What is the name of the temperament that uses 2\17 as a generator?

Actually, this question comes in three parts:

1) What is the name of the temperament that uses 2\17 as a generator
in which 4 steps is mapped to 9/7?
2) What is the name of the temperament that uses 2\17 as a generator
in which 4 steps is mapped to 14/11?
3) What is the name of the temperament that uses 2\17 as a generator
in which 4 steps is mapped to 5/4?

#3 is the one that I hope has a really good name.

-Mike

On Fri, Apr 8, 2011 at 5:08 PM, Mike Battaglia <battaglia01@...> wrote:
> Actually, this question comes in three parts:
>
> 1) What is the name of the temperament that uses 2\17 as a generator
> in which 4 steps is mapped to 9/7?
> 2) What is the name of the temperament that uses 2\17 as a generator
> in which 4 steps is mapped to 14/11?
> 3) What is the name of the temperament that uses 2\17 as a generator
> in which 4 steps is mapped to 5/4?
>
> #3 is the one that I hope has a really good name.

http://x31eq.com/cgi-bin/rt.cgi?ets=8_9&error=34.070&limit=13&invariant=5_3_7_4_6_1_1_2_2_3_3

The answer to #3 is "progression" temperament, and that's quite a hell
of a name it has.

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> Actually, this question comes in three parts:
>
> 1) What is the name of the temperament that uses 2\17 as a generator
> in which 4 steps is mapped to 9/7?

I suggest "puke" as a name, but anything with a val <17 27 * 46| will map 9/7 to 8, and there are several choices, all bad.

> 2) What is the name of the temperament that uses 2\17 as a generator
> in which 4 steps is mapped to 14/11?

Again, more than one choice here.

> 3) What is the name of the temperament that uses 2\17 as a generator
> in which 4 steps is mapped to 5/4?

I suggest "insane temperament tempering out 5184/3125 in which we pretend 141 cents is a good approximation to 6/5" as a name.

> #3 is the one that I hope has a really good name.

Do you like my suggestion?

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

> The answer to #3 is "progression" temperament, and that's quite a hell
> of a name it has.

How do you figure 5/4 is four steps?

I meant 3 steps. I forget sometimes that tuning arrays start from zero.

Sent from my iPhone

On Apr 9, 2011, at 12:34 AM, "genewardsmith" <genewardsmith@...>
wrote:

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

> The answer to #3 is "progression" temperament, and that's quite a hell
> of a name it has.

How do you figure 5/4 is four steps?

   Let me get this right: this temperament hits about 1.37 (545 cents) 1.54 (753 cents) and 1.646 (863.cents)?

  In that case, yep, that's pretty bad...and 753 cents is a really bad "fifth" IMVHO, right up there with 16/11 and 40/27.  How about Teen Nightmare (since so many of the numerators and denominators in the dyads go well into the teens)?

--- On Fri, 4/8/11, genewardsmith <genewardsmith@...> wrote:

From: genewardsmith <genewardsmith@...>
Subject: [tuning] Re: What is the name of the temperament that uses 2\17 as a generator?
To: tuning@yahoogroups.com
Date: Friday, April 8, 2011, 9:23 PM

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

>

> Actually, this question comes in three parts:

>

> 1) What is the name of the temperament that uses 2\17 as a generator

> in which 4 steps is mapped to 9/7?

I suggest "puke" as a name, but anything with a val <17 27 * 46| will map 9/7 to 8, and there are several choices, all bad.

> 2) What is the name of the temperament that uses 2\17 as a generator

> in which 4 steps is mapped to 14/11?

Again, more than one choice here.

> 3) What is the name of the temperament that uses 2\17 as a generator

> in which 4 steps is mapped to 5/4?

I suggest "insane temperament tempering out 5184/3125 in which we pretend 141 cents is a good approximation to 6/5" as a name.

> #3 is the one that I hope has a really good name.

Do you like my suggestion?