RE: [tuning] Re: Schismas, meantone, well-temperaments (for Graha m Breed)

Just wanted to say, keep up the good work Graham. You're the man!

P.S. You seem uncomfortable assigning a name to "the 22, 34, 46, ...
family". What's wrong with "diaschismic", which you yourself suggested?
These are the cardinalities you get from periodicity blocks where one of the
unison vectors is a diaschisma, right?

Paul Erlich wrote:

> Just wanted to say, keep up the good work Graham. You're the man!

Thanks, and mutual respect all round. I've got a lot more sympathy with
your idea of alternative-tonality that when I originally read that 22all
paper.

> P.S. You seem uncomfortable assigning a name to "the 22, 34, 46, ...
> family". What's wrong with "diaschismic", which you yourself suggested?
> These are the cardinalities you get from periodicity blocks where one
> of the
> unison vectors is a diaschisma, right?

Ah, well, the first thing wrong with it is that it's a four syllable
Greek-derived word. I'm hoping for something simpler. "Split positive"
is the best I thought of. Same number of syllables, but more English.
Although it didn't catch on.

The other thing wrong with it is that the "diaschisma" has a former life
as a kind of semitone. So the term "diaschismic" could be misleading to
those who know this older meaning. I didn't know that when I originally
came up with the word. In that case, a truly meaningless Greek-derived
word would be better. So how about "metaschismic"?

Graham

Graham wrote,

>The other thing wrong with it is that the "diaschisma" has a former life
>as a kind of semitone. So the term "diaschismic" could be misleading to
>those who know this older meaning.

Well, words like "Phrygian" and "enharmonic" have former lives with other
meanings, but that doesn't prevent widespread use today with the current
meaning. The same should go for "diaschismic", particularly if it's going to
be a parallel to "schismic".

Graham wrote,

>Thanks, and mutual respect all round. I've got a lot more sympathy with
>your idea of alternative-tonality that when I originally read that 22all
>paper.

Nice to hear -- I wonder if you have any reactions to other people's
approaches to alternative tonality, for example Bohlen/Pierce,
Balzano/Zweifel, Clough/Carey/Clampitt, Kraehenbuehl/Schmidt, Yasser,
Euler/Fokker, Goldsmith, Von Hoerner . . . ?

Paul Erlich wrote:

> Graham wrote,
>
> >The other thing wrong with it is that the "diaschisma" has a former
> life >as a kind of semitone. So the term "diaschismic" could be
> misleading to >those who know this older meaning.
>
> Well, words like "Phrygian" and "enharmonic" have former lives with
> other
> meanings, but that doesn't prevent widespread use today with the current
> meaning. The same should go for "diaschismic", particularly if it's
> going to
> be a parallel to "schismic".

The redefinition of "Phrygian" et al has caused no end of confusion.
That's exactly the kind of thing I'm trying to avoid. If we're going to
be re-defining terms, Bosanquet's "double positive" would be the obvious
one. This kind of temperament is characteristic of the equal temperaments
with 2+12n notes. Although the terms aren't identical (96- and 118-equal
are double positive but schismic) they're close enough that something like
"continuous double positive" should be clear.

By association, schismic scales could be referred to as "continuously
single positive" and meantones as "continuously double negative".

That also means the family of meantone-like scales where the whole tone is
divided into two equal parts, and t/2 + s is associated with 7:8, can be
described as "continuously double negative". These are 14, 26, 38, 50,
etc. Note that 50-equal is both singly and doubly negative in this
continuous realm.

The neutral third MOS can also be neatly described as "continuously
septimally double positive" after Wilson.

At the bottom of his 1975 paper where he introduces the term "septimally
positive" Erv Wilson does say "By `system' I do not limit the meaning to
closed equal cycles. If the beginning member of a linear series forms (in
this case) a `quasi-fifth' to the ending member of the series, which
subtends the same number of scale-degrees as the remaining (typical)
`fifths' of the series -- a moment of symmetry is formed having scale-like
and systematic properties. These are important, and I will go into them
at another time." Which looks like it means "septimally positive" refers
primarily to systems with a "`Fifth' larger than 4/7 `Octave'" and only
secondarily to the scales with 5+7n equal steps to the "octave".

However, Wilson doesn't consider doubly positive or negative scales. That
conveniently avoids the confusion between 5-equal being "double negative"
by Bosanquet's ET-based definition, but "single negative" by the MOS one.
In which case "septimally double positive" may be a neologism, although
it's an obvious combination of Bosanquet and Wilson's ideas.

If confusion's unavoidable, I'd prefer the general naming scheme that
covers 5 of my favourite temperament families, and has the potential to
name a lot more, than to keep inventing Greek looking words.

Graham

Paul Erlich wrote:

> Nice to hear -- I wonder if you have any reactions to other people's
> approaches to alternative tonality, for example Bohlen/Pierce,
> Balzano/Zweifel, Clough/Carey/Clampitt, Kraehenbuehl/Schmidt, Yasser,
> Euler/Fokker, Goldsmith, Von Hoerner . . . ?

The simple answer is that I don't know much about them. And if there
isn't anything on the web, I'm not likely to find out much more. But
let's got through in order.

>Bohlen/Pierce

The Bohlen/Pierce scale sounds pleasant enough. On the "BP Tonality" page
<http://members.aol.com/bpsite/tonality.html> there isn't very much. A
primary consonance and some scales, but no standard progressions or
characteristic dissonances.

>Balzano/Zweifel

I've heard of Balzano. Can't remember why.

>Clough/Carey/Clampitt

My response to that "Self-Similar Pitch Structure" paper is much as I said
at the time. It doesn't seem to have much connection to music. The basic
idea ties in with Wilson's MOS anyway, "Well Formedness" seems to be
useful, in that chords or tunes can be transposed and still make sense.
Again, nothing about chord progressions, only defining the scales.

>Kraehenbuehl/Schmidt

Don't know

>Yasser

The bits I've heard about sound fairly nutty, so I haven't looked any
further.

> Euler/Fokker

They both talk good sense from what I've seen. But not really what I was
calling "alternative tonality". More alternative consonances, in the
meantone tradition.

> Goldsmith, Von Hoerner

Don't know

> . . .

The first thing that sprang to mind was Walter O'Connell's "The Tonality
of the Golden Section" from Xenharmonikon 15. The interesting feature is
that it uses inharmonic timbres but preserves the coincidence between
partials and resultant tones you get from the harmonic series. So it
might allow for a deeper sense of tonality than other inharmonic timbres.

Well, I decided to set it up and find out. It doesn't sound as convincing
as the Bohlen-Pierce scale, which is partly because Golden ratio timbres
don't sound as nice as square waves. Also because the consonances aren't
so consonant. Although the sense of "octave equivalence" is very strong
-- more so than with the usual octaves and harmonic timbres. And the dyad
of pretend and real octave is consonant. So there could be some value in
dyadic music.

The paper doesn't even give any chords, let alone progressions or
characteristic dissonances. So again, not really "alternative tonality",
but then tonality wasn't fashionable back then.

It may be Setharian techniques could yield a better scale for that timbre.
I don't know if that would be any help for the general problem of
inharmonic tonality, because there are still only two timbres with the
special property. And the harmonic series probably has a special place in
our brains, more important that its acoustic properties.

That aside, I still think there's potential in inharmonic timbres. My
experiments with the neutral third scales show strong chord progressions
can work with out otonal, or even particularly consonant, chords. So find
an inharmonic timbre that gives something like fifths and octaves, and see
what happens. It's a field I'm interested in, but I need to find the time
to collect samples, find scales and the like. I'm thinking of something
like what the music in Dancer in the Dark should have been. Have it grow
out of incidental sounds, instead of using a few samples in the
introduction and then fade them out when the orchestra kicks in. But
still mix in harmonic sounds where they're needed.

So there you go. In summary, I haven't seen anything as relevant as your
or Margo's work, but that may be because it wasn't pushed at me through
this list.

Graham

--- In tuning@y..., graham@m... wrote:
>
> That aside, I still think there's potential in inharmonic timbres.
My
> experiments with the neutral third scales show strong chord
progressions
> can work with out otonal, or even particularly consonant, chords.
So find
> an inharmonic timbre that gives something like fifths and octaves,
and see
> what happens. It's a field I'm interested in, but I need to find
the time
> to collect samples, find scales and the like. I'm thinking of
something
> like what the music in Dancer in the Dark should have been. Have
it grow
> out of incidental sounds, instead of using a few samples in the
> introduction and then fade them out when the orchestra kicks in.
But
> still mix in harmonic sounds where they're needed.
>

Graham,

This is really fantastic to hear, and I'll be personally very
interested to hear what you come up with from this research.

I think if one is able to resynthesize timbres or outright create
them, then it would be possible to make an existing tuning match to
the timbre - by changing the timbres partials, but where one desires
to use pre-existing timbres, which you may not care to resynthesize,
and would care to use as-is, then I think a whole different logic
must come into play. Almost seems as two polar opposite approaches to
timbre and tuning.

Thanks,

Jacky Ligon

--- In tuning@y..., graham@m... wrote:

>
> The redefinition of "Phrygian" et al has caused no end of confusion.

Really? Outside of this list, there seems to be no confusion: E F G A B C D E is E Phrygian.

> That's exactly the kind of thing I'm trying to avoid. If we're going to
> be re-defining terms, Bosanquet's "double positive" would be the obvious
> one. This kind of temperament is characteristic of the equal temperaments
> with 2+12n notes.

You mean 12n - 2?

> Although the terms aren't identical (96- and 118-equal
> are double positive but schismic)

And 56-, 64-, and 76-equal are not double positive but are some of scales we're talking about

> they're close enough that something like
> "continuous double positive" should be clear.

I don't see how the word "continuous" alleviates that problem, but I do see it suggesting many
things that aren't true about 22, 46, etc.

> If confusion's unavoidable, I'd prefer the general naming scheme that
> covers 5 of my favourite temperament families, and has the potential to
> name a lot more, than to keep inventing Greek looking words.

Again, I don't see why "diaschismic" falls into a different class than "schismic". What potentially
contradictory meaning could be suggested by "diaschismic"?

--- In tuning@y..., ligonj@n... wrote:

> I think if one is able to resynthesize timbres or outright create
> them, then it would be possible to make an existing tuning match to
> the timbre - by changing the timbres partials, but where one desires
> to use pre-existing timbres, which you may not care to resynthesize,
> and would care to use as-is, then I think a whole different logic
> must come into play. Almost seems as two polar opposite approaches to
> timbre and tuning.

That very duality, of course, was the thrust of Sethares' original JASA paper, and is featured
heavily in his book as well.

Paul Erlich wrote:

> > The redefinition of "Phrygian" et al has caused no end of confusion.
>
> Really? Outside of this list, there seems to be no confusion: E F G A B
> C D E is E Phrygian.

It confused me when I first read that stuff in Plato. Also that the
neutral scales in Manuel's mode list follow the Greek ordering. It seems
to confuse most people when they start to find out about Ancient Greek
music.

> > That's exactly the kind of thing I'm trying to avoid. If we're going
> > to be re-defining terms, Bosanquet's "double positive" would be the
> > obvious one. This kind of temperament is characteristic of the equal
> > temperaments with 2+12n notes.
>
> You mean 12n - 2?

Yes, or 12n+10. 12n+2*5n would be the best way of capturing "doudecimally
double-positive".

> > Although the terms aren't identical (96- and 118-equal
> > are double positive but schismic)
>
> And 56-, 64-, and 76-equal are not double positive but are some of
> scales we're talking about

The change-over occurs when the syntonic comma is best represented by 2
steps.

> > they're close enough that something like
> > "continuous double positive" should be clear.
>
> I don't see how the word "continuous" alleviates that problem, but I do
> see it suggesting many things that aren't true about 22, 46, etc.

It suggests that the Pythagorean comma is positive, and can be divided
into two equal parts for all members of the family. I proposed "split
positive" to mean a positive tuning with an octave split into equal parts
so as to avoid confusion with double positive scales.

If you really mean the set of tunings Bosanquet described as "double
positive" you can call them "10+12n" (and hope you get the right one :).
I see this concept as less important than the "diaschismic" one, so I'd
prefer the friendly name to be applied to "diaschismic" scales than
"12n+10" scales.

I also suggest we abbreviate "septimally double positive" to "7++". That
way we avoid confusion with "septimal" referring to 7-limit harmony. It
would then follow that diaschismic scales are 12++. As "12++" is my own
coinage, and has nothing to do with Bosanquet or Wilson, that also leaves
me free to define it however I like.

> > If confusion's unavoidable, I'd prefer the general naming scheme that
> > covers 5 of my favourite temperament families, and has the potential
> > to name a lot more, than to keep inventing Greek looking words.
>
> Again, I don't see why "diaschismic" falls into a different class than
> "schismic". What potentially contradictory meaning could be suggested
> by "diaschismic"?

So was there already an interval called a schisma? The word "schismic"
(or at least "skhismatic") was already being used do describe schismic
scales before I came along. It's also 1 or 2 syllables shorter. The word
"diaschismic" was starting to catch on because I used it on my website.
As I'd stopped liking the word by then, I thought I'd stop promoting it.
I do have alternatives, so I'll see what other people start using.

I would reconsider if you can show that "disachisma" would usually be
understood to have the newer meaning. Mathieu uses it that way, so it has
appeared in print.

Graham

Jacky Ligon wrote:

> This is really fantastic to hear, and I'll be personally very
> interested to hear what you come up with from this research.

I have 4 weeks holiday a year. I think it'll take me at least 5 weeks to
get this done ;)

> I think if one is able to resynthesize timbres or outright create
> them, then it would be possible to make an existing tuning match to
> the timbre - by changing the timbres partials, but where one desires
> to use pre-existing timbres, which you may not care to resynthesize,
> and would care to use as-is, then I think a whole different logic
> must come into play. Almost seems as two polar opposite approaches to
> timbre and tuning.

But if I find a timbre I like, I don't want to ruin it by forcing it to
match a different scale. There has to be some sort of compromise, like
finding a scale that half-fits all timbres being used, and bend them to
fit that. Also to morph between different timbres and tunings so that one
part can be wholly inharmonic, and another more conventional. I think
this would suit the escapism of Dancer in the Dark much better than they
way they did it. Start with the noise of a factory, then have the noises
coming in tune with one another, and have them sound more and more like
orchestral instruments.

Oh yes, I have lots of ideas ...

Graham