"When you double the third of a major chord
it sounds more minor,
and
when you double the third of a minor chord
it sounds more major."
(Pete in Zenoland)

Origin
This paradox is named for one of our correspondents,
     who seems to have noticed,
               uniquely by aural perception,
          the modal modification operated by a doubling.
We felt that it deserved recognition and commentaries.
     Naming this a "paradox" will seem all the more appropriate
          with the reading of the following paragraphs.

No Change
Let's start by looking at it this way -
     1. The mode of a Triad is determined by the disposition of its MEDIAN,
          major if the MEDIAN is a major third from the root, and
          minor if the MEDIAN is a major third from the fifth.
     2. The mode of a Triad can be altered by chromaticizing the MEDIAN,
          sharper to make a minor Triad major, and
          flatter to make a major Triad minor.
     3. Since there is no question of Chromaticism here, only doubling,
               the MEDIAN remaining exactly what it was,
          one can hardly see how there could be any change of mode,
               or even any "feeling" of change of mode.

Wrong Change
Now, let's look at it this way -
     1. In the absence of the MEDIAN, the FRAME of a chord,
               (i.e.COMMON TONE and PROPER TONE)
          will not convey any sense of mode whatever,
               it could be either major or minor.
     2. A Triad with an undoubled MEDIAN
          will evidently convey the mode of its solitary MEDIAN.
     3. A Triad with a doubled MEDIAN,
           could be expected to confirm the initial mode sensation even more strongly,
                    more major or more minor,
               and not even attempt to over-rule the initial sensation we had with one MEDIAN.

Right Change
Finally, let's look at it this way -
     1. Doubling a note, above all, confers on that note the quality of fundamentality.
          In other words, one doubles a Primary Note of the chord,
               COMMON TONE or PROPER TONE,
          and not a Secondary Note of the chord,
               MEDIAN or MOTRIX.
     2. Thus doubling the MEDIAN of a Triad,
          would imply the perception of the doubled MEDIAN as a Primary Note,
               in this case the PROPER TONE.
     3. More precisely, one could say that doubling the MEDIAN
          would suggest the impression that we are dealing with a Deceptive Triad,
               the result of a Substitution 1(0), with no COMMON TONE left.
     4. In this typical kind of Deceptive Triad,
          the apparent doubling of the MEDIAN
               is, in reality, the doubling of the PROPER TONE of the complete Tetrad,
                    this Tetrad being of the opposite mode to that of the Deceptive Triad.

Examples
1. If we double the "third of an Em chord" (evidently a Triad), the note G,
     we will hear this note G as the PROPER TONE of a C⁺⁷ chord, the TONIC,
               with the COMMON TONE, the note C, missing,
          whose normal resolution would evidently be the chord of F⁶, the COUNTER.
2. This COUNTER Chord, F⁶, could also be represented by its Deceptive Triad, Dm,
     in which the "doubling of the third" would be the note F,
          in reality, the PROPER TONE of F⁶,
               with, once again, the COMMON TONE, the note C, missing.
3. If we double the "third of an Am chord", the note C,
     we will hear this note C as the PROPER TONE of a C⁶ chord, the TONIC,
               with the COMMON TONE, the note G, missing,
          whose normal resolution would evidently be the chord of G⁷, the DOMINANT.
     In these 3 cases, doubling the third of a minor Triad produced Deceptive Triads of major Tetrads.
4. We could repeat this procedure in the ANTES, to discover that
          doubling the third of a G Triad would produce a Deceptive Triad of Em⁷,
          doubling the third of a C Triad would produce a Deceptive Triad of Am⁷, and
          doubling the third of an F Triad would produce a Deceptive Triad of Dm⁷,
     In these 3 cases, doubling the third of a major Triad produced Deceptive Triads of minor Tetrads.

The Real Test
The weak link in the presentation of this paradox
     is that there is no other justification for the "Right Change"
          than the unusually astute and perceptive ears of our correspondent.
However, if we magnify the process of "doubling" sufficiently,
     the "Right Change" can be immediately perceived
          by even the most mindless and insensitive individual.
Instead of doubling, let us quadruple the MEDIAN of the chord.
     1. Play any music (or chord pattern) in the Key of C, ending on the TONIC chord of C.
     2. Then play, in octaves, 4 Es, and see if they are perceived as part of the same chord of C.
     3. Immediately we hear that we are in minor, A minor to be precise,
          on the chord of E⁷, to be more precise,
               on its COMMON TONE, to be even more precise.
It is impossible to "double" a Secondary Note to this extent
     and still hear it as a Secondary Note !

Coda
Let's end with a more technical and precise paraphrase of the original paradox -

When you double the third of a major Triad
you draw attention to the fundamental minor Tetrad of which it is a part,
and
when you double the third of a minor Triad
you draw attention to the fundamental major Tetrad of which it is a part.

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