Ḍha (Indic)

Ḍha (also romanized as Ddha) is a consonant of Indic abugidas. In modern Indic scripts, Ḍha is derived from the early "Ashoka" Brahmi letter  after having gone through the Gupta letter . As with the other cerebral consonants, ḍha is not found in most scripts for Tai, Sino-Tibetan, and other non-Indic languages, except for a few scripts, which retain these letters for transcribing Sanskrit religious terms.

Āryabhaṭa numeration

Aryabhata used Devanagari letters for numbers, very similar to the Greek numerals, even after the invention of Indian numerals. The values of the different forms of ढ are: 
ढ  = 14 (१४)
ढि  = 1,400 (१ ४००)
ढु  = 140,000 (१ ४० ०००)
ढृ  = 14,000,000 (१ ४० ०० ०००)
ढॢ  = 1,400,000,000 (१ ४० ०० ०० ०००)
ढे  = 14 (१४×१०१०)
ढै  = 14 (१४×१०१२)
ढो  = 14 (१४×१०१४)
ढौ  = 14 (१४×१०१६)

Historic Ḍha
There are three different general early historic scripts - Brahmi and its variants, Kharoṣṭhī, and Tocharian, the so-called slanting Brahmi. Ḍha as found in standard Brahmi,  was a simple geometric shape, with variations toward more flowing forms by the Gupta . The Tocharian Ḍha  did not have an alternate Fremdzeichen form. The third form of ḍha, in Kharoshthi () was probably derived from Aramaic separately from the Brahmi letter.

Brahmi Ḍha
The Brahmi letter , Ḍha, is probably derived from the altered Aramaic Dalet , and is thus related to the modern Latin D and Greek Delta. Several identifiable styles of writing the Brahmi Ḍha can be found, most associated with a specific set of inscriptions from an artifact or diverse records from an historic period. As the earliest and most geometric style of Brahmi, the letters found on the Edicts of Ashoka and other records from around that time are normally the reference form for Brahmi letters, with vowel marks not attested until later forms of Brahmi back-formed to match the geometric writing style.

Tocharian Ḍha
The Tocharian letter  is derived from the Brahmi , but does not have an alternate Fremdzeichen form.

Kharoṣṭhī Ḍha
The Kharoṣṭhī letter  is generally accepted as being derived from the altered Aramaic Dalet , and is thus related to D and Delta, in addition to the Brahmi Ḍha.

Devanagari Ḍha

Ḍha (ढ) is a consonant of the Devanagari abugida. It ultimately arose from the Brahmi letter , after having gone through the Gupta letter . Letters that derive from it are the Gujarati letter ઢ, and the Modi letter 𑘛.

Devanagari-using Languages
In all languages, ढ is pronounced as  or  when appropriate. Like all Indic scripts, Devanagari uses vowel marks attached to the base consonant to override the inherent /ə/ vowel:

Conjuncts with ढ
Devanagari exhibits conjunct ligatures, as is common in Indic scripts. In modern Devanagari texts, most conjuncts are formed by reducing the letter shape to fit tightly to the following letter, usually by dropping a character's vertical stem, sometimes referred to as a "half form". Some conjunct clusters are always represented by a true ligature, instead of a shape that can be broken into constituent independent letters. Vertically stacked conjuncts are ubiquitous in older texts, while only a few are still used routinely in modern Devanagari texts. Lacking a vertical stem to drop for making a half form, Ḍha either forms a stacked conjunct/ligature, or uses its full form with Virama. The use of ligatures and vertical conjuncts may vary across languages using the Devanagari script, with Marathi in particular avoiding their use where other languages would use them.

Ligature conjuncts of ढ
True ligatures are quite rare in Indic scripts. The most common ligated conjuncts in Devanagari are in the form of a slight mutation to fit in context or as a consistent variant form appended to the adjacent characters. Those variants include Na and the Repha and Rakar forms of Ra. Nepali and Marathi texts use the "eyelash" Ra half form  for an initial "R" instead of repha.
 Repha र্ (r) + ढ (ḍʱa) gives the ligature rḍʱa: 

 Eyelash र্ (r) + ढ (ḍʱa) gives the ligature rḍʱa:

 ढ্ (ḍʱ) + rakar र (ra) gives the ligature ḍʱra:

 ढ্ (ḍʱ) + न (na) gives the ligature ḍʱna:

 प্ (p) + ढ (ḍʱa) gives the ligature pḍʱa:

 ष্ (ṣ) + ढ (ḍʱa) gives the ligature ṣḍʱa:

Stacked conjuncts of ढ
Vertically stacked ligatures are the most common conjunct forms found in Devanagari text. Although the constituent characters may need to be stretched and moved slightly in order to stack neatly, stacked conjuncts can be broken down into recognizable base letters, or a letter and an otherwise standard ligature.
 छ্ (cʰ) + ढ (ḍʱa) gives the ligature cʰḍʱa:

 ड্ (ḍ) + ढ (ḍʱa) gives the ligature ḍḍʱa:

 द্ (d) + ढ (ḍʱa) gives the ligature dḍʱa:

 ढ্ (ḍʱ) + ब (ba) gives the ligature ḍʱba:

 ढ্ (ḍʱ) + भ (bʰa) gives the ligature ḍʱbʰa:

 ढ্ (ḍʱ) + च (ca) gives the ligature ḍʱca:

 ढ্ (ḍʱ) + छ (cʰa) gives the ligature ḍʱcʰa:

 ढ্ (ḍʱ) + द (da) gives the ligature ḍʱda:

 ढ্ (ḍʱ) + ड (ḍa) gives the ligature ḍʱḍa:

 ढ্ (ḍʱ) + ढ (ḍʱa) gives the ligature ḍʱḍʱa:

 ढ্ (ḍʱ) + ध (dʱa) gives the ligature ḍʱdʱa:

 ढ্ (ḍʱ) + ग (ga) gives the ligature ḍʱga:

 ढ্ (ḍʱ) + घ (ɡʱa) gives the ligature ḍʱɡʱa:

 ढ্ (ḍʱ) + ह (ha) gives the ligature ḍʱha:

 ढ্ (ḍʱ) + ज (ja) gives the ligature ḍʱja:

 ढ্ (ḍʱ) + झ (jʰa) gives the ligature ḍʱjʰa:

 ढ্ (ḍʱ) + ज্ (j) + ञ (ña) gives the ligature ḍʱjña:

 ढ্ (ḍʱ) + क (ka) gives the ligature ḍʱka:

 ढ্ (ḍʱ) + ख (kʰa) gives the ligature ḍʱkʰa:

 ढ্ (ḍʱ) + क্ (k) + ष (ṣa) gives the ligature ḍʱkṣa:

 ढ্ (ḍʱ) + ल (la) gives the ligature ḍʱla:

 ढ্ (ḍʱ) + ळ (ḷa) gives the ligature ḍʱḷa:

 ढ্ (ḍʱ) + म (ma) gives the ligature ḍʱma:

 ढ্ (ḍʱ) + ङ (ŋa) gives the ligature ḍʱŋa:

 ढ্ (ḍʱ) + ण (ṇa) gives the ligature ḍʱṇa:

 ढ্ (ḍʱ) + ञ (ña) gives the ligature ḍʱña:

 ढ্ (ḍʱ) + प (pa) gives the ligature ḍʱpa:

 ढ্ (ḍʱ) + फ (pʰa) gives the ligature ḍʱpʰa:

 ढ্ (ḍʱ) + स (sa) gives the ligature ḍʱsa:

 ढ্ (ḍʱ) + श (ʃa) gives the ligature ḍʱʃa:

 ढ্ (ḍʱ) + ष (ṣa) gives the ligature ḍʱṣa:

 ढ্ (ḍʱ) + त (ta) gives the ligature ḍʱta:

 ढ্ (ḍʱ) + थ (tʰa) gives the ligature ḍʱtʰa:

 ढ্ (ḍʱ) + ट (ṭa) gives the ligature ḍʱṭa:

 ढ্ (ḍʱ) + ठ (ṭʰa) gives the ligature ḍʱṭʰa:

 ढ্ (ḍʱ) + व (va) gives the ligature ḍʱva:

 ढ্ (ḍʱ) + य (ya) gives the ligature ḍʱya:

 ङ্ (ŋ) + ढ (ḍʱa) gives the ligature ŋḍʱa:

 ट্ (ṭ) + ढ (ḍʱa) gives the ligature ṭḍʱa:

 ठ্ (ṭʰ) + ढ (ḍʱa) gives the ligature ṭʰḍʱa:

Bengali Ḍha
The Bengali script ঢ is derived from the Siddhaṃ , and is marked by a similar horizontal head line, but less geometric shape, than its Devanagari counterpart, ढ. The inherent vowel of Bengali consonant letters is /ɔ/, so the bare letter ঢ will sometimes be transliterated as "ḍho" instead of "ḍha". Adding okar, the "o" vowel mark, gives a reading of /d̳ʱo/.
Like all Indic consonants, ঢ can be modified by marks to indicate another (or no) vowel than its inherent "a".

ঢ in Bengali-using languages
ঢ is used as a basic consonant character in all of the major Bengali script orthographies, including Bengali and Assamese.

Conjuncts with ঢ
Bengali ঢ exhibits a few conjunct ligatures, as is common in Indic scripts.
 ঢ্ (ḍʱ) + র (ra) gives the ligature ḍʱra, with the ra phala suffix:

 ঢ্ (ḍʱ) + য (ya) gives the ligature ḍʱya, with the ya phala suffix:

 ণ্ (ṇ) + ঢ (ḍʱa) gives the ligature ṇḍʱa:

 র্ (r) + ঢ্ (ḍʱ) + য (ya) gives the ligature rḍʱya, with the repha prefix and ya phala suffix:

Gujarati Ḍha

Ḍha (ઢ) is the fourteenth consonant of the Gujarati abugida. It is derived from the Devanagari Ḍha  with the top bar (shiro rekha) removed, and ultimately the Brahmi letter .

Gujarati-using Languages
The Gujarati script is used to write the Gujarati and Kutchi languages. In both languages, ઢ is pronounced as  or  when appropriate. Like all Indic scripts, Gujarati uses vowel marks attached to the base consonant to override the inherent /ə/ vowel:

Conjuncts with ઢ
Gujarati ઢ exhibits conjunct ligatures, much like its parent Devanagari Script. While most Gujarati conjuncts can only be formed by reducing the letter shape to create a "half form" that fits tightly to following letter, Ḍha does not have a half form. A few conjunct clusters can be represented by a true ligature, instead of a shape that can be broken into constituent independent letters, and vertically stacked conjuncts can also be found in Gujarati, although much less commonly than in Devanagari. Lacking a half form, Ḍha will normally use an explicit virama when forming conjuncts without a true ligature.
True ligatures are quite rare in Indic scripts. The most common ligated conjuncts in Gujarati are in the form of a slight mutation to fit in context or as a consistent variant form appended to the adjacent characters. Those variants include Na and the Repha and Rakar forms of Ra.
 ર્ (r) + ઢ (ɖʱa) gives the ligature RḌha:

 ઢ્ (ɖʱ) + ર (ra) gives the ligature ḌhRa:

 ઢ્ (ɖʱ) + ઢ (ɖʱa) gives the ligature ḌhḌha:

 ઢ્ (ɖʱ) + ન (na) gives the ligature ḌhNa:

Javanese Ḍha

Telugu Ḍha

Ḍha (ఢ) is a consonant of the Telugu abugida. It ultimately arose from the Brahmi letter . It is closely related to the Kannada letter ಢ. Most Telugu consonants contain a v-shaped headstroke that is related to the horizontal headline found in other Indic scripts, although headstrokes do not connect adjacent letters in Telugu. The headstroke is normally lost when adding vowel matras.
Telugu conjuncts are created by reducing trailing letters to a subjoined form that appears below the initial consonant of the conjunct. Many subjoined forms are created by dropping their headline, with many extending the end of the stroke of the main letter body to form an extended tail reaching up to the right of the preceding consonant. This subjoining of trailing letters to create conjuncts is in contrast to the leading half forms of Devanagari and Bengali letters. Ligature conjuncts are not a feature in Telugu, with the only non-standard construction being an alternate subjoined form of Ṣa (borrowed from Kannada) in the KṢa conjunct.

Malayalam Ḍha

Ḍha (ഢ) is a consonant of the Malayalam abugida. It ultimately arose from the Brahmi letter , via the Grantha letter  Ḍha. Like in other Indic scripts, Malayalam consonants have the inherent vowel "a", and take one of several modifying vowel signs to represent syllables with another vowel or no vowel at all.

Conjuncts of ഢ
As is common in Indic scripts, Malayalam joins letters together to form conjunct consonant clusters. There are several ways in which conjuncts are formed in Malayalam texts: using a post-base form of a trailing consonant placed under the initial consonant of a conjunct, a combined ligature of two or more consonants joined together, a conjoining form that appears as a combining mark on the rest of the conjunct, the use of an explicit candrakkala mark to suppress the inherent "a" vowel, or a special consonant form called a "chillu" letter, representing a bare consonant without the inherent "a" vowel. Texts written with the modern reformed Malayalam orthography, put̪iya lipi, may favor more regular conjunct forms than older texts in paḻaya lipi, due to changes undertaken in the 1970s by the Government of Kerala.
 ഡ് (ḍ) + ഢ (ḍʱa) gives the ligature ḍḍʱa:

 ണ് (ṇ) + ഢ (ḍʱa) gives the ligature ṇḍʱa:

Odia Ḍha

Ḍha (ଢ) is a consonant of the Odia abugida. It ultimately arose from the Brahmi letter , via the Siddhaṃ letter  Ḍha. Like in other Indic scripts, Odia consonants have the inherent vowel "a", and take one of several modifying vowel signs to represent syllables with another vowel or no vowel at all.

As is common in Indic scripts, Odia joins letters together to form conjunct consonant clusters. The most common conjunct formation is achieved by using a small subjoined form of trailing consonants. Most consonants' subjoined forms are identical to the full form, just reduced in size, although a few drop the curved headline or have a subjoined form not directly related to the full form of the consonant. The second type of conjunct formation is through pure ligatures, where the constituent consonants are written together in a single graphic form. ଢ generates conjuncts only by subjoining and does not form ligatures.

Tibetan

Ḍha is a consonant of the Tibetan abugida. Tibetan Ḍha is not genealogically related to Ḍha in other Indic scripts, but is rather a "compound" letter composed from Ḍa + Ha. As a cerebral consonant, it is not used for writing native Tibetan words, but can be found in terms borrowed from Sanskrit and other Indo-Aryan languages.

Kaithi Ḍha

Ḍha (𑂛) is a consonant of the Kaithi abugida. It ultimately arose from the Brahmi letter , via the Siddhaṃ letter  Ḍha. Like in other Indic scripts, Kaithi consonants have the inherent vowel "a", and take one of several modifying vowel signs to represent syllables with another vowel or no vowel at all.

Conjuncts of 𑂛 
As is common in Indic scripts, Kaithi joins letters together to form conjunct consonant clusters. The most common conjunct formation is achieved by using a half form of preceding consonants, although several consonants use an explicit virama. Most half forms are derived from the full form by removing the vertical stem. As is common in most Indic scripts, conjucts of  ra are indicated with a repha or rakar mark attached to the rest of the consonant cluster. In addition, there are a few vertical conjuncts that can be found in Kaithi writing, but true ligatures are not used in the modern Kaithi script.

 𑂩୍ (r) + 𑂛 (ḍʱa)  gives the ligature rḍʱa:

Kaithi Ṛha

Ṛha (𑂜) is a consonant of the Kaithi abugida and is derived from the Kaithi 𑂛 Ḍha.

Conjuncts of 
As is common in Indic scripts, Kaithi joins letters together to form conjunct consonant clusters. The most common conjunct formation is achieved by using a half form of preceding consonants, although several consonants use an explicit virama. Most half forms are derived from the full form by removing the vertical stem. As is common in most Indic scripts, conjucts of  ra are indicated with a repha or rakar mark attached to the rest of the consonant cluster. In addition, there are a few vertical conjuncts that can be found in Kaithi writing, but true ligatures are not used in the modern Kaithi script.

 𑂩୍ (r) +  (ṛʱa)  gives the ligature rṛʱa:

Comparison of Ḍha
The various Indic scripts are generally related to each other through adaptation and borrowing, and as such the glyphs for cognate letters, including Ḍha, are related as well.

Character encodings of Ḍha
Most Indic scripts are encoded in the Unicode Standard, and as such the letter Ḍha in those scripts can be represented in plain text with unique codepoint. Ḍha from several modern-use scripts can also be found in legacy encodings, such as ISCII.

References

 Conjuncts are identified by IAST transliteration, except aspirated consonants are indicated with a superscript "h" to distinguish from an unaspirated cononant + Ha, and the use of the IPA "ŋ" and "ʃ" instead of the less dinstinctive "ṅ" and "ś".

Indic letters