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Can anyone help me understand why second inversion triads are considered less stable than 1st inversion triads even though the intervals between the bass (chordal 5th), root, and chordal 3rd of a second inversion triad actually have more consonant frequency ratios of Perfect 4th (4:3) and Major third (9:8) when compared to that of 1st inversion triads with a minor third (16:15) and perfect fourth (4:3)?

The only thing I have found online that makes any sense besides several subjective, "that's just how it is" articles, is that the perfect fourth above the bass can sound kind of like a suspended chord? Although even this explanation seems a but suspect to me because there is still the sixth between the bass and soprano voices (to separate it from a typical suspended chord in root position) and the upper parts of the second inversion triad might still be displaced by octaves to make any kind of suspension feeling even less convincing. Any insight is greatly appreciated, thanks.

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I consider second inversions less stable, because to me they sound less stable. Not because I made calculations and got such and such numbers.

If there's people to whom second inversions give different feelings than they give me, then maybe those people might say that they don't consider seconds inversions less stable.

Theory describes, theory does not prescribe. At most, theory might help you predict, but that's all.

To me, second inversion sounds like it's going to a dominant, halfway there already. C/G - G7 - C. First inversion doesn't sound like it's almost a dominant already. It might go to subdominant or maybe back to tonic. But the pressure for movement imposed by the second inversion is greater.

So. Who is it who considers second inversions less stable than first inversions? Have you conducted a study of their cultural backgrounds - maybe their considerations are due to conventions and practices, things they've got so used to that they expect the things? Perhaps there's no physical or mathematical explanation. And even if there was, how do you show that that's the "true" explanation, and that culture and learned things don't play a role in this.

To give this inversion stability thing some perspective, let's look at this example which uses first and second inversion chords in two different contexts.

What do you think - what contributes more to the feeling of stability here, chord inversion or chord degree? Which one feels more stable, a clear tonic in second inversion, or a subdominant in first inversion? Or do you think that in the first part the F/A feels like a tonic, not the C/G?

Let's add some a lower bass:

In the first section, does the F/A give you more "stable" feelings than the C/G? How about after the G/B has been introduced and the C/G is clearly played as a final chord?

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    1st inversion sounds like (to me) it's going to sub-dominant. It's halfway there with the sub-dominant's leading note supporting it. – Tim Oct 9 at 10:28
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    I would have to disagree. That is like saying octaves simply sound good because they just do. It is because they have a ratio of 2:1. Music theory and the harmonic series is rooted in nature and physics and can be very insightful if understood correctly. Furthermore, I would argue 'prediction' is essential in mastery of any art or craft as it can lead to better informed decisions instead of repetitive trial and error, which does not lead to an increase in speed or proficiency over time, and hurts composition flow. You can't break rules in a creative manner unless you know them first. – 4Matt Oct 9 at 10:37
  • I suspect that "Second inversion sounds like it's going to a dominant" because we have been conditioned to (possibly by classical music's use of I 6/4 and IV 6/4). I don't think Beethoven's use of i 6/4 as the first, stable chord of the 2nd movement of his Symphony No. 7 is a complete anomaly or exception--I've also used 2nd-inversion chords in more stable contexts. – Dekkadeci Oct 9 at 11:15
  • @Dekkadeci Good point. The cultural and "learned" aspect may have a lot to do with it. It's hard to say, and myself, I can't unlearn my cultural history, so I can only say that it sounds that way :) And I suspect that the people who classify it as less stable, feel that way too. If we find people to whom it sounds different, they might say, "we don't consider it less stable". – piiperi Reinstate Monica Oct 9 at 11:20
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Off the top of my head, when I think of textbook descriptions, I don't remember that 1st and 2nd inversion and their treatment are stated in terms of a consonance measure.

My understanding is both are unstable simply because they aren't in root position.

If we consider...

I I6/3 IV

and

I V6/4 I6/3

...I don't think much attention is given to comparing the consonance/stability of I6/3 versus V6/4. Both are unstable and you would follow voice leading/harmony conventions about moving to the next chord.

Textbooks definitely describe the handling of 2nd inversion chords as more restricted than 1st inversion chords. Meaning there are fewer conventional options about where a 2nd inversion chord goes. But that's usually explained as convention rather than a result of a consonance measure.

I think you need to read individual theory texts closely to be sure what they mean. Some may try to explain inversions in terms of interval ratios and comparative consonance. Others may not.

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Purely my own ideas here - so do what you like with them!

There are usually some harmonics involved when listening to any played note. More audible on some instruments than others, not available in pure sine waves.

When the triad is in root position, i.e. C at the bottom of a C major chord, that note has its own harmonics - built from another C note, then a higher G, then another C, then an E. So, pretty well, the harmonics from that lowest note align with the other notes being played.

Now put the G underneath: 2nd inversion. Its harmonics are G, D and B initially. None of which align with a C triad (except G). But, since the G note itself is the first harmonic not to be an octave copy of the original, it 'fits'.

Now put E underneath: 1st inversion. Its harmonics are E B and G♯. Again, not in line with any others (except the B, which messes up my idea a bit!) - and F♯ isn't diatonic.

Of course it could be that 'stacked thirds' are deemed more consonant, due to our listening history.

Comments gratefully accepted!

  • Thanks for your time writing that up. Although I'm a bit confused. So if you look at the bass note's harmonic series for root position, 1st invert, and 2nd invert you get C-C-G-C-E (root), E-E-B-E-G# (1st), G-G-D-G-B (2nd). For first inversion and second inversion the bass note only has harmonics pairings with itself (when compared with all the chord tones). So I don't believe this would explain why 2nd inversion triads are less stable than 1st, unless I missed something? – 4Matt Oct 9 at 9:55
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The second inversion appears as passing chord I-V64-I6 or as I64 as suspension of the dominant chord (GCE -> GBD) while the first inversion the 3rd will be a leading tone I6 - IV or V6 - I, and in the minor degrees it is the root of its related chord ii6=F =>IV, iii6 = G =>V, vi6=>C => I, vii6=D = ii or V34 unclompete, without root G).

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