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The cuneiform ha sign comes in two common varieties in the 1350 BC Amarna letters. It is also found in the large 12-chapter (Tablets I-XII) work of the Epic of Gilgamesh. Cuneiform ha is used as a syllabic for ha, and an alphabetic for h, or a; from the Epic of Gilgamesh it also has two sumerogramic uses (capital letter (majuscule)), for HA (Akkadian language zittu, for "share"), and KU6, for nūnu, "fish".
The digitized version of ha has 4, short vertical strokes, 2-pairs-of-2, in a square; it is ligatured at the right, typically with a large, or medium-large sized wedge-stroke. The 2nd type of cuneiform ha is consistent as: 2-verticals, with a wedge between, and a (typical) large wedge ligatured at right; (thus both types contain the wedge at the right).
Type I of the sign with four short vertical strokes , (1-pair, above another pair), is the za (cuneiform) sign, which is used for linguistic items like: ṣa, za, ZA, ZA being a sumerogram.
In the Epic of Gilgamesh the usage numbers for the ha sign is as follows: ha-(145 times), HA-(2), KU6-(4).
Selected list of Amarna letter usage by type
Selected Amarna letter usage by type, with some explanation of the letter texts:
Type I
Type II (2nd vertical and wedge often larger)