# Talk:Generator-offset property

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# Billiard scale

What is a billiard scale? Mike Battaglia (talk) 00:28, 28 May 2022 (UTC)

- See this definition. (I think the definition is the right one possibly modulo a subtlety.) I'd of course also have to justify why SGA scales are billiard scales and thus EMOS. Inthar (talk) 02:03, 28 May 2022 (UTC)
- Interesting - also possibly related: https://en.wikipedia.org/wiki/Bresenham%27s_line_algorithm Mike Battaglia (talk) 02:26, 28 May 2022 (UTC)

## Error In Part 3 Of the Definition

I don't want to be presumptuous, as am only just now learning about GOs and so forth, but I believe there is an error in part 3 of the definition in the opening section. Specifically, in a GO "[t]he lengths of the chains differ by at most one" yet also, in the summary of parts 1-3, the only claim made about the lengths of the chains is that they "do not necessarily take up the same number of steps" which does not seem to imply that it can be only 0 or 1. So, which one is it? Or is it neither? Or are they actually just the same, in which, can the definitions be made more clear? Thank you.

AjaxDirtWormton (talk) 03:19, 2 January 2023 (UTC)

- I meant that one alternant a
_{1}does not necessarily occur as the same number of steps as a_{2}. This is the case in 5-limit blackdye, where the alternants are 10/9 (a 1-step interval) and 6/5 (a 3-step interval). Thanks for notifying me of the problematic wording; I clarified it. Inthar (talk) 03:39, 15 February 2023 (UTC)