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I recently started working my way through Hindemith's Traditional harmony Book 1 on my own. The instructions are short and simple, but sometimes too much so for a self-learner.

I have reached Chapter II; so far, the book is based on harmony for SATB voices. Hindemith starts this chapter with rules to connect the principal triads in their "simplest" form i.e. with the root tone doubled "in the octave or unison":

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I am confused by this rule. Could someone clarify what is the reference point for the doubling interval? Is it relative to the Bass voice? The Tenor voice? (Other?) Please help me understand how it works.

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  • The doubled note in each of these chords is the root of the chord, has nothing to do with SATB. (Actually it looks like the Bass note is always the root in this so maybe thats wrong) – Legorhin Oct 24 at 16:00
  • There's always going to be a common note between I and V, and between I and IV. In the 1st example, it's the B note of E and B chords. In the 2nd, it's the Bb note, and in 3rd, betwee the Eb and the Ab it's Eb. There really should be double bar lines between each example. As an educational item, it lacks a lot of clarity. – Tim Oct 24 at 16:28
  • Starting with Hindemith! You are a brave person. – Carl Witthoft Oct 25 at 12:48
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The doubled tone in these exercises will always be the root of the chord. For now, since you're only using root-position chords, this pitch will always be in the bass.

But as you progress, you'll need to learn the distinction between the root and the bass. The bass is simply the lowest sounding note, and it can be any member of the chord (root, third, fifth, seventh, etc.).

The idea of the chordal root, however, is somewhat abstract. In short, the root is the lowest pitch when you stack the chord in thirds. Given the collection E C G, we have to actively order the pitches so that each is third above the previous one. G C E doesn't work, because G up to C is a fourth; G E C is organized in thirds, but notice that these are descending thirds. Finally, C E G does work, and therefore C is the root.

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In fourth-related chords (V-I and I-IV) the 8va and 5th in the upper voices are interchanged; also compare the leading tone 3rd <=> 8va and 5th <=> 3rd.

I don’t understand why Hindemith didn’t demonstrate the progression just in the cadence of C-F-C-G-C.

In this basic progression - when the bass plays the root tone and the root is doubled - it is most clear that in a sequence of chords clockwise in the circle of fifths (tonic -> dominant or subdominant -> tonic) the fifth of the first chord keeps laying and becomes the octave of the new chord while the octave and the third are moving down-step and become the third respectively the fifth of the following chord - and vice versa when the progression goes counterclockwise in the circle of fifths (tonic -> subdominant and dominant -> tonic).

This must sound pretty confuse and complicated but it is very evident if you look at the movement of the fingers on keyboard or at the voicing on a sheet.

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