A major 7th chord is a major chord plus the "true" 7th note of the scale. I use the word "true" to allow me to point out that when we refer to a 7th chord we are talking about the major chord plus a flattened 7th.
|C major is;
|C E G
|C 7th is;
|C E 'G' Bflat
|C major 7th is;
|C E G B
Don't forget that a Stradella system only plays three notes in a chord (more >>) so the 7th chord buttons do not sound the 5th (in this case G) note of the scale.
Now we have to work out how to get C, E, G and B to sound. The answer is to hold down the C major button and the E minor button at the same time. Because of the way the Stradella system works this simply opens only one more valve on the left side than the chord alone so it does not mean that twice as much pumping is required. In addition, every note of the chord sounds (that is, including the major 5th).
Based on this you can play any major 7th chord on the left hand.
If you are playing quickly so that the major 7th chord is just a passing sound, I use the correct fundamental bass (in this case C) and the appropriate minor chord (in this case E minor).
Often, the music calls for a sequence of chords going from the tonic chord (in this case C), passing through the major 7th chord (in this case C major7 with the major 7th note - B - sounding in the bass) to the relative minor chord (in this case A minor). Here I play C major (finger 4 for C bass and finger 3 for C major chord) then C major7 (finger 4 on B, the counter bass of G and finger 2 on the E minor chord) and then A minor (finger 4 for A bass and finger 3 for the A minor chord).
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