## Does Trojan use valid commas?

Dave Keenan
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### Does Trojan use valid commas?

The file sag_12R.par tells us the following. I've shown secondary commas in red.

Lower bound	Symbol	Ratio		Name	Most common semitone fraction
-------------	------	-----------	----	-----------------------------
-3.99999999		1/1			0
3.99999999		4131/4096	17C	1/12
9.090909101		41553/40960	5:19C	1/10
11.99999999		81/80		5C	1/6
16.66666668		3645/3584	5:7C	1/5 (5:7C is  and not a valid secondary comma for  )
22.22222223		2048/2025	25C	1/4 (25C is  and not a valid secondary comma for  )
28.57142856		64/63		7C	1/3
33.33333334		55/54		55C	3/8
38.88888888		46/45		5:23S	2/5
42.85714285		36/35		35M	4/9
48.00000001		33/32		11M	1/2
51.99999999		8505/8192	35L	5/8
57.14285715

To my horror, I find that Trojan is using secondary commas that are no longer valid (if they ever were), as you can see here: http://sagittal.org/SagittalJI.gif

Here are some spreadsheets I used in designing the Trojan notation.
Attachments
12N+-7 SymbolDegrees.xls
12R Boundaries - 240-EDO.xls
12R Trojan Boundaries.xls

cmloegcmluin
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Real Name: Douglas Blumeyer (he/him/his)
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### Re: Does Trojan use valid commas?

Oh my!
Nice catch.

I can't believe I didn't notice those columns when checking over the .par files... I suppose I was too busy focusing on the bounds.

I expect you're calling for replacement primary commas for these two Trojan symbols. The criteria would be:
1. inside the comma zone* for the symbol in the JI notation
2. the tempered version falls inside the Trojan capture zone
If that is what you're asking for, it should be easy enough.

I haven't gone through the attached spreadsheets in detail yet, but it looks like "12N+-7 SymbolDegrees" will be the most relevant one in terms of the comma selection.

volleo6144
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### Re: Does Trojan use valid commas?

Comma Tempered
----- --------
5:7 C 17.48781 - difference between 5:7 tritone and 12edo tritone, also equal to tempered 5:7k
7:11C 17.50796 - difference between 7:11 aug. 5th and 12edo mi. 6th

25  C 27.37257 - difference between 16:25 aug. 5th and 12edo mi. 6th
23  C 28.27435 - difference between 16:23 tritone and 12edo tritone

I don't see anything wrong with just using 7:11C and 23C here, right?

...Also "12R Trojan Boundaries.xls" already uses the tempered 7:11C and 23C cents values.
Last edited by volleo6144 on Mon Jul 26, 2021 5:26 am, edited 2 times in total.
I'm in college (a CS major), but apparently there's still a decent amount of time to check this out. I wonder if the main page will ever have 59edo changed to green...

cmloegcmluin
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### Re: Does Trojan use valid commas?

cmloegcmluin wrote: Tue Jun 16, 2020 3:00 am I can't believe I didn't notice those columns when checking over the .par files... I suppose I was too busy focusing on the bounds.
Actually, I see now that I did notice, but I simply corrected them to their primary commas, the 7:11C (45927/45056) and 23C (736/729), respectively.
volleo6144 wrote: Tue Jun 16, 2020 4:10 am I don't see anything wrong with just using 7:11C and 23C here, right?

...Also "12R Trojan Boundaries.xls" already uses the tempered 7:11C and 23C cents values.
As @volleo6144 points out, they do show up in the "12R Trojan Boundaries" sheet in tempered cents form. I also note they appear in the "12N+-7 SymbolDegrees" sheet explicitly (in ratio form).

@Dave Keenan, in your comment on my PR linked above, you said they are "supposed" to use secondary commas. Must they? Echoing volleo6144's question, is there some reason to not prefer the primary commas for these two? Their tempered values are inside the respective Trojan capture zones:

17.508 b/t 16.666 and 22.222
28.274 b/t 22.222 and 28.571

cmloegcmluin
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### Re: Does Trojan use valid commas?

Man, I gotta read more carefully! @Dave Keenan went on to say in that same comment "But perhaps the primaries are valid after all. I haven't yet checked, but I doubt it."

So if that was your only concern, Dave, and if volleo6144 and I haven't run the numbers wrong, then maybe we just use the 7/11C and 23C, yeah?

Dave Keenan
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### Re: Does Trojan use valid commas?

Phew! That's a relief. I agree it's just that the wrong commas were listed in the .par file. Perhaps due to a previous failure to update them. As you both say, they should just be the current primaries for those symbols (and so for all the symbols).

I love these time-zone handoffs. I wake up and find that the elves have fixed the problem overnight (or shown that it was imaginary).

Trojan was designed back in 2003/2004, so I've forgotten much of the detailed reasoning. Hence just dumping the spreadsheets on you, late at night my time.

Thanks again, guys.