size category bounds in the half apotome

cmloegcmluin
Posts: 1689
Joined: Tue Feb 11, 2020 3:10 pm
Location: San Francisco, California, USA
Real Name: Douglas Blumeyer (he/him/his)
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size category bounds in the half apotome

Woke up this morning and wanted this diagram. I hope it's valuable to others. Feedback welcome! I just whipped it up in a spreadsheet quickly.

Attachments
size category bounds in the half apotome.jpg

Dave Keenan
Posts: 2092
Joined: Tue Sep 01, 2015 2:59 pm
Location: Brisbane, Queensland, Australia
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Re: size category bounds in the half apotome

That's wonderful! Thank you, Douglas.

I note, for other readers, that this is not something you need to know in order to use Sagittal notation. But it is very helpful in order to follow discussions about Sagittal JI notation, relating to the assignment of commas to symbols. And it has much wider application as a systematic comma naming scheme outside of Sagittal.

For more information on this, see these posts in the topic: "List of 7-prime limit / 6125-odd limit accidentals"
viewtopic.php?p=582#p582
viewtopic.php?p=598#p598

Of course I can immediately think of many other things that could be shown on such a diagram. In decreasing order of importance:
• the title seems wrong, since it shows a full apotome of size categories. Perhaps "size category bounds mirrored about the half apotome".
• a legend showing what the abbreviations stand for.
• cent numbers on the right (from top to bottom) 64, 74, 84, 94, 104, 114 (or perhaps 63.7, 73.7, 83.7, 93.7, 103.7, 113.7).
• perhaps cent numbers every 5 cents instead of every 10 cents.
• a semicircular arrow at the top.
• Continue it to the double-apotome with two more columns and semicircular arrows top and bottom.
• Show marks where the Pythagorean comma and Pythagorean limma fall.
• Show a mark for the single-point "category" of "u" for unison.
• Show the width of each category in cents to one decimal place.
• Show the bounds of each category up to the half-apotome in cents and as a monzo/2.
• Show some alternative names in the legend, such as fifthtone, quartertone, thirdtone, limma, wholetone.

cmloegcmluin
Posts: 1689
Joined: Tue Feb 11, 2020 3:10 pm
Location: San Francisco, California, USA
Real Name: Douglas Blumeyer (he/him/his)
Contact:

Re: size category bounds in the half apotome

Cool. Glad you like the idea. And thank you for contextualizing it for the uninitiated.

A few of your suggestions are things I thought of as well, but didn't want to invest any more time until I'd gotten a general thumbs up. And I agree with all the suggestions. I'll include such a more refined version of this diagram in the educational materials eventually, but not super high priority of course.

Dave Keenan