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I have the following sheet music excerpt for Spanish guitar:

Odeon. Tango Brasileiro

What is the meaning of the ₵2 and C3 on the 2nd and 4th measures?

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I haven't seen those symbols in that context before, but they must mean that you use your first finger to barre the indicated fret (fret 2 in the second half of the first bar, and fret 3 in the third bar).

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    This makes a lot of sense. Barring the fret is the easiest way to hit the chords in the first chord. I suppose the crossed C indicates half barre (strings E,B,G) and the uncrossed C indicates a full barre. – Renan Gemignani Oct 2 '18 at 19:43
  • @RenanGemignani: Yes, smart that you figured out the half vs the full barre; I'm sure that's the difference between those two symbols. – Matt L. Oct 3 '18 at 7:52
  • The C with a slash through it is also noted as 1/2 C, e.g. 1/2 C5 is a partial barre in the 5th position. – ggcg Oct 4 '18 at 16:59
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The symbols in question represent in fact barre chords. The numerals following the C indicates the position (i.e., fret) of the barre chord. As OP already has figured out, ₵ refers to a partial barre chord—it does, however, not indicate how many strings should be barred.

A nice overview of the many different styles to notate barre chords is given in the respective Wikipedia article.

  • This is the correct answer. – ggcg Oct 3 '18 at 17:39
  • The notation rarely spoonfeeds yo by telling you how many strings to bar – Neil Meyer Oct 18 '18 at 8:39

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