what would you call a 1-b5-6?

[thephilosopher]

what would you call that chord? why?

[Eli M.]

I can't think of what you'd call 1-b5-6. In C, for example, it would be:

C-Gb-A

If you spell it enharmonically as C-F#-A, you have an F# diminished triad in second inversion.

[Alvaro Martín Gómez A.]

There are two options for this:

1- According to traditional harmony, the fifth of a chord may be omitted without "harmful" effects, so it can be a minor sixth chord minus the fifth: C-Eb-G-A without the G (it works fine).

2- The second inversion of a diminished chord. If you put the sixth on bottom (A-C-Eb) you have the root inversion of a diminished chord, which is made of two minor thirds.

[Alvaro Martín Gómez A.]

Oops... I read "b3" instead of "b5". According to this, Eli is right.

[Phil Smith]

It's a diminished chord. If C was the root it would probably be notated Gbdim/C if this is the specific voicing you're after. It's an F# or Gb Dim chord and also a Cdim, Ebdim, Adim chord which are all spelled the same i.e. they all have the same notes.