# How is the ninth a fifth below a fifth?

I am reading Vincent Persichetti's "Twentieth Century Harmony" and in the first chapter he mentions that

The most effective support tones are the fifth and the ninth, the fifth because it's a strong resonant interval and the ninth because it's the fifth below a fifth.

I didn't understand the reason the ninth is a an effective support tone is because it's the fifth below a fifth.. because if our bottom tone is an A (its fifth is an E and its ninth is a B) the fifth below the E is an A, not a B So how is the ninth a fifth below a fifth?

• Hi @Gilgamesh. The problem here is that you haven't quoted the book correctly. You've posted what looks like a quote in your question, but is actually text paraphrased by you! See my answer (below) for an explanation. Feb 2 '20 at 17:39

The ninth of a chord is, of course, not a fifth below the fifth of a chord.

However, I have just re-read the page in question from Persichetti's excellent Twentieth Century Harmony. Context is everything. This section of the book is dealing with resonance of chords, in particular in relation to the spacing of the Harmonic Series. The confusion here may be largely due to the passage being misquoted in the OP's question. Here is the full passage preceding the sentence quoted by the OP:

The principal of supporting resonance by lower sonority is occasionally applied to chordal structures. This colour device is used primarily when the composer works with chords in the upper register and needs to fill in toward the bass. In lower registers, the addition of tones is limited by the danger of muddy progressions. Most effective supporting tones are the fifth or ninth below the bottom tone of the chord because the fifth is a strong and resonant interval and the ninth is a fifth below the fifth.

Persichetti is describing notes a fifth below the existing bottom note of a chord and a ninth below the existing bottom note of a chord. This "ninth below" is a fifth below the "fifth below"! The passage below should make this clear:

• I've only answered the question...
– Tim
Feb 2 '20 at 20:24
• Yes! Always a SE problem - giving a great answer for a flawed question. I would never have spotted this had I not read the book years ago, and just started re-reading it today...! Feb 2 '20 at 20:27
• All I can say is - +1... It probably helps to be ...well read amongst other things!
– Tim
Feb 2 '20 at 21:38

Seems a strange way to portray notes and intervals!

Taking A as root, a P5 above it is E. You're correct. A P5 above E is B. As in E>B =P5. I guess that's what the writer has in mind. It's generally accepted that intervals are counted from lower note upwards. It could have been phrased a whole lot better!

• Actually, see Bob Broadley's answer: It's not that the phrasing is poor but that the quotation is taken out of context. In context, it is clear that the "fifth" is the fifth below, so the ninth below is actually a fifth below the fifth. Feb 2 '20 at 19:07
• Even worse - it isn't actually a quotation at all... Feb 2 '20 at 20:29

To address the 9th issue given any starting note (in the bass) the 9th is a 5th above the 5th of that note. So in the key of C the 5th is G and the 5th of G is D, the second (or ninth) of C. This pattern follows through the circle of 5ths. In fact there is a harmony text (I forget the author) that demonstrates building the major scale in just tuning from three triads built on the I, the 5th above V, and the "5th" below IV. And I place quotes to illustrate the possible confusion of a 5th below. It is possible that when the author says 5th below he/she means descending to the 5 of the tonic. But that would be an interval of a 4th (C-->G is a 5th, and G-->C is a 4th). Notice that an interval of 5th below is the 4th of the tonic (walking down a 5th from C gets you to F). The 5th below that (in my notation) is the dominant 7th of the tonic (as your example illustrates), e.g. the 5th below F is Bb.

Not sure how this author uses the term "5th below". If it is consistent throughout the text the other occurrences should help. It is also possible that the author means is judging these intervals relative to the lowest and not the tonic (but that's a stretch imo). As for these being "supporting" intervals does the author discuss why this is in more detail? Is it presumably based on resonance between harmonics? If so then relative to what note are these intervals supporting?