JI based on Fundamentals

Hey list,

Forgive me for being a JI greenie, but I have a rather
elementary question for y'all. I was reading about how
all the pitches used by La Monte Young in The
Well-Tuned Piano are overtones from a particular
subsonic (?) E flat. Is this a common way to devise a
just intonational system? Are there other composers
before Young who approached it this way? For a little
cultural studies project I'm working on I'm trying to
read a particular symbolic significance into LY's low
E flat, and I'm wondering if there are other pieces
using such a system that would bolster/bust my idea.

Thanks for your thoughts.

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Hello Jeremy,

--- In tuning@y..., Jeremy Grimshaw <jngrimshaw@y...> wrote:
> Forgive me for being a JI greenie, but I have a rather
> elementary question for y'all. I was reading about how
> all the pitches used by La Monte Young in The
> Well-Tuned Piano are overtones from a particular
> subsonic (?) E flat. Is this a common way to devise a
> just intonational system? Are there other composers
> before Young who approached it this way?

I can only answer briefly, about Harry Partch. Partch's system of 43-
tone, 11 limit JI generates from one central tone, which happens to
be a G natural (392 hz, I think I remember). The mystery of this
starting point? Harry had a good, resonant low G in his voice, and he
started there! As for LY's choice of the sub E flat, David Beardsley
could answer this better than I; I have read theories (even recently)
that the universe emits or resonates to a very subharmonic E flat.
Whether this is part of LY's system, I couldn't say.

Cheers,
Jon

--- In tuning@y..., Jeremy Grimshaw <
jngrimshaw@y...> wrote:
> Hey list,
>
> Forgive me for being a JI greenie, but I have a rather
> elementary question for y'all. I was reading about how
> all the pitches used by La Monte Young in The
> Well-Tuned Piano are overtones from a particular
> subsonic (?) E flat. Is this a common way to devise a
> just intonational system?

It's somewhat common, but not overwhelmingly
so. Harry Partch, for example, did not proceed this
way. He did start with G as a central pitch.Then he
added the first 12 overtones of G (5 more pitch
classes), the first 12 subharmonics of G (5 more
pitch classes), and all the notes that are within the
first 12 overtones of the subharmonics (and thus
also within the first 12 subharmonics of the
overtones) (18 more pitch classes). The set of 29
pitch classes so derived is just the set of pitches
forming an 11-limit consonance with the central G.
Then he filled the gaps of this rather uneven
"scale" with closely related JI pitches (14 more
pitch classes). Erv Wilson has created JI systems
that emphatically lack a central or generating pitch,
used by composers such as Kraig Grady. Other
composers who use JI systems not derived as a
single overtone series include Ben Johnston, Jon
Catler, Lou Harrison, and Michael Harrison.
Wendy Carlos wrote a piece where each of the
tones of 12-tone equal temperament is used as the
fundamental for a large harmonic series tuning
(through the 21st harmonic, with the 27th added).

> Are there other composers
> before Young who approached it this way? For a little
> cultural studies project I'm working on I'm trying to
> read a particular symbolic significance into LY's low
> E flat, and I'm wondering if there are other pieces
> using such a system that would bolster/bust my idea.

I know Pat Pagano uses a harmonic series tuning
with a special significance given to the fundamental
frequency, while others (such as Carter Scholz)
have used a harmonic series tuning where the
choice of fundamental is arbitrary.

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:

/tuning/topicId_26158.html#26164

>
> It's somewhat common, but not overwhelmingly
> so. Harry Partch, for example, did not proceed this
> way. He did start with G as a central pitch.Then he
> added the first 12 overtones of G (5 more pitch
> classes),

sure..., but what are they again?

D, B, F, A, C# (??)

the first 12 subharmonics of G (5 more
> pitch classes),

OK... similar logic, the other way...

and all the notes that are within the
> first 12 overtones of the subharmonics (and thus
> also within the first 12 subharmonics of the
> overtones) (18 more pitch classes).

I *kind of* get this, Paul, but could you please break this out a bit
if you have time??

The set of 29
> pitch classes so derived is just the set of pitches
> forming an 11-limit consonance with the central G.

Well, of course, this is because he goes up to 12 overtones, yes??

> Then he filled the gaps of this rather uneven
> "scale" with closely related JI pitches (14 more
> pitch classes).

Right... and *Miracle or not* is what we have been discussing...

Thanks, Paul!

_______ _______ ______
Joseph Pehrson

In a message dated 7/12/2001 1:18:17 AM Eastern Daylight Time,
paul@stretch-music.com writes:

> I know Pat Pagano uses a harmonic series tuning
> with a special significance given to the fundamental
> frequency, while others (such as Carter Scholz)
> have used a harmonic series tuning where the
>

Just out of curiousity Paul. What kind of "significance" are you talking
about?

Andy

La Monte tunes his Bb to 60 cycles.
In North America (I don't know about Central or
South America) electricity runs at 60 cycles.

David Beardsley
http://mp3.com/davidbeardsley

----- Original Message -----
From: Jon Szanto <JSZANTO@ADNC.COM>

> Hello Jeremy,
>
> --- In tuning@y..., Jeremy Grimshaw <jngrimshaw@y...> wrote:
> > Forgive me for being a JI greenie, but I have a rather
> > elementary question for y'all. I was reading about how
> > all the pitches used by La Monte Young in The
> > Well-Tuned Piano are overtones from a particular
> > subsonic (?) E flat. Is this a common way to devise a
> > just intonational system? Are there other composers
> > before Young who approached it this way?
>
> I can only answer briefly, about Harry Partch. Partch's system of 43-
> tone, 11 limit JI generates from one central tone, which happens to
> be a G natural (392 hz, I think I remember). The mystery of this
> starting point? Harry had a good, resonant low G in his voice, and he
> started there! As for LY's choice of the sub E flat, David Beardsley
> could answer this better than I; I have read theories (even recently)
> that the universe emits or resonates to a very subharmonic E flat.
> Whether this is part of LY's system, I couldn't say.
>
> Cheers,
> Jon
>
>
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--- In tuning@y..., jpehrson@r... wrote:
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
>
> /tuning/topicId_26158.html#26164
>
> >
> > It's somewhat common, but not overwhelmingly
> > so. Harry Partch, for example, did not proceed this
> > way. He did start with G as a central pitch.Then he
> > added the first 12 overtones of G (5 more pitch
> > classes),
>
> sure..., but what are they again?
>
> D, B, F, A, C# (??)

With the 72-tET accidentals we've been using, it would be

D, Bv, F<, A, C#[.
>
> the first 12 subharmonics of G (5 more
> > pitch classes),
>
> OK... similar logic, the other way...
>
> and all the notes that are within the
> > first 12 overtones of the subharmonics (and thus
> > also within the first 12 subharmonics of the
> > overtones) (18 more pitch classes).
>
> I *kind of* get this, Paul, but could you please break this out a
bit
> if you have time??

It's just the Tonality Diamond, as Partch describes in his book --
you understand that, right?
>
> The set of 29
> > pitch classes so derived is just the set of pitches
> > forming an 11-limit consonance with the central G.
>
> Well, of course, this is because he goes up to 12 overtones, yes??

And 12 undertones, yes. If he had taken overtones of overtones or
undertones of undertones, this wouldn't hold. But since it's
overtones of undertones, aka undertones of overtones, it does.

--- In tuning@y..., JoJoBuBu@a... wrote:
> In a message dated 7/12/2001 1:18:17 AM Eastern Daylight Time,
> paul@s... writes:
>
>
> > I know Pat Pagano uses a harmonic series tuning
> > with a special significance given to the fundamental
> > frequency, while others (such as Carter Scholz)
> > have used a harmonic series tuning where the
> >
>
> Just out of curiousity Paul. What kind of "significance" are you
talking
> about?
>
> Andy

Some kind of mystical or numerological meaning associated with the
fundamental frequency, or an association with the ambient 60Hz, or
any significance that would cause the composer to be less than happy
with the result of attempting to transpose his or her music to a
different fundamental.