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What is the dance etiquette at a milonga when asking a Tango dancer to dance?
At a traditional milonga the music is played in tandas separated by cortinas - a short section of a different music style. A tanda comprises 3 or 4 pieces of tango music, 3 pieces of tango vals music, or 3 pieces of milonga music. Usually tandas are in the order: T, T, V, T, T, M, T, T, V, T,..... (3 or 4 depends on location, country, or tradition - but only for tango, not vals or milonga). Tango, vals and milonga are different dances. You don't/can't dance tango to milonga music.
Invitation to dance is usually by cabeceo/mirada, but that depends on the culture of the event. If the cabeceo is responded to by a mirada, then you usually dance the whole tanda, unless you're injured or insulted, in which case it's 'Thank you' and goodbye.
If you turn up at a milonga with a SO as partner, then the first and last dances are usually with them - as well as any 'specials'. It's not usual to dance 2 consecutive tandas together, except with a SO.