What is the origin of Indian music? I've heard that music is derived from "Samaveda".
Is it right? If yes, then what type of music is mentioned in Samaveda?
Yes, Indian Music originated from the Sama Veda. This is a very prominent view of many, and is accepted by everyone who learns Carnatic Music.
The Rig Veda and Yajur Veda mainly use only three notes which correspond to modern Shadja, Rishabha and Nishada, with the occasional Gandhara svara.
But the Samaveda is sung with all seven svaras (which include in addition to the above four, Madhyama, Panchama and Dhaivata). The way Samaveda is sung resembles to an extent the scale of Raga Kharaharapriya, a major Raga in Carnatic Music, which corresponds to the Kafi Thaat of Hindusthani Music.
Almost all composers in Carnatic Music refer to music as originating from the Samaveda. Prominent among them are the Musical Trinity of Muttusvami Dikshitar, Shyama Shastri and Tyagaraja. Saint Tyagaraja has dedicated many songs to the glory of Music, and in one of his songs, titled 'Nada tanum Anisham Shankaram', (or, 'Lord Shiva, the Embodiment of Music), he proclaims,
Modakara Nigamottama Samaveda Saaram Vaaram Vaaram (Nada Tanumanisham)
"(I repeatedly worship the embodiment of music), which was born from the Samaveda, the foremost of Vedas."
He also says in another Kriti, 'Shobhillu Saptasvara', (or, 'The Seven Svaras Shine Brightly'),
Dhara Rig Samadulalo Vara Gayatri Hrdayamuna
"(The Seven Svaras shine), in the Vedas headed by the Rig and Sama Vedas, as well as in the core of the sacred Gayatri Mantra (or, in the sacred Gayatri Hridaya)".
In yet another song, 'Vidulaku Mrokkeda', (or, 'I salute the maestroes of Music'), he says
Mudamuna Shankara Krita Sama Nigama Vidulaku Nadatmaka Saptasvara (Vidulaku)
"(I salute the maestroes) who are aware of the knowledge of the seven notes, the embodiment of Music, found in the Samaveda, which was originated from Lord Shiva (as the embodiment of Music)."
Thus, we can understand that Indian Music has originated from the Sacred Sama Veda.
I heard during a lecture sometime ago that carnatic music has its roots in Sama veda. Also sama veda is considered to be the melodious among all vedas. The shloka included along with the Bhagwat gita text on one of the lines reads "vedaisaanga padakramopanishadaihi gaayanthi yam saamagaaha". Saamagas actual chant the mantras of the sama veda. But here the vedas are referred to in general but the reference to saamaveda us due to its melody. I think Krishna also makes a similar reference in the Bhagwat gita. But I do not know the correct verse from the top of my head.
I am not sure if Sama Veda goes into 'types of music'.
The Sama Veda has a lot of chants and melodious rhythmic shlokas. Some of the audio can be found here.
Also, it talks about Swaras and musical notes etc. This page mentions multiples documents relating to this context which are available for download.