It's simple really. When you do not drive the harmonies by MIDI or audio input, then the only other possibility is to tell the harmonizer what scale you're singing in, so it will create the proper notes in the respective chord, in a fixed mode. So then, of course you need to tell the box when you change the key, otherwise will come out badly. For instance, when moving from C major in D major, if you do not tell it you changed the key, instead of F sharp (the 3rd) it will probably create either F or G, which is obviously wrong.
The only problem I see with fixed mode is that it will mathematically create the harmonies, with less musicality. No 7ths, no variations, no particular flavors...
Well, I am only guessing here. I have not experienced at all with this. But I am interested. The most I am interested in what harmonizer and in what mode would work best with an arranger like Roland Bk-9.
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Yamaha S770, Studio One 3, EMU 0404USB, ESI, ATH, Dell. And others.