Unlike Rúmil, Fëanor considered vowels as indepedent sounds and not just “colours” of the consonants, so he devised the “full writing” (Quanta Sarmë). However he also used a more 'conservative' system which seem to have been proved far more popular. Fëanor held the idea of syllabic analysis of the words by the Sarati, and made also use of signs for vowels (instead of the full letters).
When the Noldor rebelled and came to Middle-earth, they adapted their writing for the new languages they learned. This led to the Mode of Beleriand, obviously a Quanta Sarmë modification for writing Sindarin. It is also possible that the Tengwar influenced the evolution of the Cirth, mainly in their shape and arrangement.
Tengwar are known to be used on Númenor by Men during the Second Age. In Eregion the Elves used new 'General' Modes of the Tengwar that could be used for a variety of languages, and it was in such a mode that the Inscription of the One Ring was formed.
The Exiles brought this Mannish usage to the Realms in Exile on Middle-earth, and was used to write the Common Speech. Different modes were used between Arnor and Gondor. Noticeable, the Northern Mode of Arnor was a modification of the Mode of Beleriand, still used in Rivendell. Men also made use of the so called General Use Modes and their variations.
The shape of the Tengwar were unirofmely consisted of two elements, the telco (stem) to which is attached a lúva (bow). It is noticeable that some of the letters of the Sarati resembled the telco/lúva shape seen on the Tengwar, therefore it is possible that those particular letters influenced stylistically the Tengwar.
The telco could be normal, raised, shortened or heightened. The lúva would be single or doubled, and these could be open or closed. All the above combinations can create 31 different shapes of letters. These shapes mirrored phonological significances: The basic form of a tengwa was used for the patakar, the voiceless fricatives; telcor determined how the sound was articulated, and the lúvar where in the mouth it was made.
According to their shape, the 32 different glyphs could be arranged and presented consistently on a table
By the end of the Third Age, the Tengwar were somehow standardized. Their Quenya names became standard for all modes, and less used ones were not included (although still used), such as those of the extended stems and the Tyelpetéma. The table displayed 36 letters: the 24 standard Tengwar, plus 12 of the additional Tengwar.
Also, the Tengwar were assigned numeric values
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 Quenya Tengwar
 Sindarin Tengwar
 Westron Tengwar
The word Tengwa has the meaning of 'sign representing audible phonemes' and is translated simply as 'letter'. The Sindarin name was Tîw (singular Têw).