Alphasyllabic numeral systems are a type of numeral systems, developed mostly in India starting around 500 AD. Based on various alphasyllabic scripts, in this type of numeral systems glyphs of the numerals are not abstract signs, but syllables of a script, and numerals are represented with these syllable-signs.[1] On the basic principle of these systems, numeric values of the syllables are defined by the consonants and vowels which constitute them, so that consonants and vowels are - or are not in some systems in case of vowels - ordered to numeric values. While there are many hundreds of possible syllables in a script, and since in alphasyllabic numeral systems several syllables receive the same numeric value, so the mapping is not injective.
The basic principle of the Indian alphasyllabaries is a set of 33 consonant-signs, which are combined with a set of about 20 diacritic marks that indicate vowels of the brahmi scripts, these produce a set of signs for syllables; unmarked consonant-signs denote the syllable with the inherent vowel ’a’.
Starting around 500 AD, Indian astronomers and astrologers began to use this new principle for numeration with assigning numeral values to the phonetic signs of various Indian alphasyllabic scripts – the brahmi scripts.[2] Earlier 20th-century scholars supposed that the Indian grammarian Pāṇini used alphasyllabic numerals already in the 7th century BC.[3] Since there is no direct evidence for any alphasyllabic numeration in India until about 510 AD, recently this theory is not supported.[4]
These systems, known collectively as varnasankhya systems, were considered to be distinct from other Indian systems – i.e. brahmi or kharosthi numerals - that had abstract numeral-signs.[5] Alike the alphabetic systems of Europe and the Middle East, these systems used phonetic signs of a script for numeration, but they were more flexible than those. Three significant systems of them: Āryabhaṭa numeration, katapayadi system, and the aksharapalli numerals.
Alphasyllabic numeration are very important for understanding Indian astronomy, astrology, and numerology, since Indian astronomical texts were written in Sanskrit verse, which had strict metrical form. These systems had the advantage of being able to give any word a numerical value, and to find many words corresponding to one given number. This made possible the construction of various mnemonics to aid scholars and students, and would have served a prosodic function.
Structure of the Indian alphasyllabic numeration systems differs basically from one another. Though in each of the systems consonants and vowels are ordered to numeric values, thereby each syllable has a numeric value, but on the base of each system's own rules. In various systems the V, CV, CCV syllables receive different values, and the methods, how the numbers are represented by these syllables, are quite different.
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 0 | |
|---|---|---|---|---|---|---|---|---|---|---|
| ka क క ക | kha ख ఖ ഖ | ga ग గ ഗ | gha घ ఘ ഘ | nga ङ జ్ఞ ങ | ca च చ ച | cha छ ఛ ഛ | ja ज జ ജ | jha झ ఝ ഝ | nya ञ ఞ ഞ | |
| ṭa ट ట ട | ṭha ठ ఠ ഠ | ḍa ड డ ഡ | ḍha ढ ఢ ഢ | ṇa ण ణ ണ | ta त త ത | tha थ థ ഥ | da द ద ദ | dha ध ధ ധ | na न న ന | |
| pa प ప പ | pha फ ఫ ഫ | ba ब బ ബ | bha भ భ ഭ | ma म మ മ | - | - | - | - | - | |
| ya य య യ | ra र ర ര | la ल ల ല | va व వ വ | śha श శ ശ | sha ष ష ഷ | sa स స സ | ha ह హ ഹ | - | - |