Chakra nature of Tailed Beasts As we all know that Kurama's chakra is of the healing nature type. This is known from many mentions about it in the wiki page of Naruto Uzumaki.

My question is, what is the nature type of the chakra of the other Tailed beasts?

Note: This is my thinking why there should have been a nature type to each of the tailed beasts. 

As we all know that when Rikudō Sennin was about to die, he split his powers among his two sons (the older son inherited his powerful chakra and spiritual energy, and the younger son inherited his powerful life force and physical energy). Similarly, when creating the nine tailed beasts from the Shinju, he must have split the chakra based on their nature so that each tailed beast had a unique natured chakra.

Any insight on this would be very much welcomed.
A few facts first:


Kurama's chakra isn't healing type. Minato sealed Yang-Kurama in Naruto, which resulted in the chakra Kurama gave him to be Yang oriented. This adds the healing properties to that chakra.
Not all tailed beasts have a known nature, but some do.


So the natures:


Shukaku - Wind, evident by the Drilling Air Bullet he fired at Gamabunta.
Matatabi - Fire, evident by the fireball she fired at Hidan and Kakuzu when they battled her.
Isobu - Water, obvious.
Son Goku - Lava (Earth and Fire), evident by multiple lava techniques reanimated Roshi used while in Jinchuuriki form.
Kokuo - Not revealed. His Jinchuuriki was said to use the Steam element (Fire and Water)
Saiken - Not revealed. His Jinchuuriki uses Water element and specializes in bubbles. Saiken himself was shown to be able to spit acid.
Chomei - Not revealed. Not much was revealed about its Jinchuuriki too.
Gyuuki - Not revealed, but presumed Lightning. His Jinchuuriki uses Lightning.
Kurama - Not revealed, but presumed Yin-Yang. His Jinchuuriki was shown to have remarkable stamina and healing properties, which suggest Yang nature which is compatible with the half of Kurama he had. The other half's chakra was not explained thoroughly.
Last but not least


   Shinju (God Tree; Juubi) - Natural Energy and Yin-Yang. Evident by the techniques Obito uses after becoming its Jinchuuriki, as well as what was revealed in the manga.