Is it possible that listening same music with your partner can synchronize emotionally? Music forces us to feel emotions. Some music calms us, some music give us energy. What emotions music makes us feel can be different in each person but generally gives same emotions to us. 

We have emotional turbulence in our daily routine. Sometimes our emotions sync with our partner but sometimes not. Is it possible that listening the same music with your partner can synchronize emotionally? Is there any scientific research for that? My field is not psychology so I am asking to you.
I think that one of the most basic and universal responses a person can have to music is engagement. When listeners are engaged with music, they follow the sounds closely connecting in an affective way to what they hear.
Moreover, music listening and music therapy is becoming an important topic of social neuroscience scientific inquiry (Kamioka et al., 2014).
This branch of research is facilitated by Hyperscanning EEG which provides the opportunity to explore dynamic brain activities between two or more participants (Liu et al., 2018).
I'd like to suggest to you the following study by Lindenberger and colleagues (2009).
The authors recorded EEG from the brains of pairs of guitarists playing a short melody together to investigate the rate of cortical synchronization in the course of music-driven actions.
In order to measure the rate of brain synchronization, they implemented the phase-locking index (PLI) which reflects invariants of phases across trials measured from single electrodes. As you can see in the first figure both the participants playing and listening to each other music showed fronto-central activity and Synchronization measured by the PLI index suggested that the activity is the highest at fronto-central sites. Especially, in the image below you can see the PLI distribution in the fronto-central brain regions at the theta frequency.

Finally, they used another index called Interbrain Phase Coherence (IPC) which represents the degree of constancy in phase differences across trial between two electrodes measuring the activity from two different brains.
In the figure below you can see synchronization between brains as measured by IPC: coherence was also strongest for fronto-central connections.

I hope that this paper partly answered your doubts. I do not know any study directly investigating brain synchronization in romantic couples, but if you think that romantic couples can be a discriminating factor to study brain synchronization while listening or practising music you could put on an experiment that considers romantic couples as an experimental group and friends/acquaintances as a control group.
Always remember, however, that you must justify the choice of your experimental groups with strong literature.
REFERENCES

Kamioka H, Tsutani K, Yamada M, Park H, Okuizumi H, Tsuruoka K, Honda T, Okada S, Park S. (2014)Effectiveness of music therapy: a summary of systematic reviews based on randomized controlled trials of music interventions. DOVEPRESS. http://dx.doi.org/10.2147/PPA.S61340
Difei Liu, Shen Liu, Xiaoming Liu, Chong Zhang, Aosika Li, Chenggong Jin, Yijun Chen, Hangwei Wang and Xiaochu Zhang. Interactive Brain Activity: Review and Progress on EEG-Based Hyperscanning in Social Interactions. Front. Psychol., 08 October 2018 | https://doi.org/10.3389/fpsyg.2018.01862
Ulman Lindenberger, Shu-Chen Li, Walter Gruber and Viktor Müller. Brains swinging in concert: cortical phase synchronization while playing guitar. BMC Neuroscience 2009, 10:22 doi:10.1186/1471-2202-10-22