Which is True?

Which moral(s) is the reason behind the koto having 13 strings?
They took 12 strings from the number of months in a year and one more from the leap year to make it 13 strings.
An instrument called Shitsu had 25 strings yet since the father wanted to split the instrument between his 2 daughters, one received a 13 stringed instrument and the other received the 12 string instrument. Historians say that the 13 stringed koto was then brought into Japan and the 12 stringed was brought to Korea.
13 was the inventors favourite number so they chose to put 13 strings.
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