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I've seen people standing next to Torah readers and making hand signals during the Torah reading, presumably to prompt the reader in the trope. I think @Shalom mentioned this in Method for practicing Torah reading. What recognized systems exist for this, if any?

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I doubt you'll find an official system. I know a couple different gabbaim who each have differences on certain trop. –  Double AA Mar 26 '12 at 16:20
    
I have at least 3 systems that I use with various readers –  Baal Shemot Tovot Mar 26 '12 at 16:44
    
@l' did you devise them ad hoc with the readers in question? –  yitznewton Mar 26 '12 at 16:46
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While looking for the article @msh210 referenced in his presently-removed answer, I came across this: books.google.com/… –  Dave Mar 26 '12 at 18:35
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@Dave They have a sign for Karnei Farah!! –  Double AA Apr 19 '12 at 1:48
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Based on observations in a Sepharadic environment:

I have signed ta'amim for several readers using systems they taught me. They all seem to be based around the same signs, even if there are nuances between various methods. They are more or less imitations of the ta'am symbol, using your hand against the inside edge of the Sefer Torah case (upright, of course). Here are those which seem to me to be more-or-less universal in Sepharadic circles (if not exactly, then slightly variant):

  • רביע- Stick out index finger at a horizontal angle. Some swivel it about 15 degrees back and forth.
  • זרקה- Sideways figure-eight with index finger
  • תילשא- Index and thumb touch, remaining 3 fingers held up (like an "okay" gesture)
  • אזלא גריש- Move my index finger upwards in a 90 degree arc - first from the left then from the right
  • פזר גדול- Wave index finger up and down about three times, each time going a little higher than the last
  • פסק- One swift vertical chopping movement with whole hand
  • דרגא-תביר- Some form of an up-and-down movement. (My favorite is an upwards Z motion with index finger (דרגא) followed by a downwards-inwards curve (תביר))
  • שני גרשין- Hold out index and second finger together vertically, wave them inwards (sort of like a beckoning motion)
  • אתנח\סוף פסוק- Either tap the reader's hand, or downwards motion with whole hand. Reader is usually well-enough versed to differentiate. מאריך טרחא is generally assumed
  • זקף קטן- Index and middle finger held out, apart and vertically
  • זקף גדול- single upwards motion with index finger

I'm not sure if this is what you're looking for or if it will help you; I hope it will. I hope the explanations aren't too abstract (they look good to me, but I know what I'm referring to in each one so I can't tell objectively).

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And for Karnei Farah?? –  Double AA Mar 26 '12 at 22:38
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@DoubleAA It doesn't exist as far as I am concerned. –  Baal Shemot Tovot Mar 26 '12 at 22:39
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You may have a different name, but you want to tell me there is some other trop on אלפים באמה in sephardi sifrei torah? –  Double AA Mar 27 '12 at 4:47
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@DoubleAA Kodem Kol, a Sepharadic Sefer Torah doesn't have ta'amim in it; as a matter of fact it has nothing but the letters :P Seriously though, after speaking it over with my peers, apparently it does exist. Everyone I've spoken to vocalizes it differently. Rav Mazouz, in his Tikkun called Ish Matzliach, says it's like a Pazer Gadol. I've never signed it before, nor have I seen it been signed, and I have no clue how its commonly done, but if I was stuck signing one on the spot I'd prob do the Tilsha sign with two hands. Also, my readers generally know if a really rare ta'am is in the aliya –  Baal Shemot Tovot Mar 27 '12 at 16:51
    
@Vram It has some dots in it too, I imagine. –  Double AA Apr 18 '12 at 21:17
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Asher Laufer (אשר לאופר) wrote a paper "תנועות ידיים וראש בשעת קריאת התורה" on this subject. He describes (in my own very loose translation and sometimes condensation):

In Rabat, Morocco, the Torah reader himself moved his right hand or his head when reading words with mafsik (pausal) cantillation. That is, the motions constituted an "accompaniment":
zarka – he moves his head leftward
s'golta, zakef katon, asnach, sof pasuk – the index finger is situated on the table vertically; the other fingers form a fist
pazer gadol, karne fara, sh'ne g'rishin, shalsheles – he lifts his hand above his shoulder; the index finger is extended and the other fingers are in a fist
talsha – some (not all) make a circle with the hand, with the hand at shoulder-height
azla g'rish – he moves his head leftward and then rightward (back and forth)
r'via – he moves his hand downward (one movement)
kadma – he lifts his index finger a little upward. (It's the identical sign as for pazer except that he lifts the finger less than to shoulder-height.)
zakef gadol – he shakes his head down-up-down (three movements)
t'vir – the palm is open and is moved on a slant downward to the left to the table

In Fez, Morocco, they practiced two sets of motions. One was "accompaniment" of the head by the reader himself. The other set was done only when the reader was inexpert in the cantillation: then the "somech", standing to his left, helped him with "assisting" signs executed with the right hand or both hands. The assisting motions were not done simultaneous with the reading, as the accompaniment was, but beforehand, so the reader would know what cantillation was coming up. The use of assisting motions is disliked and generally unused, but is used freely in teaching cantillation to children.
zarka – the index finger is extended and the others form a fist. Move the hand upward slowly. Head accompaniment: the reader moves his head downward; some also raise their eyebrows.
s'golta – After raising the hand for zarka, lower the palm. At the end, the palm is open and not resting on the table.
pazer – Move the hand slowly leftward once. Head accompaniment: turn the head in small circles.
talsha and karne fara – the somech draws circles in the air until the reader starts reading the talsha. Head accompaniment: arcing rightward.
azla g'rish – the somech lifts both hands in parallel (each finger opposite its mate), and bends the fingers inward (thereby indicating the Tiberian symbol). Head accompaniment: move the head leftward, then rightward.
pasek – as for zarka but faster. Head accompaniment: suddenly lifting the head.
r'via – the hand is at shoulder height and the index finger is turned slowly slightly backward toward the shoulder. Head accompaniment: turn the head slowly to the right.
kadma – the hand is at shoulder height and is moved leftward to be at the base of the throat. Head accompaniment: turn the head down and leftward (similar to the hand motion).
zakef katon – from the end of the hadma sign, the hand is then moved slowly to rightward. Head accompaniment: move the head downward.
zakef gadol – the palm is open and moves upward slowly. Head accompaniment: move the head downward.
shalsheles – a slow arc rightward. Head accompaniment: an arc rightward.
sh'ne g'rishin – standing the index and middle fingers connected (like the Tiberian symbol)
darga – the palm is opposite the middle of the chest and lifts until it's at shoulder height and on the somech's right side.
t'vir – opposite hand motion to that of darga. Head accompaniment: move the head downward.
maarich, tarcha, asnach – the somech shows the symbols at [the height he's at already?]. Head accompaniment: none.
y'siv – the palm is opposite the middle of the chest and moves fast rightward. Head accompaniment: none.
sof pasuk – lift the extended palm slightly.

In Djerba, a "masmich" would aid the reader by putting his right-hand fingers on the reader's back (near his left shoulder) during the reading; this is still done in the Djerba synagogue in Jerusalem. Another informant says that to teach children the reading, a teacher would use his right hand as follows:
zarka – with the index finger extended and the others in a fist, make three or four fast clockwise circles
s'golta – vertical motion
pazer gadol, zakef gadol – slow upward motion
talsha, karne fara – slow clockwise circles
azla g'rish – with the index finger extended and the others in a fist, make the azla shape twice, slowly
pasek – a fast right-and-upward motion (with the index finger extended and the others in a fist)
r'via – like for pazer but faster
kadma – like for s'golta but shorter
zakef katon, darga, t'vir, asnach, sof pasuk – like for s'golta but slower
shalsheles – with the index finger extended and the others in a fist, make two slow circles and then throw the hand upward fast
sh'ne g'rishin – with the index finger extended and the others in a fist, make two slow circles

The ancient community of Rome:
mercha-tip'cha-esnach/sof pasuk – the open hand, palm down, is placed on the back of the reader's hand as he points to the words
mahpach-pashta-munach-zakef katon – the open hand, palm down, moves up and down repeatedly, increasing in amplitude
pasek – the open hand, with pinky side down, moves downward once
t'vir – with the index finger extended and the others in a fist, and with the hand oriented so the index finger points downward, the hand moves downward once
mercha t'vir – as for t'vir alone, but the hand starts off oriented so the finger is pointing upward and arcs around
sh'ne pashtin – the open hand, with pinky side down, moves back and forth
kadma v'azla, darga, gershayim, r'via – with the index finger extended and the others in a fist, and with the hand oriented so the index finger points upward, the hand moves upward once
talsha – with the hand in a fist and oriented so the back of the hand is upward, move the hand downward once

He notes that all these traditions are still live but are dying.

Note also that this paper indicates that it was presented with a videotape of the signs, including some of the above and some not listed above (from Egypt and Sana).

I have also seen (and used) chironomy different from all the above. I suspect any synagogue, reader, or gabay can make up whatever suits him, so long as the reader understands it.

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The someich described in the paragraph about Fez reminds me of the one time I was in a Teimani shul on Shabbat and the gabbai would sign the next passuk's trop to the oleh as the meturgeman was translating. (There was no designated ba'al keriyah.) –  Double AA Apr 18 '12 at 21:21
    
@DoubleAA, even without a m'turg'man, I think it makes much more sense to sign before the relevant word than during it, and that's what I've always done when signing. –  msh210 Apr 18 '12 at 21:38
    
Sorry, but the Roman cheironomy is anything but dying. It is still widely practised in any Roman temple, being it during the reading by a professional or by a member of the minyan. And the Lybian Jews in Rome have a practically identical system, which they always use. This is true also for two of the three Italian minyanim in Israel, the Jerusalem one (a mish mash of different Italian rite traditions), and the Italian minyan of Tel Aviv (basically Tripolitanian, with anybody free to sing, chant, conduct the prayer they way he likes, according tot he tradition he comes from: Tripoli, Rome, Leba –  user2007 Oct 16 '12 at 7:41
    
@MassimoTorrefranca, thanks, that's good to know. Welcome to Mi Yodeya. I hope you stick around and enjoy the site. –  msh210 Oct 16 '12 at 15:23
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