## 5n edos

William Lynch
Posts: 45
Joined: Mon Sep 21, 2015 9:27 pm

### Re: 5n edos

How about enharmonics so that scales like porcupine don't look terrible? I propose that F = G and B = C so that porcupine comes out looking sensible and tertian harmony doesn't look random and scattered.

Porcupine thus is notated as C D E F G A Bb:/|: C such that F and G are equated and B and C are equated? It could be written in the score but this way you kind of get the best of both worlds.

Fb:/|: is the same pitch as Gb:/|: in 5n EDOs.
Last edited by William Lynch on Wed Apr 20, 2016 1:07 am, edited 1 time in total.

Dave Keenan
Posts: 1940
Joined: Tue Sep 01, 2015 2:59 pm
Location: Brisbane, Queensland, Australia
Contact:

### Re: 5n edos

I hope you meant F = E and B = C.
F = G makes no sense to me.

Dave Keenan
Posts: 1940
Joined: Tue Sep 01, 2015 2:59 pm
Location: Brisbane, Queensland, Australia
Contact:

### Re: 5n edos

I made a US-Greek keyboard layout for Windows.

After it's installed, you can simply hold down the right-hand Alt key (or the Ctrl key and the left-hand Alt key) to type Greek characters using the corresponding Latin letter keys. Otherwise, everything should work as usual.

http://sagittal.org/us-techn.zip
Unpack the zip file and run the setup.exe that's inside it. Then Restart. Then choose "US-technical symbols keyboard" as your current keyboard layout from the right-hand end of the task bar.
Use at your own risk -- no warranty etc. Let me know if you find any problems.

Dave Keenan
Posts: 1940
Joined: Tue Sep 01, 2015 2:59 pm
Location: Brisbane, Queensland, Australia
Contact:

### Re: 5n edos

William Lynch wrote:Ok, I'm trying to get this to all work in MUS2 with Bravura font but I cannot seem to find Shai and Shao. Am I supposed to combine something? I'm using the mixed sagittal btw, is it like a Gao Flat or something?
No. No combining required. These 5n accidentals are all single-shaft, so there's no difference between mixed and pure Sagittal in this case. Shai and shao come immediately after slai and slao . They are all way down in the Promethean single-shaft section.

See page 117 (PDF-page 11) of this http://sagittal.org/smufl-0.9-sagittal.pdf

Dave Keenan
Posts: 1940
Joined: Tue Sep 01, 2015 2:59 pm
Location: Brisbane, Queensland, Australia
Contact:

### Re: 5n edos

William Lynch wrote:Ok, I'm trying to get this to all work in MUS2 with Bravura font but I cannot seem to find Shai and Shao. Am I supposed to combine something? I'm using the mixed sagittal btw, is it like a Gao Flat or something?
OK. I think I can guess what's happening. I assume you can't find slai and slao either, because you are actually using the BravuraMSS font where the mixed spartans were mapped to the Latin alphabet. So you're not used to having to look outside the first 256 characters.

I'm not familiar with how you select characters as accidentals in MUS2. Can you type in a unicode specification like "U+E394"? Can you scroll a palette of characters way way down, until you get to the "E-thousands" and start to see musical symbols? Can you find them using the Windows Character Map accessory, (Win10 Start/AllApps/WindowsAccessories/CharacterMap) then copy and paste them into MUS2?

Juhani
Posts: 31
Joined: Sun Sep 06, 2015 12:14 am

### Re: 5n edos

I'm not familiar with how you select characters as accidentals in MUS2. Can you type in a unicode specification like "U+E394"? Can you scroll a palette of characters way way down, until you get to the "E-thousands" and start to see musical symbols?
Dave, could you consider purchasing Mus2 as it's the most versatile and handiest Microtonal notation program on the market (with playback, and without pitchbend), it's both for PC and Mac, and it's very inexpensive indeed. Or maybe you could at least download the demo? Anyway, the character selection window for accidentals only shows 136 at the time but there's a character range menu that has a list that starts like this: 1: U+0...U+7F 2: U+80...U+FF 3: U+100...U+17F and so on; there are 512 ranges like that on the menu. However, on none of them can I see any more Sagittal symbols when the Bravura font has been selected - only in the first 'range'. What about you, Willliam?

About the notation. So 15edo is notated as three circles of fifths a syntonic comma apart where the tuning is such that the fifth is 720 cents and the syntonic comma is so big that it's close to a 12edo half-step, ie. 80 cents? A Pythagorean third, then is 480 c, enharmonically a fourth, and when that's narrowed by the comma, we'll get a "5/4" of 400 cents (as it's also tuned in 12et). Yes?
So, what's the rationale behind the 35M diesis symbol in 10edo?

Dave Keenan
Posts: 1940
Joined: Tue Sep 01, 2015 2:59 pm
Location: Brisbane, Queensland, Australia
Contact:

### Re: 5n edos

Juhani wrote:Dave, ... maybe you could at least download the demo? Anyway, the character selection window for accidentals only shows 136 at the time but there's a character range menu that has a list that starts like this: 1: U+0...U+7F 2: U+80...U+FF 3: U+100...U+17F and so on; there are 512 ranges like that on the menu. However, on none of them can I see any more Sagittal symbols when the Bravura font has been selected - only in the first 'range'.
That's very strange, because when I install Mus2 and go to Score > Symbols, click the Add button, select "New Accidental", click Acquire from Font, select Font: Bravura and Character Range: 456: U+E380...U+E3FF, I see the expected Sagittals.

Incidentally, you can get to that character range quickly by clicking in the Character Range field and typing "456↵" with no pause between digits. The more common Sagittals are in Character Range: 455: U+E300...U+E37F.
About the notation. So 15edo is notated as three circles of fifths a syntonic comma apart where the tuning is such that the fifth is 720 cents and the syntonic comma is so big that it's close to a 12edo half-step, ie. 80 cents? A Pythagorean third, then is 480 c, enharmonically a fourth, and when that's narrowed by the comma, we'll get a "5/4" of 400 cents (as it's also tuned in 12et). Yes?
Yes. That is all correct. Of course this is only one way of notating these 5n edos—the way that William asked for. They could instead be notated as subsets of 60-edo. In that case the notational fifth would be 700c as in 12edo.
So, what's the rationale behind the 35M diesis symbol in 10edo?
Gai is actually being used there in its secondary role as the 13 M-diesis symbol (or you can say we dropped the accent mark), because 10edo has a very good (within 0.5 cent) approximation of 13/8, at 7 degrees, e.g. C : A. Strictly-speaking, in that example it is behaving as the 13 L-diesis (26:27) but in 10edo both 13M and 13L map to 1 degree, so we only need the one 13 symbol.

Juhani
Posts: 31
Joined: Sun Sep 06, 2015 12:14 am

### Re: 5n edos

...Bravura and Character Range: 456: U+E380...U+E3FF, I see the expected Sagittals.
Excellent, there they are. I just didn't know where to look and gave up after some tries.

Thanks for the 13 diesis explanation - very neat.

Juhani

Dave Keenan
Posts: 1940
Joined: Tue Sep 01, 2015 2:59 pm
Location: Brisbane, Queensland, Australia
Contact:

### Re: 5n edos

We now have a better rationale for 5n-edo notations (and other "bad fifth" EDOs), thanks to suggestions by Cryptic Ruse / Igliashon Jones. See this thread:
viewtopic.php?f=5&t=256

The proposal looks like this for 5n-edos (in mixed Sagittal):
5n-edos: A:B C:D D:E F:G G:A = 1\5, B:C E:F = 0, # b = 1\5
5-edo																	  5-edo
10-edo																	 10-edo
15-edo																	 15-edo
20-edo																	 20-edo
25-edo																	 25-edo
30-edo																	 30-edo
Apotome fractions:	1/6	1/5	1/4	1/3	2/5		1/2		3/5	2/3	3/4	4/5	5/6		1 apotome
In pure Sagittal:
5n-edos: A:B C:D D:E F:G G:A = 1\5, B:C E:F = 0,   = 1\5
5-edo																	  5-edo
10-edo																	 10-edo
15-edo																	 15-edo
20-edo																	 20-edo
25-edo																	 25-edo
30-edo																	 30-edo
Apotome fractions:	1/6	1/5	1/4	1/3	2/5		1/2		3/5	2/3	3/4	4/5	5/6		1 apotome
Use the horizontal scroll bar below to see the rest of the accidentals above.

Dave Keenan
Posts: 1940
Joined: Tue Sep 01, 2015 2:59 pm
Location: Brisbane, Queensland, Australia
Contact:

### Re: 5n edos

The only difference between the notation above, and that given earlier in this thread (for 5 nominals), is that has been eliminated, and the use of has been extended to include 1/4 and 1/5 apotome. So only the 20-edo and 25-edo notations have changed.

5edo: C D E G A
10edo: C D D E E G G A A C
15edo: C C D D D E E G G G A A A C
20edo: C C D D D D E E E E G G G G A A A A C C
25edo: C C C D D D D D E E E E E G G G G G A A A A A C C
30edo: C C C D D D D D D E E E E E E G G G G G G A A A A A A C C C