Comma as unison vector

Hi there,

A composer may sometimes want to make tunings that
exploit commas as scale steps - the syntonic comma
is plenty large enough to use as a scale step.

Here is a tune in a scale using the syntonic comma
as a scale step - the scale is:

10/9 9/8 5/4 3/2 5/3 27/16 2/1

http://www.robertinventor.com/syntonic_comma_as_scale_step.mid

- lattice diagram:

1 ... 3 ... 9 ... 27
\ /
5/9 ...5/3 ... 5

Rather than the 81 ~= 5 of

1 ... 3 ... 9 ... 27
\ / \ / \ /
5.....15.....45

To find the periodicity block it is in,
we want 81 ~= 5/9 so use unison vectors 729/640 and 25/24

1/1 10/9 9/8 5/4 4/3 45/32 3/2 5/3 27/16 16/9 15/8 2/1

1/9 ... 1/3 ... 1 ... 3 ... 9 ... 27
\ / \ / \ / \ / \ /
5/9 ... 5/3 ... 5 ...15 ...45

In Scala:
File | New | Product Scale and then Modify | key | to centre

How about a seven tone scale from those notes, for instance:
10/9 9/8 5/4 3/2 5/3 27/16 15/8 2/1

Here is an improvisation in that tuning:

http://www.robertinventor.com/syntonic_comma_as_scale_step_seven_tones.mid

in a tuning which has a comma that isn't a comma :-).

Robert

--- In tuning@yahoogroups.com, "Robert Walker" <robertwalker@n...> wrote:
> Hi there,
>
> A composer may sometimes want to make tunings that
> exploit commas as scale steps - the syntonic comma
> is plenty large enough to use as a scale step.
>
> Here is a tune in a scale using the syntonic comma
> as a scale step - the scale is:
>
> 10/9 9/8 5/4 3/2 5/3 27/16 2/1

Here's a scale with both 81/80 and 64/63 as steps:

10/9 9/8 5/4 21/16 4/3 3/2 5/3 27/16 15/8

You could use it to investigate the care and feeding of commas.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:

> Here's a scale with both 81/80 and 64/63 as steps:
>
> 10/9 9/8 5/4 21/16 4/3 3/2 5/3 27/16 15/8
>
> You could use it to investigate the care and feeding of commas.

If we really want to do this right, we can go for twelve notes to the
octave. That way we can retune and then reharmonize a 12-equal melody:

10/9 9/8 5/4 21/16 4/3 3/2 5/3 27/16 7/4 16/9 15/8 2

This scale has two complete otonal quintads, and all that goes with
that, including two major tetrads and two subminor tetrads. It also
has four major triads, three minor triads, two subminor triads two
1-6/5-7/5 diminished triads and a supermajor triad. Hence, its ability
to harmonize is undoubted.

Hi Gene,

Thanks :-)

> Here's a scale with both 81/80 and 64/63 as steps:

> 10/9 9/8 5/4 21/16 4/3 3/2 5/3 27/16 15/8

> You could use it to investigate the care and feeding of commas.

Tune smithy fractal tune.
http://www.robertinventor.com/comma_and_septimal_diesis_steps.mid

Robert

Hi Gene,

Thanks for the twelve tone scale with all the commas and dieses
and the harmonies - I'm enjoying improvising in it as you can hear
here :-):

http://www.robertinventor.com/comma_and_septimal_diesis_steps_improv3.mid

10/9 9/8 5/4 21/16 4/3 3/2 5/3 27/16 7/4 16/9 15/8 2/1

Robert

--- In tuning@yahoogroups.com, "Robert Walker" <robertwalker@n...> wrote:
> Hi Gene,
>
> Thanks for the twelve tone scale with all the commas and dieses
> and the harmonies - I'm enjoying improvising in it as you can hear
> here :-):
>
>
http://www.robertinventor.com/comma_and_septimal_diesis_steps_improv3.mid
>
> 10/9 9/8 5/4 21/16 4/3 3/2 5/3 27/16 7/4 16/9 15/8 2/1

Loads of fun, eh? I did a retuning of Prokoviev, which is really quite
musical and sounds like what might have happened if he had
collaberated with Lou Harrison. JI Prokoviev! It's on my Mad Science page:

http://66.98.148.43/~xenharmo/mad.html

From: "Gene Ward Smith" <gwsmith@s>

> 10/9 9/8 5/4 21/16 4/3 3/2 5/3 27/16 7/4 16/9 15/8 2

It's quite a pitty but I can't tune such a scale on my synth because the
largest detuning from 12-equal comes out as about 94 cents to either side
(even if I remove the offset). Unfortunately, the Yamaha XG tuning messages
allow only a retuning of no more than -64..+63 cents.
Well, what about this?

! parizek_syndiat.scl
!
Petr Parizek, diatonic scale with syntonic alternatives
12
!
10/9
9/8
5/4
4/3
27/20
40/27
3/2
5/3
27/16
50/27
15/8
2/1

Petr