1. A method for generating a magnetic resonance tomography image with spectral fat saturation or spectral water excitation in a tissue region of a patient, comprising the steps of: (1) placing a patient, comprising a tissue region, in a magnetic resonance tomography data acquisition unit comprising a radio-frequency antenna arrangement comprising a plurality of sub-coils, each having a field of view that encompasses at least a portion of said tissue region, and making a frequency adjustment measurement of said tissue region using a sub-coil entity, comprised of at least one of said sub-coils, to obtain a first frequency spectrum in which fat and water respectively exhibit resonant frequencies due to the field of view of said first sub-coil entity; (2) in a processor, precisely determining the resonant frequency of water in said first frequency spectrum; (3) making another frequency adjustment measurement of said tissue region of the patient using a second sub-coil entity, different from and adjacent to said first sub-coil entity, to obtain a second frequency spectrum from said tissue region in which fat and water exhibit respective resonant frequencies due to the field of view of said second sub-coil entity, and precisely determining the resonant frequency of water in said tissue region in said second frequency spectrum; (4) implementing a magnetic resonance data acquisition sequence for the patient in the data acquisition unit to acquire a k-space data record using a diagnostic data sub-coil entity that includes one of said first sub-coil entity or said second sub-coil entity, and operating said data acquisition unit at a frequency corresponding to the resonant frequency of water determined for the sub-coil entity that is used as said diagnostic data coil entity; (5) repeating Step (4) with other sub-coils in said plurality of sub-coils until magnetic resonance data from an entirety of said tissue region are acquired; (6) combining the respective k-space data records acquired in Steps (4) and (5), to obtain a combined k-space data record; and (7) in an image computer, generating a magnetic resonance image of said tissue region from said combined k-space data record.