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Are minor sevenths allowed in baroque counterpoint? I ask because in the first measure of Bach's Invention No. 1 the upper voice and lower voice have an interval of a minor seventh (the upper voice plays C while the lower voice plays D).

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@jjmusicnotes already answered the question with yes. The particular example you mention goes like:

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(2nd half of the first bar).

The d occurs in the lower voice in a rising line of steps in between c and an e; It's on a weak count and as it is a short sixteenth it immediately dissolves into an e which is consonant with the c in the uppoer voice. So this is a simple passing note and its effect is to smoothen the melody line. In this example, the seventh may sound harsh if the tempo is too low and if you deliberately emphasize the counter beat (the second half of the 3rd count); If it does, it probably means you got the tempo and/or the emphasis wrong.

Another typical case where you see minor sevenths (in classsic and in Baroque) is when the seventh actually has the function of the seventh degree in a (major or minor) 7th chord (typically the 5th degree of the scale or dominant 7th chord). This is not such an instance.

In such cases the seventh would typically descend to the third of the chord that lies a fourth above the seventh chord, forming a (semi)cadence.

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They are absolutely allowed and are treated in many different ways. In order to avoid a continuance of asking so many specialized questions, I would urge you to study Johann Fux's Gradus ad Parnassum which is the foundation for counterpoint and studied by all composers.

Also, for future reference, if Bach does it, then it's okay.

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Who waz johan fux –  Chris Olszewski May 16 '13 at 17:36
@ChrisOlszewski en.wikipedia.org/wiki/Johann_Joseph_Fux –  NReilingh May 16 '13 at 18:14
There are even instances where Bach used parallel octaves and fifths intentionally! –  ecline6 May 16 '13 at 18:46
@11684 - You are half correct here. Yes, during his lifetime he was actually more famous as an organist, and it is true that after his death, he was almost immediately forgotten for a few decades before being rediscovered. At his teacher's instruction, Mendelssohn began studying Bach's works and began championing them, which made them more accessible to the public, whereas before Bach was more of a musician's composer. Bach's music is widely, widely regarded has being the pinnacle of all Baroque style and forms. We would be doing ourselves a disservice to look to anyone else. –  jjmusicnotes Jun 2 '13 at 16:31
English translation of the book by Fux referred to by @jjmusicnotes can be found over here: opus28.co.uk/Fux_Gradus.pdf If you want to go through it, I'd suggest to also get this worksheet with commentary, as it explains some of the apparent contradictions in Fux' work. tc.umn.edu/~ston0235/pdf/fux_workbook_0.1.pdfb –  Roland Bouman Dec 28 '13 at 2:43
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