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In strict counterpoint, it is forbidden to have a B in one voice and then, in the very next chord, an F in another voice, or vice versa. This is called the false relation of the tritone.

George John Bennett, in his Combined and Florid Counterpoint (p.7), cites this as a reason why one shouldn't move from root position triad V to root position IV. Fair enough. But why does this author not mention the reverse progression IV-V, which also involves the tritone? Is this to be considered an exception, on account of IV-V being a very ordinary progression in tonal harmony? Or is root position IV-V altogether out of the question in strict counterpoint?

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    I don't know this rule. Of course not in the same voice but ... different voices? Root position is of course always possible, this means other voice -> counter movement (opposite direction). – Albrecht Hügli Apr 7 at 13:40
  • I've never heard this rule either. I've got a PhD in Theory and I teach theory every day in a US conservatory. I guess you really can teach an old dog new tricks! – Richard Apr 12 at 3:12
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My Piston Harmony mentions the rule only in regard to V to IV. Kostka/Payne doesn't appear to mention it at all. That description on p.7 of Bennett doesn't seem to give much of an explanation.

This description from Schenker (my first time reading it) seems clear in what the concern is...

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I'm not very familiar with German theory so the reading is a bit tough for me. But the basic gist I get is: you don't cadence on the subdominant. You cadence only on the tonic or dominant. In German theory vi has a "tonic" identity which in the theory familiar to me is called a deceptive cadence.

It seems important to point out that Piston and Schenker both illustrate the false relation of the tritone as a progression of ^7 to ^4 in the outer voices of soprano and bass. Piston specifically shows the progression as acceptable if one of the tones is in an inner voice. Both Piston and Schenker show the ^7 in the soprano moving to ^1.

Another way to think of it is: how to harmonize ^7 to ^1, the leading tone moving up to the tonic. If we consider the basic harmonic implication of that melodic movement to be V to I, then harmonizing the second chord as the subdominant IV sort of contradicts the basic idea of resolution inherent in ^7 to ^1, a resolution to the tonic.

If the harmony is reversed, we aren't just changing the order of two chords. We are change the chord to which the music resolves. Moving ^1 to ^7 is a resolution to a chord harmonizing ^7 which will be a chord of the dominant V. The ^1 can be harmonized as tonic or subdominant (ex. I or ii6/5) it's harmonization is flexible, because we aren't cadencing to it.

Piston specifically illustrates root position IV to V in voice leading for all three voices moving with ^1 to ^7 in the soprano. Of course that means ^4 is in the bass followed by ^7 in the soprano. So, at least according to Piston, the rule does not apply vice versa. The order matters.

This rule has always frustrated me. I don't understand why it's called false relation of the tritone when Piston shows an acceptable example of this tritone relationship in the outer voices in IV to V. Clearly the problem is not simply any tritone between outer voices. And the problem isn't about root position chords moving by step. It seems to me the rule is more like: don't harmonize ^7 (leading tone) to ^1 as a retrogression. I think Schenker's description is clearer in that regard.

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  • Thanks, Michael .That all sounds very plausible. By the way, I've seen the "no tritone"-rule in more than one counterpoint treatise, the one by Gore Ouseley for example (who seems to have taken most of his rules from Cherubini). Now that I think of it, Gore Ouseley mentioned the rule specifically in relation to two-part counterpoint. Perhaps the rule is more stringent in that case. – Kim Fierens Apr 7 at 18:00
  • I had thought the 'false relation of the tritone' wording is more of a counterpoint thing, compare that with my 'don't harmonize a retrogression' which is clearly a functional harmony point of view rather than counterpoint. But, definitely this rule is common. – Michael Curtis Apr 7 at 18:28
  • Yes, one of the reasons for the old mi contra fa tritone prohibitions (certainly not the only one) is that they can deny proper resolution of a leading tone. Later theorists (like Schenker) seem to extend this principle even when leading tone resolution is NOT denied (as in the example here), but chordal resolution isn't correct according to functional harmony. This extension of the contrapuntal principles makes little sense, but oh well. The basic answer to the OP's question is that theorists are often very inconsistent and use a lot of ad hoc justifications. – Athanasius Apr 11 at 17:19
  • I always love Michael's well-researched and well-cited answers; bravo! – Richard Apr 12 at 3:13
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I'd like to give a historical account of this, where the question becomes "under what conditions did cross relations of the tritone become permitted?".

The wider definition of false relations comes from any perfect interval which has been augmented or diminished, although this type of false relation "of the tritone" is listed under "Mi contra Fa" by many of the older theorists, and quoted in Grove. As defined by Gioseffo Zarlino (1558) in Le Istitutioni Harmoniche (Book III Chapter 30) this includes the tritone (both in its original augmented fourth form as well as its diminished fifth form) as well as the augmented and diminished octaves.

Parallel major thirds (and parallel minor sixths) are particularly problematic because of this, and Zarlino suggests avoiding all such progressions in compositions of two voices (III.31). However, in compositions of more than two voices, he argues that just as there are in medicine "deadly ingredients which in combination with other substances are healthful", so in music, "there are intervals and relations that give little pleasure in themselves, but have wonderful effect when combined with others."

Interestingly, the outlined / diagonal tritone was more directly criticised than the simultaneous tritone in late Renaissance theory, specifically allowing for the diminished fifth as a vertical interval even in two-part harmony.

This difference in treatment between the vertical tritone and the diagonally adjacent tritone comes to the fore in the baroque - in an analysis from c. 1700 of Lully's Proserpine, vertical tritones resolve very differently from other dissonances, and at one point states that a vertical tritone "moderates the inharmonical relation" of a diagonal tritone!

Indeed, Zarlino himself is inconsistent with his own rules, including writing tritone cross-relations between tenor and bass. This appears to be related to cadences in his examples: where from a functional harmony perspective we would see dominant to tonic functions, Zarlino would see a leading tone moving to its final with an appropriate(ly prepared) dissonance over the tenor clause. Cadences with such dissonant suspensions (which at this point includes the perfect fourth) are given their own category by Zarlino, a cadenza diminuita (Book III Chapter 53).

The idea of the elaborated cadence accepting such dissonances is carried forward in late 17th century and 18th century treatises, under various names (cadenza composta, cadentia ligata). It is this contrapuntal dissonance that defines such a cadence: an admission and acceptance of dissonance (including, indeed especially tritones) in cadential contexts that we would now see as IV-V or ii-V harmonic progressions.

However, non-cadential progressions did not gain the license to be so liberal with their dissonances, whilst cadences became the "instigation and release of tension by means of dissonance" with the rise of harmony-based thinking after Rameau. As V - IV was vanishingly rare in cadences, even in "evaded" ones (now called "interrupted" cadences), older guidelines persisted from earlier considerations of tritone dissonance, and also served to "justify" the salience of the tritone's value in cadential harmony as opposed to non-cadential progressions.

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  • This is all very interesting (and potentially relevant) background, but I'm not sure you directly answer the question: why is the tritone objectionable in V-IV, but not in IV-V? – Athanasius Apr 11 at 17:06
  • @Athanasius The final paragraph summarises it in one word: cadences. – Michaelyus Apr 11 at 17:48
  • Yes, I agree it has to do with cadences, but I'm just pointing out your answer doesn't explain why that means the contrapuntal rules only apply to one type of progression (as Michael's sort of does). And if the general answer is, "Well, cadences!" then I'm not sure of the relevance of all of the preceding information, as it's irrelevant backstory to an inconsistent ad hoc grafting of a contrapuntal principle onto a situation that was actually about harmony. (Just my opinion, though I thought you were getting at something deeper with your background sources.) – Athanasius Apr 11 at 18:16
  • @Athanasius I concede that there is a much large backstory, which I will make clearer in the final paragraph - I actually wrote a much larger answer, which required a severe cut-down. – Michaelyus Apr 11 at 22:27

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