A meantone analogue of Blackjack

Rather than employing the miracle generator in a way analogous to the
meantone, we could use a meantone in a way analogous to Blackjack or
other miracle scales. We find for instance 4141414141411 as a scale
of 13 steps in the 31-et. I don't know if anyone will think this is
much of a miracle, but it certainly has both an exotic sound and a
lot of good thirds. If someone wants to try it, we than use:

! 13-31-mean.scl
!
13 out of 31 scale, a meantone analogue of Blackjack
13
!
154.8387097
193.5483871
348.3870968
387.0967742
541.9354839
580.6451613
735.4838710
774.1935484
929.0322581
967.7419355
1122.580645
1161.290323
2/1

--- In tuning@y..., genewardsmith@j... wrote:
> Rather than employing the miracle generator in a way analogous to
the
> meantone, we could use a meantone in a way analogous to Blackjack
or
> other miracle scales. We find for instance 4141414141411 as a scale
> of 13 steps in the 31-et.

It's pretty strange to think of this as a meantone analogue of
Blackjack -- not a lot of perfect fifths (the generator of meantone),
let alone complete consonant chords. But I'm pretty sure Robert
Valentine has discussed this scale. Robert?

--- In tuning@y..., genewardsmith@j... wrote:

> We find for instance 4141414141411 as a scale
> of 13 steps in the 31-et. I don't know if anyone will think this is
> much of a miracle, but it certainly has both an exotic sound and a
> lot of good thirds.

The generator of this scale is close to that of Graham Breed's top-
ranking linear temperament for the 7-limit: 193.8722 cents.
Unfortunately, you don't get a single 7-limit tetrad in this 13-tone
scale. To be at all useful for 7-limit harmony (with a maximum error
of only 1.43¢!), you have to go to the next MOS, which is an improper
one with 19 notes. Then you get an improper MOS with 25 notes, a
proper one with 31 notes, improper 37, improper 68, proper 99,
improper 130, proper 229 . . .

By the way, the #2 rank in the 7-limit goes to something like 9-tET
with 44.4¢ errors, while the #3 rank goes to the MIRACLE temperament.

Please, Paul !

Here is one forum TUNNING, and not only one
microtonal... !
Stop, pls :)
Ok, ask who understand and use all of yours microtonal
thinngs ...
It's horrible to hear, truelly !
Why do you spam all of space here with ?
Or you want to stay "only you" to discute ?
It's time to think about :)
Too much formules and numbers=no music !!!

Dimitrov

--- Paul Erlich <paul@stretch-music.com> a �crit�: >
--- In tuning@y..., genewardsmith@j... wrote:
>
> > We find for instance 4141414141411 as a scale
> > of 13 steps in the 31-et. I don't know if anyone
> will think this is
> > much of a miracle, but it certainly has both an
> exotic sound and a
> > lot of good thirds.
>
> The generator of this scale is close to that of
> Graham Breed's top-
> ranking linear temperament for the 7-limit: 193.8722
> cents.
> Unfortunately, you don't get a single 7-limit tetrad
> in this 13-tone
> scale. To be at all useful for 7-limit harmony (with
> a maximum error
> of only 1.43�!), you have to go to the next MOS,
> which is an improper
> one with 19 notes. Then you get an improper MOS with
> 25 notes, a
> proper one with 31 notes, improper 37, improper 68,
> proper 99,
> improper 130, proper 229 . . .
>
> By the way, the #2 rank in the 7-limit goes to
> something like 9-tET
> with 44.4� errors, while the #3 rank goes to the
> MIRACLE temperament.
>
>

___________________________________________________________
Do You Yahoo!? -- Un e-mail gratuit @yahoo.fr !
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--- In tuning@y..., Latchezar Dimitrov <latchezar_d@y...> wrote:
> Please, Paul !
>
>
>
> Here is one forum TUNNING, and not only one
> microtonal... !
> Stop, pls :)
> Ok, ask who understand and use all of yours microtonal
> thinngs ...
> It's horrible to hear, truelly !
> Why do you spam all of space here with ?

Hi Latchezar.

If you go to the home page of this list, you will see the following:

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Welcome to the Alternate Tunings Mailing List.
(Originally based at Mills College in Oakland, California, USA.)
(AKA "The Tuning List", "The Tuning Group".)

This mailing list is intended for exchanging ideas relevant to
alternate tunings: just intonation; paratactical tunings;
experimental musical instrument design; non-standard equal
temperaments; MIDI tuning system exclusive specs; concert postings;
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the experimental tunings of Harry Partch, Lou Harrison, Martin
Bartlett, James Tenney, and so on; software reports; recordings;
books; research sources, etcetera.

Happy retuning!

*********************************************************************

I don't think what I'm posting is off-topic at all. Yes, much of the
material often seems overly mathematical . . . but I assure you it's
all based on qualities I can hear when I use these tunings on my
keyboard (or guitars). And not just me -- there is a long history of
musicians working from very similar principles -- just read the
volumes of the journals Xenharmonikon and Interval, for a start.

Earlier this year I started an additional list, tuning-
math@yahoogroups.com. I then conducted an anonymous poll as to
whether that more mathematical list should stay separate, or whether
more mathematical topics should be covered here on this list. The
result was 11 votes for the first option, 23 votes for the second
option (I did not vote). Nevertheless, I kept the other list, which
is still quite active. But clearly there are at least 23 people here
who are interested in such matters, and for their benefit I think
it's worth making a few very concise and information-rich posts such
as this one.

If anyone doesn't understand anything in my posts, I encourage them
to ask questions . . . I am very patient and will be happy to explain
all the concepts I'm referring to! You are new to this list, so
perhaps many of the concepts are unfamiliar to you, but many of us
have been here for years so we have a bit of a language of our
own . . . I should think that would be understandable.

Besides, this post was a _reply_ to a post by Gene. Why not just
allow me to reply to him, and ignore this discussion if you so desire?

-Paul