This may be a little different TOTW. It is a traditional Swedish song, it is a song (even if it is known as an instrumental), it is played very slow, it is more known a piano piece and it has a touch of jazz.
Here is the most famous recording by the jazz pianist Jan Johansson in 1964.
The song is very old. The original title is O Tysta Ensamhet (in English: O Silent Solitude), but is known as Visa från Utanmyra (Tune from Utanmyra) because it origins from the village of Utanmyra (which is located on the island Sollerön in the lake of Siljan. Today Utanmyra has about 100 inhabitants (and has just got broadband connection).
The Swedish Tune Archive has a record from 1907 with the melody and lyrics (it is #55 on the lower half of the first page on http://fmk.musikverket.se/browselarge.php?lang=en&katalogid=Dr+29&bildnr=00024). The lyrics were written by the Swedish poet Olof von Dalin who lived 1708 – 1763. So probably the tune is from the late 1700’s or early 1800’s. In the Tune Archive there are also other melodies to the same lyrics.
The tune became famous in 1964 when the Swedish jazz pianist Jan Johannsson made an album with old traditional Swedish songs. The album is named Jazz På Svenska, which means Jazz in Swedish. However, is not at all ordinary jazz music, but it was a creative and artistic approach to traditional music. All tunes on the album was played by Jan Johansson on grand piano an Georg Riedel on bass. Jan Johansson was a student of technology, but ended his studies just before he was ready, and became a full time jazz pianist. He played with a lot of prominent jazz musicians such as Stan Getz , but he also had a feeling and an interest for traditional music. He made also music of Russian traditional music, and he composed some children’s songs. He was born in 1931 and was killed in a car accident in 1968.
The song is a kind of shepard’s song. In highland areas the farmers used to have a summer resident for the cattle and goats, often located far away. These summer places were called “säter” (mountain pasture). The plots at home was needed for ordinary crops during the summer season, so the cattle and goats were brought to other far pasture places. Usually it was young ladies who took care about the cattle and goats and they had to spend long times alone far from other people (I think they can be like Swedish cowgirls). There are several other "cowgirl" songs in the tradiotinal Swedish music. The song may very well have sounded like this when the girls where watching the cattle.
The tune is based on the melodic A minor scale but with occasional flattened 7th and occasionally raised 4th. The harmonies used is based on Am and E or E7 with occasional additions of B7, C, F6 and G. It is not too advanced harmonies, for a jazz pianist. I found it suits well in sawmill tuning.
I have heard the tune on several different instruments, but not yet on banjo or fiddle:
There is a lead sheet (melody and chords) here.
On this YouTube clip there is a guitar tab:
On this YouTube clip there is music notation for Jan Johansson's piano and Geogre Riedel's bass.
I have made two OT banjo tabs that are posted in the tab archive. I play in sawmill tuning (aEADE) and I prefer to play it slowly and with a bluesy bounce. In the last part of the thumb lead version I play it in double time (it can be played in double time in clawhammer but I have not tabbed it)
Clawhammer (TablEdit, pdf and midi)
Thumb lead ((TablEdit, pdf and midi)
I will add a recording during the weekend I hope. I have a new computer I have have not got the recording functions to work yet 
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