Key Signatures and MOS Notation

William Lynch
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Key Signatures and MOS Notation

Postby William Lynch » Mon Oct 10, 2016 12:28 am

I have debated for a while on how to use sagittal for key signatures. It makes a score much cleaner looking to put all the needed signs in the key for a set of 7 pitches but it also MIGHT make it more difficult to read the score for some. I personally do not know what is best yet as I have only just now begun to put time into mastering sagittal at least for 22 EDO.

Take my piece endless flow. It pretty much uses a fixed set of 7 pitches for the majority of the piece or at least half of it. The pitches are B C:#: D:\!::#: E F:#: G:#: A . My first reaction based on the simplicity of chain of fifths notation is to put keys as superpyth[7] MOS only with deviations being written into the score as accidentals because it shows we are dealing with a MODMOS of superpyth. In that case we get a E Major Superpyth[7] key signature, F:#: C:#: G:#: D:#: since we're essentially dealing with a mixolydian thing given that 4:5:6:7 is on the tonic B. Then I used a :\!::#: for all instances of D. This makes sense because we're keeping ratios of 5 as modifications to the superpyth MOS which is easy to understand. However, there were D:\!::#: all through the piece.

The other option is of course to allow any set of 7 pitches in the key signature marking thus have the key be F:#: C:#: G:#: D:\!::#: instead making the score much cleaner to read but I'm not sure if this is a bad idea to use 5 commas in the key itself. Given that the piece is in that key however, D:#: never occurs in the piece, of if it does it's in the weird key change part.

My simple question is, if in superpyth MODMOS should we stay out of putting 5-comma in the key signature entirely or allow it?

Then this brings up the question of using key signatures for all MOS and MODMOS if held for an extended period of time. Porcupine key signatures make sense of course but we need some sort of consistency of key markings. We don't want to have several ways of writing the same key signature.
Last edited by William Lynch on Tue Oct 11, 2016 11:11 pm, edited 1 time in total.

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herman.miller
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Re: Key Signature Approaches?

Postby herman.miller » Mon Oct 10, 2016 6:23 am

The one thing that might be confusing is that if you have D:\!::#: (or D:||\:) in the key signature but you occasionally might need a D:#:, it might be confusing that D:#: is only a comma sharper than the unmarked D. But the general idea of allowing any combination of accidentals in the key signature seems like a reasonable thing to do. Maybe if you're using mixed Sagittal notation you could set up a convention where you only need to write D:\!: for D:\!::#: if D:#: is in the key signature, but then if you really need a D:\!: you'd have to write it as D:\!::h:.

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Dave Keenan
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Re: Key Signature Approaches?

Postby Dave Keenan » Mon Oct 10, 2016 10:03 am

Hi William and Herman,

My personal feeling is that, following the historical Pythagorean[7] and Meantone[7] conventions, a key signature should only be used to establish a MOS, not a MODMOS, and it would be good to say what the MOS is, at the start of the score, in addition to the EDO, e.g. "Porcupine[7] in 22-edo" or "15&22[7] in 22-edo".

Cam, George and I discussed naturals and the overriding of compound accidentals here:
http://forum.sagittal.org/viewtopic.php?f=14&t=131
The conclusion was that we should use the convention that already exists in the case of a conventional double-flat, namely that any combination of accidentals against the same note is treated as if it were a single accidental and so can only be cancelled or replaced as a whole.

i.e. If there is a :bb: in a key signature (or earlier in the same bar), it is completely cancelled by a single :h: and it is completely replaced by a simple :b:. It is never necessary to write :h::h: or :b::h:. Similarly, if there is a :\!::#: in a key signature (or earlier in the same bar), it is completely cancelled by a single :h: and it is completely replaced by a simple :#: or :\!:. There is never any need to write :h::h: or :h::#: or :#::h: or :\!::h:.

So another way to remember this convention is: Naturals always stand alone. They never need to be combined with anything else.

William Lynch
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Re: Key Signature Approaches?

Postby William Lynch » Mon Oct 10, 2016 11:07 pm

Dave I think that's probably a good idea because its easier to understand the score that way. Can someone explain porcupine keys signatures though? I cannot seem to understand how they change based on going down quills (the generator).

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Re: Key Signature Approaches?

Postby Dave Keenan » Mon Oct 10, 2016 11:48 pm

I probably should have addressed Herman's actual example.

herman.miller wrote:Maybe if you're using mixed Sagittal notation you could set up a convention where you only need to write D:\!: for D:\!::#: if D:#: is in the key signature, but then if you really need a D:\!: you'd have to write it as D:\!::h:.

So the convention we recommend is, if D:#: is in the key signature (or earlier in the same bar) and you want D:\!::#:, then you have to write D:\!::#: in full, and so if you want D:\!: you only need to write D:\!:, not D:\!::h:.

A nice thing about this convention is that it is the same whether you are using pure-Sagittal or mixed-Sagittal.

I'll leave porcupine key signatures to Herman. :)

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Dave Keenan
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Re: Key Signature Approaches?

Postby Dave Keenan » Tue Oct 11, 2016 11:40 am

William Lynch wrote:... we need some sort of consistency of key markings. We don't want to have several ways of writing the same key signature.

A valid Superpyth[7] key signature in 22-edo would be any consecutive 7 notes from one of the columns below. Notes on the same line are enharmonic, but you would not mix spellings from different columns in one key signature. The preferred key signatures are those whose nominals are shown in red below, and are those that do not involve :x: :bb: :/|::#: :\!::b: or F:b: C:b: E:#: B:#: (with or without :/|: or :\!:). Others would only be arrived at via successive modulations.

D:/|::bb:
A:/|::bb:
E:/|::bb:
B:/|::bb:
F:/|::b:
C:/|::b: D:bb:
G:/|::b: A:bb:
D:/|::b: E:bb:
A:/|::b: B:bb:
E:/|::b: F:b:
B:/|::b: C:b: D:\!::bb:
F:/|: G:b: A:\!::bb:
C:/|: D:b: E:\!::bb:
G:/|: A:b: B:\!::bb:
D:/|: E:b: F:\!::b:
A:/|: B:b: C:\!::b:
E:/|: F G:\!::b:
B:/|: C D:\!::b:
F:/|::#: G A:\!::b:
C:/|::#: D E:\!::b:
G:/|::#: A B:\!::b:
D:/|::#: E F:\!:
A:/|::#: B C:\!:
E:/|::#: F:#: G:\!:
B:/|::#: C:#: D:\!:
F:/|::x: G:#: A:\!:
C:/|::x: D:#: E:\!:
G:/|::x: A:#: B:\!:
D:/|::x: E:#: F:\!::#:
B:#: C:\!::#:
F:x: G:\!::#:
C:x: D:\!::#:
G:x: A:\!::#:
D:x: E:\!::#:
B:\!::#:
F:\!::x:
C:\!::x:
G:\!::x:
D:\!::x:

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Dave Keenan
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Re: Key Signature Approaches?

Postby Dave Keenan » Tue Oct 11, 2016 12:09 pm

William Lynch wrote:Can someone explain porcupine keys signatures though? I cannot seem to understand how they change based on going down quills (the generator).

A valid Porcupine[7] key signature in 22-edo would be any consecutive 7 notes from the column below (a chain of quills). The preferred keys would be those near the middle of the chain. Notice that the chain can be seen as 3 interleaved chains of fourths. The simplest key is the one whose nominals are shown in red.

D:\!::#:
E:/|:
F:#:
G:\!::#:
A:/|:
B
C:\!::#:
D:/|:
E
F:\!::#:
G:/|:
A
B:\!:
C:/|:
D
E:\!:
F:/|:
G
A:\!:
B:/|::b:
C
D:\!:
E:/|::b:
F
G:\!:
A:/|::b:
B:b:
C:\!:
D:/|::b:

William Lynch
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Re: Key Signatures and MOS Notation

Postby William Lynch » Tue Oct 11, 2016 11:17 pm

Ok, I changed the title to include MOS notation since that is also a big issue here even if not a key signature pursue.

How about Pajara and the decatonics? These I find hard to notate consistently even though I know Cam mentioned an easy way to do it logically but I cannot seem to remember. Should 7/6 be notated as a large tone in that temperament? Paul did something like C E G A:/|: for the tonic 4:5:6:7 I think.

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Re: Key Signatures and MOS Notation

Postby Dave Keenan » Wed Oct 12, 2016 12:44 am

William Lynch wrote:How about Pajara and the decatonics? These I find hard to notate consistently even though I know Cam mentioned an easy way to do it logically but I cannot seem to remember. Should 7/6 be notated as a large tone in that temperament? Paul did something like C E G A:/|: for the tonic 4:5:6:7 I think.

Here is Pajara as two chains of fifths a half-octave apart. An example of a 4:5:6:7 in 22-edo is C E:\!: G B:b:, or if we swap all identities to the other chain, an example is C:/|: E G:/|: B:/|::b:.

D:b:	A:/|::bb: or	G:\!:
A:b: E:/|::bb: or D:\!:
E:b: B:/|::bb: or A:\!:
B:b: F:/|::b: or E:\!:
F C:/|::b: or B:\!:
C G:/|::b: or F:\!::#:
G D:/|::b: or C:\!::#:
D A:/|::b: or G:\!::#:
A E:/|::b: or D:\!::#:
E B:/|::b: or A:\!::#:
B F:/|: or E:\!::#:
F:#: C:/|: or B:\!::#:
C:#: G:/|: or F:\!::x:
G:#: D:/|: or C:\!::x:
D:#: A:/|: or G:\!::x:

William Lynch
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Re: Key Signatures and MOS Notation

Postby William Lynch » Wed Oct 12, 2016 2:57 am

Dave Keenan wrote:
William Lynch wrote:How about Pajara and the decatonics? These I find hard to notate consistently even though I know Cam mentioned an easy way to do it logically but I cannot seem to remember. Should 7/6 be notated as a large tone in that temperament? Paul did something like C E G A:/|: for the tonic 4:5:6:7 I think.

Here is Pajara as two chains of fifths a half-octave apart. An example of a 4:5:6:7 in 22-edo is C E:\!: G B:b:, or if we swap all identities to the other chain, an example is C:/|: E G:/|: B:/|::b:.

D:b:	A:/|::bb: or	G:\!:
A:b: E:/|::bb: or D:\!:
E:b: B:/|::bb: or A:\!:
B:b: F:/|::b: or E:\!:
F C:/|::b: or B:\!:
C G:/|::b: or F:\!::#:
G D:/|::b: or C:\!::#:
D A:/|::b: or G:\!::#:
A E:/|::b: or D:\!::#:
E B:/|::b: or A:\!::#:
B F:/|: or E:\!::#:
F:#: C:/|: or B:\!::#:
C:#: G:/|: or F:\!::x:
G:#: D:/|: or C:\!::x:
D:#: A:/|: or G:\!::x:


So this means if I pick D G C G B:b as one chain, then G:\!::#: C:\!::#: F:\!::#: B:\!: E:\!: can form the other pitches of the pajara MOS.
I'm wondering if I should use multiple versions of the same pitch to spell chords correctly even in the same key. Kinda weird.


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