the idea of avoiding the 1/2 critical band point of dissonance by a slight cushioning "margin".

    At least to my ears, this sounds a good deal more natural than any other scale I've heard with sine waves with 8+ notes.  Try it yourself, what do you think?

-Michael

--- On Wed, 6/11/08, Aaron Wolf <aaron@...> wrote:
From: Aaron Wolf
<aaron@...>
Subject: [tuning] Re: Blues/theory
To: tuning@yahoogroups.com
Date: Wednesday, June 11, 2008, 8:04 AM

Dear Neil,

How much do you think what you are calling blues is just a

cultural/stylistic thing and in that sense not some sort of absolute

expression? My question may sound dumb and obvious, let me clarify.

Do you think the timing and tuning of blues is in itself expressive in

a different way than other aural-based folk traditions, or is it

uniquely expressive only within its culture?

Let me clarify once more. Does a Ukrainian folk singer, well versed

in subtle details of his aural tradition, find blues to have something

particularly unique compared to any other aural tradition that is

foreign to him? Is the subtlety of expression in his tradition vs

blues comparable or no? Would a Ukrainian and a blues guy each trying

each other's tradition feel equally uncertain of the other or judge

each other equally inauthentic?

I guess my point is this:

I think that there are absolute theoretical things within blues that

are totally valid to understand. Use of 7th harmonics has a clearly

bluesy feeling. But deviating from pure harmonies or from the simple

shell of the form is clearly part of the tradition as well. My

feeling is that the things that are special to blues compared to other

aural traditions CAN be discussed theoretically. I'd assert that any

aspect of blues that cannot be easily discussed theoretically is

either common to aural traditions in general, or is arbitrary to the

culture (not important that it is one way or another, just that people

got used to it being one particular way).

I totally agree about the classical interpretations of blues -

nonsense awful junk. However, the idea of "authentic" blues is harder

to pin down since it is an evolving aural tradition. Everyone has

slightly different ideas about what does or doesn't exist in "blues."

I am not a total blues guy, and my degree is classical guitar, but I

was raised on blues to some degree, have listened to a very wide range

of blues from pop to obscure, and am very influenced by guitarists who

themselves are blues influenced (such as my hero Frank Zappa). I am

not a classical interpreter of blues by any means. I do not think in

any sort of classical way about what I play when I'm playing blues,

but I may think theoretically at times.

Anyway, blues being an American style, I'd argue that the language

relationships (which are definitely there) are very influenced by

English in addition to the African language roots. Most blues is

certainly sung in English.

As for theory, it seems to me that harmonic intervals - particularly

7th harmonic relatives - seem to be the foundational grid for a lot of

blues, and what you are saying about not applying theory is more about

not being strict to the grid. Classical musicians are often not free

enough with interpretations. The blues feel isn't just playing a

stiff 7th harmonic, but deviating around it expressively. But I think

there are still focal points around which deviation happens, and both

those points as well as the forms of deviation can be discussed

theoretically.

Best,

Aaron Wolf

--- In tuning@yahoogroups. com, <microstick@ ...> wrote:

>

> Actually, I've played blues for so long (over 40 years), that I

don't think much about the theory behind it...I just DO it. And, in

many years of reading interviews with great blues artists, I can't

recall ever seeing one of them discuss how they arrive at the pitches

they use. I am also a bit wary these days of overanalyzing a culture's

music (or anything else) when one is not part of that culture...sure,

we can learn a lot by reading, and that's often the only way to learn

about a subject. But, being a part of something is way different than

trying to analyze it from afar, for the most part.

> That being said, there are 2 really interesting books on blues

with valuable info..."Africa and the Blues" (Gerhard Kubik), and "Deep

Blues," by Robert Palmer. Both make the observation that the "blue"

notes could be related to the African concept of language and music

being related; pitches are very fluid here, and the pitch of a spoken

word gives it different meanings (and of course this is found in other

cultures as well). The "blue" notes (and this is a term used by

writers and observers, not by the artists) are often flat to the

Western idea of where the pitch lies, and can really add depth and

meaning to blues phrases. And, where you put a pitch, even in the same

song, can change from performance to performance. ..it all depends on

the FEELING you are trying to convey.

> In the book "Louis Armstrong's New Orleans," Louis talks about

hanging out with the rag pickers, and how they played cheap bugles to

draw the kids around. The pitches they played were not at all like

Western notes, for the most part. And, in the same book, it is

mentioned that certain people sounded like they were singing when they

talked. This makes big sense to me...but, I totally learned blues from

copying other players, and then from playing a great deal of blues in

live situations. And of course, this is how Arabic and Indian music

has been taught for a long time...listen and copy, then develop your

own thing.

> As far as "neutral" 3rds, flat 5ths and 7ths...I can put those

pitches where I want 100% of the time, but there's a lot more "blue"

notes than those, that's for sure. Most of my students are blues guys,

and for the most part, hitting those "blue" notes is VERY

difficult... it has to be done by feel, and any sort of intellectual

knowledge of ratios would be of no help whatsoever. And, I'm not

against understanding the theory behind blues, it's good fun. And, you

can't fake blues...within seconds, it's obvious to tell if someone

knows what the hell they're doing...it isn't just the pitches, either;

it's the rhythms and timing, which are just as difficult as the

pitches. (hearing classically trained folks try to play blues or jazz

is a hoot). Anyway, a few thoughts...best. ..Hstick microstick.net

myspace.com/ microstick

>