Talk:3L 4s

Tuning ranges incomplete?

Is there any particular reason the "tuning ranges" ("ultrasoft", "quasisoft" etc.) don't completely cover the range? Like where does a 351 cent generator fall? —Keenan Pepper (talk) 22:18, 19 April 2021 (UTC)

It seems to only cover ranges that are "notable". A 351 cent generator would fall in the parasoft range. This range likely isn't covered because the fifth isn't good for meantone or archy. This range includes optimal neutral tunings, but the simplest good extension of it is hemififths, which doesn't even contain simple intervals of 5 and 7 in the 3L 4s MOS, so whether it should be included or not is debateable. --Overthink (talk) 22:11, 24 October 2025 (UTC)

Intervals of 11 vs 13

I wonder if there would be a noticeable difference between a piece in 3L 4s played in 17edo compared to 24edo. Many of the intervals in 17edo are closer to simple 2.3.13 ratios than 2.3.11 ones, while in 24edo the intervals are closer to simple 2.3.11 ratios than 2.3.13 ones, so they may have different flavors. However, the neutral third itself is ambiguously between 11/9 and 16/13 in 17edo, while it is much closer to 11/9 in 24edo. Also, since the temperament tempering out 512/507 is less accurate than the one tempering out 243/242, the 17edo version may be less consonant.--Overthink (talk) 22:17, 24 October 2025 (UTC)