How many sibilants did Old Akkadian cuneiform distinguish?

Question

According to fdb's answer to another question:

It is believed that Old Akkadian (at least) still retained the Semitic distinction of s₁, s₂ and s₃ and used different signs for syllables containing each of these. This is reflected by the transcription of those signs.

I know that Akkadian cuneiform eventually had four series of signs for different sibilants: S, Z, Ṣ, and Š. The third of these wasn't present in Sumerian (which only had three sibilant series) and was a fairly late development.

However, Old Akkadian (aka Sargonic) cuneiform was somewhat different than the later sorts, and represented a very different dialect than classical Babylonian or Assyrian. Did it ever distinguish more sibilants than these, such as a separate reflex of Proto-Semitic *s₂ (aka *ś aka *ł aka sin)? And if so, how? (As in, what signs did they use?)

Answer 1

Gelb proposes that there were four sibilant series, somewhat confusingly named z, š₁₂, š₃, and š₄.

• The z series was written with signs ZA, ZÉ, ZI, ZU, and represented the outcome of what Semiticists now generally consider affricates (i.e. PSem *s, *ṣ, etc).
• The š₁₂ series was written with signs SA, SE₁₁, SI, SU, and represented the outcome of Semitic s₁ (PSem *š) and s₂ (PSem *ś).
• The š₃ series was written with signs ŠA, ŠI, ŠI, ŠU, and represented the outcome of Semitic s₃ (PSem *θ).
• The š₄ series was written with signs SÁ, ŠÈ, ŠÈ, SU₄ and represented the outcome of Semitic *ð, which doesn't seem to have ever been called s₄ anywhere else that I can find.

(As a side note, I'm more used to s₃ being a name for PSem *s, rather than *θ. But the reflexes Gelb lists make it clear he's talking about *θ, not *s.)

Hasselbach disagrees, claiming that there were only three series, which she calls z, s, and θ (corresponding to Gelb's z, š₁₂, š₃ respectively). Regarding š₄, she says "[Gelb's] analysis does not conform to the etymologies of the words written with these three signs, which usually is [*š]", and "[t]here is no indication that SÁ, SE₁₁ and SU₄ represent different sibilants than SA, SI and SU."

Both authors (and also von Soden, whose work is not freely available online) seem to agree that there was no written distinction between Semitic s₁ (*š) and s₂ (*ś) in any stage of Akkadian; they're both reflected as s (š₁₂) in Sargonic, and š in later dialects.

Answer 2

I think you have examined this issue thoroughly. I was misled by von Soden's confusing notation. It does indeed seem that no known variant of Akkadian distinguished between Semitic s1 and s2.

Answer 3

Your question about Old Akkadian is also a question about what kinds of phonological contrasts were offered by Sumerian and what kinds of contrasts in Semitic had to be written.
It seems that four groups of phonemes can be distinguished:

1. *s (heb. shin ~ Arabic s)
2. *θ
3. *ś, originally a lateral fricative, but presumably a palatal sibilant in Akkadian and its descendants
4. affricates like *(d)z, tsade, tsamekh. group4 was also used to write the emphatic lateral dad, presumably because Sumerian offered no way to write that kind of sounds with specific signs.

Old Akkadian and Eblaite apparently had a full distinction between the four groups, but it seems that in Paleo-Babylonian *s and *θ had fused.
Eblaite and Old Akkadian concord on the fact that *s and *ś were written with sa, si, su, but in Paleo-Babylonian, sa, si, su were only used for *ś.
Eblaite and Old Akkadian consistently write *θ with specific signs, ša, etc. In Paleo-Babylonian, PS *s and PS *θ are no longer distinguished and written with the signs that used to be reserved for *θ. It seems that Assyrian did not choose the same signs to write the pair *s/θ as Babylonian.

From what I see in your account, it seems Gelb is mistaken about some sign values.

Besides, it can be noted that the signs *Sa have their equivalents *aS (three groups *as, *aθ, *ats). Generally speaking, it appears that Sumerian had only three series of sounds: roughly *s, *ts and *θ, while Semitic was in need of much more differentiation.