The search for an "ideal" blues/jazz piano tuning

When I was listening to some Mardi Gras music last Tuesday, I was contemplating how it might sound in 7-limit JI or something close to it. I also thought of well-temperaments and am experimenting with some of my own. (I'd love to hear WTs used a lot more in popular music.)

I first came up with a quick-and-dirty tuning: a type of _temp�rament ordinaire_ which lowers all fifths between the perfect prime and augmented fifth/minor sixth by a quarter of a Pythagorean comma, then raises the remaining fifths by a quarter of a P-comma:

1/1
72.63
192.18
276.54
384.36
492.18
576.54
696.09
768.72
888.27
984.36
1080.45
2/1

This tuning is doable in 100-edo, with the two fifths being 58 and 59 steps.

The basic idea is to have just-flavored major intervals and septimal-like minors. I have 7/5 in mind for a tritone, not 11/8 or 18/13. This obviously works much better for keys with the fewest sharps and flats, but a retuned MIDI of Chopin's twenty-four Preludes doesn't sound that bad, just surreal at times.

I'm searching the group archives right now for more information. My knowledge of well-temperaments is still rather limited; I wouldn't know how to improve a WT very much.

~D.

--- In tuning@yahoogroups.com, "Danny Wier" <dawiertx@...> wrote:

> I'm searching the group archives right now for more information. My
> knowledge of well-temperaments is still rather limited; I wouldn't
know how
> to improve a WT very much.

This seems to be a great deal like the modified 2/7-comma
meantone "zartre84.scl" in the Scala directory; I wonder what the
history is for that. It's also interesting to compare your scale with
grail; you have two major thirds close to 14/11, and one close to 9/7,
and grail makes these exact. Grail also surrounds the chain of four
sharp thirds by two quite flat ones on either side, bringing the thirds
down to meantone range faster.

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

> Grail also surrounds the chain of four
> sharp thirds by two quite flat ones on either side, bringing the
thirds
> down to meantone range faster.

Sharp fifths.

From: "Gene Ward Smith"

> --- In tuning@yahoogroups.com, "Danny Wier" <dawiertx@...> wrote:
>
>> I'm searching the group archives right now for more information. My
>> knowledge of well-temperaments is still rather limited; I wouldn't
> know how
>> to improve a WT very much.
>
> This seems to be a great deal like the modified 2/7-comma
> meantone "zartre84.scl" in the Scala directory; I wonder what the
> history is for that. It's also interesting to compare your scale with
> grail; you have two major thirds close to 14/11, and one close to 9/7,
> and grail makes these exact. Grail also surrounds the chain of four
> sharp thirds by two quite flat ones on either side, bringing the thirds
> down to meantone range faster.

It's "schulter_zarte84.scl" in the Scala archives, and it turned out to be the best match, except my tuning is C-G# instead of F-C#.

(And we were discussing grail and other WTs not too long ago; I need to pay attention more.)

From: me

>> This seems to be a great deal like the modified 2/7-comma
>> meantone "zartre84.scl" in the Scala directory; I wonder what the
>> history is for that. It's also interesting to compare your scale with
>> grail; you have two major thirds close to 14/11, and one close to 9/7,
>> and grail makes these exact. Grail also surrounds the chain of four
>> sharp thirds by two quite flat ones on either side, bringing the thirds
>> down to meantone range faster.
>
> It's "schulter_zarte84.scl" in the Scala archives, and it turned out to be
> the best match, except my tuning is C-G# instead of F-C#.
>
> (And we were discussing grail and other WTs not too long ago; I need to > pay
> attention more.)

I did some more archive searching, and found one of your tunings called "smithgw_ratwolf.scl"; which is very close to what I'm really looking for, except transposed. I made another scale, an intersection of a meantone with something I've called an "antimeantone" (fifths tempered up a fraction of a septimal comma). What I did is temper fifths 2/7-comma lower nine fifths up and 2/5-septimal comma higher three fifths down:

0: 0.000
1: 70.672
2: 191.621
3: 262.293 (or 261.418)
4: 383.241
5: 487.139
6: 574.862
7: 695.810
8: 766.483
9: 887.431
10: 974.279
11: 1079.052
12: 1200.000

(The most extreme form of this idea of tuning would be a combination 7-tet and 5-tet with the 1/1 repeated.)

> 0: 0.000
> 1: 70.672
> 2: 191.621
> 3: 262.293 (or 261.418)
> 4: 383.241
> 5: 487.139
> 6: 574.862
> 7: 695.810
> 8: 766.483
> 9: 887.431
> 10: 974.279
> 11: 1079.052
> 12: 1200.000

Wait, that is closest to "zarte84", never mind.

It's really just 2/7-comma, nine fifths up and none down; the rest are third-wolves.

--- In tuning@yahoogroups.com, "Danny Wier" <dawiertx@...> wrote:

> I did some more archive searching, and found one of your tunings
called
> "smithgw_ratwolf.scl"; which is very close to what I'm really looking
for,
> except transposed.

Ratwolf is a meantone, actually. It tries to slightly tame the wolf by
making the wolf fifth=diminished sixth an exact 20/13, which counts as
a 13-limit consonance for what that is worth. The ratwolf wolf fourth
is 13/10. Anyway there's very little difference between it and 2/7-
comma meantone, except for the wistful hope we will get some kind of JI
lock with the exact 13-limit wolf fifth.