How does one sign an ascending melodic minor scale using hexachordal solmization?
Here is an example, it's the famous Bourreé by Bach, from the Suite in E minor, BWV 996:
We know that Bach used this system of solmization, so the obvious question is, how would Bach sing this using solmization and teach it to his students?
The syllables that I've written, I'm fairly sure about. First we start in the hexachord on D, which is the natural hexachord here, and we have: re mi fa mi re. The note D sharp, is the cadential raised 7th degree, sung ut (or do... in Renaissance and earlier music, this would be "causa pulchritudinis"), so we stay in the same hexachord on D. Then follow re and mi. Now what?
One is tempted to mutate to the hexachord on B (♮), but this hexachord is not related to the hexachord on D, so this seems to me to be out of the question, since only hexachords on G (soft) and A (hard) are allowed in this transposition of the gamut. So this ascending tetrachord in melodic minor is causing me confusion. Descending is easy, we just proceed like in natural minor: (in soft hexachord) la sol fa (mutate to natural hexactord) la sol fa mi re.
To recapitulate, here we have...
What syllables should one sing in place of question marks?
Since this scale is not a subset of the transposed gamut, I suspect the syllables are going to be the same as in natural minor, just with a raised intonation (re mi fa re mi ♯fa ♯sol la), but I would like someone to confirm this to me (preferably with a quote from a source with authority) or tell me that I'm wrong and show me what is correct.
Another possibility that occurred to me is that I'm wrong about the allowed hexachords and that we temporarily treat this as modal mixture (pretend we are in E major and not E minor), and then the hexachord on B would be allowed as the hard hexachord. But what would be the point of mutation in that case? The raised sixth degree: re mi fa sol la re mi fa?
A third possibility that occurred to me is to sing it like a dorian scale, just with a raised seventh degree ("causa pulchritudinis"): re mi fa re mi ♯fa sol. I find it very practical but a bit odd.