19-tet pentaenharmonic MIDI

http://www.angelfire.com/mo/oljare/images/lilies.mid

This 19-tet tune uses a 9-tone scale i dubbed pentaenharmonic,together with diatonics and some transpositions.Something like this:

sLsLLsL
(small steps 1,large steps 3)

Or with meantone note naming starting from C:

C C# D# Eb F G G# A# Bb

The scale is based on a generator that divides the fifth in half from above,creating a 9-tone MOS that includes the regular pentatonic scale as a subset(C Eb F G Bb).

The other four notes,of course,form a incomplete pentatonic scale by themselves.Transposing the scale pattern by the generator makes it complete.So the pentatonics are used as a mode of transition between the 9-note and the diatonic sounds at the beginning,middle and end of the piece.

This is only one of a few interesting MOSes i�ve discovered in equal temperaments.I�ll cover more as i finish the pieces i am writing with them(i find such"reference implementations"very important,and it is one of my main reasons for composing within the limited range of 1-instrument MIDI)

-=-=-=-=-=-=-
MATS �LJARE
http://www.angelfire.com/mo/oljare
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--- In tuning@y..., "Mats Öljare" <oljare@h...> wrote:
> http://www.angelfire.com/mo/oljare/images/lilies.mid
>
> This 19-tet tune uses a 9-tone scale i dubbed
pentaenharmonic,together with
> diatonics and some transpositions.

Interesting.

> Something like this:
>
> sLsLLsL
> (small steps 1,large steps 3)

You mean sLsLLsLsL?

> Or with meantone note naming starting from C:
>
> C C# D# Eb F G G# A# Bb
>
> The scale is based on a generator that divides the fifth in half
from
> above,

You mean it divides the fourth in half?

>creating a 9-tone MOS that includes the regular pentatonic
scale as a
> subset(C Eb F G Bb).
>
> The other four notes,of course,form a incomplete pentatonic scale by
> themselves.Transposing the scale pattern by the generator makes it
> complete.So the pentatonics are used as a mode of transition between
the
> 9-note and the diatonic sounds at the beginning,middle and end of
the piece.

You could increase the available harmonies in that scale, without
greatly impacting it's melodic nature, by either sharpening all the
notes of the incomplete pentatonic (C# D# G# A#) by about 10 cents,
or flattening them all by about 10 cents.

If you sharpen them by 10 cents, you get usable subminor triads
(approximate 6:7:9's) on Bb, F,and C. You also get supermajors on C#,
G# and D#. In this case C#, G#, D#, A# would be more accurately named
Dbb, Abb, Ebb, Bbb.

If you flatten them by 10 cents, you get supermajors on Eb, Bb, F, and
subminors on C#, G#, D#.

Regards,
-- Dave Keenan

> Subject: 19-tet pentaenharmonic MIDI
>
> http://www.angelfire.com/mo/oljare/images/lilies.mid
>
> This 19-tet tune uses a 9-tone scale i dubbed pentaenharmonic,together with
> diatonics and some transpositions.Something like this:
>
> sLsLLsL

I believe you meant sLsLLsLsL.

Very interesting, I'll try to give it a spin. I have been very interested
in trasposable diatonic scale systems in EDOs like this one. (For those
interested, transposition by a sharp looks like

s L s L L s L s L
+ L-s s-L
---------------------------
s L L s L s L s L

and by a flat looks like

s L s L L s L s L
+ s-L L-s
---------------------------
s L s L s L L s L

A generalized version of a transposable diatonic system is

n*[ q*A, r*B ], [ q*A, (r+-1)*B ]

In this case

n = 3
q = 1
r = 1
r+-1 = 2
A = s = 1
B = L = 3

so

sL sL sL sLL

The axis of transposition is related to 'n'. In traditional pentatonic
and septatonic systems, n = 1, so transposition is by approximately a
half of the octave... Of course, the system doesn't have to be
constrained to an octave, just to repeating diatonic patterns...)

Depending on your useage (I haven't heard your composition) and your
tools, you may try renderring the piece in 43 or 67 EDO. Both of
these support your scale (7 and 2, 11 and 3 respectively) and have
a better "3/2" and a likely more pleasing (if not more accurate)
"5/4" than does 19. What may be a drawback is that the "sL" and "s"
intervals get smaller.

Looks very interesting, the simultaneous inclusion of #2 and b3 looks
like some neat room for ambiguous resolution (like, did that really
resolve...)

I have been looking into the resources of a similar octonic scale
in a variety of EDOs

LLsLsLLs

In 31tet, L=5 and s=2 giving a meantone spelling of

C D E E# Fx Abb Bbb Cb

I still have to code it into a tuning table and see whether the
interesting properties outweigh the fact that it doesn't have
a real "3/2" in any mode.

One thing that is attractive in your scale from a chording system
in that tetrads just 'fit' in a 9-note scale. My approach (on paper)
is to have a 'normal' system of tetrads with three steps on the
second term, for instance

LL sLs LL s
C E Abb Cb is a "I maj 7 +5"

and then there is a passing system of 'diminished chords' based
on the symmetric division of the scale.

Who knows, I'll play with both of them. Thanks for posting it!

Bob Valentine

Hey Dave,

Regarding Mats piece, you wrote:
> Interesting.

And then:

> You could increase the available harmonies in that scale...

and then:

> If you sharpen them by 10 cents, you get usable subminor triads...

and then:

> If you flatten them by 10 cents, you get supermajors...

So, my question is: did you listen to it first, and then suggest
the 'improvements', or have you not listened to it at all? I'm really
*hoping* it was the former, even though I didn't see a "Call for
Commentaries".

Your local musical curmudgeon,
Jon

Dave,

--- In tuning@y..., JSZANTO@A... wrote:
> Hey Dave,
>
> Regarding Mats piece, you wrote:

...and the rest. This is weird, because I wrote this last night, but
at the last minute I decided not to post it. And then this morning I
see is on the list, long after I went to bed. Maybe I hit post
instead of preview.

Oh well.

Rgds,
Jon