## Key Signatures and MOS Notation

Dave Keenan
Posts: 1082
Joined: Tue Sep 01, 2015 2:59 pm
Location: Brisbane, Queensland, Australia
Contact:

### Re: Key Signatures and MOS Notation

William Lynch wrote: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.
I realise that's a typo, and you meant, if D G C F B is one chain, then G C F B E can form the other. Yes, that's correct. You always have a pai/pao chain and a plain chain. I don't know whether you should use both pai and pao spellings of the same pitch in the same key. I agree it's kinda weird. Maybe it's another of those cases where you should feel free to do so while composing, but should choose one spelling for each pitch if you're presenting it to others.

But I think it's fine, even when presenting to others, to use pai-spelling at one end of the chain and pao-spelling at the other.
e.g. D G C F B and A D F B E. And then maybe only the middle pitch F will sometimes change spelling to G.

But you're the pioneer here. Let us know what works for you.

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

### Re: Key Signatures and MOS Notation

So what key signature would be used for Pajara, pentachordal major: D D E F G G A B C C ?
F B , I presume.

Dave Keenan
Posts: 1082
Joined: Tue Sep 01, 2015 2:59 pm
Location: Brisbane, Queensland, Australia
Contact:

### Re: Key Signatures and MOS Notation

Juhani wrote:So what key signature would be used for Pajara, pentachordal major: D D E F G G A B C C ?
F B , I presume.
Since those are the only nominals that don't have both natural and altered notes in the scale, they are the only ones that might be worth putting in a key signature. But its debatable whether it's worth using a key signature at all with the decatonics. Perhaps better not to, so that you can readily recognise perfect fourths and fifths and subminor-sevenths (same chain) and minor and major thirds (different chains).

Just to explain for other readers: The symmetrical decatonic scales are MOS and so consist of two chains of fifths a half octave apart and hence at the same height on the diagram below, while the pentachordal decatonic scales have an offset of one position (up or down) between the two chains. The two chains for the pentachordal scale described above are C G D A E and B F C G D (shown in red below). Note that if the right-hand chain had been notated using pai-flats instead of pao-sharps there would have been no nominal that did not have both natural and altered forms, and hence no point in any key signature. It would also be poor use of the resources of the standard staff since two positions per octave would be completely unused.

One could consider the preferred spellings for all 10 tetrads in the scale and see if perhaps pai-flats might occur more often than pao-sharps for some of the notes in the right-hand chain. But once that's decided, I agree with Cryptic Ruse that you don't change the spelling of a note within the same key. You just learn to love the remaining misspellings.
D	A or	G
A	E or	D
E	B or	A
B	F or	E
F	C or	B
C	G or	F
G	D or	C
D	A or	G
A	E or	D
E	B or	A
B	F  or	E
F	C  or	B
C	G  or	F
G	D  or	C
D	A  or	G

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

### Re: Key Signatures and MOS Notation

Dave Keenan wrote:
One could consider the preferred spellings for all 10 tetrads in the scale and see if perhaps pai-flats might occur more often than pao-sharps for some of the notes in the right-hand chain. But once that's decided, I agree with Cryptic Ruse that you don't change the spelling of a note within the same key. You just learn to love the remaining misspellings.
D	A or	G
A	E or	D
E	B or	A
B	F or	E
F	C or	B
C	G or	F
G	D or	C
D	A or	G
A	E or	D
E	B or	A
B	F  or	E
F	C  or	B
C	G  or	F
G	D  or	C
D	A  or	G
I disagree because it seems like reading that would be very annoying. I personally do not see why using multiple enharmonics is a bad thing, I have read alot of 20th century scores with enharmonic trade offs. I think it's better to preserve chord spelling as long as double accidentals aren't used. A good example: Say we're in the key of F major, we have a C7#9 which has an D# in it. Then we shift to a Cm7 chord which obviously has an Eb in it. Now, let's say this piece uses that chord movement over and over again in it. Would it really be better to use a single D# or Eb just to avoid an enharmonic shift? I can't imagine how.

Regardless, 12 edo sight readers already know standard 7th chords and read them like that. It's a pain, seriously to have to read C# F G# B as a C#7 chord. Even though I might pronounce notes that way, on paper it needs to be spelled right or it's 50 times harder to read. Same as pajara, I really wouldn't want those tetrads to be misspelled just to keep accidentals simpler. The music becomes weirder to read intervallically as a trade off of using only one enharmonic. Is it worth it?

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

### Re: Key Signatures and MOS Notation

I agree with Dave that key signatures should not be used with decatonics. They should be reserved for rather special cases of microtonal music, anyway. In the case of decatonics, they certainly make reading the notation slower and prone to mistakes.
In classical music - the most notation-based genre - marking every single note with an accidental has been quite a common practice for hundred years now and educated musicians are used to that. Key signatures are not common even in tonal 20th Century music.
For easily readable notation of contemporary music, performers expect more accidentals rather than less. For example, natural signs should be used even when the note would be a natural anyway, if it has been chromatically altered in some previous bar. In chromatic music, an accidental should be repeated when a note comes back in a bar, even if the accidental affects the whole bar. Otherwise players will invariably ask which one it should be, and valuable rehearsal time will be lost. If an un-inflected note (say, D) follows an inflected note (D) right after a bar line, it is actually a strict rule in all music publishing houses (if not in music theory books) that the latter note has to be cancelled out with a natural sign (D).
In microtonal music, it's particularly important to use a lot of cautionary accidentals. Key signatures may be useful but it's important to decide case by case whether they make the music easier or more difficult to read.

Dave Keenan
Posts: 1082
Joined: Tue Sep 01, 2015 2:59 pm
Location: Brisbane, Queensland, Australia
Contact:

### Re: Key Signatures and MOS Notation

You make good points William. Perhaps one just needs to learn the 5 enharmonic pairs in whatever decatonic key one is using, despite the fact that they are very different from enharmonic pairs in 12-EDO. It seems to me that the easiest to learn would be the 5 in the middle where a pai-flat is always enharmonic with a pao-sharp, never a plain pai or pao. So the easiest symmetric key might be:
C	G or	F
G	D or	C
D	A or	G
A	E or	D
E	B or	A
And the easiest pentachordal key might be:

G or	F
G	D or	C
D	A or	G
A	E or	D
E	B or	A
B
No key signatures.

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

### Re: Key Signatures and MOS Notation

Juhani wrote:I agree with Dave that key signatures should not be used with decatonics. They should be reserved for rather special cases of microtonal music, anyway. In the case of decatonics, they certainly make reading the notation slower and prone to mistakes.
In classical music - the most notation-based genre - marking every single note with an accidental has been quite a common practice for hundred years now and educated musicians are used to that. Key signatures are not common even in tonal 20th Century music.
For easily readable notation of contemporary music, performers expect more accidentals rather than less. For example, natural signs should be used even when the note would be a natural anyway, if it has been chromatically altered in some previous bar. In chromatic music, an accidental should be repeated when a note comes back in a bar, even if the accidental affects the whole bar. Otherwise players will invariably ask which one it should be, and valuable rehearsal time will be lost. If an un-inflected note (say, D) follows an inflected note (D) right after a bar line, it is actually a strict rule in all music publishing houses (if not in music theory books) that the latter note has to be cancelled out with a natural sign (D).
In microtonal music, it's particularly important to use a lot of cautionary accidentals. Key signatures may be useful but it's important to decide case by case whether they make the music easier or more difficult to read.
Juhani I'm really starting to see what you mean. I'm leaning towards using keys with superpyth[7] keys because we're just changing out chain of fifths to a different place in the cycle. But in case of anything else, it makes sense because you can see on paper, it's literally spelled out what intervals and JI is being played on where as if you have a key, you might get confused and have to check the key signature again and again. So IF we're in a superpyth[7] piece or possibly superpyth[12] I think key sigs are ok but yeah it depends on the piece.

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

### Re: Key Signatures and MOS Notation

It would appear I forgot something. In trying to notate a score which is in A Major with some 5-comma shifts, I ended up using a key signature which has a B E A D so I'm finding that we need pai and pao key signatures for the other chain of fifths so our key signatures don't look insane. Try notating G# major which is the only other way with a A major.

Dave Keenan