To improvise and to expand weaving together the notes in a fast tempo is a taan. Taans are very technical and
shows the training, practice and dexterity in weaving complicated patterns of the notes with variations in the rhythm.
Taans also are sung in Akaar. Speed is an important factor of the taan.
Some important types of the taan
Bol Taan : Taan can also be sung by utilizing the words of the Cheez (Composition). This is a difficult type of a taan as in this correct pronunciation, the beauty of the words, meaning of the composition, every thing has to be taken in to consideration.
Shuddha/Sapat (Straight)Taan : The notes are placed in an order in one or more octaves.
Koot Taan : The notes do not remain in order. It's complicated in nature.
Mishra Taan : Combination of the above two taans.
Gamak Taan : Gamak is a technique by which a force is added to notes and each note is repeated atleast twice.
Also there are many other types of taan called Ladant taan, Zatkaa taan, Gitkari taan, Jabde ki taan, Sarok Taan, Halak Taan, Palat taan.
Although the terms can be explained the raag is a tonal complex. The listener has to listen to several pieces of the raag in order to recognize the raag. Each raag is presented differently depending upon the Gharana of the artist, the artist's own nature, and his/her mood at that time, also on the form he/she chooses to perform the raag in i.e. whether it's a khayal, a Dhrupad, Thummri, Bhajan etc. The presentation is also different in case of vocal and instrumental music. This is why a Indian Classical Music can only be learnt properly by listening and repetition.