Re: The Parízek shruti scale

From: "Gene Ward Smith" <gwsmith@s>
> I found an interesting property of this scale. If we take the
> Pythagorean scale on 22 notes, and Hahn reduce it via the schisma, we
> get a scale where the maximum Hahn distance is 4 from the 1/1, which
> is simply a transposition of this scale. I was going to call it
> indian-hahn, but Paul Hahn already has his version of shrutis in the
> Scala archive!

Do you mean that the posted scales also go into Manuel's scale archive?

> If we replace the 256/135 with something a schisma
> higher, 243/128, we get the Tenney-reduced shruti scale; but this has
> Hahn size 5 and the other choice seems better.

This is really strange. I'm beginning to think there must be some kind of
"super-real power" that delivers my ideas to you (and yours to me) even
before they
manage to appear on the list. When you sent the scale the first time, I
realized I didn't specify the position of the 1/1 and I was a bit wondering
why you took it from -19 to +2 fifths (if I forget about the schisma).
Though, I said to myself: "Well, it's essentially what it should be like."
And about a day later, what a surprise, you sent it again just in the same
form as I use it.
It's all quite an interesting matter. At the time I joined the list, you
discussed some good thoughts about various commas in which I mostly agreed
with you. Then, it was the strongest surprise for me when you spoke about
your idea of using 11/8 and 13/8 in a meantone tuning in just the same way
as I tried some two years ago. There were also other topics like this I
can't recall now. And, correct me if I'm wrong, I believe in one of your
posts I found a few words mentioning your fondness for 50-equal. I'm getting
ready for everything. If I should discover, for example, that you like music
full of otonal scales, that you've also experimented with quasi-meantone
tunings, or perhaps that you've examined equal-beating meantones, I don't
think I need to be surprised. I'm rather curious what's gonna be the next
topic on the list we both think of almost at the same time.
Petr
PS: Do you think someone ever used a meantone tuning with a minor second of
15/14? I recently made some music this way and now I'm trying to find out if
I was or wasn't the first.

--- In tuning@yahoogroups.com, Petr Parízek <p.parizek@w...> wrote:
> From: "Gene Ward Smith" <gwsmith@s>
> > I found an interesting property of this scale. If we take the
> > Pythagorean scale on 22 notes, and Hahn reduce it via the schisma, we
> > get a scale where the maximum Hahn distance is 4 from the 1/1, which
> > is simply a transposition of this scale. I was going to call it
> > indian-hahn, but Paul Hahn already has his version of shrutis in the
> > Scala archive!
>
> Do you mean that the posted scales also go into Manuel's scale archive?

They go in of Manuel puts them in, but I put yours in my own scl
directory.

And, correct me if I'm wrong, I believe in one of your
> posts I found a few words mentioning your fondness for 50-equal.

It's my favorite. It seems just about right so far as the sound goes,
it has a 12-note scale wolf pretty close to 20/13 and major thirds in
the extreme keys nearly 9/7. It gives nice round numbers for the scale
steps besides.

I'm getting
> ready for everything. If I should discover, for example, that you
like music
> full of otonal scales, that you've also experimented with quasi-meantone
> tunings, or perhaps that you've examined equal-beating meantones, I
don't
> think I need to be surprised.

I don't know what you mean by "quasi-meantone" but I certainly might
have. I spent a lot of time pondering "brats" (beat ratios) and the
Wilson fifth, as well.

> PS: Do you think someone ever used a meantone tuning with a minor
second of
> 15/14? I recently made some music this way and now I'm trying to
find out if
> I was or wasn't the first.

That's a fifth of (112/15)^(1/5), and I don't think I've heard of it.
It's pretty close to 50-equal, of course; even closer than my
"ratwolf" fifth of (416/5)^(1/11).

Parizek fifth: 696.11 cents
Ratwolf fifth: 695.84 cents
50-et fifth: 696 cents exactly

Can you upload your music somewhere?

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:

> That's a fifth of (112/15)^(1/5), and I don't think I've heard of it.
> It's pretty close to 50-equal, of course; even closer than my
> "ratwolf" fifth of (416/5)^(1/11).
>
> Parizek fifth: 696.11 cents
> Ratwolf fifth: 695.84 cents
> 50-et fifth: 696 cents exactly

Something else I've mentioned along these same lines is (224/9)^(1/8),
which gives pure 9/7 supermajor thirds.

supermajor thirds fifth: 695.61 cents

This is actually more a 69-equal idea, but 69 is also an interesting
equal temperament, with a fifth very close to the Wilson equal beating
fifth.

69-et fifth: 695.62 cents
Wilson fifth: 695.63 cents

To my ears this is not quite as nice as the 696 cent fifth, but
obviously there is very little difference. I'm not quite sure why I
have the reaction I do.