121-et: pushing this sharp fifths thing to the limit

121 is actually a good system, particularly for 19-21 limit harmony. It
also features a sharp fifth, not as sharp as 17 but at over two cents
sharp, sharp enough to make a difference. In the 17 limit, the lowest
Graham complexity (60) occurs with the linear temperament with a fifth
as a generator; in the 19-limit, that becomes, at 71, the second
lowest. There are MOS of size 46 and 75. All of the primes to 19 are
tuned on the sharp side, and it is 19-limit consistent.

Now, how likely it is anyone will find this useful I don't know, but it
does fit into the range between 58 and 46 fifths-tuning-wise, and is
actually closer to 46. It's the last of what seem to me to be
interesting equal temperaments to do that.

I had given plenty consideration to 121 during my search that lead me to
choose 79/80 MOS 159-tET. You can have complete cycles with both the
meantone fifth and the Superpythagorean... That means we get lovely
alterations between Rast and Mahur/Suzidilara everywhere. Besides, it is
equal, so transpositions are exact. It also does an excellent job
approximating lots of common JI intervals... but it is way too voluminous! I
can see no way in implementing it to the qanun, which is a fundamental
criterion for Maqam Music in my opinion.

Oz.

----- Original Message -----
From: "Gene Ward Smith" <genewardsmith@coolgoose.com>
To: <tuning@yahoogroups.com>
Sent: 20 Ekim 2006 Cuma 12:11
Subject: [tuning] 121-et: pushing this sharp fifths thing to the limit

> 121 is actually a good system, particularly for 19-21 limit harmony. It
> also features a sharp fifth, not as sharp as 17 but at over two cents
> sharp, sharp enough to make a difference. In the 17 limit, the lowest
> Graham complexity (60) occurs with the linear temperament with a fifth
> as a generator; in the 19-limit, that becomes, at 71, the second
> lowest. There are MOS of size 46 and 75. All of the primes to 19 are
> tuned on the sharp side, and it is 19-limit consistent.
>
> Now, how likely it is anyone will find this useful I don't know, but it
> does fit into the range between 58 and 46 fifths-tuning-wise, and is
> actually closer to 46. It's the last of what seem to me to be
> interesting equal temperaments to do that.
>
>

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:

> I had given plenty consideration to 121 during my search that lead me
to
> choose 79/80 MOS 159-tET. You can have complete cycles with both the
> meantone fifth and the Superpythagorean... That means we get lovely
> alterations between Rast and Mahur/Suzidilara everywhere. Besides, it
is
> equal, so transpositions are exact. It also does an excellent job
> approximating lots of common JI intervals... but it is way too
voluminous!

Unfortunately, there isn't anything smaller which works as well. If you
are willing to stretch a point and not worry much about exact tuning,
there's 78-et. 80-et has a really, really flat meantone fifth of 690
cents but is better in terms of tuning.

80 is quite dysfunctional. 78 won't do either. Now take mine, I have neatly
working fifths in 79/80 MOS 159-tET.

----- Original Message -----
From: "Gene Ward Smith" <genewardsmith@coolgoose.com>
To: <tuning@yahoogroups.com>
Sent: 21 Ekim 2006 Cumartesi 2:14
Subject: [tuning] Re: 121-et: pushing this sharp fifths thing to the limit

> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> > I had given plenty consideration to 121 during my search that lead me
> to
> > choose 79/80 MOS 159-tET. You can have complete cycles with both the
> > meantone fifth and the Superpythagorean... That means we get lovely
> > alterations between Rast and Mahur/Suzidilara everywhere. Besides, it
> is
> > equal, so transpositions are exact. It also does an excellent job
> > approximating lots of common JI intervals... but it is way too
> voluminous!
>
> Unfortunately, there isn't anything smaller which works as well. If you
> are willing to stretch a point and not worry much about exact tuning,
> there's 78-et. 80-et has a really, really flat meantone fifth of 690
> cents but is better in terms of tuning.
>
>