Talk:Arithmetic tuning

Proposed changes

First, I propose freeing the word arithmetic in the sense of arithmetic-like, and thereby changing:

• Arithmetic tuning to arithmetic-like tuning;
• AFS to EFS (equal frequency sequence), and alternatively as I much prefer, arithmetic sequence, in which case arithmetic means equal frequency;
• APS to EPS (equal pitch sequence), and alternative as I much prefer, equal sequence, in which case pitch is assumed;
• ALS to ELS (equal length sequence), and alternatively as I much prefer, inverse-arithmetic sequence, in which case inverse-arithmetic means equal length.

I don't see a reason why AFS and ALS shouldn't follow the naming convention of EFD and ELD.

Second, I don't believe most of these concepts need "specifications", or at least their use should be discouraged due to the lack of orthogonality. Iow one specification is often encompassed by another, and specifying a tuning system in these ways can be confusing.

For example, AS25/24 is equivalent to 1ed25/24. It's good to keep these concepts and good to know 1ed25/24 is an equal multiplication or ambitonal sequence (in fact they can be defined as 1ed-p), but 1ed25/24 should be its standard identifier.

Similarly, otonal division holds well as a concept, but n-od-p isn't a great way to specify it. It should be specified as n-efd-p i.e. n-ad-p (and mode 12 since that's a distinct naming system). Consider also we've agreed that EFD is now intended to be a generic term and not reserved for irrational tunings.

FloraC (talk) 12:12, 3 March 2023 (UTC)

The reason why "AFS" is used instead of "EFS" is because an arithmetic sequence is an established mathematical concept with a logical name, whereas the name "equal sequence" is neither logical nor established. I have edited the article to clarify this.

For an individual, standardization to something such as exclusively using EDs may be fine, but Paul, Billy, and I designed this system to work for the wider community, a collection of individuals with diverse wants and needs, and I think it's clear that for some people in some circumstances, conceptualizing tunings as sequences will be more intuitive or appropriate.

EFD was never "reserved" for irrational. It should support either irrational or rational. If that’s not clear in an article, please feel free to correct it or point it out to me. --Cmloegcmluin (talk) 16:34, 3 March 2023 (UTC)

Well, that again narrows down to how we use the term arithmetic. Just as I expected, there are geometric progression and harmonic progression besides arithmetic progression aka sequence. I don't find it very cool to only take arithmetic progression without also taking geometric progression – adapted as equal here, and harmonic progression – adapted as inverse-arithmetic here.

I guess you have a fair point at least for an alias of those unity divisions. But still, I believe identifiers like "12odo" should be discouraged due to lack of orthogonality. It's either 12ado aka 12efdo or mode 12.

FloraC (talk) 18:49, 3 March 2023 (UTC)

Our approach was to use only "arithmetic", which we took from Shaahin's existing work. "Geometric sequence" and "harmonic sequence" are unnecessary when instead one is specific about the resource being arithmetically sequenced, i.e. frequency, pitch, or length. I suppose as with most of these xenharmonic theory issues, there's as many ways to approach concepts as there are ways to hear music composed with them.

Sorry I didn't ask for clarity on this earlier, but I still don't understand what you mean by "orthogonality" here. --Cmloegcmluin (talk) 19:06, 3 March 2023 (UTC)

Yes, applying arithmetic sequences on the different scales of measurement is one possible logic. The approach I much prefer is to think of a kind of sequence as indicating the scale of measurement.

I explained the lack of orthogonality as "one specification is often encompassed by another", and so by having orthogonality our specifications would be minimal and disjoint from each other. Note that this is not abouting deprecating the concepts and the names, only how we specify individual tuning systems.

FloraC (talk) 19:43, 3 March 2023 (UTC)

I have made the change re: rational vs. irrational that you explain here.

I note that you posted on Facebook about this idea to change AFS to EFS here: https://www.facebook.com/groups/xenwiki/permalink/3341743592758288 As I expected, Paul (with whom I co-designed the naming system which includes AFS) reiterated the same point I made above, which is that "equal sequence" is insufficient to convey the idea of a sequence which iterates by an equal amount, while "arithmetic" captures that idea exactly and succinctly. Mike Battaglia (who was not involved in the creation of this system, by the way) also noted that "EPS" would suggest a sequence of all the same pitch, not a sequence of changing pitches. --Cmloegcmluin (talk) 23:55, 31 March 2023 (UTC)

The conversation about "orthogonal" moved to Talk:IDO. --Cmloegcmluin (talk) 19:58, 1 April 2023 (UTC)