The web page on Scale and Temperament by Justin Senryū contains extensive discussion of Japanese temperaments and tunings, including relationships to 12-TET. In particular, he writes (about his own adaptation of the system)
The following chart shows Akebono Chōshi in Adjusted 12TET, and in Senryū I by the number of cents difference from standard 12TET, and for Senryū I also showing the ratio (please read up on Just Intonation if this doesn’t make sense), which represents the note’s natural relationship to the mother note, in this case ...
(c) 2020 by Justin Senryū. Used by kind permission of the author.
Note that the chart applies specifically to "shakuhachi honkyoku [music] and Edo period shakuhachi ensemble music", but would not necessarily apply to other instruments.1 Further,
we transpose that one scale into various keys. The chart of mine that you are using, presents that scale in 'akebono key' (akebono chōshi). The same scale is also played in other keys - hon chōshi, kumoi chōshi etc, for which everything in the chart would remain unchanged except for the far left column, which are the tablature-style kana that we use for shakuhachi notation.2
1Email communication. October 7, 2020.
In "The Role of Tone-colour in Japanese Shakuhachi Music", Nick Bellando and Bruno Deschênes mention Akebono:
The “modes” are simply transpositions of a single scale to different starting points on the flute. Because of the transposition and the physical limitations of the flute, however, pieces composed in different modes tend to have a unique
intervallic interplay, taking on a gradiantly brighter or darker feel, which is expressed in the names of some modes (akebono, meaning daybreak, or yugure, meaning twilight). Tokita notes that the terms “mode” and “scale” are often used interchangeably in Japanese music. (page 55)
Earlier in the paper, they explain that early Shakuhachi were constructed with evenly spaced finger holes, rather than attempting to adhere to a set of precisely tuned harmonic ratios. This evolved over time, so that more precise tuning came into vogue.
Almost all shakuhachi made during the Edo era ... used finger hole position calculation methods termed towari or kyu-han wari (literally “divided by ten” or “divided by 9.5”) wherein the spacing between each of the four finger holes on the front of the flute is set at 1/10 or 1/9.5 of the total length of the flute. The result is ergonomically pleasing, but the notes are not precisely in tune according to a scale or a mode. Rather, some are a bit low, others are a bit high, and due to the natural bore shape, octaves are slightly off. The assumption is that the tones will be adjusted with the breath, according to the player’s aims.
In the Meiji era (1868-1912), after Japan opened itself to Western influence, musical values began to shift in a more pronounced fashion. ... [Since, due to technological development, instrument construction was] no longer subject to the variety in natural bamboo bore diameters and textures, they can also be more precisely tuned. ... Each shakuhachi would be more precisely in tune with Western pitches.... The goal in the modern construction style is to produce a beautiful and tuned sound for the sake of entertainment, even in honkyoku playing, which means that factors like pitch-precision ... become more important. (pages 46-47)