Yahoo Tuning Groups Ultimate Backup tuning is this scale special?

> 0: 1/1
> 1: 73.534 cents
> 2: 350.978 cents
> 3: 424.511 cents
> 4: 498.045 cents
> 5: 775.489 cents
> 6: 849.022 cents
> 7: 1126.466 cents
> 8: 2/1

It seems weird to me -- many folks give the output of scala's
show command instead of the contents of the .scl file...

> generator is (8/3)^(1/4) or about 424.5 cents. Mapped
> linearly to the keyboard and playing notes that look
> like a major third apart, one finds that every note
> can be harmonized with another note either an exact 3/2
> and/or 4/3 away.
>
> Special? Or dime a dozen?

Well, the scale

!
Chain of six 3:2s (pythagorean).
6
!
9/8
81/64
3/2
27/16
243/128
2/1
!

has the same property, but fewer notes.

Your scale is interesting. It has nice neutral 3rds.
I'm not aware of another one like it off the top of
my head. I've saved it in my 'to try out' folder.

-Carl

🔗Keenan Pepper <keenanpepper@gmail.com>

On 4/9/06, Jacob <jbarton@rice.edu> wrote:
> 0: 1/1
> 1: 73.534 cents
> 2: 350.978 cents
> 3: 424.511 cents
> 4: 498.045 cents
> 5: 775.489 cents
> 6: 849.022 cents
> 7: 1126.466 cents
> 8: 2/1
>
> generator is (8/3)^(1/4) or about 424.5 cents. Mapped linearly to the
> keyboard and playing notes that look like a major third apart, one
> finds that every note can be harmonized with another note either an
> exact 3/2 and/or 4/3 away.
>
> Special? Or dime a dozen?

It's a moderately good {2,3,7,11} temperament with wedgie

|| +4 +9 +10 +3 +2 -3 >>

so it tempers out 99/98 and 243/242. If you want to extend it to a
full 11-limit temperament you can also temper out 385/384 and get

|| +4 -15 +9 +10 -33 +3 +2 +63 +75 -3 >>

It's supported by 14, 17, 31, and 48-edo.

Keenan

🔗Gene Ward Smith <genewardsmith@coolgoose.com>

🔗Jacob <jbarton@rice.edu>

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> > 0: 1/1
> > 1: 73.534 cents
> > 2: 350.978 cents
> > 3: 424.511 cents
> > 4: 498.045 cents
> > 5: 775.489 cents
> > 6: 849.022 cents
> > 7: 1126.466 cents
> > 8: 2/1
>
> It seems weird to me -- many folks give the output of scala's
> show command instead of the contents of the .scl file...

I never made a .scl file. I'm not a big Saver.
>
> > generator is (8/3)^(1/4) or about 424.5 cents. Mapped
> > linearly to the keyboard and playing notes that look
> > like a major third apart, one finds that every note
> > can be harmonized with another note either an exact 3/2
> > and/or 4/3 away.
> >
> > Special? Or dime a dozen?
>
> Well, the scale
> Chain of six 3:2s (pythagorean).
> has the same property, but fewer notes.

I wasn't clear. With this scale one can play a P4 or P5 and move
parallel up the scale and have this interval always be P4 or P5.
That's the magic. With pythagorean, you get wolves (tritones) in your
parallel motion.

The even-number cardinality has a lot to do with it. Tcherepnin mode
of 12 (3 1 3 1 3 1) does the same. As does 8-tone scale with
(4/3)^(1/4) as generator. Hmm...so what about (16/3)^(1/4)? Yup. But
not 32/3.

The only case of interval-class-pairs being inversions of one another?

I don't know what I'm doing. Move to tuning-math at will.

🔗Yahya Abdal-Aziz <yahya@melbpc.org.au>

Hi Jacob,

On Sun, 09 Apr 2006, Jacob Barton wrote:
>
> 0: 1/1
> 1: 73.534 cents
> 2: 350.978 cents
> 3: 424.511 cents
> 4: 498.045 cents
> 5: 775.489 cents
> 6: 849.022 cents
> 7: 1126.466 cents
> 8: 2/1
>
> generator is (8/3)^(1/4) or about 424.5 cents. Mapped linearly to the
> keyboard and playing notes that look like a major third apart, one
> finds that every note can be harmonized with another note either an
> exact 3/2 and/or 4/3 away.
>
> Special? Or dime a dozen?

That certainly is unusual melodically.

The generator is a quarter (fourth part) of a pure
eleventh.

How about using:
- a third, fifth, sixth or seventh (etc) of a pure
eleventh?
- a third, quarter, fifth, sixth or seventh (etc) of a
pure twelfth?
- a third, quarter, fifth, sixth or seventh (etc) of
any other pure fourth or fifth plus a whole number
of octaves?

Any of these should give you the "harmonized with
another note either an exact 3/2 and/or 4/3 away"
property.

However, mapping to the keyboard might not be as
neat as playing apparent major thirds.

Regards,
Yahya

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🔗Hudson Lacerda <hfmlacerda@yahoo.com.br>

Jacob escreveu:
> --- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
> >>> 0: 1/1
>>> 1: 73.534 cents
>>> 2: 350.978 cents
>>> 3: 424.511 cents
>>> 4: 498.045 cents
>>> 5: 775.489 cents
>>> 6: 849.022 cents
>>> 7: 1126.466 cents
>>> 8: 2/1
>>
>>It seems weird to me -- many folks give the output of scala's
>>show command instead of the contents of the .scl file...

Is there any option (for ``show'') to print the scale on screen without the pitch indexes, or yet better, in .scl format?

(BTW, I am having problems to paste data to Scala from X clipboard.)

[...]
> I wasn't clear. With this scale one can play a P4 or P5 and move
> parallel up the scale and have this interval always be P4 or P5.
> That's the magic. With pythagorean, you get wolves (tritones) in your
> parallel motion.
> > The even-number cardinality has a lot to do with it. Tcherepnin mode
> of 12 (3 1 3 1 3 1) does the same. As does 8-tone scale with
> (4/3)^(1/4) as generator. Hmm...so what about (16/3)^(1/4)? Yup. But
> not 32/3.
> > The only case of interval-class-pairs being inversions of one another?

I would describe that as: a single interval class with exactly two sizes: 3/2 and 4/3. For the scales referred to, with 8 tones, ic4 is the central interval class. Perhaps the number `n' in (3^x/2^y)^(1/n) is related to the number of steps the scale should have to show that property?

Here is an scale based on ((3/2)^(1/3)):

!
chain of 6 intervals of (3/2)^(1/3) reduced into 2/1
6
233.985
467.970
701.955
935.940
1169.925
2/1
!

The intervals are:

1: 1 30.075 cents
1: 5 233.985 cents
2: 2 264.060 cents
2: 4 467.970 cents
3: 3 498.045 cents
3: 3 701.955 cents
4: 4 732.030 cents
4: 2 935.940 cents
5: 5 966.015 cents
5: 1 1169.925 cents

Here, ic3 is either 3/2 or 4/3.

Cheers,
Hudson

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🔗Carl Lumma <clumma@yahoo.com>

> > Well, the scale
> > Chain of six 3:2s (pythagorean).
> > has the same property, but fewer notes.
>
> I wasn't clear. With this scale one can play a P4 or P5 and move
> parallel up the scale and have this interval always be P4 or P5.
> That's the magic. With pythagorean, you get wolves (tritones) in
> your parallel motion.

Try the 6-tone chain of 5ths.

> The only case of interval-class-pairs being inversions of one
> another?

I shouldn't think so.

-Carl

🔗Carl Lumma <clumma@yahoo.com>

> Jacob escreveu:
> > --- In tuning@yahoogroups.com, "Carl Lumma" <clumma@> wrote:
> >
> >>> 0: 1/1
> >>> 1: 73.534 cents
> >>> 2: 350.978 cents
> >>> 3: 424.511 cents
> >>> 4: 498.045 cents
> >>> 5: 775.489 cents
> >>> 6: 849.022 cents
> >>> 7: 1126.466 cents
> >>> 8: 2/1
> >>
> >>It seems weird to me -- many folks give the output of scala's
> >>show command instead of the contents of the .scl file...
>
> Is there any option (for ``show'') to print the scale on screen
> without the pitch indexes, or yet better, in .scl format?

I don't know. I save the file and open it with my text
editor (I have .scl associated with the editor).

> (BTW, I am having problems to paste data to Scala from X clipboard.)

How odd. It works fine for me on Windows, and it's gtk.

-Carl

🔗Hudson Lacerda <hfmlacerda@yahoo.com.br>

Carl Lumma escreveu:

>>(BTW, I am having problems to paste data to Scala from X clipboard.)
> > > How odd. It works fine for me on Windows, and it's gtk.
> > -Carl

On GNU/Linux there are two clipboard arenas. One is normally used just with the mouse (selecting text is sufficient to copy it, middle button does pasting), the other one is used with commands like Ctrl-C Ctrl-V (used by many gtk programs).

Pasting with the mouse doens't work in Scala when copying from a terminal or from Emacs; however, it does work with other gtk programs like GEdit. To paste something to Scala, I need paste it to GEdit and then copy it again...

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🔗Ozan Yarman <ozanyarman@ozanyarman.com>

One can have Scale nr.1 with the following mode out of my improved 79-tone tuning:

5 18 5 5 18 5 18 5

And Scale nr.2 with the following mode:

6 16 6 22 6 17 6

Cordially,
Oz.
----- Original Message -----
From: Mohajeri Shahin
To: tuning@yahoogroups.com
Sent: 11 Nisan 2006 Salı 16:23
Subject: FW: [tuning] Re: is this scale special?

Hi all

this scale :

>>>0: 1/1
>>> 1: 73.534 cents
>>> 2: 350.978 cents
>>> 3: 424.511 cents
>>> 4: 498.045 cents
>>> 5: 775.489 cents
>>> 6: 849.022 cents
>>> 7: 1126.466 cents
>>> 8: 2/1
>>

has this structure :

a=73.534

b=277.444

abaababa

now , I change it to

a=90

b=250

c=a+b = 340

to have 2 pack of (aba) and center of (c) as : abacaba

90.

340.

430.

770.

860.

1110.

1200.

Sounding good to me!! Between arabic taste and persian chahargah.