Re: C6 v Am7

>How would you tune C6 differently from Am7?

C6
1/1 5/4 3/2 27/16

Am7
1/1 7/6 3/2 7/4

Both
1/1 5/4 3/2 5/3
1/1 6/5 3/2 9/5

>Hrm, maybe I'm wrong, and C6 and Am7 should be tuned
>the same. 27:20 makes a bad 4th.

You haven't given any examples to be wrong about. Bad? For what?

Maybe we shouldn't call any of these chords C6 or Am7, since these names
are in terms of the diatonic scale. These chords can also arise from other
scales, not the least of which are harmonic series segments.

Even if we keep the names, only those who insist on playing their diatonic
scale with 7 total pitches will have a problem. And they will miss the
ability to inflect these chords in different ways.

>Would your default tuning for C6 be different that your default tuning for
>Am7?

That depends. If I actually decided to use the Justonic chord detector ---
which could play all autoharp parts in the repertoire --- I would probably
set up different combos for different situations (the Justonic people were
good enough to allow this, and it does provide a partial solution to the
uniqueness and inversion problems)...

Combo Am7(+1&3) C6(+1&3) Answer
---------------------------------------------------
classical 6/5 9/5 5/4 5/3 no
septimal 7/6 7/4 9/7 12/7 no
mixed 7/6 7/4 5/4 5/3 yes
strange 13/11 20/11 5/4 13/8 yes
neutral 11/9 16/9 16/13 22/13 yes
---------------------------------------------------

-C.