U+1D000 Byzantine Musical Symbol Psili

The Wikipedia has the following information about this codepoint:

The smooth breathing (Ancient Greek: ψιλὸν πνεῦμα, romanized: psilòn pneûma; Greek: ψιλή psilí; Latin: spiritus lenis) is a diacritical mark used in polytonic orthography. In Ancient Greek, it marks the absence of the voiceless glottal fricative /h/ from the beginning of a word.

Some authorities have interpreted it as representing a glottal stop, but a final vowel at the end of a word is regularly elided (removed) when the following word starts with a vowel and elision would not happen if the second word began with a glottal stop (or any other form of stop consonant). In his Vox Graeca, W. Sidney Allen accordingly regards the glottal stop interpretation as "highly improbable".

The smooth breathing mark ( ᾿ ) is written as on top of one initial vowel, on top of the second vowel of a diphthong or to the left of a capital and also, in certain editions, on the first of a pair of rhos. It did not occur on an initial upsilon, which always has rough breathing (thus the early name ὕ hy, rather than ὔ y) except in certain pre-Koine dialects which had lost aspiration much earlier.

The smooth breathing was kept in the traditional polytonic orthography even after the /h/ sound had disappeared from the language in Hellenistic times. It has been dropped in the modern monotonic orthography.