Bringing order to the caos #2

The tritone bandoneón's keyboards

Published on January 17th, 2021 under Various

Let's continue with the second article of the topic "Bringing order to the chaos". Today we'll talk about the tritone and its location in the keyboards of the bandoneón. As with the previous article I will consider the layouts Rheinische 142 and Einheits 144.

For this article it is necessary to make a minimum reference to music theory, which I will try to simplify as much as possible.

The tritone

In the temperate system, the tritone is an interval made up of three whole tones (or six semitones). The tritone has three fundamental characteristics:

1. Divide the scale into two equal parts;
2. the ascending tritone interval is equal to the descending one (i.e. the diminished fifth is equal to the augmented fourth);
3. the tritone is present in the dominant seventh chord.

From the point of view of acoustics, the tritone represents the maximum dissonance and instability, so much so that its execution was forbidden or limited for centuries.

For mathematical reasons, from the first two properties derives the fact that in the tempered system we have a total of 6 tritones.

1. C - G♭
2. D - A♭
3. E - B♭
4. F - B
5. G - D♭
6. A - E♭

How is it possible then that each tritone is in the dominant chords, which are 12 in all (one for each tonality)? We should have 12 tritones.

But the tritones are always and only 6. From this it follows that each tritone stands in two dominant chords. As you can see:

• G - B - D - F
• D♭ - F - A♭ - C♭

Stop, have a break. Clarifications are urgently needed.
First of all, you will all have recognized the two dominant seventh chords G7 and D♭7. Then, you know that B and C♭ for the temperate system are actually the same note (enharmonic interval: same note, different name). If I want, I could write the second chord as D♭ - F - A♭ - B, which is good to understand (but I would fail all the theory and solfeggio exams, even those of Mickey Mouse Club Choir).

Once it is therefore established that the tritone is the same even with different names, some of you will recognize in D♭7 the tritone substitute of G7.

Tritone substitute

The tritone substitute is a dominant chord that replaces harmonically another dominant chord. The two dominant chords share the tritone and the respective fundamental notes are at a distance of a diminished fifth. Also in the circle of fifths the two tonalities are exactly the opposite of each other.

The G7 can therefore be replaced by the D♭7 and harmonically none will be able to argue. In fact, what matters is the resolution of the tritone, which solves by opposite motion "opening" (as in G7 - C) or "closing" (as in D♭ - C). For jazz musicians I'm not saying anything new, in fact they use it constantly. One of the most common uses of tritone replacement it is in the famous II-V-I cadence where we can substitute the V with its tritone substitute, obtaining a chromatic movement at the bass II-II♭-I. The Neapolitan sixth chord is also an application of the tritonal substitution.

Here you can find all the dominant chords, grouped in pairs each with its own tritone substitute (the acronym of the chord in red, the shared tritone in bold).

C - E - G - B♭ (C7)
G♭ - B♭ - D♭ - F♭ (G♭7)

D - F♯ - A - C (D7)
A♭ - C - E♭ - G♭ (A♭7)

E - G♯ - B - D (E7)
B♭ - D - F - A♭ (B♭7)

F - A - C - E♭ (F7)
B - D♯ - F♯ - A (B7) (*)

G - B - D - F (G7)
D♭ - F - A♭ - C♭ (D♭7)

A - C♯ - E - G (A7)
E♭ - G - B♭ - D♭ (E♭7)

(*) To be formally correct and precise, this chord should be C♭ - E♭ - G♭ - B♭♭; (C♭7), but it's the enharmonic of B7, because B♭♭ it's just an A.

How to use this article's info

Too much info, right? Now let's be practical and adapt these things to the bandoneón.

I assigned a color to each tritone and reported the location of the tritone in the keyboards of the bandoneón. Each color has two shades, one darker and one lighter. The notes retain their assigned gradations even if they are in different octaves.

The goal is to quickly learn where the tritone is because, as you should have understood, each tritone has two dominant chords as a possibility: just add that note that makes it clear what chord you are playing.

For example, if I'm playing the tritone B - F, I just need to add a G to create a G7. Or instead of the G, I play a D♭ and I get a D♭7 (the fifth is often omitted, especially if you are a jazz musician and you can't resist playing none and thirteenth).

Below you can find the diagrams for the Rheinische and Einheits layouts. After the schemes, some ideas for how to exercise.

Bandoneón 142 Rheinische

Tritones 1 & 2
(C - G♭ | D - A♭)

Tritones 3 & 4
(E - B♭ | F - B)

Tritones 5 & 6
(G - D♭ | A - E♭)

Bandoneón 144 Einheits

Tritones 1 & 2
(C - G♭ | D - A♭)

Tritones 3 & 4
(E - B♭ | F - B)

Tritones 5 & 6
(G - D♭ | A - E♭)

Exercise tips

1. Familiarize yourself with tritones by playing them opening and closing on both keyboards. Also experiment with combinations of tritonal intervals that go beyond the octave.
2. Play the tritone on the right keyboard and add the bass with the left. Do the same with the bass of the other dominant chord related to that tritone. Practice opening and closing. Then reverse the keyboards: tritone to the left and tonic on the right keyboard.
3. Play the tritone on the right keyboard adding the fifth of the chord and accompanying it with the root at the left keyboard. Opening and closing.
4. Play the tritone on the right keyboard and add the bass, moving from one dominant chord to the other.
5. Experiment with chords beyond the octave: playing the tritone with the right hand and tonic and fifth on the left. On the right hand add the ninth or the eleventh, or the thirteenth. Opening and closing.

These are some ideas for exercises. The possibilities are several and I invite each one of you to experiment and discover your exercises.

A tritones-made scale

If we put together all the notes of the first three tritones we get an interesting scale, the whole-tones scale which divides the octave into equal parts using six whole tones. There are only two whole-tone scales:

C - D - E - F♯ - G♯ - A♯
D♭ - E♭ - F - G - A - B

Probably you recognized it, it's one of the scales indicated by Messiaen in its limited transposition modes. The whole-tone scale was used a lot by Debussy for its "indefiniteness", because it has no tonal center. In pop and jazz this scale is used a lot, for example to play on altered dominant seventh chords (i.e. augmented fifth).

Here's how it sounds with the bandoneón:

Conclusion

Here we conclude the second "episode" to get closer to the keyboard of the bandoneón experimenting with various types of approaches. In the next episode we'll see the tritone resolution (do you want to leave things unresolved !?)

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