Best First >12EDO Tuning to Explore: 16EDO:

I think the most logicalfirst EDO tunings to explore
would be the ones whose pitch class numbers are
factors of 2, in order to mimic/prioritize the
1/2 octave relationship in nature
(2,4,8,16,32, etc.).

Since we've already got 12EDO as our cultural
de facto tuning, I think the next one to explore
should be 16EDO. That way the internal equal
divisions of the octave (the microcosm)would miror
the external 1/2 octave relationship (the macrocosm),
fulfilling the dictum "as above, so below".

With all due respect to Pythagoras, The significance
of the number 3 in esoteric mysticism
(ie Gurdjieff's Law of Three Forces
[ http://www.endlesssearch.co.uk/philo_lawof3.htm ])
does NOT guarantee that the number 3 should be
automatically prioritized/festishized in musical
tuning system design.

Until the EDO tunings of the factors of 2 are
completely explored, what basis is there for
objective evaluation of any other allegedly
more complicated/sophisticated tunings?

Bill Flavell

--- In tuning@yahoogroups.com, "Bill Flavell" <bill_flavell@e...> wrote:
>
>
> I think the most logicalfirst EDO tunings to explore
> would be the ones whose pitch class numbers are
> factors of 2, in order to mimic/prioritize the
> 1/2 octave relationship in nature
> (2,4,8,16,32, etc.).

You're half-way to Balzano's theory, which says we should first look
at edos divisible by 4, and it shares the same defect--there's no
actual reason for it. In particular 1/2 octaves are hardly either
found in nature or especially pleasing to the ear.

> Since we've already got 12EDO as our cultural
> de facto tuning, I think the next one to explore
> should be 16EDO.

That's pretty grim, though I suppose Herman Miller might object here.
Far better as a candidate is 22-edo, Paul Erlich's favorite system.
Even that can leave people pretty unimpressed, alas. Three decades
back, after I filled my brother's ears with how good a system 22 was,
he gave me a pretty hard time when he heard actual music in it. Of
course, that may have been my fault, I suppose.

> With all due respect to Pythagoras, The significance
> of the number 3 in esoteric mysticism
> (ie Gurdjieff's Law of Three Forces
> [ http://www.endlesssearch.co.uk/philo_lawof3.htm ])
> does NOT guarantee that the number 3 should be
> automatically prioritized/festishized in musical
> tuning system design.

We've got three notes in a triad, and that should be enough for any
esoteric mystic.

> Until the EDO tunings of the factors of 2 are
> completely explored, what basis is there for
> objective evaluation of any other allegedly
> more complicated/sophisticated tunings?

Because factors of 2 don't sound better, and by insisting on them you
simply miss half the systems. The first system after 12 with a decent
sound to it is 19, not 22, for instance. 34 is a fine system, but so
is 31. There's absolutely no reason to prefer the even numbers.

Gene Ward Smith wrote:
> --- In tuning@yahoogroups.com, "Bill Flavell" <bill_flavell@e...> wrote:
> >>
>>I think the most logicalfirst EDO tunings to explore
>>would be the ones whose pitch class numbers are
>>factors of 2, in order to mimic/prioritize the >>1/2 octave relationship in nature >>(2,4,8,16,32, etc.).
> > > You're half-way to Balzano's theory, which says we should first look
> at edos divisible by 4, and it shares the same defect--there's no
> actual reason for it. In particular 1/2 octaves are hardly either
> found in nature or especially pleasing to the ear.

Hear, hear!

[snip]

>>With all due respect to Pythagoras, The significance
>>of the number 3 in esoteric mysticism >>(ie Gurdjieff's Law of Three Forces >>[ http://www.endlesssearch.co.uk/philo_lawof3.htm ])
>>does NOT guarantee that the number 3 should be
>>automatically prioritized/festishized in musical
>>tuning system design.
> > > We've got three notes in a triad, and that should be enough for any
> esoteric mystic.

Hmmm... this gives me an idea, which I explain below.

>>Until the EDO tunings of the factors of 2 are
>>completely explored, what basis is there for >>objective evaluation of any other allegedly >>more complicated/sophisticated tunings?
> > > Because factors of 2 don't sound better, and by insisting on them you
> simply miss half the systems. The first system after 12 with a decent
> sound to it is 19, not 22, for instance. 34 is a fine system, but so
> is 31. There's absolutely no reason to prefer the even numbers.

Well, 17 might not sound "decent" =P but it sure is interesting.

I would say the usable EDOs are just those which have fifths between the 720 cent fifth of 5EDO and the 686 cent fifth of 7EDO. So the next ones after 12 are 17, 19, 22, 24, 26, 27, 29, 31... (most of these are familiar)

However, this brings me back to my idea. You know how the Bohlen-Pierce scale rejects 2 (the octave) as a consonance and uses a 3/1 "tritave" along with intervals of 5 and 7? What if instead we kept 2 but rejected 3, and instead of a "circle of fifths" had a "circle of major thirds" or something. Then the usable EDOs would be 13, 16, 19, 22, and so on. And there should be a linear temperament in which intervals of 7 are approximated by some number of major thirds.

I'm going to go play around with this right now.

Keenan

(On tuning systems which reject intervals of 3 but include intervals of 5 and 7)

If you temper out 50/49, you get two chains of intervals separated by exactly half an octave. The interval I'm using is 4*sqrt(70*sqrt(2))/35, or about 222 cents. Is there a name for this temperament, or did I just discover/invent it?

If you use exactly 225 cents for the interval, you get 16EDO - exactly what Bill Flavell suggested. Pure coincidence, though.

Keenan

--- In tuning@yahoogroups.com, Keenan Pepper <keenanpepper@g...> wrote:

What if instead we kept 2 but rejected 3, and instead of a
> "circle of fifths" had a "circle of major thirds" or something. Then
the usable
> EDOs would be 13, 16, 19, 22, and so on. And there should be a linear
> temperament in which intervals of 7 are approximated by some number
of major thirds.

The threes in hemiwuerschmidt are pretty complex, and if we ignore
them we have the no-threes system tempering out 3136/3125. The
generator is half of a major third. The related systems of magic and
muggles have generators of a third. On your piano you find a very
simple if rather crude no-threes system called 6-edo, for that matter.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
>
> You're half-way to Balzano's theory, which says we should first look
> at edos divisible by 4, and it shares the same defect--there's no
> actual reason for it. In particular 1/2 octaves are hardly either
> found in nature or especially pleasing to the ear.

UTTER BULLSHIT! :) To my ear the 8-tone blues mode 8-26
is the most significant 12EDO subscale and it is based
on both the tritone and minor 3rd. The tritone is THE
MOST SPECIFIC PROPERTY OF 12EDO (because it's an
EVEN-NUMBERED EDO), and I haven't heard
any alternative tuning system that can match it!

Bill Flavell

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
>
> > Since we've already got 12EDO as our cultural
> > de facto tuning, I think the next one to explore
> > should be 16EDO.
>
> That's pretty grim, though I suppose Herman Miller might object
here.
> Far better as a candidate is 22-edo, Paul Erlich's favorite system.
> Even that can leave people pretty unimpressed, alas. Three decades
> back, after I filled my brother's ears with how good a system 22
was,
> he gave me a pretty hard time when he heard actual music in it. Of
> course, that may have been my fault, I suppose.

My point is that the 12EDO tritone and minor 3rd
are the basis of the best tuning/scale I've heard
so far (the 12EDO 8-tone blues mode 1-2-2-1-2-1-1-2),
so I'm interested in seeing what happens when you go
an additional 2 powers of 2 equal divisions of the
octave. I haven't heard any alternative tunings that
can match that 8-tone blues mode yet.

Bill Flavell

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:

> > Until the EDO tunings of the factors of 2 are
> > completely explored, what basis is there for
> > objective evaluation of any other allegedly
> > more complicated/sophisticated tunings?
>
> Because factors of 2 don't sound better,

TO YOU, maybe! :) I'll take a 12EDO tritone
and minor 3rd over any other alternative
tuning'scale I've heard sio far! :)

> and by insisting on them you
> simply miss half the systems. The first system after 12 with a
decent
> sound to it is 19, not 22, for instance. 34 is a fine system, but so
> is 31. There's absolutely no reason to prefer the even numbers.

You're buying the conventional anti-tritone
bias of conventional western music theory.

The African-Americans rightly recognized
the tritone as the most 12EDO-specific interval,
and based the blues and jazz mostly on it.

What other interval could you base your
music on when all you had access to was a
bunch of beat-up out of tune pianos? :)

Bill Flavell

--- In tuning@yahoogroups.com, Keenan Pepper <keenanpepper@g...> wrote:

>instead of a
> "circle of fifths" had a "circle of major thirds" or something. Then
the usable
> EDOs would be 13, 16, 19, 22, and so on. And there should be a linear
> temperament in which intervals of 7 are approximated by some number
>of major thirds.
>
> I'm going to go play around with this right now.
>
> Keenan

Hi Keenan, welcome back, it's been, like, years?

I feel I should send you the latest (8/27/04) draft of the _Middle
Path_ paper, so you can see a bit of what you missed during the years
you were away. It discusses systems like this, and more generally,
systems where some group of JI intervals ("commas") is tempered out
(the commas "vanish").

Would you kindly provide me with your snail-mail address?

Best,
Paul

--- In tuning@yahoogroups.com, Keenan Pepper <keenanpepper@g...>
wrote:
>
> (On tuning systems which reject intervals of 3 but include
intervals of 5 and 7)
>
> If you temper out 50/49, you get two chains of intervals separated
>by exactly
> half an octave. The interval I'm using is 4*sqrt(70*sqrt(2))/35, or
>about 222
> cents. Is there a name for this temperament, or did I just
>discover/invent it?

We haven't looked too much at {2,5,7} temperaments so you probably
discovered it. The TOP tuning would have the primes tempered as
follows:

prime 2 -> cents(2)-cents(50/49)*log(2)/log(50*49) = 1196.89 cents;
prime 5 -> cents(5)-cents(50/49)*log(5)/log(50*49) = 2779.10 cents;
prime 7 -> cents(7)+cents(50/49)*log(7)/log(50*49) = 3377.55 cents.

Is the approximation of 8/7 and 28/25 the generator? If so, I get
213.13 cents . . .

> If you use exactly 225 cents for the interval, you get 16EDO -
exactly what Bill
> Flavell suggested. Pure coincidence, though.
>
> Keenan
>

Keenan Pepper wrote:
> (On tuning systems which reject intervals of 3 but include intervals of 5 and 7)

Paul said we hadn't looked much at these, and sure enough there was a bug in my temperament finder that broke them. But it's fixed now. Go to

http://x31eq.com/temper/linear.html

and set the limit to 1.5.7, then play around with other things (probably lower the maximum complexity)

The simplest consistent equal temperaments are

2 3 4 5 6 9 10 11 12 13 15 16 18 19 21 22 25 26 27 28

> If you temper out 50/49, you get two chains of intervals separated by exactly > half an octave. The interval I'm using is 4*sqrt(70*sqrt(2))/35, or about 222 > cents. Is there a name for this temperament, or did I just discover/invent it?

I don't find this one on the search. Maybe there's still a bug, or it isn't so special. Do you have the full mapping?

> If you use exactly 225 cents for the interval, you get 16EDO - exactly what Bill > Flavell suggested. Pure coincidence, though.

There's this one that covers 16-edo:

2/31, 77.2 cent generator

basis:
(1.0, 0.064321646603719529)

mapping by period and generator:
[(1, 0), (1, 9), (2, 5), (3, -3)]

mapping by steps:
[(16, 15), (25, 24), (37, 35), (45, 42)]

highest interval width: 8
complexity measure: 8 (9 for smallest MOS)
highest error: 0.000320 (0.384 cents)
unique

Graham

Graham Breed wrote:
> Keenan Pepper wrote:
> >>(On tuning systems which reject intervals of 3 but include intervals of 5 and 7)
> > > Paul said we hadn't looked much at these, and sure enough there was a > bug in my temperament finder that broke them. But it's fixed now. Go to
> > http://x31eq.com/temper/linear.html
> > and set the limit to 1.5.7, then play around with other things (probably > lower the maximum complexity)

This looks interesting. Is there a manual or anything? Can I see the source code?

> The simplest consistent equal temperaments are
> > 2 3 4 5 6 9 10 11 12 13 15 16 18 19 21 22 25 26 27 28

Yes, and the best ones of those are 6 ("whole tone"), 16, 22, 25, and 28.

>>If you temper out 50/49, you get two chains of intervals separated by exactly >>half an octave. The interval I'm using is 4*sqrt(70*sqrt(2))/35, or about 222 >>cents. Is there a name for this temperament, or did I just discover/invent it?
> > > I don't find this one on the search. Maybe there's still a bug, or it > isn't so special. Do you have the full mapping?

Well, it definitely doesn't sound so great (mostly because 50/49 is too big of an interval to temper out). The one with a half a 5/4 as a generator sounds much better; I think Gene called it "hemiwuerschmidt"?

I don't know exactly what you mean by "full mapping", but 8/7 corresponds to the generator, 5/4 corresponds to the half-octave minus the generator, and 7/5 and 10/7 both correspond to the half-octave (because their difference, 50/49, is tempered out).

>>If you use exactly 225 cents for the interval, you get 16EDO - exactly what Bill >>Flavell suggested. Pure coincidence, though.
> > > There's this one that covers 16-edo:
> > 2/31, 77.2 cent generator
> > basis:
> (1.0, 0.064321646603719529)
> > mapping by period and generator:
> [(1, 0), (1, 9), (2, 5), (3, -3)]
> > mapping by steps:
> [(16, 15), (25, 24), (37, 35), (45, 42)]

Maybe if I stare at these long enough I can figure out what they mean. =P

Why can't you just say it tempers out 2^-21 * 5^3 * 7^5 ?

> highest interval width: 8
> complexity measure: 8 (9 for smallest MOS)
> highest error: 0.000320 (0.384 cents)
> unique
> > > Graham

Keenan

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

> UTTER BULLSHIT! :) To my ear the 8-tone blues mode 8-26
> is the most significant 12EDO subscale and it is based
> on both the tritone and minor 3rd. The tritone is THE
> MOST SPECIFIC PROPERTY OF 12EDO (because it's an
> EVEN-NUMBERED EDO), and I haven't heard
> any alternative tuning system that can match it!

None of this argues that it is either especially pleasing or found in
nature, except for the claim that you haven't found a tuning system to
match 12-edo. But I suspect you've not had enough experience with
various systems of tuning to compare.

I also think the tritone is not the most specific property of 12-edo;
22-edo, for instance, makes more of it, really. 12-edo has both a
diminished seventh chord consisting of four stacked minor thirds, and
an augmented triad consisting of three stacked major thirds. It has
poor thirds because of these facts, however; but its fifths are good.
I could go on about it but I don't see the tritone as very specfic to it.

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

> TO YOU, maybe! :) I'll take a 12EDO tritone
> and minor 3rd over any other alternative
> tuning'scale I've heard sio far! :)

But you don't seem to have heard any.

> > and by insisting on them you
> > simply miss half the systems. The first system after 12 with a
> decent
> > sound to it is 19, not 22, for instance. 34 is a fine system, but so
> > is 31. There's absolutely no reason to prefer the even numbers.
>
> You're buying the conventional anti-tritone
> bias of conventional western music theory.

No, I'm simply pointing out a psychoacoustic fact of life.
Conventional western music theory in any case doesn't have such a bias.

> The African-Americans rightly recognized
> the tritone as the most 12EDO-specific interval,
> and based the blues and jazz mostly on it.

Once again, I'd say tritones are even more characteristic of 22 than
of 12. You seem to be zeroing in on septimal harmony tempering out
50/49, and that suggests 12, 22, 26, 28, or 38 would be worth
exploring, along with less well-tuned systems such as 16. Certainly 22
is very well able to explore a blues and jazz idiom--in fact better
able than 12 in my view, as it can do a better job of hitting blue notes.

--- In tuning@yahoogroups.com, Keenan Pepper <keenanpepper@g...> wrote:

> Well, it definitely doesn't sound so great (mostly because 50/49 is
too big of
> an interval to temper out). The one with a half a 5/4 as a generator
sounds much
> better; I think Gene called it "hemiwuerschmidt"?

By hemiwuerschmidt I meant the temperament with a half 5/4 as a
generator, such that a 7/4 is five generators, *and* it is a
wuerschmidt system, meaning a 6 is eight 5/4s, and so 16 generators.
Since 5 and 7 are of low complexity compared to 3, there is a nice
{2,5,7} system embedded in it. Hemiwuerschmidt tempers out 3136/3125,
which is a no-threes comma, and that gives this no-threes system; it
also tempers out 2401/2400 and 6144/6125. Because it's a no-threes
system and 31 is a good {2,3,5} system, doing it in 31 works pretty
well, though if you want the 3s also, 99 or 130 would be much more
accurate. The 13-note MOS would be worth trying.

Gene Ward Smith wrote:
> By hemiwuerschmidt I meant the temperament with a half 5/4 as a
> generator, such that a 7/4 is five generators, *and* it is a
> wuerschmidt system, meaning a 6 is eight 5/4s, and so 16 generators.
> Since 5 and 7 are of low complexity compared to 3, there is a nice
> {2,5,7} system embedded in it. Hemiwuerschmidt tempers out 3136/3125,
> which is a no-threes comma, and that gives this no-threes system; it
> also tempers out 2401/2400 and 6144/6125. Because it's a no-threes
> system and 31 is a good {2,3,5} system, doing it in 31 works pretty
> well, though if you want the 3s also, 99 or 130 would be much more
> accurate. The 13-note MOS would be worth trying.

Ah, thanks for explaining. Of course you mean 31 is a good {2,5,7} system, right? Also, what is the origin of the word "wuerschmidt"?

Keenan

Keenan Pepper wrote:

> This looks interesting. Is there a manual or anything? Can I see the source code?

Everything's linked to from http://x31eq.com/temper/ except for a
newer version of the method at the wiki, riters.com/microtonal or wherever. And some C code as well

http://x31eq.com/temper/temper.c
http://x31eq.com/temper/temper.h
http://x31eq.com/temper/temper.i
http://x31eq.com/temper/temper_wrap.py

> Well, it definitely doesn't sound so great (mostly because 50/49 is too big of > an interval to temper out). The one with a half a 5/4 as a generator sounds much > better; I think Gene called it "hemiwuerschmidt"?
> > I don't know exactly what you mean by "full mapping", but 8/7 corresponds to the > generator, 5/4 corresponds to the half-octave minus the generator, and 7/5 and > 10/7 both correspond to the half-octave (because their difference, 50/49, is > tempered out).

The mapping comes from the comma in this case. It'll be (1, 1) for 50/49 I think. So a very simple one.

>>There's this one that covers 16-edo:
>>
>>2/31, 77.2 cent generator
>>
>>basis:
>>(1.0, 0.064321646603719529)
>>
>>mapping by period and generator:
>>[(1, 0), (1, 9), (2, 5), (3, -3)]
>>
>>mapping by steps:
>>[(16, 15), (25, 24), (37, 35), (45, 42)]
> > > Maybe if I stare at these long enough I can figure out what they mean. =P
> > Why can't you just say it tempers out 2^-21 * 5^3 * 7^5 ?

Because it's harder to work that out for the more complicated temperaments. It comes from the mapping by generator anyway, except for the 2^-21 bit. Also it's a full 7-limit temperament where the 3s are ignored, but still there.

Graham

--- In tuning@yahoogroups.com, Keenan Pepper <keenanpepper@g...> wrote:

> Ah, thanks for explaining. Of course you mean 31 is a good {2,5,7}
system,
> right?

Right, sorry about that.

> Also, what is the origin of the word "wuerschmidt"?

Wuerschmidt's name is attached to the comma 6/(5/4)^8 = 393216/390625,
and hence to the 5-limit temperament (31&34) tempering it out.

--- In tuning@yahoogroups.com, Keenan Pepper <keenanpepper@g...> wrote:

> Well, it definitely doesn't sound so great (mostly because 50/49 is
too big of
> an interval to temper out).

I beg to differ, particularly with the TOP tuning I put forward here.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:

> Certainly 22
> is very well able to explore a blues and jazz idiom--in fact better
> able than 12 in my view, as it can do a better job of hitting blue
>notes.

Unfortunately, and based on much relevant experience, I have to
disagree with this statement. 22 sounds funny for blues, is poorly
suited for any jazz (which has a common-practice diatonic
underpinning), and totally fails to hit the vast majority of blue notes
(neutral thirds and sevenths).

--- In tuning@yahoogroups.com, "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:
>
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
>
> > Certainly 22
> > is very well able to explore a blues and jazz idiom--in fact better
> > able than 12 in my view, as it can do a better job of hitting blue
> >notes.
>
> Unfortunately, and based on much relevant experience, I have to
> disagree with this statement. 22 sounds funny for blues, is poorly
> suited for any jazz (which has a common-practice diatonic
> underpinning), and totally fails to hit the vast majority of blue notes
> (neutral thirds and sevenths).

We've had this conversation before, or a variant of it, and I think
you are being far too narrow. You yourself write jazz-influenced music
in 22, and I think the sound of septimal harmony in general, including
in 22, tends to sounds jazzy in a more general sense than you seem to
want to consider.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
>
> --- In tuning@yahoogroups.com, "wallyesterpaulrus"
> <wallyesterpaulrus@y...> wrote:
> >
> > --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> >
> > > Certainly 22
> > > is very well able to explore a blues and jazz idiom--in fact
better
> > > able than 12 in my view, as it can do a better job of hitting
blue
> > >notes.
> >
> > Unfortunately, and based on much relevant experience, I have to
> > disagree with this statement. 22 sounds funny for blues, is
poorly
> > suited for any jazz (which has a common-practice diatonic
> > underpinning), and totally fails to hit the vast majority of blue
notes
> > (neutral thirds and sevenths).
>
> We've had this conversation before, or a variant of it, and I think
> you are being far too narrow. You yourself write jazz-influenced
music
> in 22,

True.

> and I think the sound of septimal harmony in general, including
> in 22, tends to sounds jazzy

It does.

>in a more general sense than you seem to
> want to consider.

Still, you can't open up the real book and expect a random jazz tune
to work at all in 22. I guess that's what I meant, and I overstated
the case.

P,

--- In tuning@yahoogroups.com, "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:
> Still, you can't open up the real book ...

Heh. I wonder how many people on the list know the real book (besides
Neil)?

>... and expect a random jazz tune

Is that like "free jazz"? :)

Cheers,
Jon

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

> Still, you can't open up the real book and expect a random jazz tune
> to work at all in 22. I guess that's what I meant, and I overstated
> the case.

It's certainly true that you won't find a neutral third in 22, and you
*will* find it in 34, which in general is not notable for septimal
harmony. Of course, it's also there in 31, which might be a good
choice if we wanted to adapt something out of a book.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
>
> --- In tuning@yahoogroups.com, "wallyesterpaulrus"
> <wallyesterpaulrus@y...> wrote:
>
> > Still, you can't open up the real book and expect a random jazz
tune
> > to work at all in 22. I guess that's what I meant, and I overstated
> > the case.
>
> It's certainly true that you won't find a neutral third in 22, and you
> *will* find it in 34, which in general is not notable for septimal
> harmony. Of course, it's also there in 31, which might be a good
> choice if we wanted to adapt something out of a book.

Yes, as John Starrett found, 31 works much better for most jazz tunes
than 34. It's that meantone-born, common-practice diatonic underpinning
showing its head again.

Of course, neutral thirds won't be found notated in the real book, and
you often get more convincing results by *bending* than by nailing the
neutral third on the 31-tone guitar -- blue notes are *supposed* to
have some glissando in them.

Hi Paul,

--- In tuning@yahoogroups.com, "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:
>
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> >
> > --- In tuning@yahoogroups.com, "wallyesterpaulrus"
> > <wallyesterpaulrus@y...> wrote:
> > >
> > > Unfortunately, and based on much relevant experience,
> > > I have to disagree with this statement. 22 sounds
> > > funny for blues, is poorly suited for any jazz
> > > (which has a common-practice diatonic underpinning),

While that's at least partly true, i don't think i can
totally agree with it.

> > > and totally fails to hit the vast majority of blue
> > > notes (neutral thirds and sevenths).
> >
> > We've had this conversation before, or a variant of it,
> > and I think you are being far too narrow. You yourself
> > write jazz-influenced music in 22,
>
> True.

I wrote something here a few months back explaining my
take on this: i think, despite the fact that "blue notes"
are almost always considered to be intonationally closer
to "neutral" undecimal (ratios-of-11) ratios than to
septimal (ratios-of-7) ratios, the fact that *all* chords
in blues are dominant-7th chords tends to make them seem
like concordant 4:5:6:7 proportions, as opposed to the
discordant sonorities which "common-practice" harmony
expects dominant-7th chords to be.

> > and I think the sound of septimal harmony in general,
> > including in 22, tends to sounds jazzy
>
> It does.
>
> >in a more general sense than you seem to
> > want to consider.
>
> Still, you can't open up the real book and expect a
> random jazz tune to work at all in 22. I guess that's
> what I meant, and I overstated the case.

I just wanted to point out for those who might not
get it, that "the real book" refers to the _Real Book_,
a "fake book" of all the greatest jazz standards which
is used by every jazz musician i know.

(so my point is that, properly, the title should have
been capitalized and underlined/italicized)

-monz
http://tonalsoft.com
Tonescape microtonal music software

Hi Paul and Gene,

--- In tuning@yahoogroups.com, "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:
>
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> >
> > It's certainly true that you won't find a neutral third
> > in 22, and you *will* find it in 34, which in general is
> > not notable for septimal harmony. Of course, it's also
> > there in 31, which might be a good choice if we wanted
> > to adapt something out of a book.
>
> Yes, as John Starrett found, 31 works much better for most
> jazz tunes than 34. It's that meantone-born, common-practice
> diatonic underpinning showing its head again.

Oh, i think it's more than that.

31-edo, besides being a meantone, and besides having
"neutral" versions of all the "imperfect" intervals,
also has good approximations of all the septimal
intervals too. Apparently, 31-edo is an awesome choice
for rendering a new version of jazz and blues.

> Of course, neutral thirds won't be found notated in
> the real book, and you often get more convincing results
> by *bending* than by nailing the neutral third on the
> 31-tone guitar -- blue notes are *supposed* to
> have some glissando in them.

So true. Mainly because i like the simplicity of HEWM
notation so much, i've been using 72-edo in Tonescape
to render versions of bluesy/jazzy music with what i
think is pretty good success.

I've recently been working on a Tonescape version of
Bruce Springsteen's "Jungleland" in 72-edo. In this tune,
Springsteen strikes the pose of the Jack-Kerouac-type
hipster street-poet, and does a lot of what sounds like
half-spoken/half-sung vocals, and i think i've been quite
successful in capturing that style in 72-edo.

One side note that's particularly interesting to my
opening comments in this post: there are several places
where Springsteen is singing in intervals very close
to 31-edo!

-monz
http://tonalsoft.com
Tonescape microtonal music software