What is the origin of the gojuuon kana ordering?

1.1.5. What is the origin of the gojuuon kana ordering?

The gojuuon order

		K	S	T	N	H	M	Y	R	W
A	あ	か	さ	た	な	は	ま	や	ら	わ
I	い	き	し	ち	に	ひ	み	¹	り	ゐ³
U	う	く	す	つ	ぬ	ふ	む	ゆ	る	²
E	え	け	せ	て	ね	へ	め	¹	れ	ゑ³
O	お	こ	そ	と	の	ほ	も	よ	ろ	を

There is no kana for "ye" or "yi".
See 1.1.2. Is there a kana symbol for ye or yi?
There is no kana for "wu".
The "we" and "wi" kana are seldom used.
See 1.1.3. What is the use of the "we" and "wi" kana?

There are two ways in which the hiragana and katakana are commonly ordered. One is the gojuuon ordering, and the other is the iroha ordering. Gojuu (五十) means `fifty', and on (音) means `sound', so gojuuon (五十音) means `fifty sound' ordering. The gojuuon ordering is the one that most learners of Japanese will encounter first. For details of the iroha ordering, see 1.1.6. How does the i-ro-ha ordering go?.

The gojuuon is not a modern invention. The earliest example of a gojuuon-style layout dates from the period 1004-1028. The earliest example of the iroha ordering is from 1079.

The gojuuon order of the consonants in kana originates from the consonant order of Sanskrit.

R.A. Miller, in The Japanese Language, page 128, states

"The Indic order of listing phonemes as found in the arrangement of this so-called 'siddha-m.' script, as well as in all the Indic writing systems, arranges the consonants in the following order: k, kh, g, gh, n~, c, ch, j, jh, t., t.h, d., d.h, n., t, th, d, dh, p, ph, b, bh, m, y, r, l, v, s', s., s, and h. ... Here the juxtaposition of modern 'h', Old Japanese 'F', with Indic 'p' is interesting and significant; the only other point which needs particular comment is the location of modern Japanese 's' following 'k'. This is easily understood since modern Japanese 's' goes back to the Old Japanese affricate phoneme /ts/ which had an allophone [ts] before Old Japanese /a, u. o, o''/ and an allophone [s] before /i, e/." (The ., ~, '', and ' refer to diacritics.)

Acknowledgements

This answer used information from a post by Kouji Ueshiba.

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1.1.5. What is the origin of the gojuuon kana ordering?

The gojuuon order

Acknowledgements