Samaveda is the Veda of melodies and chants. It's verses are primarily derived from Rigveda (which is believed to be oldest/first and important veda from all). It includes many mysterious verses which indicates the knowledge of ultimate & absolute truth. (The most important & widely studied Chandogya Upanishad also comes from Samaveda.) Singing and listening these verse musically, It (comparatively) more effects the influences of devotion and spirituality. So, due to such importance/significance of Samaveda, Lord Krishna says He is Sama Veda among Vedas.
From Jnaneshvari BhagvadGeeta :
Where sentence in rectangle is similar to that of emphasized text in above explanation.
We know that realization of God is essential to attain the God; Singing can give the feeling which help us lead to the realization. (Quoting verse from Rigveda which are mentioned by Gayatri Pariwar)
अभि स्वरन्ति बहवो मनीषिणो राजानमस्य भुवनस्य निंसते ॥३॥
Full many a wise man lifts to thee the song of praise, and hails thee with a kiss as Sovran of this world.
स्वरन्ति त्वा सुते नरो वसो निरेक उक्थिनः ।
कदा सुतं तृषाण ओक आ गम इन्द्र स्वब्दीव वंसगः ॥२॥
2 Men, Vasu! by the Soma, with lauds call thee to the foremost place:
When comest thou athirst unto the juice as home, O Indra, like a bellowing bull?