Hexagonal 37

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cicada
Posts: 1
Joined: Thu Jan 26, 2023 4:15 pm

Hexagonal 37

Post by cicada »

Hello. I am looking to better understand how to notate the Hexagonal 37 system in Dorico using Sagittal. As a scala file the system presents as such.

! h.scl
hexagonal37
37

70.6724
111.731
133.238
141.345
182.404
203.91
223.463
244.969
274.582
315.641
364.807
386.314
427.373
456.986
498.045
519.551
568.717
590.224
609.776
631.283
680.449
701.955
743.014
772.627
813.686
835.193
884.359
925.418
955.031
976.537
996.09
1017.6
1058.66
1066.76
1088.27
1129.33
2/1

Dorico asks the user to define the Nominals which I have calculated in the following way according to how I am sonically hearing and approaching the system.

A 240 B
B 710 C
C 1820 D
D 2450 E
E 930 F
F 1820 G
G 2230 A

The software then asks the user to define further pitch deltas for the system.

I am unclear at what point as i am defining these pitch deltas that I presume I would consider the note sharp or flat as it relates to the Sagittal symbol. Any answers that would point me in the direction of expanding my understanding as a whole would be greatly appreciated.

Many Thanks!
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Dave Keenan
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Re: Hexagonal 37

Post by Dave Keenan »

Hi @cicada. Welcome to the Sagittal forum.

I'm sorry it has taken me so long to respond to this. It was quite a puzzle. I could not find any online resources describing "Hegagonal37", it's purpose or structure. And now that I have analysed it enough to know how it should be notated I am mystified by two things:
1. Why is it given in cents in the Scala file instead of ratios, since it is in 5-limit just intonation? Ratios would have made it much easier to understand its structure.
2. Why is it called "hexagonal" when the shape it makes on the 5-limit lattice is not a hexagon but a hexagram, a 6-pointed star, as shown below?

Anyway, here's a Sagittal notation for it. I've chosen D as the tonic because it gives a symmetrical notation, but I'm sure you can transpose it to A, C or G if you prefer.

The order of the accidentals on the staff should be the reverse of the order they appear here in text. I'm sorry I don't know much about how to achieve this notation in Dorico.


						D:x::\\!::\\!:
						 141

					B:#::\\!::\!:	F:x::\\!::\!:
					 955	 457

 F:#::\\!:	 C:#::\\!:	 G:#::\\!:	 D:#::\\!:	 A:#::\\!:	 E:#::\\!:	 B:#::\\!:
 365	1067	 569	  71	 773	 275	 977

	  A:\!:	  E:\!:	  B:\!:	 F:#::\!:	 C:#::\!:	 G:#::\!:
	 680	 182	 884	 386	1088	 590

		  C		  G		  D		  A		  E
		 996	 498	  0		 702	 204

	 A:b::/|:	 E:b::/|:	 B:b::/|:	  F:/|:	  C:/|:	  G:/|:
	 610	 112	 814	 316	1018	 520

 F:b:://|:	 C:b:://|:	 G:b:://|:	 D:b:://|:	 A:b:://|:	 E:b:://|:	 B:b:://|:
 223	 925	 427	1129	 631	 133	 835

					B:bb:://|::/|:	F:b:://|::/|:
					 743	 245

						D:bb:://|:://|:
						1059
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Dave Keenan
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Re: Hexagonal 37

Post by Dave Keenan »

I noticed that the diagram above has some notations out of place when viewed in some browsers, due to slightly different widths relative to the tabs I used. If the above is messed up in your browser, the following should look better, and vice versa.


						D:x::\\!::\\!:
						 141

					B:#::\\!::\!:		F:x::\\!::\!:
					 955	 457

 F:#::\\!:	 C:#::\\!:	 G:#::\\!:	 D:#::\\!:	 A:#::\\!:	 E:#::\\!:	 B:#::\\!:
 365	1067	 569	  71	 773	 275	 977

	  A:\!:	  E:\!:	  B:\!:	 F:#::\!:		 C:#::\!:		 G:#::\!:
	 680	 182	 884	 386	1088	 590

		  C		  G		  D		  A		  E
		 996	 498	  0		 702	 204

	 A:b::/|:		 E:b::/|:		 B:b::/|:		  F:/|:	  C:/|:	  G:/|:
	 610	 112	 814	 316	1018	 520

 F:b:://|:	 C:b:://|:	 G:b:://|:	 D:b:://|:	 A:b:://|:	 E:b:://|:	 B:b:://|:
 223	 925	 427	1129	 631	 133	 835

					B:bb:://|::/|:	F:b:://|::/|:
					 743	 245

						D:bb:://|:://|:
						1059
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