There is a proverb about the true nature of syllables which says that a syllable actually means the construction of letters, and thus, a letter may also be called a syllable—
akṣaraṃ barṇanirmāṇaṃ barṇamapyakṣaraṃ viduḥ.
A lot of research has gone into analysing whether a letter itself is a syllable, or whether a syllable is a letter. In the end, it can be found that the philosophical reasoning behind letters and syllables is the same as that behind Upaniṣadas (Upanishadas) and Gītā (Gita). Since a syllable encompasses an idea, and it does not stray from the idea, it is known as ‘akṣara‘. Because it is not decayble or na kṣarati—
“How far varṇa coincides, and is synonymous with akshara, ‘syllable’, or not, is obvious: it coincides with the latter term when it means vowel, otherwise not. The distinction between these terms may therefore be comprised in the following definition: kára denotes the pronounceable sound, which must always be one syllable, but may also consist of more than one syllable; if denoting one syllable, it may mean a simple vowel (a, á, i, í, u, ú, ṛi, ṛí, lṛi), or a complex vowel (e, o, ai, au), or a simple consonant made pronounceable by a vowel (usually the vowel a); karana denotes more especially the pronounceable sound represented either by more than one syllable or by one syllable containing more than one consonant. Varṇa, on the contrary, implies merely the simple letter,— among vowels, especially the simple vowel; among consonants, merely the single consonant, not accompanied with a vowel sign. Lastly, akshara means ‘syllable’ in our sense of the word, and may sometimes therefore coincide in value with kára, or varṇa in the same way that kára and varṇa are apparently convertible terms when they are the latter parts of compounds, the former of which are a, á, i, í, u, ú, ṛi, ṛí, lṛi.
I have, in the foregoing observations, purposely abstained from alluding to the use which has been made of these terms in the existing Prátiśákhyas of Śaunaka and Kátyáyana; in the first place, because it was my object to show their meaning in Páṇini’s work, as well as in those old Commentaries which have strictly adhered to his terminology, and because it would have been an uncritical proceeding to confound the meaning or bearing of these terms in works belonging to a different class of Hindu literature; Secondly, because the date of these works, themselves,—or, at least, their relative position towards Páṇini,— will have to be ascertained, before any conclusion can be drawn from a difference which may have existed between them in the use of these terms. Though I shall recur to this point, I may now state my belief, that even if grammatical works older than Páṇini had used varṇa in the general sense of akshara, such a circumstance would not disprove the fact that varṇa might have meant a written sign even before Páṇini’s time. There is, for instance, an introductory Várttika of Kátyáyana which countenances the assumption that varṇa had such a sense in some older grammarian; but the very manner in which it is brought before the reader shows that Kátyáyana contrasts the use of this word in Páṇini with that in his predecessor, and confirms, therefore, the definition I have given before. At the same time, it leaves the question undecided whether varṇa was, or was not, a written letter in this older work. The Várttika I am alluding to occurs at the end of the general introduction, and refers to the following Vaidik passage mentioned in the beginning of the introduction: ‘Whoever establishes this speech according to its words, its accent, and its syllables, he is fit to institute or to perform sacrificial work’; and that it is a duty to study grammar, follows from the words, ‘let us be fit to institute, or to perform sacrificial work.’ The Várttika then says: ‘akshara, you must know, means na kshara, i.e. not perishable,’ and continues, ‘or akshara comes from aś, ‘to pervade’, with the affix sara (Kaiyyaṭa: ‘because it pervades the sense’); and concludes, ‘or they call varṇa so in the Sútra of a former (grammarian)’ [Patanjali: i.e. ‘or in the Sútra of a former (grammarian) varna has the name akshara.’ Kaiyyaṭa: ‘For it is said in another grammar, that the varṇas are aksharas.’ Nagojibhatta: ‘In a similar manner the term aksharasamámnáya means a multitude of varṇas, as seen in the Vedas].”
[Ex. Theodor Goldstucker, Panini: His place in Sanskrit Literature, London: Trubner and Co, 1861, Pp. 42–44]