: Species counterpoint vs jazz I have many books on theory and I’m wondering if these two certain books can coincide or if they are just not able to work together. All my textbooks with counterpoint only allow intervals 1

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Some of the two-part voice leading is useful in pop as well as jazz. Between the melody and the bass is most important as these two stand out. Parallel fifths or octaves may cause it to sound like either the bass or melody dropped out.

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Of course they are different styles. And as there is a development in classical music from early Renaissance to Baroque, Classic and Romantic eras there is also a development in Jazz styles. So there are not only different styles between the two groups but also different styles within the two groups concerning chordbuilding and voice leading. The difference is as large as the difference between middle age church latin language and afro-american slang!

If you want to write Jazz music you can forget the rules of classical counterpoint, the only thing you have to know is the concept of counterpoint that concerns the idea of independent voices like imitation or countermelody (polyphony opposite to homophony) and you can work absolutely free in the realm of Jazz harmony.
And of course parallels of perfect fifths are not forbidden. :)

In Jazz and modern music you are free to create all kind of chords 1,3,5,7,9,11,13 ... and all kind of intervals and alterations. So don't study any longer those old counterpoint rules (except you have to ... or if you are interested in early music and history as I am in ancient music, renaissance music and in latin language, this is a wonderful world!)

Just start to play and write Jazz and you are free to create your own style.

I've found for you this interesting dissertation I'd like to share (it's much too broad to make a resume, but even the abstract, the table of contents and the list of tables shows the large treasure of information:
getd.libs.uga.edu/pdfs/sterrs_tamika_s_201305_phd.pdf
(I did download it and hope to find the leisure to read it in short time.)

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...only allow intervals 1 3 5 6 on accented parts ...parallel 5ths/8ths

Those are two separate issues. The fact that species counterpoint wants you to use consonances doesn't prohibit parallel fifths and octaves. The parallel concern is about relative motion and how you get to those consonances.

Does jazz care about parallel fifths?

There certainly is not a jazz prohibition like there is in species counterpoint.

...can voice leading somehow work with chord extensions from jazz.

One of the key factors of voice leading is moving voices the smallest distance to the tones of the next chord. By that measure I think jazz does use voice leading. Standard progressions like thse use voice leading...