Solfège
Syllables that name each scale degree for singing
Solfège assigns a spoken syllable to each scale degree, enabling you to more easily sing melodies using such a root-relative system. For example, a melody like 1 ♭3 5 ♭7 becomes do me so te. So, the purpose of solfège is to better allow you to connect these systems with your voice. The trade-off is that it doesn't express certain relationships as simply as the number system.
Like the degrees themselves, the syllables are built on the major scale: do, re, mi, fa, so, la, ti are degrees 1 through 7, and a lowered degree is formed by a regular vowel change — mi becomes me, la becomes le, ti becomes te. So a flat follows from its major-scale parent much as its number does: once you know the 7th is ti, the ♭7 is te.
Weighed against the bare numbers, solfège's strength is the voice — a syllable is easier to sing than a spoken number, the natural tool for carrying degrees onto a melody. Its cost is mild: the base syllables and the vowel rule have to be learned up front, and they can't be reasoned about arithmetically the way numbers can. Once known, though, the system is regular — so the two are best used together: numbers to reason with, syllables to sing.