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 2. Letters

Śiva Sūtras, Phonemes, Script and Pratyahāra
Śiva Sūtras (Sanskrit: शिवसूत्राणि) are a collection of fourteen apohisms consisting of phonemes spoken in (Classical) Sanskrit. Phonemes are called वर्ण (varṇa) in Sanskrit. These phonemes constitute स्वर (śvara) or vowels and व्यञ्जन (vyañjana) or consonants of Sanskrit. Vowels and consonants are represented using लिपि (lipi) or script letters when writing. A letter which represents a phoneme is also called a वर्ण. Śiva Sūtras are not a part of Aṣṭādhyāyī but they have usage in it. They are given in as follows, they are represented using Devanagari script, their IAST counterparts are also given, each phenome has a separate cell: The last phoneme (or letter) of each apohism have the term इत् (IAST: IT) in Aṣṭādhyāyī (AA - 1.3.3). In IAST इत् letters are capitalized. Pāṇini used Śiva Sūtras to create प्रत्याहार (pratyāhāra). He used pratyāhāras in Aṣṭādhyāyī to mnemonically represent sets of letters. A pratyāhāra is a representation of a set of letters. A pratyāhāra is formed by taking a non-इत् letter and a इत् letter occuring in the same apohism or in succeeding apohisms. These two letters constitute a pratyāhāra which represents its first letter and all non-इत् letters occuring between them (AA - 1.1.71), (AA - 1.2.9). For example:  अच् (aCH pratyāhāra) — It is constituted of two letters, the first one is non-इत् and the latter one is an इत् letter, the first letter is from the first apohism and the last letter is from the fourth apohism. Thus, this pratyāhāra represents its first letter which is अ and all the non-इत् letters across अ and च्, they are {इ, उ, ऋ, ऌ, ए, ओ, ऐ, औ}, IAST: {i, u, ṛ, ḷ, e, o, ai, au}. In conclusion अच् pratyāhāra represents these letters: {अ, इ, उ, ऋ, ऌ, ए, ओ, ऐ, औ}, IAST: {a, i, u, ṛ, ḷ, e, o, ai, au}. The अच् pratyāhāra represents all the vowels of (Classical) Sanskrit. Note: 1. From the fifth apohism, non-इत् letters are consonants and have the inherent vowel which is, for Devanagari script, अ (a) adjoined with the letters, because those letters have no diacritics added to them. And inherent vowel is ajoined to those letters which have no diacritics. Pratyāhāras do not represent the inherent vowel. For example:  यण् (yaṆ) pratyāhāra — It represents the letters {य्, व्, र्, ल्}, IAST: {y, v, r, l} (the  ् diacritic signifies absence of any vowel with that letter). Not {य, व, र, ल}, IAST: {ya, va, ra, la}, which have the inherent vowel adjoined. 2. Notice that there are two ण् (Ṇ) as इत् letters, one in apohism 1 and the other in apohism 6. So what will be the set of letters if a pratyāhāra which consists of any of the non-इत् letters of the first apohism and ण्? Will the pratyāhāra represent the letters across apohism 1 and 6 or just 1? There are pratyāhāras used by Pāṇini where such condition is met. They are अण् (aṆ) and इण् (eṆ) pratyāhāras. अण् pratyāhāra represents letters accross apohism 1 to 6 in AA - 1.1.67, elsewhere in Aṣṭādhyāyī, अण् is limited to the first apohism. इण् is also spread across apohism 1 to 6, there is no exception for this. 3. There are two ह (ha) letters in Śiva Sūtras, one in apohism 5 and the other in apohism 14. But Pāṇini used only one pratyāhāra that is constituted of ह — the हल् pratyāhāra, it represents all non-इत् letters across apohism 5 to 14. ह is taken into account only once. हल् pratyāhāra represents all the consonants of Sanskrit, they are: {ह्, य्, व्, र्, ल्, ञ्, म्, ङ्, ण्, न्, झ्, भ्, घ्, ढ्, ध्, ज्, ब्, ग्, ड्, द्, ख्, फ्, छ्, ठ्, थ्, च्, ट्, त्, क्, प्, श्, ष्, स्}.

The Devanagari Alphabet
Although Sanskrit has been written in different scripts over history. In modern days, the use of Devanagari script is most popular. Vowels, consonants and diacritics of Devanagari that are used in (Classical) Sanskrit are given here. The letter sequence of Devanagari alphabet is different from the sequence of Śiva Sūtras.

Vowels
As stated before, अच् (aCH) pratyāhāra represents all the vowels in (Classical) Sanskrit. Those vowels can be divided or categorized based on - ए (e) is the combination of अ/आ (a/ā) sound with इ/ई (i/ī) sound (AA - 6.1.87). ओ (o) is the combination of अ/आ (a/ā) sound with उ/ऊ (u/ū) sound (AA - 6.1.87). ऐ (ai) is the combination of अ/आ (a/ā) sound with ए (e) sound (AA - 6.1.88). औ (au) is the combination of अ/आ (a/ā) sound with ओ (o) sound (AA - 6.1.88). Categorisation shown above has been summarized in this table:
 * Vowel length
 * ह्रस्व or Short: Short vowels have the duration of one मात्रा (mātrā). They are अ, इ, उ, ऋ and ॠ, IAST: a, i, u, ṛ and ḷ.
 * दीर्घ or Long: Long vowels have twice the duration of a short vowel, i.e., two mātrās. They are long forms of the short vowels. They are आ, ई, ऊ, ॠ and ॡ, respective to the short vowels, IAST: ā, ī, ū, ṝ, and ḹ. ए, ऐ, ओ, and औ, IAST: e, ai, o, and au, are also long vowels. ॡ is not used in Classical Sanskrit.
 * प्लुत or Prolonged: Prolonged vowels have thrice the duration of a short vowel, i.e., three mātrās. They are prolonged forms of short vowels and complex vowels. They are denoted by adding ३ symbol with vowel letters.
 * Composition of Sounds
 * Simple: Simple vowels, also known as monophthongs, are vowels that are pronouned with a single mouth position and are consisted of only one sound. A simple vowel may be short or long. The अक् (aK) pratyāhāra represents all the simple vowels.
 * Complex: Complex vowels, also known as diphthongs, are vowels that are pronounced with two consecutive mouth positions and are combination of two vowel sounds. A complex vowel is always long. A comple vowel is called संयुक्त स्वर (saṃyukta śvara) in Sanskrit. The एच् (eCH) pratyāhāra represents all the complex vowels.
 * Combinations of complex vowels are given:
 * उच्चारणस्थान (uccāraṇasthāna) or Place of Articulation
 * Of simple vowels
 * कण्ठ्य (kaṇṭhya) or Guttural: Place of articulation is throat. Thay are अ (a) and आ (ā).
 * तालव्य (tālavya) or Palatal: Place of articulation is palate. They are इ (i) and ई (ī).
 * ओष्ठ्य (oṣṭhya) or Labial: Place of articulation is lips. They are उ (u) and ऊ (ū).
 * मूर्धन्य (mūrdhanya) or Retroflex: Place of articulation is between alveolar ridge and hard palate. They are ऋ (ṛ) and ॠ (ṝ).
 * दन्त्य (dantya) or Dental: Place of articulation is teeth. They are ऌ (ḷ) ॡ (ḹ).
 * Of complex vowels
 * कण्ठतालव्य (kaṇṭhatālavya) or Palatoguttural: Two consecutive points of articulation — throat and palate. They are ए (e) and ऐ (ai).
 * कण्ठोष्ठय (kaṇṭhoṣṭhaya) or Labioguttural: Two consecutive points of articulation — throat and lips. They are ओ (o) and औ (au).
 * अनुनासिक स्वर (anunāsika śvara) or Nasal vowel : A vowel can be nasalised. When a nasalized vowel is pronounced, air flows through mouth as well as nose. The  ँ diacritic is used to denote a nasal vowel.  ँ (IAST: m̐) is called चन्द्रबिन्दु (candrabindu) in Sanskrit. But when it is marked above a vowel letter or diacritic that extends above the top line, अनुस्वार (anusvāra) diacritic —  ं (IAST: ṃ) is used instead.

Consonants
हल् pratyāhāra reresents all the consonants in (Classical) Sanskrit. They too can be categorized, based upon -
 * उच्चारणस्थान (uccāraṇasthāna) or Place of Articulation
 * कण्ठ्य (kaṇṭhya) or Guttural
 * तालव्य (tālavya) or Palatal
 * मूर्धन्य (mūrdhanya) or Retroflex
 * दन्त्य (dantya) or Dental
 * ओष्ठ्य (oṣṭhya) or Labial
 * कण्ठोष्ठ्य (kaṇṭhayoṣṭhya) or Labioguttural: Two consecutive places of articulation — throat and lips.
 * Airflow and Touch
 * स्पर्श व्यञ्जन (sparśa vyañjana) or Stop consonant: Consonants that are produced when two उच्चारक (uccāraka) or articulators touch each other or the throat shrinks to completely block airflow and then suddenly realease it. ञय् (ñaY) pratyāhāra represents all the stop consonants.
 * Stop consonants can be divided into classes with the letters having a fixed sequence
 * क ख ग घ ङ, IAST: ka kha ga gha ṅa, constitute the क वर्ग (ka varga), as the varga begins with ka. Varga means class. क वर्ग is known as कु (ku) in Aṣṭādhyāyī. It consists of all guttural stop consonants.
 * च छ ज झ ञ, IAST: ca cha ja jha ñ, constitute the च वर्ग (ca varga). It is known as चु (chu) in Aṣṭādhyāyī. It consists of all palatal stop consonants.
 * ट ठ ड ढ ण, IAST: ṭa ṭha ḍa ḍha ṇa, constitute the ट वर्ग (ṭa varga). It is known as टु (ṭu) in Aṣṭādhyāyī. It consists of all retroflex stop consonants.
 * त थ द ध न, IAST: ta tha da dha na, constitute the त वर्ग (ta varga). It is known as तु (tu) in Aṣṭādhyāyī. It consists of all dental stop consonants.
 * प फ ब भ म, IAST: pa pha ba bha ma, constitute the प वर्ग (pa varga). It is known as पु (pu) in Aṣṭādhyāyī. It consists of all labial stop consonants.

Note that each varga letter has the inherent vowel adjoined. It is for the ease of pronounciation as consonants cannot be produced without a vowel.
 * अन्त:स्थ व्यञ्जन (antahstha vyañjana) or Approximant consonant: Consonants that are produced when two articulators come close or touch each other, but the airflow is not blocked. यण् (yaṆ) pratyāhāra represents all the approximant consonants.
 * ऊष्म व्यञ्जन (ūṣma vyañjana) or Fricative consonant: Consonants that are produced by forcing air through a narrow opening made by placing two articulators close together or when air is forced through a shrinked throat. शल् (śaL) pratyāhāra represents all the fricative consonants.
 * Aspiration
 * महाप्राण व्यञ्जन (mahaprāṇa vyañjana) or Aspired consonants: Consonants that are accompanied by a strong burst of breath when produced. They are first, third and fifth letters of every varga and all approximant consonants.
 * अल्पप्राण व्यञ्जन (alpaprāṇa vyañjana) or Unaspired consonants: Consonants that are not accompanied by a strong burst of breath. They are second and fourth letter of every varga and all fricative consonant.
 * Voicing
 * सघोष व्यञ्जन (saghoṣa vyañjana) or Voiced consonants: Consonants that are produced along with the vibration of vocal cords. हश् (haŚ) pratyāhāra represents all the voiced consonants.
 * अघोष व्यञ्जन (aghoṣa vyañjana) or Unvoiced consonants: Consonants that are not produced along with the vibration of vocal cords. खर् (khaR) pratyāhāra represents all the unvoiced consonants.
 * अनुनासिक व्यञ्जन (anunāsika vyañjana) or Nasal consonant
 * The last letter of every varga, i.e., ङ ञ ण न म, IAST: ṅa ña ṇa na ma are nasal consonants. Air air flows through mouth as well as nose when a nasal consonant is pronounced. They are represented by the ञम् (ñaM) pratyāhāra.

In the tables above, the letters have the inherent vowel अ (a) adjoinded with them for the ease of pronounciation. A vowel can be adjoined with a consonant. A vowel adjoins with a consonant with its diacritic. When a vowel other than अ (a) adjoins with a consonant, it replaces the inherent vowel.
 * Vowel diacritics

अ (a) is the inherent vowel in Devanagari, thus, it has not any diacritic. It is adjoined to consonant letters without any diacritic. A consonant without any vowel has  ् diacritic, it is called विराम (virāma) in Sanskrit.

Conjunct Consonants
Conjunct consonants are consonants that have not intervening vowels between them and are produced consecutively. They are conjucted when they are very close to each other. Conjunction is called संयोग (saṃyoga) in Sanskrit (AA - 1.1.7). Example:  व् (v) + य (ya) = व्य (vya); व् is the former letter,  ् diacritic is added to signify that there is no vowel after it. य has its inherent vowel अ (a) adjoined to it, but it does not affect the conjunction since it is not between the consonants. When conjuncted, the conjunct letter will be व्य. The  ् is no longer used when the letter, to which it is added, undergo conjunction with a next consonant letter and forms a conjunct letter. When consonants conjunct, they conjunct in different manners for different combinations of consonant letters. For example:  1. व् (v) + य (ya) = व्य (vya) 2. द् (d) + य (ya) = द्य (dya) Conjunction 1 is different from 2. In 1, व्'s vertical stroke is removed and is attached to य to form व्य. While in conjunction 2, द्'s diagonal line and य's upper curved line is removed, and the remaining part of द् is inserted where was य's upper curved line. Some conjunct consonant letters are not formed from the parts of their previous and next letters. Example:  क् (k) + ष (ṣa) = क्ष (kṣa) ज् (j) + ञ (ña) = ज्ञ (jña)
 * Conunction with र् (r)
 * 1. If र् comes before a consonant, it becomes a curved stroke and is attached on the top of the consonant. Example:

 र् (r) + क (ka) = र्क (rka) र् (r) + र (ra) = र्र (rra)
 * 2. If र् comes after a consonant having a vertical stroke, it becomes a diagonal stroke and gets attached to the vertical stroke. Example:

 क् (k) + र (ra) = क्र (kra) Here, र has the inherent vowel अ (a) is added to it.
 * 3. If र् comes after a consonant not having a vertical stroke, it becomes two diagonal strokes having a common vertex and gets attached to the below of the consonant letter.

 छ् (ch) + र (ra) = छ्र (chra) ट् (ṭ) + र (ra) = ट्र (ṭra) ड् (ḍ) + र (ra) = ड्र (ḍra)
 * In case of द्, ह्, श् and त्:

 द् (d) + र (ra) = द्र (dra) ह् (h) + र (ra) = ह्र (hra) श् (ś) + र (ra) = श्र (śra) त् (t) + र (ra) = त्र (tra)
 * Remember
 * 1. द्ग is not as same as ग्द

 द्ग (dga) = द् (d) + ग (ga) ग्द (gda) = ग् (g) + द (da)
 * 2. द्ध is not not as same as ध्द. ध्द is not possible to pronounce.

 द्ध (ddha) = द् (d) + ध (dha) ध्द (dhda) = ध् (dh) + द (da)
 * 3. द्न is not as same as न्द

 द्न (dna) = द् (d) + न (na) न्द (nda) = न् (n) + द (da)
 * 4. द्ब is not as same as ब्द

 द्ब (dba) = द् (d) + ब (ba) ब्द (bda) = ब (b) + द (da)
 * 5. द्भ is not as same as भ्द

 द्भ (dbha) = द् (d) + भ (bha) भ्द (vda) = भ् (bh) + द (da)
 * 6. द्व is not as same as व्द

 द्व (dva) = द् (d) + व (va) व्द (vda) = व् (v) + द (da)
 * 7. ह्ण is not as same as ण्ह

<div style="background: white; border: 1px solid rgb(153, 153, 153); padding: 4px"> ह्ण (hña) = ह् (h) + ण (ña) ण्ह (ñha) = ण् (ñ) + ह (ha)
 * 8. ह्न is not as same as न्ह

<div style="background: white; border: 1px solid rgb(153, 153, 153); padding: 4px"> ह्न (hna) = ह् (h) + न (na) न्ह (nha) = न् (n) + ह (ha)
 * 9. ह्म is not as same as म्ह

<div style="background: white; border: 1px solid rgb(153, 153, 153); padding: 4px"> ह्म (hma) = ह् (h) + म (ma) म्ह (mha) = म् (m) + ह (ha)
 * 10. ह्ल is not as same as ल्ह

<div style="background: white; border: 1px solid rgb(153, 153, 153); padding: 4px"> ह्ल (hla) = ह् (h) + ल (la) ल्ह (lha) = ल् (l) + ह (ha)