How should one describe that some solfege notes rhyme?
How should one describe that some solfege notes rhyme or perhaps share the same role?
The two examples are do and so (I and V) and mi and ti (III and VII).
C D E F G A B
(I) (II) (III) (IV) (V) (VI) (VII)
do re mi fa so la ti
The V is harmonically closest to the I, so it almost sounds like a resolving scale if one plays C,D,E,F,G.
Is the role of III and VII similar in that they are harmonically the 'middle' notes between I and V and V and the following I?
In other words the III and VII are harmonically the next closest notes to the I (or the V).
Is this why they have rhyming names? Is it to demonstrate the (diatonic) hierarchy of harmony?
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The names of the solfege notes are derived from the hymn "Ut Queant Laxis", and as such, have no connection with their function whatsoever. The first name, "ut", has now been replaced by "do", and "ti" didn't exist in the original hexachord (six tone) solfege system.
upload.wikimedia.org/wikipedia/commons/9/92/Ut_Queant_Laxis_MT.png
In terms of function FA and TI are harmonically related rather than MI and TI.
Harmonically FA and TI are respectively the chord tones 7th and 3rd of the V7 dominant seventh chord.
And functionally, as tendency tones, FA and TI resolve by half-step (in major keys) FA going down to MI and TI going up to DO giving us the progression V7 to I.
There is an interesting review of the FA-MI & TI-DO relationships in Music in the Galant Style, by Gjerdingen. While it isn't about the actual solfege syllable names (which is sort of the heart of your question) it does give a nice historic review of solfege concepts and the tonal role of the scale tones.
It is kind of interesting that DO and SOL and FA and LA verbally rhyme and are paired together in the I and IV chords, but that is just a coincidence.
Not directly. Solfege syllables can be modified (in moveable Do) to show chromaticism. For instances, if you raise "fa" by a half-step, it becomes "fi," or if you lower "mi" it becomes "me" (sounds like "may"). Syllables with a [ay] ending are flattened to [ah], so "re" becomes "ra."
The system works because it shows that you can't raise "mi" or "ti" because those notes are already "fa" and "do" respectively.
So there are definitely some parallels between a scale degree's function and it's solfege syllable, but I wouldn't say that the function determines why certain syllables are used.
The six solfège syllables ut, re, mi, fa, sol, and la were, as mentioned in another answer, derived from a hymn, so there's no reason to seek functional similarity between, for example, fa and la.
Ut was later replaced in Italy with do. (France still uses ut.) The guy who came up with this, a fellow by the name of Doni, had a bit of a hard sell, and one of the points he made was that it is the first syllable of dominus, meaning lord, but I don't see any suggestion that it was thought to be advantageous to have the same syllable there as in sol, though there is certainly such a case to be made. (It doesn't seem that he stressed the fact that it is also the first syllable of his own name, though he does seem to have had this in mind.)
At some point in the eighteenth century, si was added, which became ti in the English-speaking world. In this case, I think it is pretty clear that the vowel i was chosen because of the very similar melodic function of the third and seventh degrees of the major scale.
While it is true, as noted in another answer, that fa and ti are both found in the very important dominant seventh chord, there are other contexts in which ti is more closely related to mi than to fa. In particular, mi and ti have similar melodic function because they are both a half step below their upper neighbor in the scale. Before the invention of si, an ascending C-major scale would have been solmized ut, re, mi, fa, sol, la, mi, fa.
Indeed, it is this property of the i vowel representing a melodic (upward) leading tone that led to the choice of the same vowel to indicate upward chromatic alteration in di, ri, fi, etc.
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