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Biwa as pantheon
In his Biwa hōshi, Hyōdō Hiromi 兵藤裕己 quotes Fukishima Junkai 福貴島順海 of Kagoshima on "the interpretation [or buddhas] of the biwa" (琵琶の釈):
如是衆妙音琵琶、即ち世界大五行般若の体、四つの緒は四節、撥は土用なり。弾ずる声は十方諸々の国土に響く。諸仏神のましませば、この家の地神を祭るに、妙音薩埵愛染の法となる。
The "with-many-wondrous-sounds-as-these" biwa is the five world-element prajñā body; the four strings are the four seasons [associated with Wood (Spring), Fire (Summer), Metal (Autumn), and Water (Winter)], the pick is the Earth [that makes them turn]. The voice, once plucked, reverberates across the land in all directions. The myriad buddhas and gods are present within it, making the biwa the method most beloved by the Boddhisattva "Miraculous Sound" 妙音菩薩 for paying homage to house gods.
Or does that "愛染" refer to Rāgarāja a.k.a. Aizen Myō-ō 愛染明王?
Anyway, what does he mean by "the myriad buddhas and gods are present within it"? (諸仏神のましませば — actually now that I think of it maybe that's 仏神 as in just plain buddhas, who are like unto gods.) Well, it turns out that the various parts of the biwa are associated with bits and pieces of the Buddhiverse.
抑々、頂は須弥山と名づく。反手さとうはちまんを学ぶ。だいはつは下界とす、四つの転手は四天王、承弦は大地諸仏、六つの柱は六観音、の口は釈迦牟尼仏如来、腹うのかたは天象を形取り、中にも忍柱たていわなはせんえと交わす、ひょうしょう落帯は無量寿如来、遠山は不動明王、石突は毘盧遮那仏、陰月はほうじゅんにょらい、つつは薬師の十二神、覆手は栴檀こうおう仏、撥は普賢文殊の王よ号す。半月は日月を学び請じ奉る。
Now, the head of the biwa is called Sumeru. The pegbox learns [derives?] from Satō Hachiman [?]. The daihatsu [?] is our [human] world, the four pegs are the Four Heavenly Kings, the nut is the various buddhas of the earth, the six frets are the six forms of Kannon, the kyō no kuchi [??] is Sakyamuni...
I'm going to give up there. I think that the gist is pretty clear, I'm at a distinct loss not knowing anything more than you could find in a standard reference book about biwa construction, Kagoshima dialect, or regional/chronological variations on the "official" names of Buddhist entities.
For example, what is the daihatsu? And: "Satō Hachiman"? Really? Maybe satō is an adverbial form of satoi? Or sa is a particle? I thought that was a Tōhoku thing.
Avery:
Here's my lame attempt to be helpful: 栴檀こうおう = 栴檀香王 = sandalwood Gandharaja ~= 香王菩薩
"栴檀仏というのは、昔、釈迦がこの世にあったとき、インドの優填王が栴檀（せんだん--中国語では「旃檀」 ただし、これは香木のビャクダンをいう）の木で釈迦の形を作ったことに由来している。この形が、立像で左手を下げ、右手を上げて、いずれも手のひらを表にする、いわゆる与願（よがん）、施無畏（せむい）の印相を持っているところから、その後、この形で作った釈迦像を栴檀仏と呼ぶようになったものである。"
I can't really further elucidate on this yamabushi-esque esoteric exposition of the biwa, but I would like to add an irrelevant comment about biwas, because it weighs heavy on my soul. I was reading the Japanese Wikipedia article on 三種の神器 recently and noticed a link to 絃上 in the "See also" section. Apparently 絃上 was the name of a biwa handed down from Emperor Murakami which was part of the Imperial regalia in the Middle Ages. Or maybe this is just a story that some medieval Noh director made up. The Internet failed to elucidate this for me, which is surprising because I thought people would go nuts over extra Imperial regalia.