Restoration: 1998-2000, organ restoration by Pieter Visser, finished by his assistant Ignacio Zapata; the case was restored by Agustín Espinosa. The project directors were Gustavo Delgado and Ofelia Gómez of the Academia Mexicana de Música Antigua para Órgano (AMMAO); the restoration was financed by Fomento Cultural Banamex.

The organ of the Basílica de la Soledad is one of the oldest and most imposing organs in all of Mexico. The profile and dimensions, as well as the exquisite carved, painted, and gilded decoration, resemble those of the organ of Yanhuitlán, which may have been built around the same time. The Soledad organ was originally located in a raised tribune to the right of the main altar, with its four large bellows in a room behind. The tribune was built for the organ in 1718, and the organ was built and installed there during the following year, 1719. These projects, as well as the entire construction of the church and convent, were financed by the estate of the late Pedro de Otálora; the works were in process when he died in 1691. A railing encircled the tribune with a curve in the middle where the organist sat. The splendid decoration of the organ, including the whimsically painted lower case, would have been visible to all parishioners. Since the Basilica de la Soledad was a point of departure along the route (Camino Real) for travelers headed to the coast, there would have been ongoing activity in this church. The organ was moved up to its current location in the expansive choir loft in 1908, but only three bellows fit beside the organ. The IOHIO discovered the fourth bellows in 2019 in a store room in the Basilica. 

An inventory of church goods in 1767 cites four statues of angels standing on the side towers of the organ, with the archangel Michael in the center; 19th-century carved decoration now fills the spaces. Until the Reform Period of the 1860s, the choir loft was connected to the Augustinian nuns’ convent to the right of the church, currently the seat of the Oaxaca Municipal government. The façade pipes were originally decorated with grotesque faces (mascarones) and multicolored floral designs, probably similar to those of Yanhuitlán. 

The organ was surely modified in 1908 when the Casa Wagner disassembled it for its move to the choir loft, although it is impossible to distinguish such changes from later interventions.  During the 1970s, supposedly by the order of the priest, the organ was again modified, reflecting the aesthetic shift from the lavish baroque to the quieter neo-classical. The pipe decoration was painted over with silver enamel, although fortunately it was not scraped off as in the Oaxaca Cathedral organ: much of the original floral decoration still remains under the overpainting. At the same time, the richly decorated case was repainted in muted gray and green tones. The organ was also modernized with a pedal board and new keyboard, a reservoir bellows, the cancelation of the reed stops, and the reconstruction of the wind chest. Two decades later, an appreciation for historic instruments led to a restoration project to reverse the modifications and recover the 18th-century baroque character of the organ. The keyboard, key action, and windchest were reconstructed, the pedal board removed, a new horizontal reed installed, and the original case painting recovered. Unfortunately, the façade pipes were painted white on top of the silver coat from the 1970s, incongruent for this elegant baroque instrument. Although intended as a temporary protective cover, decades later it has still not been removed.

Two-dimensional painting imitates three-dimensional carving