12EDO Specificities:

In my continued harping on the fact that
the potential of 12EDO hasn't been begun to
be realized yet, I'll just point out these
specificities:

1. the tritone/minor 3rd: this is actually
the most specific thing in 12EDO, since the
tritone/minor 3rd only appear in an EDO with
an even number of pitch classes.

2. Inversion: truly free inversions are only
possible in EDO tunings, and those inversions
lead to different superscale tonalities when
the inversions are on different pitch classes,
so for 12EDO there are a potential of 12 different
superscale tonalities for each of the 330 subscale
structures of 12EDO pitch class set theory.

Bill Flavell

--- In tuning@yahoogroups.com, "Bill Flavell" <bill_flavell@e...> wrote:

> 2. Inversion: truly free inversions are only
> possible in EDO tunings,

What is the basis for this claim?

> and those inversions
> lead to different superscale tonalities when
> the inversions are on different pitch classes,
> so for 12EDO there are a potential of 12 different
> superscale tonalities for each of the 330 subscale
> structures of 12EDO pitch class set theory.

This sounds like the stuff occasionally discussed on the tuning-math
list, where you might find a more interested audience for it.

--- In tuning@yahoogroups.com, "Bill Flavell" <bill_flavell@e...> wrote:
>
>
> In my continued harping on the fact that
> the potential of 12EDO hasn't been begun to
> be realized yet, I'll just point out these
> specificities:
>

I am also of the opinion that 12EDO is far from "spent". Not that it
matters much here, since *alternative* tunings are the purpose of this
group...

>
> 1. the tritone/minor 3rd: this is actually
> the most specific thing in 12EDO, since the
> tritone/minor 3rd only appear in an EDO with
> an even number of pitch classes.
>

You mean the fully symmetrical tritone? Yes, fully symmetric ttritones
appear only in even-number EDOs. And fully-symmetric diminshed seventh
chords appear only in EDOs where the number of pitches is a multiple
of 4, and fully symmetric augmented triads appear only in EDOs where
the number of pitches is a multiple of 3 - and so on! Symmetrical
chords are very good for modulations. And 12, as a relatively low
number with an exceptional high number of divisors, is indeed quite a
good choice in this aspect.
OTOH, if you want something like a non-symmetrical whole-tone scale,
an odd-number EDO is needed.

> 2. Inversion: truly free inversions are only
> possible in EDO tunings,

or in just intonation tunigs with an unlimited number of pitches per
octave.
--
Hans Straub

Hans, I am of the opinion that any tuning becomes quite boring after it
establishes monopoly over the alternatives for an extended period of time.
Not that I have anything against 12-tET as a means of making music of
course... It's rather that this particular tuning has been abused enough by
sloppy electronic gadgets and the ever-growing mass media. Thankfully,
traditional genres made their way into the world music market in time.

----- Original Message -----
From: "hstraub64" <hstraub64@telesonique.net>
To: <tuning@yahoogroups.com>
Sent: 16 Aral�k 2005 Cuma 14:39
Subject: [tuning] Re: 12EDO Specificities:

> --- In tuning@yahoogroups.com, "Bill Flavell" <bill_flavell@e...> wrote:
> >
> >
> > In my continued harping on the fact that
> > the potential of 12EDO hasn't been begun to
> > be realized yet, I'll just point out these
> > specificities:
> >
>
> I am also of the opinion that 12EDO is far from "spent". Not that it
> matters much here, since *alternative* tunings are the purpose of this
> group...
>

SNIP

Ozan Yarman wrote:

> Not that I have anything against 12-tET as a means of making music of
> course... It's rather that this particular tuning has been abused enough by
> sloppy electronic gadgets and the ever-growing mass media. Thankfully,
> traditional genres made their way into the world music market in time.

My impression is rather the opposite: that the world music _market_ spreads 12-et, keyboardified, ethnically influenced pop music. Tarkan comes to mind (and the woman with the more complicated name who composed for him and who I actually liked better).

klaus

You have a point there Klaus. But still, there are microtonal brands too.

Oz.

----- Original Message -----
From: "klaus schmirler" <KSchmir@online.de>
To: <tuning@yahoogroups.com>
Sent: 17 Aral�k 2005 Cumartesi 14:33
Subject: Re: [tuning] Re: 12EDO Specificities:

> Ozan Yarman wrote:
>
> > Not that I have anything against 12-tET as a means of making music of
> > course... It's rather that this particular tuning has been abused enough
by
> > sloppy electronic gadgets and the ever-growing mass media. Thankfully,
> > traditional genres made their way into the world music market in time.
>
> My impression is rather the opposite: that the world music _market_
> spreads 12-et, keyboardified, ethnically influenced pop music. Tarkan
> comes to mind (and the woman with the more complicated name who
> composed for him and who I actually liked better).
>
> klaus
>
>

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@o...> wrote:
>
> Hans, I am of the opinion that any tuning becomes quite boring
> after it establishes monopoly over the alternatives for an
> extended period of time.
> Not that I have anything against 12-tET as a means of making music
> of course... It's rather that this particular tuning has been
> abused enough by sloppy electronic gadgets and the ever-growing
> mass media. Thankfully, traditional genres made their way into the
> world music market in time.
>

Well, there is one thing that happens when something gets a quasi-
monopoly or just big success in the mass market: a lot of stuff will
be produced with more money than music in mind, and a lot of this
will be of bad quality.
This is, however, not the fault of the tuning system, nor of
electronics. If a lot of bad stuff is produced, this does not mean
there cannot be good things any more.
--
Hans Straub

Certainly. But to promote more good things, we must endorse the alternative
practicable tunings with greater vigor.

----- Original Message -----
From: "hstraub64" <hstraub64@telesonique.net>
To: <tuning@yahoogroups.com>
Sent: 18 Aral�k 2005 Pazar 15:24
Subject: [tuning] Re: 12EDO Specificities:

> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@o...> wrote:
> >
> > Hans, I am of the opinion that any tuning becomes quite boring
> > after it establishes monopoly over the alternatives for an
> > extended period of time.
> > Not that I have anything against 12-tET as a means of making music
> > of course... It's rather that this particular tuning has been
> > abused enough by sloppy electronic gadgets and the ever-growing
> > mass media. Thankfully, traditional genres made their way into the
> > world music market in time.
> >
>
> Well, there is one thing that happens when something gets a quasi-
> monopoly or just big success in the mass market: a lot of stuff will
> be produced with more money than music in mind, and a lot of this
> will be of bad quality.
> This is, however, not the fault of the tuning system, nor of
> electronics. If a lot of bad stuff is produced, this does not mean
> there cannot be good things any more.
> --
> Hans Straub
>

--- In tuning@yahoogroups.com, "hstraub64" <hstraub64@t...> wrote:

> > 2. Inversion: truly free inversions are only
> > possible in EDO tunings,
>
> or in just intonation tunigs with an unlimited number of pitches per
> octave.
> --
> Hans Straub

Or in any regular system of tuning, be it a temperament (such as a
meantone, schismatic, diaschismatic, miracle, or whatever), a tuning
whose intervals derive from an inharmonic spectrum, or what have you.