Paul's Arabic diatonic - Beware - This posting is not for tuning novices

--- In tuning@y..., "paulerlich" <paul@s...> wrote:

> The Arabic Diatonic can be notated, for example, as
> > Ab A# Cb Db Eb E# Gb (Ab)
> > or
> > A# Cb C# D# E# Gb G# (A#)
> >

Transposed this gives
A Ax C D E Ex G (Let's analyse it in C)

C Cx Eb F G Gx Bb

on a spiral of fifths this gives

Eb Bb F C G D A B F# C# G# D# A# E# B# Fx Cx Gx
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
y y y y y n n n n n n n n n n n y y

So a chain of 17 steps - 6 thru 16 are missing - tonic is 4

Therefore scalecoding is
17/678910111213141516/4
A span of 17 is fairly long for Western tunings, so I suggest that what has happened is the Cx has been substituted for the more usual Db and Gx for the usual Db.

This would gives us.

C Db Eb F G Ab Bb

On a spiral of fifths this would be a contiguous chain:

Db Ab Eb Bb F C G
1 2 3 4 5 6 7

which is 6/0/6

giving us the Phrygian or Bhairavi scale
i.e. white notes only descending from E

see http://www.harmonics.com/lucy/lsd/scalemak.html

for total explanation of this system.

I suggest that what you have done is to sharpen two notes from b to the adjacent x, in LucyTuning a difference of approx 4.5 cents

Early morning in London. I'm half asleep, so please forgive any detail errors or typos.

--
~====================================================~
Charles Lucy - lucy@harmonics.com (LucyScaleDevelopments)
------------ Promoting global harmony through LucyTuning -------
for information on LucyTuning go to http://www.harmonics.com/lucy/
or Lucytuned Lullabies go to
http://www.lucytune.com or http://www.lucytune.co.uk or http://www.lullabies.co.uk

So the C Db Eb F G Ab Bb scale is a phrygian (13 limit variety?)

In any case this is identical to the pentatonic chain to be found in Lendvai
as Mi Pentatony

G Bb C Eb F Ab Bb Db (and continuable indefinitely in either direction).
Assume 4ths are just, and choose your minor third or similar (15/13 or 16/13
for a really authentic effect)

> From: tuning@yahoogroups.com
> Reply-To: tuning@yahoogroups.com
> Date: 30 Jan 2002 08:38:10 -0000
> To: tuning@yahoogroups.com
> Subject: [tuning] Digest Number 1856
>
> Paul's Arabic diatonic - Beware - This posting is not for tuning novices

--- In tuning@y..., Charles Lucy <lucy@h...> wrote:
> --- In tuning@y..., "paulerlich" <paul@s...> wrote:
>
> > The Arabic Diatonic can be notated, for example, as
> >
> > Ab A# Cb Db Eb E# Gb (Ab)
> >
> > or
> >
> > A# Cb C# D# E# Gb G# (A#)
> >
> >
>
> Transposed this gives
> A Ax C D E Ex G
>
>
> (Let's analyse it in C)
>
> C Cx Eb F G Gx Bb
>
> on a spiral of fifths this gives
>
> Eb Bb F C G D A B F# C# G# D# A# E# B# Fx Cx Gx
> 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
> y y y y y n n n n n n n n n n n y y
>
> So a chain of 17 steps - 6 thru 16 are missing - tonic is 4
>
> Therefore scalecoding is
> 17/678910111213141516/4
> A span of 17 is fairly long for Western tunings, so I suggest that
>what has happened is the Cx has been substituted for the more usual
>Db and Gx for the usual Db.

"What has happened"? Where?

> This would gives us.
>
> C Db Eb F G Ab Bb

Oh no! The "Arabicness" is totally lost! Why did you do that,
Charles? :)

--- In tuning@y..., Mark Gould <mark.gould@a...> wrote:

> So the C Db Eb F G Ab Bb scale is a phrygian (13 limit variety?)

My apologies Mark, but where are you getting 13-limit from? Charles
Lucy took my original 31-tET Arabic Diatonic scale, and recast it as
a Western Diatonic in LucyTuning, a tuning very close to 19-tET (the
major third is 1/pi octave) and hence the scale became a Renaissance
meantone Phrygian.

> In any case this is identical to the pentatonic chain to be found
in Lendvai
> as Mi Pentatony
>
> G Bb C Eb F Ab Bb Db (and continuable indefinitely in either
direction).
> Assume 4ths are just, and choose your minor third or similar (15/13
or 16/13
> for a really authentic effect)

Oh so is that where you were getting 13-limit from?

Sounds fascinating -- I'll have to try this on my keyboard when I get
home. By the way, 15:13 is 248 cents, and 16:13 is 359 cents -- in my
experience, I haven't found that ratios of 13 have any
audible "attraction" until you play Otonal chords of three or more
notes, thus I personally would tend to think of these intervals as
particular cents values as opposed to ratios.

But where do you get "identical"? The Arabic diatonic scales I posted
each had five notes in one chain of fifths, and two notes in another -
- while your "Mi Pentatony" derivation would have four notes in one
chain of fifths and three in another. Correct?