Nitaboh

Obviously if you love shamisen, you'll enjoy both of these anime. Both characters are looking for their own sound although their personalities are completely different from each other. 

Both stories are about a traditional japanese art which must face either evolving or remaining routed in tradition in a modernised japan during the edo period. 

This is probably the only non-mystery recommendation for this show but Ayatsuri Sakon had another major theme, Bunraku. This is a form of Japanese puppetry and is reference in the show often since one of the main characters is a Bunraku puppet. Nitaboh, while not a mystery anime, shares the same likeness when it comes to sharing a cultural aspect about Japan. Nitaboh was created a 5 years after Ayatsuri Sakon but both their execution and sound tracks are top notch. Nitaboh focuses on an instrument called a Shamisen, a three stringed instrument and is often used in Bunraku performances during narrative songs. Both movie and show share dark moments with times of joyous triumphant, and both protagonists (Nitaboh and Sakon) find their places through partnering with inanimate objects that held a special place in their hearts. read more 

Both tell a story of one person trying to realize a dream against the background of the modernization of Japan. 

Both involve the main character trying to learn to play their intrument (well enough) in time for the main event. 

The bittersweet struggle for music. Both show the powerful journey of music, & the devolvement of characters as they dive deep into the world of Music. Although, Nodame has a lot of Comedy & Romance you won't find in Nitaboh. Also, Nitaboh story is based on Japanese Folk Music while Nodame focuses on Westren Classical Music. 

How is this similar to Nitaboh? The answer is Music, main character from both anime comes from a poor family, and later on they find out that they are both gifted in one way or another in playing music. Piano no Mori and Nitaboh are two beautiful movies (visually stunning).