Ajna, the Third Eye chakra, appears in the classical Sanskrit tantric sources with its own seed syllable and symbolism centred on inner sight and intuition, with no reference to Western musical pitch. Its pairing with the note A in the modern chakra-tone system follows the same ascending mapping used throughout these entries, the sixth scale degree matched to the sixth chakra, a twentieth century Theosophical and New Age construction rather than an element of the older tradition.
A carries a separate and much more concrete significance in Western music entirely apart from any esoteric correspondence: A above middle C is the international standard reference pitch, fixed at 440 Hz by the ISO 16 standard adopted in the mid twentieth century, against which every other pitch in equal temperament tuning is calculated. Some modern esoteric writers note this practical primacy and read it as reinforcing A's pairing with a chakra concerned with perception and awareness, an interpretive flourish added after the fact rather than a reason drawn from the chakra-tone system's actual twentieth century origin.
Sources The Serpent PowerSir John Woodroffe (Arthur Avalon) with Rainbow Body: A History of the Western Chakra System from Blavatsky to BrennanKurt Leland, ISO 16:1975, Acoustics, Standard tuning frequency (Standard musical pitch)International Organization for Standardization