Blinking snake

The Z and Y Glyphs of the Lunar Supplementary Series

Constellation band

The only useful reference for these Glyphs is Yasugi and Saito (1991). I quote Schele, Grube and Fahsen: “.They demonstrated that Z and Y fall into a cycle of seven, although they did not know what the cycle counted.”

Yasugi and Saito’s hypothesis is that Glyph Y, or the “Beetle Glyph,” represents a terrestrial god in a cycle of seven; the “Seven Lords of the Earth,” similar to the Nine Lords of the Night/Underworld and the Thirteen Lords of the Day/Sky/Heaven. The Nine Lords’ collective name in Ch’ol is Bolon ti k’u, the Thirteen Lords (equivalent to the first thirteen integers), Oxlahun ti k’u. Therefore, by extension, the collective name of the Seven Lords of the Earth would be Wuk ti k’u.

What Yasugi and Saito have shown is that Glyph Y doesn’t ordinarily appear with a numerical coeffecient, but when it does, there is no associated Glyph Z. Glyph Z comes with a coeffecient; examples in the inscriptions are limited to 5 and 7. Glyph Y’s coeffecients, however, include 2, 3, 4, 5, 6, but no 1 and no 7.

Therefore, Glyph Y is the collective name of the Lord of the Earth, and Glyph Z’s coeffecient names the particular Lord being evoked on a specific day. Additionally, Yasugi and Saito have pointed out that Glyph Y with a coeffecient of 9 seems to appear in clauses where G6 is expected:
Glyph Y as proposed G6 Glyph Y as proposed G6

These glyphs, then, would be alternate forms of G6.

This hypothesis is strengthened when we note that 819-day stations, all of which are ruled by G6, require Z or Y7. Yasugi and Saito also suppose that the absence of a coeffecient on the Y glyph would stand for a coeffecient of 1.

Mathematics

First, find the 819-day station for your date. Apply the formula

    z=d819 % 7

If the answer is 0, use a Z or Y glyph with the coeffecient of 7. If the answer is 1, use a coeffecient at your discretion. All other answers, use as is.

Here's another algorithm which doesn't depend on the 819-day station.
Set e=3;
If md is a date [12.19.14.14.0], then
Set l=[0,14,14,19,12];
For l[0], set c=1;
For l[1], set c=6;
For l[2], set c=3;
For l[3], set c=4;
For l[4], set c=3;
For all l[n] where n>1, set c=3 if n is odd and c=4 if it is even;
For all l[n], apply the formula

            e=(e+(i*c))%7

Unless md is negative, in which case, apply the formula

            e=(e-(i*c))%7

When l is exhausted, e is the answer.  Use a Z or Y glyph according to the rules above.

What I’ve done below is manufacture Z glyphs with appropriate coeffecients; Z1, Z2, Z3, Z4 and Z6 are not attested in either the inscriptions or the codices. Z7 functions as a mathematical 0, exactly like 13 in the trecena and G9 in the Nine Lords of the Night cycle.
Z Glyphs
Coeffecient 1 Coeffecient 2 Coeffecient 3 Coeffecient 4 Coeffecient 5 Coeffecient 6 Coeffecient 7
Glyph Z 1 Glyph Z 1 Glyph Z 2 Glyph Z 2 Glyph Z 3 Glyph Z 3 Glyph Z 4 Glyph Z 4 Glyph Z 5 Glyph Z 5 Glyph Z 5 Glyph Z 5 Glyph Z 5 Glyph Z 5 Glyph Z 5 Glyph Z 5 Glyph Z 5 Glyph Z 5 Glyph Z 6 Glyph Z 6 Glyph Z 7 Glyph Z 7 Glyph Z 7 Glyph Z 7 Glyph Z 7 Glyph Z 7 Glyph Z 7 Glyph Z 7
Y Glyphs
No coeffecient (1) Coeffecient 2 Coeffecient 3 Coeffecient 4 Coeffecient 5 Coeffecient 6 Coeffecient 7, No examples
Glyph Y Glyph Y Glyph Y Glyph Y Glyph Y Glyph Y Glyph Y Glyph Y Glyph Y 2 Glyph Y 2 Glyph Y 2 Glyph Y 3 Glyph Y 3 Glyph Y 4 Glyph Y 5 Glyph Y 5 Glyph Y 6 Glyph Y 6  

Finally, Yasugi and Saito suggest the following interpretations for certain glyphs found in the 819-day series.

Wuk ti K’u Bolon ti K’u Oxlahun ti K’u
One squirrel, Wuk ti K’u One squirrel, Wuk ti K’u Bolon ti K’u 819-day introductory glyph, Oxlahun ti K’u 819-day introductory glyph, Oxlahun ti K’u
Seven Lords of the Earth Nine Lords of the Night or Underworld Thirteen Lords of the Day, Sky or Heavens

References

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