604s of any era are pretty awesome speakers, but the design of the beasts is not the same as what normally works well in open baffle type applications.

A quick search on the net, I could find a set of T/S parameters which help to understand the design and workings of drivers but, similarly designed Altecs I own are meant to be used with a ported or horn loaded cabinet almost exclusively.

A spec of relatively high Qts is usually more desirable for open baffle use. Somewhere in the range above .5 seems to work well.

The published info I found for various Altec products on the Lansing Heritage site shows the 604s of various configurations as having Qts of  .21 to .27.  
In simple terms, that usually means they need an enclosure.

The drivers which often excel in an open baffle design tend to show a Qts in the .7 range.  Lighter cones, smaller magnets, highly efficient, compliant suspensions, etc.

However, YOU HAVE THEM!  So I might try it to hear what they sound like, just for my own satisfaction.
I have done so in the past with similarly built drivers from JBL and Altec (although JBL does not offer a Duplex design) and always found them, to sound amazing for midrange, BUT the bass rolls off  like 8 to 12 dB below about 500Hz.
While there is nothing wrong with a 15" midrange/upper range driver that can maybe reach 200Hz with authority, you would not be getting the full capacity of these drivers in an open baffle, in my opinion.

Equalization might seem to help that massive roll off of low tones, but EQ introduces other issues which kind of defeat the crystal pure clarity of open baffle designs.

It is hard to beat the sound a single point source like the 604 designs can produce, though.

Hoping others will chime in for you since I seem to have given you too many answers.

Dirtdawg,
Thanks for that!  I did see the QT was low and saw some convos about using them in an O/B config but not a whole of experience out there.  I do agree that these are best in a cabinet so I will have to find some or have somebody build them.  They tend to get bulky.  I got lucky and found these along with 601C that are in cabinets that are in fair condition for a great price locally and they sound great!  I still have the original crossovers and that will be another quest to eventually replace.  
Bob

Are these not the mid/high units from the fabled Big Red studio monitors? The ones I know had a 15” for bass side by each in an infinite baffle.

Ah! Very good, so you are already an OB guy.

Sorry for giving you info you already knew, but I tend to be gentle with people asking such questions. We want you in our fold. :^)