User talk:CompactStar/Arithmetic MOS scale

How does this work?

Since there are currently no explanations other than the definition, I'm trying to understand whether this concept holds itself together logically or not. So far, I'm left wondering how one would deal with scale rotations (aka modes). For example, with the diatonic scale, you can have Ionian mode LLsLLLs, Aeolian mode LsLLsLL, etc. and the MOS properties are true for all of these modes. However, with an "arithmetic MOS scale", let's say 12:14:16:17:19:21:23:24 to keep the comparison simple, you'll encounter problems when you move to another mode. If this was "Ionian" and you moved to "Aeolian", then the new scale would be 21:23:24:28:32:34:38:42. There are now differences of sizes 1, 2 and 4 in this new scale, so it's no longer an arithmetic MOS by definition. This is just an example, but I'm questioning overall how useful of a generalization this is if you lose important properties such as this one relative to rotations, especially if you use the term "MOS" which carries a lot of assumptions with it. --Fredg999 (talk) 01:52, 22 March 2023 (UTC)

Agreed with all above. —-Cmloegcmluin (talk) 03:48, 22 March 2023 (UTC)

There's also the issue that if "arithmetic" is interpreted as it was used for ADO as originally defined by Shaahin Mohajeri — which was propagated in the arithmetic sequences of the arithmetic tuning systems catalogued by myself, Paul Erlich, and Billy Stiltner back in 2021 — then this is a contradictory name. This is because Shaahin used "arithmetic" as a reference to "arithmetic progressions" which are those where each next entry is found by repeatedly adding the same amount. In our application this amount could be of frequency, pitch, or length (of string or resonating chamber, etc.) (note that Shaahin assumed frequency in his usage). Because MOS involves adding two different amounts, however, "arithmetic MOS" is a contradiction in terms. I understand that Flora has been using "arithmetic" under an alternative interpretation, referring to the arithmetic mean, as a way to adapt pitch-based concepts to frequency-based concepts, and under this interpretation there is no self-contradiction, however, the original intention and established usage can not be ignored, and they make this extension confusing and problematic. --Cmloegcmluin (talk) 18:16, 22 March 2023 (UTC)

An alternative name for this concept which would not be problematic in this way would be a "frequency-based moment of symmetry" or FMOS. Similarly, you'd have a LMOS for length-based. But I'm still concerned about the use of "MOS" at all for this, per the concerns Fredg999 expressed above. --Cmloegcmluin (talk) 18:57, 23 March 2023 (UTC)

I suggest that since this way of using "arithmetic" is contentious, this page (along with Arithmetic interval chain) should be withdrawn from the main wiki and changed to user pages. See ADO#History for more information. --Cmloegcmluin (talk) 18:35, 30 March 2023 (UTC)