Yes, there is evidence to suggest that music tuned to A = 432 Hz induces both physiological and affective changes in comparison to A = 440 Hz, and that those effects point to a general "relaxation" of mind and body.
The journal EXPLORE, in 2019, published the article "Music Tuned to 440 Hz Versus 432 Hz and the Health Effects: A Double-blind Cross-over Pilot Study."1 That study found that
432 Hz tuned music was associated with a slight decrease of mean (systolic and diastolic) blood pressure values (although not significant), a marked decrease in the mean of heart rate (−4.79 bpm, p = 0.05) and a slight decrease of the mean respiratory rate values (1 r.a., p = 0.06), compared to 440 Hz. The subjects were more focused about listening to music and more generally satisfied after the sessions in which they listened to 432 Hz tuned music. (SOURCE)
2020 saw the publication of two studies.
A randomized trial of 42 dental patients2 demonstrated
Significantly lower anxiety level values were observed at 432 Hz (8.7±2.67) and 440 Hz (8.4±2.84) compared to the control group (17.2±4.60; p<0.05). The salivary cortisol level at 432 Hz (0.49±0.37 μg/dL) was significantly lower than 440 Hz (1.35±0.69 μg/dL) and the control group (1.59±0.7 μg/dL; p<0.05). (SOURCE)
And later that year, an Italian study3 of the sleep effect of tuning on 12 spinal cord injury patients found that
After listening to music at 432 Hz there was a significant improvement in sleep scores (+3.6, p=0.02), while there was no improvement in sleep scores listening to music at 440 Hz (-1.50, p=0.34). (SOURCE)
In 2021, International Journal of Human Sciences published "The magic of frequencies - 432 Hz vs. 440 Hz: Do cheerful and sad music tuned to different frequencies cause different effects on human psychophysiology? A neuropsychology study on music and emotions". That study concluded that
In the most comprehensive analysis with no reference to the cheerful or sad character of the sample, the participants who listened 440 Hz pieces reported rather negative mood after listening music compared to the participants who listened 432 Hz pieces. Moreover, men were observed to report even higher levels of negative mood after listening 440 Hz pieces, compared to their mood after listening 432 Hz pieces. All the findings thus reached imply that different tunes lead to variation in reported moods, even though they do not bring about changes in sympathetic and parasympathetic activation levels. (SOURCE)
An earlier study was made in 2018 by an undergraduate student in Sweden.3 That study concluded that there was no significant difference in emotional responses; it did not look at physiological responses.
1 Calamassi, Diletta, and Gian Paolo Pomponi. 2019. "Music Tuned to 440 Hz Versus 432 Hz and the Health Effects: A Double-blind Cross-over Pilot Study." EXPLORE, 15 (4): 283-290. https://doi.org/10.1016/j.explore.2019.04.001
2 Ravena, Pedro Christian, Camila Almonacid, and Marcelo Ignacio Mancilla. 2020. "Effect of music at 432 Hz and 440 Hz on dental anxiety and salivary cortisol levels in patients undergoing tooth extraction: a randomized clinical trial." Journal of Applied Oral Science, 28, e20190601. Epub May 11, 2020. https://doi.org/10.1590/1678-7757-2019-0601
3 Calamassi, Diletta, Alessia Lucicesare, Gian Paolo Pomponi, and Stefano Bambi. 2020. “Music Tuned to 432 Hz Versus Music Tuned to 440 Hz for Improving Sleep in Patients With Spinal Cord Injuries: A Double-Blind Cross-over Pilot Study”. Acta Bio Medica Atenei Parmensis 91 (12-S), e2020008. https://doi.org/10.23750/abm.v91i12-S.10755.
4 Erdal, Barış, Yeliz Kındap Tepe, Serdar Çelik, Büşra Güçyetmez, Burhanettin Çiğdem, and Suat Topaktaş. 2021. “The Magic of Frequencies - 432 Hz Vs. 440 Hz: Do Cheerful and Sad Music Tuned to Different Frequencies Cause Different Effects on Human Psychophysiology? A Neuropsychology Study on Music and Emotions: Frekansların Sihri – 432 Hz 440 Hz’e karşı: Ayrı Frekanslara göre akortlanmış neşeli Ve hüzünlü müzikler Insan Psikofizyolojisi üzerinde Farklı Etkiler yaratır mı? Müzik Ve Duygular üzerine Bir nöropsikoloji araştırması”. Journal of Human Sciences 18 (1):12-33. https://doi.org/10.14687/jhs.v18i1.6108.
5 Palmblad, S. 2018. "A = 432: A superior tuning or just a different intonation? How tuning standards affects emotional response, timbre and sound quality in music." Lisans bitirme tezi, Medya Sanatları, Estetik ve Anlatımı, Skövde Üniversitesi, İsveç. http://www.diva-portal.org/smash/get/diva2:1215149/FULLTEXT01.pdf