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In my music theory class, the text book has in an example, all of the 7th chords in a G harmonic minor scale. Why, in the chords on 1 and 3, is the 7th is lowered? While the chords on the 5 and 7 are raised, making it clear that it is a harmonic scale.

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These are not the seventh chords of G harmonic minor, but just one possible collection of seventh chords in G minor. As you've noticed, only the V and the VII chord are from harmonic minor. The reason is that these chords (usually) have a dominant function where the leading tone (F#) plays an important role. The other chords are based on the natural minor scale, which is more commonly used for the chords on I and III, because this results in the less exotic sounds of a Im7 and a IIImaj7 chord, instead of a Im/maj7 and a IIImaj7/#5. Note that these latter chords are also used but they are much less common. So the chords listed in your text book are simply the most common chords in a minor key, some of them taken from the natural minor scale, some (the ones with a dominant function) from the harmonic minor scale.

  • Indeed, the primary reason to raise the seventh is when it is functioning as a Leading Tone, as it does for V and vii. It doesn't generally have this function for i and III. – Caleb Hines Oct 27 '14 at 18:03
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The I,III don't have their 7th lowered. The scale you are looking at is most likely the G natural minor scale and not the G Harmonic minor scale. The notes that are included in the G natural minor scale are the same that consist the Bb Major scale (Bb, C, D, Eb, F, G, A). The correct thing to say here is that on the V and the VII, some notes are raised. These two chords are called Dominant Chords.

What you need to understand is the role of the Dominant chord. This chord is the V degree of your scale (and can also be substituted by the VII) and it

has the role of creating instability that requires the tonic for resolution.

So, you see, point of a dominant chord is to lead the chord progression to the first degree of you tonality (in your case G minor).

When you add F# to a chord, it becomes the leading tone of your scale. The leading tone is a note that leads to the tonic. So, in your example, if you have a F#, it has to be resolved to the tonic -> G.

To make it even more simple: In a chord progression, after you play V (or VII), most likely, the next chord will be I. (this being the point of the dominant chords). Thus, you need the leading tone to make it clear to the ear of the listener.

The rest of the chords (II,III,IV,VI) don't necessarily preceed I, so there is no point to include the leading tone.

Quoting Wikipedia on Leading Tone:

Melodically strong affinity for and leads to tonic.

Of course, there are exceptions for all the -rules- I mentioned above; I just tried to mention the really basic stuff, so you can understand it.

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The title of that part says 'G minor scale'.No mention of harmonic. There are different minor scales: natural, harmonic, classical melodic and jazz melodic. All have the same first five notes, rising, but it all changes after that. From the 5th (D) Eb, E, F and F# are available from the different minors. So there will be several different incarnations of chords spelled from those notes on top of others from G minor.

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