The Sagittal Xenharmonikôn article updated

[Dave Keenan]

I have, at long last, updated the Sagittal Xenharmonikôn article at https://sagittal.org/sagittal.pdf. The most significant changes are the improvements to the standard notations for the EDOs with bad fifths in Figures 8 & 9 on pages 16 & 17, as agreed with George Secor, and as shown in the Periodic Table of EDOs since November 2019.

[Dave Keenan]

I made a very minor correction to the Sagittal Xenharmonikôn article at https://sagittal.org/sagittal.pdf. In footnote 20 on page 25 I changed "130-EDO uses the entire 'Spartan' symbol set" to "130-EDO uses almost the entire 'Spartan' symbol set".

[Dave Keenan]

A minor improvement: On 2024 Aug 29 I added three occurrences of "(TBD)", short for "(to be determined)", in Figures 8 and 9 on pages 16 and 17, so they now read:
"or 45 notated as a subset of 135 (TBD)"
"or 64 as a subset of 128 (TBD)"
"or 49 notated as a subset of 147 (TBD)"

This is to save readers from wasting their time looking for these notations in the paper. This issue was raised by Roee Sinai over a year ago, here: viewtopic.php?t=562, but Douglas recently made me realise that my solution back then was less than ideal.

[Dave Keenan]

I updated the notation that 68-EDO and 75-EDO have in common in Fig 9 on page 17 of the XH article.
https://sagittal.org/sagittal.pdf

The first symbol changed from to and consequently its apotome complement changed from to  .

This is because as the 7-comma has a lower prime limit than as the 55-comma. was not used previously because it made bad flag arithmetic with and  , but was replaced with in 2019 prior to the publication of the Periodic Table. We only just realised this made the flag arithmetic problem go away.

[Dave Keenan]

I updated https://sagittal.org/sagittal.pdf to replace all the tildes ~ whose intended meaning was "approximately" with approximately equals signs ≈, because tilde should be reserved to mean "tempered". See https://en.xen.wiki/w/~