Talk:352/351

13/11-kleisma

How can this name be derived that it's called fairly intuitive? Please help me understand! --Xenwolf (talk) 08:26, 28 September 2020 (UTC)

Fact 1: 352/351 = (32/27)/(13/11). This says it is how much 13/11 deviates from a Pythagorean interval, hence "13/11-kleisma".

Fact 2: 352/351 = (1053/1024)/(33/32). This says it is the difference between the tridecimal quartertone and undecimal quartertone, hence "13/11-kleisma".

The reason why it's of significance is that there's a dedicated symbol for 352/351~5120/5103 in sagittal notation, and this is how they call it. FloraC (talk) 08:48, 28 September 2020 (UTC)

Needs to be made clear for future. It should be "11/13-kleisma" as 11 is in the numerator and 13 is in the denominator. FloraC (talk) 09:57, 26 November 2020 (UTC)

Is 352/351~5120/5103 the official notation for tempering out the interval between the both explicitly given intervals? I also read = instead some days ago. Both seem quite intuitive, the equals sign is catchier but also more challenging from the mathematical POV. --Xenwolf (talk) 10:10, 26 November 2020 (UTC)

I like the first form, but I have no idea how I learned it (it doesn't show up in official materials of Sagittal notation). The tilde is more commonly accepted to be used like this: 5120/5103 ~5.758¢, where it means "approximately". FloraC (talk) 11:48, 26 November 2020 (UTC)

I hope the new sagittal notation section adequately addresses the original question. Dave Keenan (talk) 13:20, 9 October 2024 (UTC)

Right, but now I wonder if something has recently changed. Since when did the downward version become the "main" Sagittal accidental? FloraC (talk) 14:46, 9 October 2024 (UTC)

No, nothing has changed in that respect. I wonder how you got that impression. I recently added a bunch of new sections to comma pages about their use in Sagittal. Maybe you only happened to see the ones where the sagittal was pointing downward? This happens about half of the time, because it's more important for the comma's 2,3-free form to be superunison than it is for the comma itself. So in this case, when speaking of the 13/11k, we look at the ratio 351/352 = (13 * 3³) / (11 * 2⁵). It also happens this way for the 5C, because it's the 80/81 form where the 5 is in the numerator. But if you look at the 11M, for an example of the other type, it's the 33/32 form where both the 2,3-form and the comma itself are super together, when the 11 is in the numerator and 33 > 32.

Ah, but I see that Dave heard your concern too and already went around to all the pages we worked on already and added the other sagittal direction. Hope these together help to clarify. --Cmloegcmluin (talk) 15:37, 9 October 2024 (UTC)