diesic (was: new equal temperament 5-limit error lattices)

> From: paulerlich <paul@stretch-music.com>
> To: <tuning@yahoogroups.com>
> Sent: Thursday, February 21, 2002 4:39 AM
> Subject: [tuning] Re: new equal temperament 5-limit error lattices
>
>
> --- In tuning@y..., "monz" <joemonz@y...> wrote:
> > re:
> > http://www.ixpres.com/interval/dict/eqtemp.htm
>
> ... about 12-equal -- what do you mean it's 'just barely' diesic?
> i can't understand why you would say 'just barely'.

i knew i needed to write more about that to clarify. it's
just that i've been busting my butt working on this page so
much lately, i haven't gotten around to that yet.

basically what i mean is that because the diesis gives
a pitch which is so far away from either of the nearest
two 12edo degrees which may represent it, if a harmonic
progression is used in 12edo which features the diesis,
the "move" into that new lattice territory (near the diesis)
would be better implied by a 12edo degrees one step away
from the ones that actually do apply.

i don't know if that's any more clear ...? in fact, i'm
not quite sure if what i'm saying even has any validity.
i haven't actually examined any examples. how about if
we do this? i'm really not even too clear on what a
"diesic" temperament does or how it works.

-monz

>
> also, even more important than diesic, is the linear temperament based on
648:625, whose mos scales include diminished and octatonic, and which falls
on a straight line (in the first graph) connecting 12 with 28. this usage of
12 is extremely important in the music of the romantic period, where
diminished sevenths can resolve four ways, and even more important in the
music of liszt, stravinsky, bartok, bloch, late scriabin, and most jazz
musicians since dizzy gillespie, including john coltrane. meanwhile, the
'diesic' usage of 12 shows up only occasionally, i can only think of two
examples -- schubert and coltrane.
>
>
>
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--- In tuning@y..., "monz" <joemonz@y...> wrote:
>
> > From: paulerlich <paul@s...>
> > To: <tuning@y...>
> > Sent: Thursday, February 21, 2002 4:39 AM
> > Subject: [tuning] Re: new equal temperament 5-limit error lattices
> >
> >
> > --- In tuning@y..., "monz" <joemonz@y...> wrote:
> > > re:
> > > http://www.ixpres.com/interval/dict/eqtemp.htm
> >
> > ... about 12-equal -- what do you mean it's 'just barely' diesic?
> > i can't understand why you would say 'just barely'.
>
>
> i knew i needed to write more about that to clarify. it's
> just that i've been busting my butt working on this page so
> much lately, i haven't gotten around to that yet.
>
> basically what i mean is that because the diesis gives
> a pitch which is so far away from either of the nearest
> two 12edo degrees which may represent it, if a harmonic
> progression is used in 12edo which features the diesis,
> the "move" into that new lattice territory (near the diesis)
> would be better implied by a 12edo degrees one step away
> from the ones that actually do apply.

sorry, monz, but i *totally* disagree. big time. 100%. still love ya,
buddy.

does this help -- given the use of semicolons i discussed earlier,
i'd write the diesis as 125;128 -- the idea is that the actual value
of the ratio 125:128 is irrelevant, what is relevant is that it's
made up of three 5:4 major thirds (or their best approximation in the
tuning system).

would anyone else like to comment here? i think this is a perfect
example of the major disagreement monz and i have had for years now
(yes, it always seems to be a facet of the same basic issue, though
the diesis example hadn't come up yet). it's why i don't like his
latest charts, and so many of his previous charts, analyses, etc. i
seem to have been unable to get my point across to him (with any
permanence) for years now. maybe i should give up (i'm considering
leaving the list for a while). perhaps others can help.

> i don't know if that's any more clear ...? in fact, i'm
> not quite sure if what i'm saying even has any validity.
> i haven't actually examined any examples. how about if
> we do this? i'm really not even too clear on what a
> "diesic" temperament does or how it works.

'diesic temperament' based a chain of three major thirds equal an
octave. consider a progression, as in schubert, of major triads
ascending by major thirds. is the fourth chord the same as the first?
if so, it's 'diesic temperament' . . . actually, i think 'trefoil'
temperament would be a better name, since there are so many dieses.

did you read the material below?

> > also, even more important than diesic, is the linear temperament
based on
> 648:625, whose mos scales include diminished and octatonic, and
which falls
> on a straight line (in the first graph) connecting 12 with 28. this
usage of
> 12 is extremely important in the music of the romantic period, where
> diminished sevenths can resolve four ways, and even more important
in the
> music of liszt, stravinsky, bartok, bloch, late scriabin, and most
jazz
> musicians since dizzy gillespie, including john coltrane.
meanwhile, the
> 'diesic' usage of 12 shows up only occasionally, i can only think
of two
> examples -- schubert and coltrane.

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

> would anyone else like to comment here?

You know me--so far as I am concerned, h12 is a map and 128/125 is in its kernel, and that's about the size of it. Which means I don't get Joe's point at all, but I don't always expect to be on other people's wavelength.

> maybe i should give up (i'm considering
> leaving the list for a while). perhaps others can help.

You've been relatively inactive on tuning-math--is something up?

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

/tuning/topicId_34671.html#34682

>
> would anyone else like to comment here? i think this is a perfect
> example of the major disagreement monz and i have had for years now
> (yes, it always seems to be a facet of the same basic issue, though
> the diesis example hadn't come up yet). it's why i don't like his
> latest charts, and so many of his previous charts, analyses, etc. i
> seem to have been unable to get my point across to him (with any
> permanence) for years now. maybe i should give up (i'm considering
> leaving the list for a while). perhaps others can help.
>

***Yes, I would enjoy commenting. I don't understand this
disagreement at all. Frankly, it looks *fascinating* but so far I'm
finding it impenetrable.

If someone gets a chance, could I please have a short "Gentle
Introduction" to the Monzo-Erlich conflagration??

JP

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:

> If someone gets a chance, could I please have a short "Gentle
> Introduction" to the Monzo-Erlich conflagration??

i think i'll go hide behind gene :)

seriously, gene seems to be a lot smarter than me, and to agree with
me on all these issues. and i'm considering leaving for a while. so i
appoint him as my representative in any future proceedings . . . :)

gene, i think monz respects mathematics, and you're the real
mathematician around here. so don't hold back. give him hell,
gene :) :) :) monz has got _the_ microtonal theory page on the
internet. why not help him make it better?

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

/tuning/topicId_34671.html#34704

> --- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
>
> > If someone gets a chance, could I please have a short "Gentle
> > Introduction" to the Monzo-Erlich conflagration??
>
> i think i'll go hide behind gene :)
>
> seriously, gene seems to be a lot smarter than me, and to agree
with me on all these issues. and i'm considering leaving for a
while. so i appoint him as my representative in any future
proceedings . . . :)
>

***Ummm... somehow I don't think that's going to work, all apologies
and due respect to Gene's fine abilities... :)

JP

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:

> > seriously, gene seems to be a lot smarter than me, and to agree
> > with me on all these issues. and i'm considering leaving for a
> > while. so i appoint him as my representative in any future
> > proceedings . . . :)
> >
>
> ***Ummm... somehow I don't think that's going to work, all
apologies
> and due respect to Gene's fine abilities... :)

i think david finnamore also took my side in previous manifestations
of this disagreement, iirc . . . where's mr. f these days?

On 2/22/02 4:17 PM, "paulerlich" <paul@stretch-music.com> wrote:

> i think david finnamore also took my side in previous manifestations
> of this disagreement, iirc . . . where's mr. f these days?

He's busy dozens of hours a day. He's been difficult to get in touch with
since about November.

--- In tuning@y..., "paulerlich" <paul@s...> wrote:
> does this help -- given the use of semicolons i discussed earlier,
> i'd write the diesis as 125;128 -- the idea is that the actual value
> of the ratio 125:128 is irrelevant, what is relevant is that it's
> made up of three 5:4 major thirds (or their best approximation in
the
> tuning system).
>
> would anyone else like to comment here?

Yes. [So much for cold turkey huh?] This same confusion seemed to come
up recently in the notating-ETs-with-commas discussion too. I like
your notation idea, but maybe it's not enough. We may just have to
explain what we mean every time. The idea of a comma as something that
can be made to vanish in a temperament is quite different to
considering it as an actual ratio between two frequencies, or as a
number of cents.

It's not really 5^3 * 2*-7 that we're talking about, it's more like
M10*3 + P8*-7 or M3*3 + P8*-1, where M10, M3, P8 stand for the best
approximations of 1:5, 4:5 and 1:2, i.e. major tenth, major third and
octave.

In other words, take a stack of 3 major thirds in some temperament and
see how much short of an octave that is. In various ETs it is
typically either zero, one or two steps. If it's zero steps, we call
it a diesic temperament, in the same way that meantones could be
called syntonic-commatic temperaments.

This confusion doesn't often arise for the really small commas because
no one expects to encounter them as an actual frequency ratio in a
scale, but those of the size of a diesis tend to get confused.

--- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
> --- In tuning@y..., "paulerlich" <paul@s...> wrote:
> > does this help -- given the use of semicolons i discussed
earlier,
> > i'd write the diesis as 125;128 -- the idea is that the actual
value
> > of the ratio 125:128 is irrelevant, what is relevant is that it's
> > made up of three 5:4 major thirds (or their best approximation in
> the
> > tuning system).
> >
> > would anyone else like to comment here?
>
> Yes. [So much for cold turkey huh?] This same confusion seemed to
come
> up recently in the notating-ETs-with-commas discussion too. I like
> your notation idea, but maybe it's not enough. We may just have to
> explain what we mean every time. The idea of a comma as something
that
> can be made to vanish in a temperament is quite different to
> considering it as an actual ratio between two frequencies, or as a
> number of cents.
>
> It's not really 5^3 * 2*-7 that we're talking about, it's more like
> M10*3 + P8*-7 or M3*3 + P8*-1, where M10, M3, P8 stand for the best
> approximations of 1:5, 4:5 and 1:2, i.e. major tenth, major third
and
> octave.
>
> In other words, take a stack of 3 major thirds in some temperament
and
> see how much short of an octave that is. In various ETs it is
> typically either zero, one or two steps. If it's zero steps, we
call
> it a diesic temperament, in the same way that meantones could be
> called syntonic-commatic temperaments.

monz take note ! ! ! !