empty post, > modes, megamodes, and L&s mapping of scales.

Yes Carl, empty;

I was having trouble deleting only parts of the original message with the strange Yahoo formating, and hence lost the whole thing.

The points that I wished to make were:

a) Mode can be a very slippery ambiguous term. e.g. when used by Messaien in his writings about modes he is using the word in the French sense as fashion, method, way, path, pattern etc.

e.g. His "mode" using every fourth semitone (Dim7) etc.

I have always seen it translated as "mode" in English, which is misleading and really missing his intent.

b) How about using the term "megamode" as used on this page, to describe a chain of fifths, and which positions are missing, yet not specifying which position is the tonic?

http://www.lucytune.com/new_to_lt/pitch_05.html

see point 5.

c) To describe a scale using L and s, works perfectly provided the user appreciates that both L and s can be "elastic" ; and that 5L+2s = one octave.

It works well for meantone-type tunings and can also be applied (with some approximations) to other systems. e.g. many edo's and by using additions and subtractions of L's and s's.

Charles Lucy
lucy@...

- Promoting global harmony through LucyTuning -

for information on LucyTuning go to:
http://www.lucytune.com

For LucyTuned Lullabies go to:
http://www.lullabies.co.uk

On 19 Apr 2009, at 1:13 AM, Charles Lucy wrote:
> c) To describe a scale using L and s, works perfectly provided the
> user appreciates that both L and s can be "elastic" ; and that 5L> +2s = one octave.
>

I'm sorry, but I can't help myself to mention: It looks like L and s are not enough elastic, when scales are limited only for one combination (5L+2s), and must be closed in octave.

Even such common scale like diminished mode (when you have mentioned Messiaen) is 4L+4s. Does it mean it's excluded from your Ls system?

And there's no reason to avoid scales like C C# D D# F# G A# B, which is 2L+6s.

Diatonic scales using half-tone, whole-tone and augmented second, like 131213(1) - C Db E F G Ab B (C) could be described as 2L+s+1L+4s. Isn't it valid scale, too?

How you will express for example a 15 ET tuning? I see here only 15s.

And lot of other scales (tunings) with more different sizes of steps? Even not closed in octave?

> It works well for meantone-type tunings and can also be applied (with
> some approximations) to other systems. e.g. many edo's and by using
> additions and subtractions of L's and s's.
>
> Charles Lucy
> lucy@...
>

Or am I totally misunderstanding this Ls concept?

Daniel Forro

2L+6s does not describe a scale. It describes an interval.

Diminished a la Messiaen

can become:

(L+s) (L+s) (L+s) ..... e.g. C - Eb - Gb - Bbb- Dbb - Fbb - etc - 300 cents in 12edo; yet 313.5 cents in LT.

although there are many other ways that it could be spelled.

Like this it is repeated steps of bIIIrds so after four steps it exceeds an octave in negative meantone as you suggest.

i.e. 4L+4s

although maybe the interval bIII could be interpreted as #II, which would make it into a different kettle a kippers.

i.e. (2L-s) (2L-s) (2L-s) ..... C - D# - Ex - Fxx - Gxx# etc - 300 cents in 12edo yet 260 cents in LT

and lotsa other combinations. (not necessarily identical)

For 15edo you would have 1200/15 per step = 80 cents which roughly approximates #1 or (L-s) in 68 cents in LT

although you could find various combinations and permutations to produce better approximations as you further add 80 cent units for 160, 240, 320 etc.

On 18 Apr 2009, at 18:02, Daniel Forro wrote:

>
>
>
> On 19 Apr 2009, at 1:13 AM, Charles Lucy wrote:
> > c) To describe a scale using L and s, works perfectly provided the
> > user appreciates that both L and s can be "elastic" ; and that 5L
> > +2s = one octave.
> >
>
> I'm sorry, but I can't help myself to mention: It looks like L and s
> are not enough elastic, when scales are limited only for one
> combination (5L+2s), and must be closed in octave.
>
> Even such common scale like diminished mode (when you have mentioned
> Messiaen) is 4L+4s. Does it mean it's excluded from your Ls system?
>

>
> And there's no reason to avoid scales like C C# D D# F# G A# B, which
> is 2L+6s.
>
> Diatonic scales using half-tone, whole-tone and augmented second,
> like 131213(1) - C Db E F G Ab B (C) could be described as 2L+s+1L
> +4s. Isn't it valid scale, too?
>

>
> How you will express for example a 15 ET tuning? I see here only 15s.
>
> And lot of other scales (tunings) with more different sizes of steps?
> Even not closed in octave?
>
> > It works well for meantone-type tunings and can also be applied > (with
> > some approximations) to other systems. e.g. many edo's and by using
> > additions and subtractions of L's and s's.
> >
> > Charles Lucy
> > lucy@...
> >
>
> Or am I totally misunderstanding this Ls concept?
>
> Daniel Forro
>
Charles Lucy
lucy@...

- Promoting global harmony through LucyTuning -

for information on LucyTuning go to:
http://www.lucytune.com

For LucyTuned Lullabies go to:
http://www.lullabies.co.uk

Charles wrote:

> (L+s) (L+s) (L+s) ..... e.g. C - Eb - Gb - Bbb- Dbb - Fbb - etc
> - 300 cents in 12edo; yet 313.5 cents in LT.

The point here is that there's no given restriction as to what sizes the L and S steps should have and what are the target intervals. In Bohlen-Pierce diatonic, for example, the L is very close to the ordinary 12-equal minor third and the S is a kind of "neutral" second and there are no octaves at all. Instead, 4L + 5S make the interval which sounds like a perfect 12th.

Petr