Going from Bulgarian to Turkish (Türkçe) has a composite linguistic distance of 93% (curated lexical data). Below is the dimension-by-dimension breakdown.
Shared vocabulary, cognates, and loanwords.
Morphology, syntax, word order, cases.
Shared sounds and phoneme inventory.
Cyrillic → Latin
Indo-European ↔ Turkic
The 5 languages with the lowest linguistic distance from Bulgarian:
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