Traditional Definitions
Chords (Tetrads or Triads) are said to be in "Root Position"
     when the Root of the chord is in the Bass Voice.
Chords (Tetrads or Triads) are said to be in "First Inversion"
     when the Third of the chord is in the Bass Voice.
Chords (Tetrads or Triads) are said to be in "Second Inversion"
     when the Fifth of the chord is in the Bass Voice.
Tetrads are said to be in "Third Inversion"
     when the Seventh of the chord is in the Bass Voice.
We will presently be dealing only with Triads in First and Second Inversions
               indicated "₆" and "₆₄" in subscript,
          not to be confused with Non-chordal Tones,
               indicated in superscript,
     and this work will, in general,
          apply to the Minor Mode as well as to the Major Mode.

Required or Optional
We will classify as "Required" an inversion which is essential to a progression,
     without which the progression could not take place in Root Position, and
we will classify as "Optional" an inversion which is not essential to a progression,
     without which the progression could take place in Root Position.

First Inversion

Unlike Triads in Second Inversion which can be tricky and dangerous,
     all Triads in First Inversion "sound well",
          and it is even possible to have several of them in a row,
               as inIV₆-iii₆-ii₆-I, which we will see in a moment.

Required

As we have seen inTriad Progressions 2.,
     Deceptive Triads in Root position automatically progress by ascending second,
          due to the "caving-in" process of the voice-leading.
     It is, therefore, impossible to resolve them by decending second
          without resorting to the First Inversion.
     Now is the time to examine this more closely.

Let's return to the ascendingI-ii-iii-IVchord pattern
          which we had in theCOUNTER/TONIC Swing using Voice-Leading A, 8.,
     and see what happens in the descendingIV-iii-ii-Ichord pattern, starting from the end.
          1. In theii-Iprogression -
               If theiiTriad is in Root Position,
                    the root (in the Bass) is, in reality, theMOTRIX(sixth) of the TetradIV⁶
                         which resolves to theMEDIAN(third) ofI(Orbit Line3-2),
                              forcing it to be in First Inversion, the progression now beingii-I₆ .
               If theiiTriad is in First Inversion,
                    the third (in the Bass) is, in reality, thePROPER TONEof the TetradIV⁶
                         which is free to resolve to theCOMMON TONE(root) ofI(Orbit Line1-0),
                              allowing it to be in Root Position, the progression now beingii₆-I.
               In this case, from a Deceptive to a Real Triad,
                    one of the 2 Triads (not both) must be in First Inversion.
          2. In theiii-iiprogression -
               If theiiiTriad is in Root Position,
                    the root (in the Bass) is, in reality, theMEDIANof the TetradI⁷
                         which resolves to thePROPER TONEof the TetradIV⁶ (Orbit Line2-1),
                                   which is the third of theiiTriad, forcing it to be in First Inversion,
                              the progression now beingiii-ii₆ .
               If theiiiTriad is in First Inversion,
                    the third (in the Bass) is, in reality, thePROPER TONEof the TetradI⁷
                         which is free to procure theMOTRIXof the TetradIV⁶ (Orbit Line1-3inVoice-Leading B),
                                   which is the root of theiiTriad, allowing it to be in Root Position,
                              the progression now beingiii₆-ii,
                         but this Bass note is also free to resolve to thePROPER TONEof the TetradIV⁶ (Line1-1)
                              and we will see this in the Optional First Inversions.
               In this case, between 2 Deceptive Triads,
                    at least one of the 2 Triads (possibly both) must be in First Inversion.
                         This is fairly heavy going because we are dealing with 2 Deceptive Triads,iiiandii,
                              and we must constantly refer back to the FundamentalI⁷ - IV⁶ Tetrad Swing
                                   of which they are part.
               We still have 2 possible patterns :iii-ii₆-Iandiii₆-ii-I₆ ,
                    with more to come.
          3. In theIV-iiiprogression -
               The first chord is a Real Triad with which we have more leeway.
                    It can, in Root position, resolve to theiiiTriad, also in Root Position,IV-iii(Orbit Line1(3)-2).
                    It can also, in Root position, resolve to theiii₆ Triad, in First Inversion,IV-iii₆ (Orbit Line1-1).
               We still have our 2 possible patterns, this time complete, :IV-iii-ii₆-IandIV-iii₆-ii-I₆ ,
                    with more to come in the "Optional" section.

We have not given you the voice-leading for these patterns
          but it should not be too difficult to work them out -
     1. Resolve the Deceptive Triads by "caving them in", with the Root ascending and the Fifth descending,
          regardless of the Performance Voices they are in.
     2. Resolve the Real Triad by resolving its third by step (no more than a second).

Other ascending chord patterns, likeV-vi-vii-I, can also function in descending order,
     producingI-vii-vi₆-VandI-vii₆-vi-V₆ for now,
               and here again, with more to come in the "Optional" section.

Optional

Let's return to the descendingIV-iii-ii-Ichord pattern,
     and see what we can add as further possibilities of First Inversion.
          1. In theiii-iiprogression -
               If theiiiTriad is in First Inversion, as mentioned previously,
                    the Bass note, which is thePROPER TONEof the TetradI⁷ ,
                              is also free to resolve to thePROPER TONEof the TetradIV⁶ (Orbit Line1-1),
                         which is the third of theiiTriad, producing theiii₆-ii₆ progression,
                              adding the completeIV-iii₆-ii₆-Ipattern to our list.
          2. In theIV-iiiprogression -
               The first chord is a Real Triad with which we have more leeway.
                    It will, in First Inversion, resolve to theiiiTriad in First Inversion,IV₆-iii₆ (Orbit Line2-1),
                         adding 2 more complete patterns,IV₆-iii₆-ii-I₆ andIV₆-iii₆-ii₆-I.
          3. We now have 5 different possibilities of theIV-iii-ii-Ipattern with First Inversions -
                IV-iii-ii₆-I,IV-iii₆-ii-I₆ ,IV-iii₆-ii₆-I,IV₆-iii₆-ii-I₆ , andIV₆-iii₆-ii₆-I.
          4. These 5 options would also be possible with the descendingI-vii-vi-Vpattern
                    from the FundamentalI⁶ - V⁷ Tetrad Swing -
                I-vii-vi₆-V,I-vii₆-vi-V₆ ,I-vii₆-vi₆-V,I₆-vii₆-vi-V₆ , andI₆-vii₆-vi₆-V.
One also finds optional use of First Inversion
     in a progression between 2 Real Triads by descending fifth,
          inV₆-Iwhich will sound similar tovii-Iand
          inI₆-IVwhich will sound similar toiii-IV,
               having, in both cases the same Bass and coming from the same Tetrad Swings,
                     V⁷-I⁶ in the first case andI⁷-IV⁶ in the second, (with the substitution0(3)of theMOTRIX).

Analysis and Summary

Relative Freedom
It is interesting to note how First Inversion affects the freedom of resolution of a Triad -
     

Second Inversion

Unlike Triad First Inversion which always produces a satisfactory disposition of the chord,
     Triad Second Inversion inevitably producesFRAME Inversion
          which, in general, it is preferable to avoid.
However, we will now see that one case is actually required, and others quite satisfactory.

Required

The most important required use of the Second Inversion is in what is called "The Cadential 64 Chord".
     When theV⁷-I(orV-I) cadence is preceded byI,
          thisITriad should preferably be in Second Inversion, indicatedI₆₄ ,
               to reserve the full impact of rest for the final TONIC chord.
     There has been disagreement as to whether this Cadential 64 Chord should be labeledI₆₄ orV^s6s4 ,
               whether it was essentially a TONIC chord in Second Inversion or
               whether it was essentially a DOMINANT chord with2 Non-chordal Tones, a sus6 and a sus4.
          We tend to believe that it is both -
               a TONICI₆₄ at a smaller rhythmic level, and
               a DOMINANTV^s6s4 at a larger rhythmic level.
                    (ForTwinkle, Twinkle,this would beLevel 0andLevel +1.)
     One way or the other, with one analysis or the other, cadences sound much better with it,
          and the Cadential 64 Chord (aTenant Chord) will always be on theBeat,
                reboundingto the following DOMINANT (proprietor chord) which will be on the Off-beat.

Optional

1. Optional use of the Second Inversion is usually seen in what are called "Passing Chords",
          inserted between 2 similar chords in a Swing.
     A common case is a DOMINANT between 2 TONIC chords,I-V₆₄-I₆ , orI₆-V₆₄-I,
          with the notes C-D-E in the Bass and E-D-C elsewhere, or E-D-C in the Bass and C-D-E elsewhere,
               and with the notes C-B-C and G-G-G in the remaining voices.
          One almost wonders if there is a DOMINANT chord at all,
               and if we are not dealing with 2 passing notes and an embroidery.
     This Second Inversion is considered optional in this case
          because the line D-E is a substitution1(3)for theMOTRIX
               and the "fundamental" line F-E could be used instead, withvii₆ instead ofV₆₄ .
2. One could say that, in some cases, use of the Second Inversion is unavoidable,
               being the result of the normal resolution of theMEDIANof the previous chord,
          but that does not necessarily prevent us from using this Bass Line,
               because theFRAMEInversion can be attenuated considerably.
     We sawpreviouslythat the optional use of First Inversion
          on the first of 2 Real Triads progressing by descending fifth,
               left the second in Root Position.
                    as inV₆-IandI₆-IV.
     However, if the progression is by ascending fifth,
          the second Real Triad will be in Second Inversion,
                    as inIV₆-I₆₄ andI₆-V₆₄ ,
               due to the normal resolution of theMEDIAN(third) of the first Triad which is in the Bass Voice.
          The simplest solution for the second Triad is to have the Bass play the Root after the Fifth,
               as inIV₆-I₆₄-IandI₆-V₆₄-V, with the Bass notes A / G-C, and E / D-G.
3. One must not forget the fact that, in Deceptive Triads,
     Second Inversion does not really produceFRAMEInversion
          because we are not dealing with theFRAMEof the Tetrad at all,
               the fifth of the Deceptive Triad being a Secondary Note of the fundamental Tetrad,
                    either aMEDIANif we are dealing with a sixth chord,
                         or aMOTRIXif we are dealing with a seventh chord.

We hope that our indications have been both clear and helpful.
     Let usknowif they have not.

Totop of page
ToThe Minor Mode
ToTriads in the Major Mode
To the Harmony 101Preface
To the Harmony 101Menu
To theHome Page