To determine how many songs Joe can purchase with his $15 gift card at a cost of $1.19 per song, we can divide the total amount of the gift card by the cost per song.
\[ \text{Number of songs} = \frac{\text{Total money}}{\text{Cost per song}} = \frac{15}{1.19} \]
Calculating this gives:
\[ \frac{15}{1.19} \approx 12.61 \]
Since Joe can only purchase whole songs, we round down to the nearest whole number, which is 12.
Therefore, Joe can purchase at most 12 songs.