An idea of a "nanotemperament"

Hi tuners.

I haven't followed the discussion closely for some time but anyway ... Have you ever noticed that the 19th root of 384 (~542.21 cents) is actually strikingly close to the 4th root of 7/2? This could have some use in the field of temperaments.

Petr

Petr Pařízek <petrparizek2000@...> wrote:
> Hi tuners.
>
> I haven't followed the discussion closely for some time
> but anyway ... Have you ever noticed that the 19th root
> of 384 (~542.21 cents) is actually strikingly close to
> the 4th root of 7/2? This could have some use in the
> field of temperaments.

It leads to [47,4,0,-19> or
11399736556781568/11398895185373143 being tempered out.
Yes, it's very accurate. 16 times better then Ennealimmal.
I don't have a name for it.

Graham

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:

> It leads to [47,4,0,-19> or
> 11399736556781568/11398895185373143 being tempered out.
> Yes, it's very accurate. 16 times better then Ennealimmal.
> I don't have a name for it.

Anyone wanting to give it a try could tune up their 74367 edo guitar, or if that is too many notes, 31 edo. Does Petr want to name this comma?

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

> Does Petr want to name this comma?

It's a comma of quasiorwell temperament, in case that helps.

Gene wrote:

> It's a comma of quasiorwell temperament, in case that helps.

Well, I've realized the same this morning. :-) Or more precisely, I first thought there was something else, like casablanca or some such, which didn't split it in halves in the way quasiorwell does.

As to naming it ... It's an awful mixture of words but right now I'm thinking of something like "dinoquint" -- i.e. the Italian "dicianove in un quinto" (nineteen in a fifth), which is a bit misleading because I'm speaking about 384/1, not 3/2. So I'm not still sure.

Petr

I wrote:

> Well, I've realized the same this morning. :-) Or more precisely, I first > thought there was something else, like casablanca or some such, which > didn't split it in halves in the way quasiorwell does.

Also, since no 5-limit temperament of such small error is as easily reachable as this 7-limit one, this leads to the idea of a "fiveless" temperament. An interesting possibility might be to use a period of 4/1 rather than 2/1, which would make 7/4 impossible but 2:3:7 would still be playable. And the MOSs would go in the same way as orwell MOSs go in the standard 2/1-periodic world -- no wonder, the generator is twice that of orwell.

Petr

I wrote:

> Also, since no 5-limit temperament of such small error is as easily
> reachable as this 7-limit one,

Hell, I was wrong again ... Kwazy seems to do better with even less complexity ... Wow, I see I should definitely try that one out!

Petr