Blackwood

I have great respect for the fact that Blackwood has engaged himself with
microtonality, but I am not convinced of his general thesis that different
tunings can be made to have a seven-tone diatonic. People will know where I
am coming from theoretically, but it seems to me that for a given EDO, we
should be seeking what structures are contained within it that behave
tonally, (including pentatonally, etc).

We might compile scales from EDOs and collections of ratios, using whatever
methods - pragmatic or numerological - but there must be some 'essence' of
tonality there; tonality as an organising force.

This is only my opinion. Some choose a tuning or scale for its deliberately
anti-organizing effect. But if such a scale or tuning *is* anti-tonal, then
obviously there must be some effect that needs to be avoided. Quite
how 'tonality' manifests itself is of course one of those mystical
unknowns, and I don't take the Chomskian view that there is some part of
the human brain wired for music.

way more than 2cents worth.... ramble ramble...

--- In tuning@y..., "Mark Gould" <mark.gould@a...> wrote:
> I have great respect for the fact that Blackwood has engaged
himself with
> microtonality, but I am not convinced of his general thesis that
different
> tunings can be made to have a seven-tone diatonic. People will know
where I
> am coming from theoretically, but it seems to me that for a given
EDO, we
> should be seeking what structures are contained within it that
behave
> tonally, (including pentatonally, etc).

i agree. for example, 12, 19, 31, 43, and 55 ETs work great around as
seven-tone diatonic, while most others don't. this is because of the
syntonic comma. blackwood's 22-ET piece sounds awful to my ears, for
this very reason.

> We might compile scales from EDOs and collections of ratios, using
whatever
> methods - pragmatic or numerological - but there must be
some 'essence' of
> tonality there; tonality as an organising force.

well, it seems to me the most powerful force, even before tonality
comes into the picture, is the set of native unison vectors of the
ET. these will suggest certain "directions" for scale construction
where melody and harmony will work together, rather than against one
another.

--- In tuning@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...> wrote:

> well, it seems to me the most powerful force, even before tonality
> comes into the picture, is the set of native unison vectors of the
> ET. these will suggest certain "directions" for scale construction
> where melody and harmony will work together, rather than against one
> another.

Exactly; and following closely after, the set of native linear temperaments.

--- In tuning@y..., "Gene Ward Smith" <genewardsmith@j...> wrote:
> --- In tuning@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...>
wrote:
>
> > well, it seems to me the most powerful force, even before
tonality
> > comes into the picture, is the set of native unison vectors of
the
> > ET. these will suggest certain "directions" for scale
construction
> > where melody and harmony will work together, rather than against
one
> > another.
>
> Exactly; and following closely after, the set of native linear
>temperaments.

the set of native linear temperaments is simply the set of all ways
of choosing one unison vector (of the ET) *not* to use. the set of
native planar temperaments is the set of all ways of choosing *two*
unison vectors not to use . . . etc . . .

--- In tuning@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...> wrote:

> the set of native linear temperaments is simply the set of all ways
> of choosing one unison vector (of the ET) *not* to use.

Yes, but looking at it in terms of generators tells us something about how chord progressions (and often scales) are naturally constructed, which was part of the original question.

--- In tuning@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...>
wrote:
> --- In tuning@y..., "Gene Ward Smith" <genewardsmith@j...> wrote:
> > --- In tuning@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...>
> wrote:
> >
> > > well, it seems to me the most powerful force, even before
> tonality
> > > comes into the picture, is the set of native unison vectors of
> the
> > > ET. these will suggest certain "directions" for scale
> construction
> > > where melody and harmony will work together, rather than
against
> one
> > > another.
> >
> > Exactly; and following closely after, the set of native linear
> >temperaments.
>
> the set of native linear temperaments is simply the set of all ways
> of choosing one unison vector (of the ET) *not* to use. the set of
> native planar temperaments is the set of all ways of choosing *two*
> unison vectors not to use . . . etc . . .

i guess that wasn't quite right. here it is correctly (i think): if
the dimensionality (number of primes or independent lattice basis
vectors) is N, the set of native linear temperaments is the set of
all ways of choosing N-1 unison vectors to use, the set of native
planar temperaments is the set of all ways of choosing N-2 unison
vectors to use, etc. . . unfortunately, not all these choices will
give distinct results . . . please fix me up on tuning-math (or if
there's a cleaner, easier way of saying this, say it here!) . . .

--- In tuning@y..., "Gene Ward Smith" <genewardsmith@j...> wrote:
> --- In tuning@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...>
wrote:
>
> > the set of native linear temperaments is simply the set of all
ways
> > of choosing one unison vector (of the ET) *not* to use.
>
> Yes, but looking at it in terms of generators tells us something
>about how chord progressions (and often scales) are naturally
>constructed, which was part of the original question.

but one piece of information can be derived from the other. also, for
example, you can see the scales and progressions immediately on the
bingo-card (lattice) of the ET, by simply marking out a swath of
pitches directed along the direction of the unison vector (or the
subspace spanned by the unison vectors) you want to use. then you
don't even have to worry about the generator.

--- In tuning@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...> wrote:

> i guess that wasn't quite right. here it is correctly (i think): if
> the dimensionality (number of primes or independent lattice basis
> vectors) is N, the set of native linear temperaments is the set of
> all ways of choosing N-1 unison vectors to use, the set of native
> planar temperaments is the set of all ways of choosing N-2 unison
> vectors to use, etc. . . unfortunately, not all these choices will
> give distinct results . . . please fix me up on tuning-math (or if
> there's a cleaner, easier way of saying this, say it here!) . . .

I thought we were talking about ets? If we have an et, adding another gives us a linear temperament, which means subtracting a comma, as you said, will also do it. Of course, there are different possible basis sets of commas, and you can't assume you will get all the temperaments of interest from just one of them.

--- In tuning@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...> wrote:

> but one piece of information can be derived from the other.

This is what I thought before coming to the tuning list, so it is funny to hear you say it. You guys taught me that looking at the linear temperaments also is important.

--- In tuning@y..., "Gene Ward Smith" <genewardsmith@j...> wrote:
> --- In tuning@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...>
wrote:
>
> > i guess that wasn't quite right. here it is correctly (i think):
if
> > the dimensionality (number of primes or independent lattice basis
> > vectors) is N, the set of native linear temperaments is the set
of
> > all ways of choosing N-1 unison vectors to use, the set of native
> > planar temperaments is the set of all ways of choosing N-2 unison
> > vectors to use, etc. . . unfortunately, not all these choices
will
> > give distinct results . . . please fix me up on tuning-math (or
if
> > there's a cleaner, easier way of saying this, say it here!) . . .
>
> I thought we were talking about ets?

yes of course we are!!

>which means subtracting a comma, as you said, will also do it.

right, that's what i meant by N-1 unison vectors above.

>Of course, there are different possible basis sets of commas, and
>you can't assume you will get all the temperaments of interest from
>just one of them.

exactly -- which is why my earlier proposal, of simply choosing one
unison vector *not* to use, is impractical.

--- In tuning@y..., "Gene Ward Smith" <genewardsmith@j...> wrote:
> --- In tuning@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...>
wrote:
>
> > but one piece of information can be derived from the other.
>
> This is what I thought before coming to the tuning list, so it is
>funny to hear you say it. You guys taught me that looking at the
>linear temperaments also is important.

cool, so we've all learned from each other -- yes? seriously, this
stuff needs to be written up, and fast, and not in mathematese! and
not just by one person!

--- In tuning@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...>

/tuning/topicId_41076.html#41088

wrote> well, it seems to me the most powerful force, even before
tonality
> comes into the picture, is the set of native unison vectors of the
> ET. these will suggest certain "directions" for scale construction
> where melody and harmony will work together, rather than against
one
> another.

***Hi Paul,

Well, I've ordered Blackwood's _The Structure of Recognizable
Diatonic Tunings_ and *maybe* will be able to get it this time :)

But, are you suggesting that Blackwood "bends" the interpretation of
his scales to somehow *cram* the diatonic into them, rather than
taking into account inherent features like eliminating unison vectors
and such like?? He *does* seem to always want to get a rather
conservative diatonic out of most of them, except when it's
absolutely impossible...

I need a little illumination; it's dark in here...

Joseph

--- In tuning@y..., "Joseph Pehrson" <jpehrson@r...> wrote:
> --- In tuning@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...>
>
> /tuning/topicId_41076.html#41088
>
> wrote> well, it seems to me the most powerful force, even before
> tonality
> > comes into the picture, is the set of native unison vectors of
the
> > ET. these will suggest certain "directions" for scale
construction
> > where melody and harmony will work together, rather than against
> one
> > another.
>
> ***Hi Paul,
>
> Well, I've ordered Blackwood's _The Structure of Recognizable
> Diatonic Tunings_ and *maybe* will be able to get it this time :)

i hope you didn't spend $170!!

> But, are you suggesting that Blackwood "bends" the interpretation
of
> his scales to somehow *cram* the diatonic into them, rather than
> taking into account inherent features like eliminating unison
vectors
> and such like??

well, he notes the comma problems in his book, as you'll see. but to
my ear, the problems are even worse than he makes them out to be.

> He *does* seem to always want to get a rather
> conservative diatonic out of most of them, except when it's
> absolutely impossible...
>
> I need a little illumination; it's dark in here...

i just don't think he's looked far enough in the direction of
*generalizing* diatonicity . . .

--- In tuning@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...>

/tuning/topicId_41076.html#41131

>> > Well, I've ordered Blackwood's _The Structure of Recognizable
> > Diatonic Tunings_ and *maybe* will be able to get it this time :)
>
> i hope you didn't spend $170!!
>

***Hi Paul,

No, certainly not, and certainly not from "slobberer..." I ordered
it from Barnes & Noble online and still paid too much for it, but not
*that* much, I can assure you...

> > But, are you suggesting that Blackwood "bends" the interpretation
> of his scales to somehow *cram* the diatonic into them, rather than
> > taking into account inherent features like eliminating unison
> vectors and such like??
>
> well, he notes the comma problems in his book, as you'll see. but
to my ear, the problems are even worse than he makes them out to be.
>
> > He *does* seem to always want to get a rather
> > conservative diatonic out of most of them, except when it's
> > absolutely impossible...
> >
> > I need a little illumination; it's dark in here...
>
> i just don't think he's looked far enough in the direction of
> *generalizing* diatonicity . . .

***I know the book is pretty complex, but it seems interesting. Do
you have a copy of it, Paul??

I would enjoy discussing it further with you on this list in
conjunction with Blackwood's _Microtonal Etudes_ if you get a chance.

(That is, what I can figure out of all this!... )

Joseph

--- In tuning@y..., "Joseph Pehrson" <jpehrson@r...> wrote:

> ***I know the book is pretty complex, but it seems interesting. Do
> you have a copy of it, Paul??

no, but i have a pretty photographic memory . . .

> I would enjoy discussing it further with you on this list in
> conjunction with Blackwood's _Microtonal Etudes_ if you get a
>chance.

of course!