The table below presents the differences between the more common transcription systems of Old Japanese with regard to vowels and voiced consonants. Additionally, the voiceless bilabial consonant is variously written as p, f, F (also φ, ɸ).
The indices ₁ and ₂ correspond to the Japanese use of kō 甲 and otsu 乙, respectively; sometimes the digits are replaced with the letters A and B, and sometimes superscripts are used instead of subscripts. Japanese hei 丙 or the letter C are seldom employed to mark the undifferentiated vowels.
The “traditional” system is often associated with Ōno Susumu 大野晋, author of many publications on Old Japanese and co-editor of the Iwanami kogo jiten 岩波古語辞典 (revised and enlarged edition of 1990), where the system is used.
The transcription named after Gerald B. Mathias and Roy Andrew Miller went through several stages, and its final version has only evolved gradually over the years.
For the system developed by Bjarke Frellesvig and John Whitman, see the 2008 book edited by them: Proto-Japanese – Issues and prospects (where also other common transcriptions are presented in the introduction).
The so-called Yale transcription goes back to Samuel E. Martin (cf his The Japanese language through time, 1987).
The systems used by Alexander Vovin changed over time; they are laid out in the first volume of Vovin’s A descriptive and comparative grammar of Western Old Japanese (two editions: 2005 and 2020), and used in his translation of the Man’yōshū (ten volumes out of twenty, published between 2009 and 2021).