Music has a considerable influence on human physiology and can modulate listeners' blood pressure (BP). Other physiological parameters like ECG and respiration are also impacted by music. Here, we study the potential for predicting both systolic and diastolic blood pressure (SBP and DBP) from ECG and respiration along with music features using a graph attention network (GAT). The aim is to advance the potential of music with physiological feedback in helping achieving a healthy BP range. Fifty participants (34 women, age:18-80yrs) listened to music digitally altered to have differing tempi and loudness rendered on a reproducing piano. ECG, respiration, and BP were acquired simultaneously during music listening following an initial silence baseline. We obtain time and frequency domain signal features from ECG and respiration during pre-processing, and extract loudness, tempo, and spectral centroid from the music signals. With SBP and DBP ranges as target variables, we perform regression analysis using GAT whereby physiological signals form nodes, music tracks establish the edges, and music features constitute the edge attributes. Comparison of loss curves (mean squared error, MSE vs epoch number) during baseline silence and during music showed that music listening (having music features as edges attributes for GAT) improved both SBP and DBP prediction. The regression value was 0.64 (SBP) and 0.61(DBP), in presence of music, vs. 0.39 and 0.36 in silence, respectively. Mean absolute error, MAE was 2.78 (SBP) and 3.58 (DBP) and RMSE was 3.01 (SBP) and 3.59 (DBP). On average, SBP and DBP prediction with physiology during music listening and music features reduced error by 29.3%, showing that music engagement enhanced hypertension diagnostic accuracy. Hence, we have demonstrated for the first time the potential of music-based physiological feedback in predicting SBP and DBP, providing more accurate and granular BP prediction during music listening for precision hypertension therapies.