Kagaku' means handing down their academic skills within the family or the clan.
Handing down skills and learning by 'Seshu' (hereditary) within the clan was a phenomenon seen among Japanese clans before the Yamato period, but under the Ritsuryo system (a system of centralized government based on the ritsuryo code) these customs were abolished and the education system at public institutions such as Daigakuryo (Bureau of Education), Tenyakuryo (the Bureau of Medicine), and Onmyoryo (Bureau of Divination) was adopted.
But, because of stockpiling valuable books in the instructors' (hakase's) house which their younger brothers or children could have more time to read at their younger ages and the instructors, the older brothers or father, used in their family education, their younger brother or children also came to assume the same government position as their older brothers' or fathers' if they were excellent at the skill. But in case of Seshu, they could not take over the government position until the specialized skill of each clan was handed down to them through generations, so there was a possibility of losing it unless they were skilled enough even though they were from the family line that had been in the government position for generations. That was the reason why in ancient times there were such family lines that had succeeded to the position of the hakase for generations, but failed in the end.
However, in the midst of Heian period, as hereditary government office system developed and the government post, regarded as a kind of interest, became taken over by heredity, particular clans ('hakase family') that took up the post of instructors by heredity emerged. In Myogyodo (the study of Confucian classics) and Kidendo (Literature), based upon their own interpretations, the Sugawara clan, the Oe clan, and the Kiyohara clan, and so on differently inserted 'okototen' used as markings for reading Chinese classics (kuntenho), which they made their family's theory used to teach their children or students. The same phenomena took place in other fields, and in order to take up the position of hakase by heredityparticular hakase families developed the learning itself into 'kagaku' inherited within the clan by making their family's theory esoteric and mystified, and by giving it authority and unequivocalness.
Major examples are follows:
Kidendo: The Sugawara clan, the Oe clan, and the Fujiwara clan (Hino school)
Myogyodo: The Nakahara clan and the Kiyohara clan
The Hakase family of Myogyodo almost unified it into hereditary learning as Shodo (calligraphy) (Daigakuryo) and Ondo (study of pronunciation of Chinese language).
Myobodo (study of Codes): The Koremune clan, later the Sakanoue clan and the Nakahara clan
Sando (study of mathematics): The Iehara clan, later the Miyoshi clan and the Ozuki clan
Onmyodo (way of Yin and Yang; occult divination system based on the Taoist theory of the five elements): The Abe clan
Tenmondo (astrology) and Rekido (the study of the calendar): The Kamo clan
Ido (The way of medical science): The Wake clan and the Tanba clan
Waka poetry: The Fujiwara clan (the Mikohidari school)
Also, there was a clan like the Mijkohidari school that split into two groups about the interpretation and each handed down different kagaku. Furthermore in some cases kagaku was so closed, it was transmitted only to a single pupil while in other cases it utilized a system whereby the head family was supported by having many pupils. And yet, before the Ritsuryo system and in early Seshu the competence of successors also mattered, but as hereditary was established, the competence became less related to qualification of the successors.
In the medieval period when Shisho (the Four Books of Confucianism) became valued under the influence of the Sung Study (Neo-Confucian), 'Myogyodo shisho' was newly established in Myogyodo, and in defiance of this, okototen called Gakkoten was set up to maintain the prerogative in learning in the Ashikaga School.
In the late medieval period an idea came about that 'kagaku' was consequently upheld even when it was inherited, not by relatives, but by pupils who were committed to the doctrine with a view to giving priority to the inheritance of 'kagaku' itself, as represented as follows ("Fushikaden" [The Flowering Spirit] Besshi Kuden [a separate secret teaching] written by Zeami).
The secrets of the art of our family are to be transmitted from the family to one person of another family.'
It must not be transmitted, even to a child, who is not eligible for it.'
The family should not be called so, until it is inherited by somebody.'
In this process, the 'iemoto' system (the system of licensing the teaching of a traditional Japanese art) came to be established to hand down kagaku by replacing master-pupil relationship by family relationships. While the iemoto system enhanced the authority of the head family of the iemoto, because the role of the family head changed into the one ruling kagaku through issuing a license to the pupils, the family head also assumed the role in hiding the successor who was not competent even though some family heads themselves were not competent to the iemoto.