Equal divisions

There's something about what I would consider the main equal temperaments under 100 notes per octave up now here:

http://xenharmonic.wikispaces.com/Equal

What favorite or important temperaments is this missing? I know myself the meantone types could use a discussion of 43 and 55, and plan to add that, and I am awaiting Igs and his article on the smaller temperaments before tackling 28 or 29. 36 could use a discussion of its no-5s uses. Then there's 37, 38, 56, 57, 65 ...

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
> There's something about what I would consider the main equal temperaments under 100 notes per octave up now here:
>
> http://xenharmonic.wikispaces.com/Equal
>
> What favorite or important temperaments is this missing? I know myself the meantone types could use a discussion of 43 and 55, and plan to add that, and I am awaiting Igs and his article on the smaller temperaments before tackling 28 or 29. 36 could use a discussion of its no-5s uses. Then there's 37, 38, 56, 57, 65 ...

You're missing some important multiples of good 2-digit ET's:

217 = 31*7 (a basis for adaptive JI, a natural for flexible-pitch instruments built for 31-ET;

210 = 41*5 (mainstay of Aaron Hunt's Tonal Plexus);

2460 = 12*105 = 41*60 (divides the octave into "minas")

However, IMMVHO the most serious omissions are 324296 and (especially) 2901533. ;-}

--George

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

> However, IMMVHO the most serious omissions are 324296 and (especially) 2901533. ;-}

I really don't know how I overlooked 2901533. It's uniquely consistent through to the 131-limit, so I recommend everyone use it all of the time, for everything. Especially Igs: he should use it.

I think it might be helpful to give more stress on the rank 2 possibilities of particular EDOs: 34 can do tetracot|hanson|wuerschmidt|diaschismatic(|others), 46 can do semisixths|diaschismatic|amity, 14 can do superpelog|octacot (should something requiring 18 generators for a major "third" catch our interest), 65 can do schismatic|semisixths, and so on.
What's more, there are EDOs like 87 or 37 which are capable of approximating non-3 ratios nicely, should we explore those partial-limit territories.

Petr

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
> I really don't know how I overlooked 2901533. It's uniquely consistent through to the 131-limit, so I recommend everyone use it all of the time, for everything. Especially Igs: he should use it.
>

I'll have Ron Sword fret up a 1/2-scale mandolin in 2901533-EDO for me immediately!

-Igs

On 20 June 2010 09:51, cityoftheasleep <igliashon@...> wrote:
> --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>>
>> I really don't know how I overlooked 2901533. It's uniquely consistent through to the 131-limit, so I recommend everyone use it all of the time, for everything. Especially Igs: he should use it.
>>
>
> I'll have Ron Sword fret up a 1/2-scale mandolin in 2901533-EDO for me immediately!

Well, I've already adopted this tuning exclusively. With a leeway of
0.5 millicents, anyway.

Graham

Hot damn that will rock once you glue the razor blades to your fingers.
Sent via BlackBerry from T-Mobile

-----Original Message-----
From: "cityoftheasleep" <igliashon@...>
Date: Sun, 20 Jun 2010 05:51:28
To: <tuning@yahoogroups.com>
Subject: [tuning] Re: Equal divisions

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
> I really don't know how I overlooked 2901533. It's uniquely consistent through to the 131-limit, so I recommend everyone use it all of the time, for everything. Especially Igs: he should use it.
>

I'll have Ron Sword fret up a 1/2-scale mandolin in 2901533-EDO for me immediately!

-Igs