Bleu

Here's an addition to the chromatic pairs page:

http://xenharmonic.wikispaces.com/Chromatic+pairs#Bleu

Great for people who like to ignore 5, and I know you are out there. Tempers out 78/77, 99/98 and 144/143; if you add 81/80 for your 5 you get a meantone fifth split into four as a generator.

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
> Here's an addition to the chromatic pairs page:
>
> http://xenharmonic.wikispaces.com/Chromatic+pairs#Bleu
>
> Great for people who like to ignore 5, and I know you are out there. Tempers out 78/77, 99/98 and 144/143; if you add 81/80 for your 5 you get a meantone fifth split into four as a generator.

So that's what this temperament is called, "bleu"? I have heard it described before, as a 9&17 temperament that's great for pretty much everything but the prime 5.

http://x31eq.com/cgi-bin/rt.cgi?ets=9+17&limit=2.3.7.11.13

Keenan

> --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@> wrote:
> >
> > Here's an addition to the chromatic pairs page:
> >
> > http://xenharmonic.wikispaces.com/Chromatic+pairs#Bleu
> >
> > Great for people who like to ignore 5, and I know you are out there. Tempers out 78/77, 99/98 and 144/143; if you add 81/80 for your 5 you get a meantone fifth split into four as a generator.

This temperament is also really easy to understand musically, for non-mathy types.

The 11:12:13:14 portion of the harmonic series is supposed to have three different intervals (12/11, 13/12, and 14/13). But in bleu you temper them all to the same interval, about 140 cents, and then just make a chain of that interval, so every set of four consecutive notes in the chain is supposed to sound like 11:12:13:14. Eventually you need one step of a different size to complete the octave.

But here's the real kicker: five of these 140 cent steps makes a 3/2!

The obvious equal temperament to use here is 17, but some of its intervals are more out of tune than they need to be, particularly 3/2. I think a 17-note circulating temperament would be a fun thing to try.

Keenan

> > --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@> wrote:
> > > Great for people who like to ignore 5, and I know you are out there. Tempers out 78/77, 99/98 and 144/143; if you add 81/80 for your 5 you get a meantone fifth split into four as a generator.

I forgot to mention: No offence, but adding 81/80 is a terrible idea. It just makes everything way more out of tune. It's obvious that 5 isn't really "supposed" to be there.

Also, I'm sure you meant "meantone fifth split into five".

Keenan

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

> So that's what this temperament is called, "bleu"?

Do you have another name?

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

> I forgot to mention: No offence, but adding 81/80 is a terrible idea. It just makes everything way more out of tune.

Not so much. If you use 60edo as your tuning, then the major third you get is 400 cents; this is a value people seem to be willing to live with. If you use 43 instead, it's much better of course.

It's obvious that 5 isn't really "supposed" to be there.
>
> Also, I'm sure you meant "meantone fifth split into five".

Yeah, sorry. And that puts a finger on the problem: 5*4 = 20, so the complexity of 5 is 20. It's not that it's not supposed to be there, it isn't there unless you reach for it; it's too complex.

On Fri, Jul 1, 2011 at 10:28 AM, Keenan Pepper <keenanpepper@...> wrote:
>
> > Great for people who like to ignore 5, and I know you are out there. Tempers out 78/77, 99/98 and 144/143; if you add 81/80 for your 5 you get a meantone fifth split into four as a generator.
>
> So that's what this temperament is called, "bleu"? I have heard it described before, as a 9&17 temperament that's great for pretty much everything but the prime 5.

It's usually called "progression."

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> > So that's what this temperament is called, "bleu"? I have heard it described before, as a 9&17 temperament that's great for pretty much everything but the prime 5.
>
> It's usually called "progression."

Nope. Progression is not a subgroup temperament. As a 13-limit temperament, it tempers out 26/25 and 36/35. What all that means in practice, though, is that you are willing to accept a really sharp third as what 5/4 is mapped to. If you use the same 60edo tuning as I used for the scales for bleu, you get to call 420 cents an approximation of 5/4. To bleu temperament, that's a 14/11, which makes sense. If you add 55/54 to the mix, you get the 8d&17 temperament, which if you use the POTE tuning has a good third, but the fifth has been pissed on; if you add instead 81/80 you get the 26&43 temperament. Progression, however, is what you get by adding in 36/35, getting the 8d&9 temperament, with a sharp third which you plan to claim as a 5/4.

On Fri, Jul 1, 2011 at 2:38 PM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > > So that's what this temperament is called, "bleu"? I have heard it described before, as a 9&17 temperament that's great for pretty much everything but the prime 5.
> >
> > It's usually called "progression."
>
> Nope. Progression is not a subgroup temperament. As a 13-limit temperament, it tempers out 26/25 and 36/35. What all that means in practice, though, is that you are willing to accept a really sharp third as what 5/4 is mapped to. If you use the same 60edo tuning as I used for the scales for bleu, you get to call 420 cents an approximation of 5/4. To bleu temperament, that's a 14/11, which makes sense. If you add 55/54 to the mix, you get the 8d&17 temperament, which if you use the POTE tuning has a good third, but the fifth has been pissed on; if you add instead 81/80 you get the 26&43 temperament. Progression, however, is what you get by adding in 36/35, getting the 8d&9 temperament, with a sharp third which you plan to claim as a 5/4.

So Blue is just progression with the 5 taken out of it, right? Which
is what I was trying to say.

-Mike

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:

>Progression, however, is what you get by adding in 36/35, getting the 8d&9 temperament, with a sharp third which you plan to claim as a 5/4.

I might add that there are more ways to add a comma with a 5 in it, some other good possibilites being 45/44 or 50/49.

On Fri, Jul 1, 2011 at 3:01 PM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
> >
> >
> >
> > --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
>
> >Progression, however, is what you get by adding in 36/35, getting the 8d&9 temperament, with a sharp third which you plan to claim as a 5/4.
>
> I might add that there are more ways to add a comma with a 5 in it, some other good possibilites being 45/44 or 50/49.

Splitting the octave in half would be really interesting. It would be
to progression what hedgehog is to porcupine.

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Fri, Jul 1, 2011 at 2:38 PM, genewardsmith
> <genewardsmith@...> wrote:

> So Blue is just progression with the 5 taken out of it, right? Which
> is what I was trying to say.

Right; it's 13-limit progression with a 5-ectomy.

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> > I might add that there are more ways to add a comma with a 5 in it, some other good possibilites being 45/44 or 50/49.
>
> Splitting the octave in half would be really interesting. It would be
> to progression what hedgehog is to porcupine.

It's not bad, and you can do it in 26, 34, 60 or even 94 edo. For 34, you can use the 13-limit version of the much-discussed 34d val, with the sharp 14\17 7/4. MOS of size 8, 10, 18, 26.