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I read that it is impossible to have a full cadence using all three notes of the final triad in a 4 part counterpoint piece. Here is the exact bit of info:

"we can’t easily arrive at a full triad in the final measure. The bass and alto (or whichever voice has the CF) must both go to ^1, the tenor is free to go to ^3 or ^5, but the soprano usually has ^7 in the penultimate V chord, so the leading tone must resolve to ^1. It is very normal to end on an incomplete I chord for these reasons."

Can someone please clarify if this is true and why? Most music I have listened to always has a full triad at the end of a cadence. And when I studied harmony it has always been a V > I progression, meaning that the whole I chord is used. Where am I getting confused?

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    Can you give a source of this quote? Don't know why anyone would say a 4-part harmony cannot have a full cadence, unless what is meant is 2-part-counter-point. – Neil Meyer Mar 15 at 14:49
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    "It is impossible to do x" is very different from "it is very abnormal to do not x." And is this in the 16th-century (Palestrina) style? – Richard♦ Mar 15 at 15:42
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    Where did the quote come from? Just 'cos it's on the 'net doesn't make it accurate! – Tim Mar 15 at 15:42
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    The source of the quote is needed, and there seems to be some important context missing. In particular, the quote appears to assume triad-based chord structures, but more context is needed to clarify that. – Aaron Mar 15 at 16:24
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    "not easy" is not the same as "impossible," and "very normal to end... incomplete" is not the same as "must be incomplete." But indeed you will find that most pieces that do end on a full chord defy some assumption or another under which that passage was written. – phoog Mar 16 at 22:04
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Although it's not impossible for both chords to be complete, it does require specific circumstances. The quotation offers a broad explanation for why this is.

First, the quotation implicitly assumes the bass voice is not the cantus firmus. The "rules" state that the bass must move to 1 and so must the CF. Thus, for a complete I chord, the other two voices have to land on 3 and 5.

The quotation makes a second assumption, which is that the soprano voice most often moves from 7 to 1. Thus, if the soprano moves from 7 to 1 and is not the CF, we now have a tripled root (because bass, CF, and soprano all proceed to 1), so a complete I chord is impossible.

As an example, I went through every possible combination of V - I cadences in which the bass and tenor start off doubling the root of the V chord. Of the 16 possible ways to move from there to the I chord, only 4 result in complete I chords. The remainder are either incomplete or disallowed by various voice-leading rules.

X: 1
T: V - I cadences, both triads complete
T: Tenor and Bass double the root of the V chord
M: 4/4
L: 1/1
K: C
%%score {(V1 V2) | (V3 V4)}
V:V1 
V:V2
V:V3 clef=bass
V:V4 clef=bass
[V:V1] D | E |] D | E |] D | E |] B | c |]
[V:V2] B,| C |] B,| G,|] B,| G,|] D | E |]
[V:V3] G,| G,|] G,| G,|] G,| E,|] G,| G,|]
[V:V4] G,| C,|] G,,|C,|] G,, C,|] G,|C, |]

(Note that bass and tenor share the same pitch in the first and last cadences. This is to avoid a hidden octave between the bass and upper voice moving from B to C.)

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  • Aaron, I assume there is a typo " I went through every possible combination of voicings in which the bass and tenor both have the root of the V chord" you meant "I" chord right? – armani Mar 16 at 10:01
  • @armani No, I do mean V. I looked at V- I cadences in C major, where both the bass and tenor took the G (the root) of the V chord and then moved to I. So the bass always moved from G to C, and the tenor either stayed on G or moved from G to E. I've edited the answer; please let me know whether or not that clarifies. – Aaron Mar 16 at 13:27
  • @Armani under the assumptions of the passage in question, each of the three voices other than the tenor has a different pitch of the V chord (bass, alto, soprano: ^5, ^2, ^7). The most likely pitch for the tenor is to double the root of that chord. – phoog Mar 16 at 22:13
  • @Aaron, how did you get 16 voicings? I only get two with the Bass and Tenor doubling the bass. Please see here ibb.co/yWW0Yn5 – armani Mar 17 at 10:46
  • @armani I didn't say 16 voicings. I said 16 ways to move from the V chord to the I chord when starting from a V chord voicing where the tenor and bass double the root. – Aaron Mar 17 at 14:45
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"we can’t easily arrive at a full triad in the final measure. The bass and alto (or whichever voice has the CF) must both go to ^1, the tenor is free to go to ^3 or ^5, but the soprano usually has ^7 in the penultimate V chord, so the leading tone must resolve to ^1. It is very normal to end on an incomplete I chord for these reasons."

Somehow that quote seems to be about a specific example. It's so indirect about what exactly the penultimate chord is I don't see why you would formulate a rule from it. At the very least normally ending on an incomplete tonic does not necessarily mean it is impossible to end on a complete tonic chord.

If you really want to study species counterpoint, you need to get Fux's Gradus ad Parnassum. It's the original source for species counterpoint.

Fux's four part examples end with chords voiced both with roots and fifth only and also with several examples of root, third, and fifth, full triads.

Here are Fux's four part 1:1 example endings with full triads. All transposed to C to compare the variety of voicings and melodic moves. All melodic moves are by step except the occasional ^7 to ^5 move which happens in the tenor, alto, and soprano.

Notice how the scale tone movements in Fux don't match up to the description in your quote? The quote implies ^7 is a leading tone, meaning the tone one half step below the tonic. Based on that, the stuff you're working from is probably species counterpoint applied to major/minor harmony. Fux's harmonic style is modal, and so the examples in phrygian mode have a ^7 a full step below the tonic. At least in these few examples when ^7 is a leading tone it does move up to ^1, but when ^7 is a subtonic in phrygian it either moves up to ^1 or down to ^5.

enter image description here

I think you should talk to your teacher about the quote and try to better understand the context in which it was given. If it's part of species counterpoint method, it should be reconciled with Fux. Fux is the original source for species counterpoint. And Haydn, Mozart, and Beethoven all study counterpoint from Fux!

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  • "Somehow that quote seems to be about a specific example": that seems a very likely hypothesis except for the parenthetical "or whichever voice has the cantus firmus," which seems to suggest that it is in fact a general statement. – phoog Mar 16 at 22:25
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This doesn't make sense. In a G>C (or G7>C) cadence, you can have G>C in bass, D>E or F>E in tenor, G>G in alto, and B>C in soprano. The D note (V5) does not have a unique resolution, so D>C and D>E can even both be used in the same cadence if you have a step down in soprano. The only unique resolution in a V>I and V>i cadence is V7>I3 (or i3) and V3>I1.

Another option for a D>C soprano is G>C bass, G>E tenor (the "alto cadence"), B>C alto and D>C soprano. It's completely fine to have a 3rd down in the alto cadence (in the tenor voice in this case), going from V1>I3. This is quite cool as you don't have I5 altogether; 5ths in general don't sound well in tune, so you avoid having this out-of-tune feeling in the final chord.

In a lesser number of voices, you need to cover at least one of the sensitive notes (V3 or V7), and then you might miss something. Still, you can have both: F>E (V7>I3) in the lower voice and B>C (V3>I1) in the upper one and it will work just fine.

The idea that alto has to go to I1 is a complete non-sense.

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  • If a question does not make sense rather consider asking for clarification in a comment – Neil Meyer Mar 15 at 15:33
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    The question makes sense. The quote doesn't. – yo' Mar 15 at 15:34
  • This answer doesn't take into account the presence of a cantus firmus, which is required to end on the tonic. – Aaron Mar 15 at 16:27
  • @Aaron, correct, thanks for pointing that out. And I do believe that the bass has to go to 1 too so thats two out of 4... now I would like to understand why the other two notes cannot be ^3 and ^5 – armani Mar 15 at 17:24
  • I suppose it does make sense since the soprano will do ^7 to ^1 too which only leaves 1 other note – armani Mar 15 at 17:26

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