L and S again

I am looking at the post that talks about L and S ratios,

the quote ' some are prepared to go below 1' intrigued me

So I took LLsLLLs

L = 2 and s = 1 hardly needs explaining

Let's set L = 2 and s = 3 so the ratio is now 2/3

2232223 = 16EDO.

To obtain the F to fsharp property, we must transpose upward by 7
steps, but of 16EDO, which is 525cents.

I would say that this scale most resembles the pentatonic, by
properties of structure and transposition.

Therefore, I would say that by reducing the L/s ratio to below 1, a new
scale is formed. After all it seems absurd to label an scale step as L
when really its the s scale step.

When L/s = 1, you have the degenerate case when 'pentatonic'
and 'diatonic' 'merge'

M

On Wed, 26 Oct 2005 "microtonalist" wrote:
>
> I am looking at the post that talks about L and S ratios,
> the quote ' some are prepared to go below 1' intrigued me
>
> So I took LLsLLLs
>
> L = 2 and s = 1 hardly needs explaining
>
> Let's set L = 2 and s = 3 so the ratio is now 2/3
>
> 2232223 = 16EDO.
>
> To obtain the F to fsharp property, we must transpose upward by 7
> steps, but of 16EDO, which is 525cents.

I've seen this mentioned before, but didn't understand it.
What do you mean exactly by "the F to fsharp property"?

> I would say that this scale most resembles the pentatonic, by
> properties of structure and transposition.

Could you elaborate? In particular, which are the structure
and transposition properties you see as most pentatonic-like,
and which as most diatonic-like?

> Therefore, I would say that by reducing the L/s ratio to below 1, a new
> scale is formed. After all it seems absurd to label an scale step as L
> when really its the s scale step.

Doesn't it? :-) In these terms, it might make more sense to
label the most frequently occurring step the "common" or
"default" step, and the other step the "uncommon" or
"variant" step. Then both types of scale have the same
pattern - no longer LLsLLLs, but ccucccu or ddvdddv (take
your pick).

> When L/s = 1, you have the degenerate case when 'pentatonic'
> and 'diatonic' 'merge'

Now that's an interesting insight. But I'll probably need
your answers to those questions I asked earlier in order
to be able to understand you.

Regards,
Yahya

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answers inline, hopefully

--- In tuning@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@m...> wrote:
>
>
> >
> > To obtain the F to fsharp property, we must transpose upward by 7
> > steps, but of 16EDO, which is 525cents.
>
> I've seen this mentioned before, but didn't understand it.
> What do you mean exactly by "the F to fsharp property"?
>
12EDO Cmajor: 0 2 4 5 7 9 11 (0
......Gmajor 7 9 11 0 2 4 6 (7
pitch number 5 is replaced by pitch number 6. This is the f to fsharp
property of what I deem to be a scale.

for 16EDO

2232223:

beginning on 0: 0 2 4 7 9 11 13 (0
beginning on 7: 7 9 11 14 0 2 4 (7

pitch number 13 is replaced by pitch number 14.
Note: I have my own ideas as to the tonic of this scale, but its
based on concepts which are perhaps left to another time.

All scales having this property must also be segments of a generator
of the EDO.

For 16EDO, the generator circle or circle of fourths:

0 7 14 5 12 3 10 1 8 15 6 13 4 11 2 9 0 7 ...

>
> > I would say that this scale most resembles the pentatonic, by
> > properties of structure and transposition.
>
> Could you elaborate? In particular, which are the structure
> and transposition properties you see as most pentatonic-like,
> and which as most diatonic-like?
>
groups of one interval separated by single instances of a larger
interval, for pentatonic-like scales, and

groups of one interval separated by single instances of a smaller
interval, for diatonic-like scales.

There are also other rules.

All pentatonic-like and diatonic-like scales must have the f to
fsharp property. They must also be segments of a generator circle.

>
> > Therefore, I would say that by reducing the L/s ratio to below 1,
a new
> > scale is formed. After all it seems absurd to label an scale step
as L
> > when really its the s scale step.
>
> Doesn't it? :-) In these terms, it might make more sense to
> label the most frequently occurring step the "common" or
> "default" step, and the other step the "uncommon" or
> "variant" step. Then both types of scale have the same
> pattern - no longer LLsLLLs, but ccucccu or ddvdddv (take
> your pick).
>
I don't think this is workable because if the variant step is large
it has different melodic properties to a small variant step. I am
thinking here of the leading note principle of melodic writing.

Interestingly, from my own study I feel that pentatonic-like scales
have downward leading notes while diatonic-like scales have upward
leading notes.

>

Does any of this help?