Harmonic sounds, such as voiced speech sounds and many animal communication signals, are characterized by a pitch related to the periodicity of their envelopes. While frequency information is extracted by mechanical filtering of the cochlea, periodicity information is analyzed by temporal filter mechanisms in the brainstem. In the mammalian auditory midbrain envelope periodicity is represented in maps orthogonal to the representation of sound frequency. However, how periodicity is represented across the cortical surface of primary auditory cortex remains controversial. Using optical recording of intrinsic signals, we here demonstrate that a periodicity map exists in primary auditory cortex (AI) of the cat. While pure tone stimulation confirmed the well-known frequency gradient along the rostro-caudal axis of AI, stimulation with harmonic sounds revealed segregated bands of activation, indicating spatially localized preferences to specific periodicities along a dorso-ventral axis, nearly orthogonal to the tonotopic gradient. Analysis of the response locations revealed an average gradient of -100° ± 10° for the periodotopic, and –12°±18° for the tonotopic map resulting in a mean angle difference of 88°. The gradients were 0.65±0.08 mm/octave for periodotopy and 1.07 ± 0.16 mm/octave for tonotopy indicating that more cortical territory is devoted to the representation of an octave along the tonotopic than along the periodotopic gradient. Our results suggest that the fundamental importance of pitch, as evident in human perception, is also reflected in the layout of cortical maps and that the orthogonal spatial organization of frequency and periodicity might be a more general cortical organization principle.