By the mid-1900s, the organs had grown more popular, and players began to switch from German polkas to Mexican music — songs of love and nostalgia that appealed to older generations.

These days, if a player does not own his instrument, he can rent one for about $80 a week, the union says.

For a variety of reasons — the cost of proper maintenance, the lack of repair know-how and overuse of the instruments — the melodies are often horribly off key. A cloud comes over diners’ faces when an organist pops up and begins cranking, forcing them to wait out the auditory assault.

There is also a skill that newcomers do not appreciate, the older players say. It is a craft. An organist does not just turn the lever and let the instrument do its business. One must crank consistently, which is not so easy given the instrument’s weight. The tempo must differ from song to song.

This knowledge is often passed down from one generation to the next.

Daniel Chávez, 40, works alongside his father on a bar-lined cobblestone street in the historical center of Mexico City, where he is slowly learning the trade.

“My father is the best one I know,” he said, pausing on a recent weekday to admire the older man, who has been playing for nearly 60 years.