Talk:APS
Periodicity and infiniteness?
By "if not provided, the sequence is open-ended" it seems to suggest that systems in this category are finite and aperiodic when n is provided. By "n-EPD-x = n-APS-(x/n)" it seems to suggest that this tuning system is infinite and periodic just as equal multiplications. Which one is intended? FloraC (talk) 11:17, 4 March 2023 (UTC)
- Great catch. The intention was that they are finite and aperiodic when n is provided. So they are only equivalent to a single period of a EPD. I have corrected accordingly (and the similar statements on the ALS and AFS pages). Thank you. --Cmloegcmluin (talk) 18:28, 28 March 2023 (UTC)
Vagueness in the spec
> "The pitch of the k-th step of an APS-p is quite simply k⋅p."
That implies p must be a pitch relation (i.e. log-frequency relation), such as cents or octaves.
> n-EPD-p = APS(p/n)
That is also true only if p is a pitch relation. I've tried to clarify this matter in the lastest changes.
However, in "APS⁴√2" and "APS1.189" the numbers are frequency ratios. Using pitches it should be APS(300 ¢), APS(1/4 oct), or APS(1\4). I think there are two ways to specify the tuning, one by frequency ratio, the other by pitch relations. It can work without confusion, cuz obviously frequency ratio is dimensionless, whereas pitch relations never go without a unit.
FloraC (talk) 10:45, 14 October 2023 (UTC)
- Oh dang, good catch! I clearly wasn't paying careful enough attention to what I was doing when I wrote this page back then. I suppose if even I found myself specifying APS by frequency ratios, I should imagine that others in the wild will do this too. And I see your point that because of the presence or absence of units, there is no ambiguity caused by allowing both. But yes, we'd need to acknowledge this in the page. I support it. Feel free to make the changes yourself, or if you'd rather I take care of it, I'm happy to. --Cmloegcmluin (talk) 17:20, 17 October 2023 (UTC)
How to use the example table
I'm much confused by the table in the "examples" section. The first row is labeled "frequency (f)", whose entries are 1, 1.19, 1.41, 1.68, 2, and that's perfectly clear to me. Now the second row is labeled "pitch (log2f)", and the entries, in terms of contents, are identical to those in the first row. So I wondered, maybe these are the f which should be plugged to log2f? That gives you the correct pitch relations. But interpreting them this way leads to inconsistent results in the third row. The entries in this row are 1, 0.84, 0.71, 0.59, 0.5, which are clearly lengths, and not meant to be the f as is plugged to 1/f.
I suggest the following changes:
- frequency → frequency ratio
- pitch → size
- length → length ratio
And then the "size" row can show the pitch relations, that is, 0/4 oct, 1/4 oct, 2/4 oct, 3/4 oct, 4/4 oct.
FloraC (talk) 11:00, 14 October 2023 (UTC)
- Yikes. I screwed up the middle row of this table. If I had done it correctly and consistently with how I did the tables on all the other arithmetic tuning pages (OD, EFD, OS, AFS, EPD, AS, UD, ELD, US, ALS), that row would simply be 0/4, 1/4, 2/4, 3/4, 4/4. So I've made that change already. Thanks for catching that.
- I prefer the simplicity of frequency/pitch/length which are fundamentals of this naming system, i.e. I'd rather not introduce the term "size" here. But the point you've raised about how pitch requires units while frequency and length do not (being ratios of whichever unit to the same unit, canceling out) is very compelling. So I suggest something like this:
- frequency → frequency (ratio)
- pitch → pitch (octaves)
- length → length (ratio)
- One advantage of this is that we consolidate the units into the row headers, rather than putting 'oct' into each cell of that row, which would clutter it. What do you think? If you agree, I volunteer to make the changes across all the tables, since that will be pretty tedious, and it's a problem I created in the first place. --Cmloegcmluin (talk) 17:20, 17 October 2023 (UTC)
- Wunderbar. It's done. --Cmloegcmluin (talk) 20:37, 19 October 2023 (UTC)