Jake Shimabukuro’s last album, “Nashville Sessions,” contained all-­original songs — a first for the ukulele virtuoso who made his name by performing a song by someone else: the Beatles’ “While My Guitar Gently Weeps.”

For his latest album, “The Greatest Day,” Shimabukuro said that he decided to mix in some familiar tunes with new originals, “just to try to keep a good balance.” Locals and tourists can get a preview when he stops by Blue Note Hawaii for two shows Monday before taking “The Greatest Day” on tour to Japan.

“I kind of wanted to bring back some of the recognizable tunes, because that’s something I really love doing, taking familiar songs and coming up with a new approach to them or a fun arrangement on the ukulele,” Shimabukuro said in a call from a tour stop in Iowa. “With the cover tunes, there were some oldies, there’s one from the ’80s band New Order called ‘Bizarre Love Triangle,’ the Beatles (“Eleanor Rigby”) and then the Zombies’ ‘Time of the Seasons.’ I’ve always loved that tune and I thought it worked really well on the ukulele.”

The workings of Shimabukuro’s fertile mind also are well in evidence with the new tunes. “Pangram” was inspired while having his son write pangrams – sentences that contain every letter of the alphabet, like “The quick brown fox jumps over the lazy dog.”

“I thought it would be cool to write a song that used all the notes in the Western music vocabulary,” he said. “I just took that idea and based everything on this chromatic line that I play throughout the song.”

He used a polar opposite approach for another tune, “Straight A’s.” It was inspired by “One Note Samba,” a song by the great Brazilian composer Antonio Carlos Jobim, which features a one-note melody sung to a harmonically dynamic accompaniment.

Similarly, Shimabukuro used the top string of the uke, traditionally tuned to the A, and created chords of different types with the remaining strings to support it.

“It goes through all these different key changes and modulations, so it gives the illusion that that note is changing, but it’s really not,” he said. “It goes through these different grooves and rhythms. There’s a part where it actually feels somewhat classical … almost like a Baroque-sounding melody, and then it goes into a straight-ahead jazzy blues thing, and then it goes into more of a fusion-rock thing, and then it goes into kind of a Santana thing.”

Shimabukuro’s original teacher, Roy Sakuma, likes to say that he could teach anyone to play a song using only one finger on the fretboard. With “Straight A’s” Shimabukuro’s taken it a step further.

“The idea was that if someone wanted to play that song with me and they’ve never played ukulele before, I can tell them ‘All you got to do is play quarter notes on that first string, the A string, from beginning to end and you’ll be playing along with me.”

He’ll be bringing his own twist to songs written by others. “Eleanor Rigby,” the Beatles tune famous for introducing string instruments to rock music, is set to a driving, New Wave-ish baseline, while Jimi Hendrix’s “If 6 Was 9” gets wildly virtuosic, which seems appropriate considering that Shimabukuro has been compared to Hendrix.

He will be performing with bassist Nolan Verner, whose work was heard on “Nashville Sessions,” and with guitar player Dave Preston, who is heard on “The Greatest Day.” The album is currently No. 8 on the Billboard’s World Music chart.

Shimabukuro was obviously pleased with the album, but it also passed muster with the critics most important to him: his parents.

“They both told me that it’s their favorite record of mine,” he said. “We’re still trying to get that approval from our parents, I guess.”