Harmonic scale based on 31-TET...has this been invented?

Here is the scale I came up with as a subset of 31-TET built for
harmony and chords:
>
> A (1st note IE "C")
> C (3rd note...)
> F (6)
> I (9)
>-----
> O (15)
> S (19)
> W (23)
> Y (25)
>-------
> [ (27)
>
>Is there any one else who in history has used this scale or something
>near it?
>
>That and....how do you think it sounds?

--- In tuning@yahoogroups.com, "djtrancendance" <djtrancendance@...>
wrote:
>
> Here is the scale I came up with as a subset of 31-TET built for
> harmony and chords:
> >
> > A (1st note IE "C")
> > C (3rd note...)

OK, so what's this 3rd note in degrees of 31-ET?

-Carl

Carl,

You said "In degrees"
I'm a newbie to this, what does the term "degree" mean?

When I say 3rd note I assume:
1) A has the same frequency as C in 12-TET and, like C in 12-TET, is the root note of BOTH my subset scale AND of 31-TET itself

2) 32 notes above A is the octave

3) C is 2/31 steps above C and 28/31 steps under the last note of 31 TET before the octave

Note I don't do anything in terms of 12TET (IE c-flat, c-double-flat, etc.)...so if you could teach me how such a notation works I would probably have an easier time explaining myself. :-)

One notation that i used for 31 Et went C C+ C# Db D- D

i am still confused by the A and C thing
why not just call C-? C?

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Michael Sheiman wrote:
>
> Carl,
>
> You said "In degrees"
> I'm a newbie to this, what does the term "degree" mean?
>
> When I say 3rd note I assume:
> 1) A has the same frequency as C in 12-TET and, like C in 12-TET, is > the root note of BOTH my subset scale AND of 31-TET itself
>
> 2) 32 notes above A is the octave
>
> 3) C is 2/31 steps above C and 28/31 steps under the last note of 31 > TET before the octave
>
> Note I don't do anything in terms of 12TET (IE c-flat, > c-double-flat, etc.)...so if you could teach me how such a notation > works I would probably have an easier time explaining myself. :-)
>
>

Kraig Grady wrote:
> One notation that i used for 31 Et went C C+ C# Db D- D
> > i am still confused by the A and C thing
> why not just call C-? C?

31-ET notation is one of the few ET notations that seems to be pretty well standardized (the main difference being what to do with the notes between C and C#, Db and D, etc.) It helps to think of traditional notation as a notation for meantone-like tunings (which were widely used before 12-ET became popular). Sharps and flats represent distinct notes: e.g., C - Eb is a minor third, but C - D# an augmented second. 31-ET is actually very close to 1/4-comma meantone.

When this was originally posted on MMM, I interpreted this scale as:

C C# D Eb F^ G Av A^ Bb
mode /equal 2 3 3 6 4 4 2 2 5

0: 1/1 C unison, perfect prime
1: 77.419 cents C# Db;
2: 193.548 cents D
3: 309.677 cents D#| Eb
4: 541.935 cents F| Gbb
5: 696.774 cents G
6: 851.613 cents Gx A;
7: 929.032 cents A| Bbb
8: 1006.452 cents A#| Bb
9: 2/1 C octave

this is pretty much the notation all the 31 tone people used in LA. it is consistent with what you say. notation being based on a cycle of 5th. early xenharmonikons touch upon this.

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Herman Miller wrote:
>
> Kraig Grady wrote:
> > One notation that i used for 31 Et went C C+ C# Db D- D
> >
> > i am still confused by the A and C thing
> > why not just call C-? C?
>
> 31-ET notation is one of the few ET notations that seems to be pretty
> well standardized (the main difference being what to do with the notes
> between C and C#, Db and D, etc.) It helps to think of traditional
> notation as a notation for meantone-like tunings (which were widely used
> before 12-ET became popular). Sharps and flats represent distinct notes:
> e.g., C - Eb is a minor third, but C - D# an augmented second. 31-ET is
> actually very close to 1/4-comma meantone.
>
> When this was originally posted on MMM, I interpreted this scale as:
>
> C C# D Eb F^ G Av A^ Bb
> mode /equal 2 3 3 6 4 4 2 2 5
>
> 0: 1/1 C unison, perfect prime
> 1: 77.419 cents C# Db;
> 2: 193.548 cents D
> 3: 309.677 cents D#| Eb
> 4: 541.935 cents F| Gbb
> 5: 696.774 cents G
> 6: 851.613 cents Gx A;
> 7: 929.032 cents A| Bbb
> 8: 1006.452 cents A#| Bb
> 9: 2/1 C octave
>
>

Hi Michael,

> You said "In degrees"
> I'm a newbie to this, what does the term "degree" mean?

One "degree" of 31-ET is 1 * the 31st root of 2, or about
38.7 cents, just as one degree of 12-ET is 1 * the 12th root
of 2, or 100 cents exactly.

> When I say 3rd note I assume:
> 1) A has the same frequency as C in 12-TET and, like C in
> 12-TET, is the root note of BOTH my subset scale AND of
> 31-TET itself

OK.

> 2) 32 notes above A is the octave

Right.

> 3) C is 2/31 steps above C

That makes no sense, I think you'll agree.

> and 28/31 steps under the last note of 31 TET before the octave

What's 28/31 steps?

> Note I don't do anything in terms of 12TET (IE c-flat,
> c-double-flat, etc.)

We'd call that doing things in terms of a chain of meantone
fifths -- it's not 12-ET specific. In fact, "Cb" has less
somewhat less meaning in 12-ET than in another meantone tuning
like 31-ET because it's the same pitch as B.

>...so if you could teach me how such a notation works I would
> probably have an easier time explaining myself. :-)

Let's look at your original post

> A (1st note)
> C (3rd note...)
> F (6)
> I (9)
> -------
> O (15)
> S (19)
> W (23)
> Y (25)
> -------
> [ (27)

I assume the things parenthesis are 31-ET degrees. In that
case, you'd put a 0 next to A. What should go next to C?

-Carl