regarding tonic minor and magic number 19

A pretty chord to end a piece with a feeling
of humility, resignation and bittersweet joy.
A C-maj7#11 voiced open but straight up

(low) C G Eb B F# (high)

...and the piece was fairly "C minor tonal"
throughout.

1) an overtone approach

1/1 3/2 19/16 15/8 11/8

2) fifths and thirds (major and minor) in tune

1/1 3/2 6/5 15/8 45/16

3) "upper structure triad" in tune warping minor third

1/1 3/2 75/64 15/8 45/16

4) "upper structure triad" in tune warping inner major third

1/1 3/2 6/5 48/25 36/25

5) "upper structure triad" in tune, "most rational"

1/1 3/2 7/6 14/9 7/5

Which would singers/strings/winds "naturally" tend to,
and which as a composer or director would you coerce
them to tennd to?

Bob Valentine

>From: Robert C Valentine <bval@iil.intel.com>
>
>
>A pretty chord to end a piece with a feeling
>of humility, resignation and bittersweet joy.
>A C-maj7#11 voiced open but straight up
>
>(low) C G Eb B F# (high)
>
>...and the piece was fairly "C minor tonal"
>throughout.
>
>1) an overtone approach
>
> 1/1 3/2 19/16 15/8 11/8
>
>2) fifths and thirds (major and minor) in tune
>
> 1/1 3/2 6/5 15/8 45/16
>
>3) "upper structure triad" in tune warping minor third
>
> 1/1 3/2 75/64 15/8 45/16
>
>4) "upper structure triad" in tune warping inner major third
>
> 1/1 3/2 6/5 48/25 36/25
>
>5) "upper structure triad" in tune, "most rational"
>
> 1/1 3/2 7/6 14/9 7/5
>
>Which would singers/strings/winds "naturally" tend to,
>and which as a composer or director would you coerce
>them to tennd to?

My conjecture is number 2), to which could be added a D at 9/8 to make it
even more stable:

F#

B (D)

G

C Eb

The D would work well just below the Eb or between the B and the F#. This
is not a chord that I've ever seen or used but I like it. Thanks for adding
to my vocabulary.

John Link
ALMOST ACAPPELLA

Robert C Valentine wrote,

>A pretty chord to end a piece with a feeling
>of humility, resignation and bittersweet joy.
>A C-maj7#11 voiced open but straight up

>(low) C G Eb B F# (high)

>...and the piece was fairly "C minor tonal"
>throughout.

>1) an overtone approach

> 1/1 3/2 19/16 15/8 11/8

>2) fifths and thirds (major and minor) in tune

> 1/1 3/2 6/5 15/8 45/16

>3) "upper structure triad" in tune warping minor third

> 1/1 3/2 75/64 15/8 45/16

>4) "upper structure triad" in tune warping inner major third

> 1/1 3/2 6/5 48/25 36/25

>5) "upper structure triad" in tune, "most rational"

> 1/1 3/2 7/6 14/9 7/5

>Which would singers/strings/winds "naturally" tend to,
>and which as a composer or director would you coerce
>them to tennd to?

I would use (3) if I wanted to be conventional though (1) would have a nice
"periodicity buzz" reinforcing the tonic. I think it is helpful (as I was
just explaining to Jim Savage) to look at all the intervals within the chord
-- looking at just the ratios relative to the root obscures what is
happening wih all the other intervals. Perhaps (3) is most consonant by
Sethares/Plomp measures while (1) wins in terms of harmonic entropy.