Hi, I have some questions about how to notation semaphore / godzilla with sagittal. By this I mean the linear temperament tempering out 49/48, with 81/80 probably also tempered out but not too sure about the mapping of any other primes.
I think the way you would notate it with 7 Pythagorean nominals is like this:
...E C B G F D C A G E=F D B=C A G E D B A F E C...
So, my first question is: is this correct? And my second question is, is there some way to notate this with only 5 nominals? That seems more natural to me because semaphore doesn't have a 7note MOS but it does have a 5note MOS. But I can't figure out any obvious way to do it because there's no symbol for or equivalently for the limma. Thoughts?
Semaphore / godzilla

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 Joined: Mon Apr 26, 2021 11:25 am
 Real Name: Keenan Pepper
 Dave Keenan
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Re: Semaphore / godzilla
Hi Keenan. Welcome to the Sagittal forum.
Here's a mapping from Graham's temperament finder.
Reduced Mapping
2 3 5 7 11 13
[ ⟨ 1 2 4 3 6 6 ]
⟨ 0 2 8 1 12 11 ] ⟩
TE Generator Tunings (cents)
⟨1204.4822, 254.5504]
Semafour+, the 13limit extension of semafour [sic], has:
Reduced Mapping
2 3 5 7 11 13
[ ⟨ 1 2 4 3 3 6 ]
⟨ 0 2 8 1 2 11 ] ⟩
TE Generator Tunings (cents)
⟨1207.0465, 255.2153]
They differ only in their mapping of prime 11. So we should avoid symbols that involve prime 11. And we probably won't need to go as high as 13.
Generators for use with pure octaves are given here: https://en.xen.wiki/w/Semaphore_and_Godzilla
Your notation is apparently using the octaveinversion of that approximately 251 cents subminorthird/supermajorsecond generator, the approximately 949 cent supermajorsixth/subminorseventh generator, so the bottom row of the mapping (which is all that matters for the notation, given that the period is an octave) becomes easier to think about, with mostly positive numbers, as:
⟨ 0 2 8 1 12 11 ] (godzilla) or ⟨ 0 2 8 1 2 11 ] (semafour+) so we should try to do the notation using only:
2 3 5 7
⟨ 0 2 8 1 ]
Yes. Your 7nominals chainoffifths notation is valid. And is a good choice for the accidental.
It can be seen as two interleaved chains of fifths (because there are two generators to the fifth) with the accidental distinguishing the chains.
There is a symbol equivalent to , the double septimal comma or 1/49mediumdiesis 4096/3969. It is . Unfortunately we couldn't make symbols with twoarcsonthesameside "work" graphically. Of course you can just use the two symbols together . I see that 4096/3969 is 10 generators.
The symbol has been used for the limma, when the limma can't be notated by a change of nominal, although that is not the primary role of that symbol. I see the limma is 10 generators.
I agree it makes sense to have a 5nominals notation because it has a 5 note proper MOS (and none larger below 14). But surely that would be 5 nominals in a chain of generators, not a chain of fifths? I favour what I call pseudonominals where we use notes chosen from 24edo, notated using conventional notation plus and . That way you can still use a standard 5line staff. So for our "nominals" we'd have:
G E D C A
Then we need sagittal accidentals for 5 generators and 10 generators (about 55 cents and 110 cents). As you suggest, we could use
+5 gens
+10 gens or
So a chain of generators could be notated:
G E D C A G E D C A G E D C A G E D C A G E D C A
It's often considered desirable for (the commas of) the chosen symbols to have untempered sizes that are not too different from their tempered sizes. The untempered 7comma is only about half the size that it is in godzilla/semafour. Some 7limit commas that map to 5 generators and have untempered size around 55c are:
36/35 49c 35mediumdiesis
28/27 63c 7largediesis
This 13limit comma is also valid as 5 gens.
27/26 65c 13largediesis
If you used either of the last two, you could drop the accents, and so the symbol could represent both. But it seems simpler to use .
My spreadsheet isn't set up to calculate the generator counts of multishaft sagittal commas. But you can find their 7limit monzos listed here:
viewtopic.php?p=578#p578
@herman.miller can probably suggest some 10 gen symbols with untempered size around 110 cents.
Here's a mapping from Graham's temperament finder.
Reduced Mapping
2 3 5 7 11 13
[ ⟨ 1 2 4 3 6 6 ]
⟨ 0 2 8 1 12 11 ] ⟩
TE Generator Tunings (cents)
⟨1204.4822, 254.5504]
Semafour+, the 13limit extension of semafour [sic], has:
Reduced Mapping
2 3 5 7 11 13
[ ⟨ 1 2 4 3 3 6 ]
⟨ 0 2 8 1 2 11 ] ⟩
TE Generator Tunings (cents)
⟨1207.0465, 255.2153]
They differ only in their mapping of prime 11. So we should avoid symbols that involve prime 11. And we probably won't need to go as high as 13.
Generators for use with pure octaves are given here: https://en.xen.wiki/w/Semaphore_and_Godzilla
Your notation is apparently using the octaveinversion of that approximately 251 cents subminorthird/supermajorsecond generator, the approximately 949 cent supermajorsixth/subminorseventh generator, so the bottom row of the mapping (which is all that matters for the notation, given that the period is an octave) becomes easier to think about, with mostly positive numbers, as:
⟨ 0 2 8 1 12 11 ] (godzilla) or ⟨ 0 2 8 1 2 11 ] (semafour+) so we should try to do the notation using only:
2 3 5 7
⟨ 0 2 8 1 ]
Yes. Your 7nominals chainoffifths notation is valid. And is a good choice for the accidental.
It can be seen as two interleaved chains of fifths (because there are two generators to the fifth) with the accidental distinguishing the chains.
There is a symbol equivalent to , the double septimal comma or 1/49mediumdiesis 4096/3969. It is . Unfortunately we couldn't make symbols with twoarcsonthesameside "work" graphically. Of course you can just use the two symbols together . I see that 4096/3969 is 10 generators.
The symbol has been used for the limma, when the limma can't be notated by a change of nominal, although that is not the primary role of that symbol. I see the limma is 10 generators.
I agree it makes sense to have a 5nominals notation because it has a 5 note proper MOS (and none larger below 14). But surely that would be 5 nominals in a chain of generators, not a chain of fifths? I favour what I call pseudonominals where we use notes chosen from 24edo, notated using conventional notation plus and . That way you can still use a standard 5line staff. So for our "nominals" we'd have:
G E D C A
Then we need sagittal accidentals for 5 generators and 10 generators (about 55 cents and 110 cents). As you suggest, we could use
+5 gens
+10 gens or
So a chain of generators could be notated:
G E D C A G E D C A G E D C A G E D C A G E D C A
It's often considered desirable for (the commas of) the chosen symbols to have untempered sizes that are not too different from their tempered sizes. The untempered 7comma is only about half the size that it is in godzilla/semafour. Some 7limit commas that map to 5 generators and have untempered size around 55c are:
36/35 49c 35mediumdiesis
28/27 63c 7largediesis
This 13limit comma is also valid as 5 gens.
27/26 65c 13largediesis
If you used either of the last two, you could drop the accents, and so the symbol could represent both. But it seems simpler to use .
My spreadsheet isn't set up to calculate the generator counts of multishaft sagittal commas. But you can find their 7limit monzos listed here:
viewtopic.php?p=578#p578
@herman.miller can probably suggest some 10 gen symbols with untempered size around 110 cents.