What’s behind this idea?

The Doubt

Around 1996 I went to study Jazz Composition at Berklee College of Music (Boston, US). I had already been working as a music teacher for the previous six years, while I studied every music book I could get my hands on. I thought I was ready. However, I was still far from other “formally” trained musicians, that is, those who could read and sing in tune a music score like it was as easy as anything.

When I got to Berklee, it really caught me off guard to be around people who could transcribe a Coltrane solo, while I couldn´t even sing a major scale in key. I could play faster, I had studied much more about harmony… and yet it was all useless. How could I pretend to have any control over what I was playing when I couldn’t sing it or write it down? What was the use of all that knowledge I had studied so hard if I couldn’t use it? What the hell did I think I was I playing?

All these doubts only got worse as the semesters passed, undermining my self-confidence, filling me with sadness and anger. I remember going through one of the worst episodes of my life. If there was one thing I desired with all my heart and soul it was to belong to that group of people I respected and admired so much: musicians. Could I call myself a musician when there wasn’t a real connection between my mind and what I played? No. I just couldn’t write down what I heard or played.

I spent those years trying to understand how those musicians thought about music. And I had the priviledge of meeting many great musicians.

I got obsessed with a simple question: how did they see music in their minds as they played? I went out and asked all of them.

Visualization

What do musicians think about when they think about a certain note? To my surprise, I got many different answers. But they all had something in common: every musicians imagined it, one way or the other. A common way was to imagine one’s instrument: they would just “play” it in their heads. At this point, I realized there was a clear difference between instruments and how each one had learned music.

Those who had learned using music scores from the beginning had a better sight-ear-instrument connection than whose who, like me, had learned to read (sight) after having mastered our instruments. I realized that the first musical input one has will determine our future control over our instrument and how we connected it to written music.

I learned that the easiest instrument to imagine was the piano. Each note has one key, and all the keys are perfectly lined up from low pitch (to the left) to high pitch (to the right), with the black keys repeated the same way all the way. Unsurprisingly, piano is considered a mandatory instrument for all musicians. During my time in Berklee, I also took lessons with Jerry Bergonzi and I remember asking him this question too. “Well, I started imagining a sax and its positions” he answered “because I first learned with a sax. Later on, I started studying piano so I imagined a piano keyboard. Now, I prefer to concentrate on feelings”.

So pianists imagined a piano, guitarrists imagined a guitar, trumpetists imagined a trumpet. The piano keyboard will always be tuned the same way, and there is just one key per sound. On a guitar, you can play the same melody in different places, changing fingering and shapes, which makes it harder to imagine in a single way. Additionally, strings are not always tuned the same way. With trumpets, what you have to imagine are hundreds of positions only using combinations of the three keys. In summary, each instrument demanded an entirely different way of imagining music by “playing it in your head”. And one isn’t necessarily easier than the other, because they all have advantages and disadvantages, depending on what you need. For example, string instruments make it easier to imagine transpositions (play the same tune in different keys). This is because the same shape for a particular tune, when played a semitone higher on the neck, will keep the relative relationship between notes, only sounding one semitone higher. This is not possible with other types of instruments.

But still, all these thoughts still didn’t answer the big question: then, how do I connect my instrument with written music?

Solfedge

At Berklee I learned Movable Do for the first time. Movable Do is the opposite system to the traditional one (Fixed Do) I had learned back home, which I had tried to learn properly several times but had failed. Fixed solfege is hard to understand if you don’t learn it as a child. However, I learned Movable Do in a matter of minutes: it made sense immediately and I could start using it fluently right after learning about it for the first time. I’ve been using it up to this day.

Movable Do is similar to placing a capo on a guitar: the same shape works on every fret. In other words, it deals with relative distances between notes.

Some people have absolute ear, which means that they can hear a note and know exactly which one it is. But most of us have relative ear, which means that we can point out the distance between two notes, but we don’t know which exact notes they are. For example, when someone with absolute ear hears Do, Re, Mi, they will know that those three notes were “Do, Re and Mi”. However, when someone with a relative ear hears those three notes, they will know they are the first three notes (degrees) of the major scale, but they wouldn´t be able to say which notes they are. For this reason, Movable Do is more suited to train relative ear while Fixed Do is more suited to train absolute ear.

However, I dont think one is better tan the other. Each systems has its pros and cons. I believe we should use both to train different aspects of the ear.

The Quest

As I said, I spent many months researching, asking, and reading everything that had to do with ear training, instrument visualization, and sight reading.

My conclusion was straight forward: to become a musician meant to connect ear, with sight, with instrument, in a direct and immediate manner. So I gathered all my determination and got down to the task. I spent countless hours sitting down with my guitar, pressing a note on a fret with my left hand, while using my right hand to write down on a piece of paper the note’s name, singing it’s name and imagining where it would be on a piano keyboard. All at the same time. You can’t imagine the level of concentration this exercise required, and how unbearably slow my progress was. There had to be an easier way…

My efforts to solve this problem resulted in the most amazing journey through pure music. Let me try to guide you through it.

The first time I came across the graphic representation of the C major scale happened when I was 13 years old and had just started taking guitar classes. It looked like this:

T = tone

S = semitone

For string instruments such as mine, this representation is fairly easy to understand, since it coincides with how notes are displayed on a string, each fret being a semitone separation from the previous one.

What defines each scale is the distance (tones and semitones) between it’s notes. We find 12 different major scales if we part from each note. If we then generalize this structure, we can name the notes “degrees”, ordered in relation to the first one. To a relative ear, what matters is the relationship/distance between notes, not their absolute name. In this sense, the scale would look like this: (I, II, III, IV etc is how degrees are written)

Escala mayor de Re:     Re         Mi        Fa# Sol     La         Si        Do# RE

Escala mayor de MI:    Mi        Fa#     Sol#La       Si         Do#    Re# Mi

Escala mayor de Fa:     Fa        Sol       La   Sib      Do        Re       Mi   Fa

Escala mayor de Sol:    Sol       La        Si    Do       Re        Mi       Fa# Sol

Escala mayor de Mib:  Mib     Fa       Sol  Lab      Sib       Do      Re    Mib

Escala mayor de Fa#:  Fa#      Sol#   La# Si         Do#     Re#    Mi# Fa# …

(#= sostenido; medio tono más agudo)

(b= bemol; medio tono más grave)

This way, we get all 12 major scales with different notes but with the same relative structure and same relative sound. In other words, the pitch may sound higher or lower but they all sound like the same thing: a major scale.

As you might notice, the black coloured notes in C major scale coincide with the black keys of a piano keyboard (flats and sharps), and the white ones spell the major scale. In this sense, we can say that a piano keyboard has the shape of the C major scale:

For this reason, piano has the advantage of being easy to understand when dealing with C major, but the disadvantage of following a different pattern for each of the rest of scales.

Tendencies

In music, a tendency is the note towards which you’re going to resolve. That’s mainly what music is: tension- relax.

Music comes alive the moment we play it, since we produce constant vibrations we guide. The mathematical answer lies in harmonics: double hertz per second vibrations, which are born from what we play. This is what makes some notes to be closer with others (consonants), or further away (dissonance).

This movements are constant in relation with the lowest sound, the base, which is the boss always. For example, if the second tends towards the first (tendency 2-1) and the base is Do, then Re (second of Do) will tend towards Do (first). If, in another case, the base is Sol, Re is no longer Sol’s second but it’s fifth, therefore tending towards Sol (tendency 5-1), so that La (now Sol’s second) will tend towards Sol (tendency 2-1). This is very important, because this happens the same way in every key, in other words, every key follows the same rules. This is why Movable Do was so important to me, because this structure remains the same only leaving us with just one key, Do (relative). Higher or lower, always Do. When I use Movable Do, I think Do is the base note always, regardless if Do is in fact the absolute base note.

Tendencia 1-5 (la primera tiende a la quinta, en Do sería la nota Do tiende a Sol, en Re sería la nota Re tiende a La…)

Tendencia 2-1

Tendencia 3-1

Tendencia 4-3

Tendencia 5-1

Tendencia 6-5

Tendencia 7-1 (8)

These movements of resolution are the ones that make chords sound, since every note tends to the triad of the first degree. For example, for Do, every note in the scale tends to Do, Mi and Sol. This makes every note to sound different and in relation to the base. Having this in mind, every note started to develop a texture, a shape and a color in my imagination, all of which helped me tell the apart.

You can imagine them as you wish, of course. In my mind, I imagined the first as a dot, because it’s the starting or finishing point. The second one is yellow to me, for no particular reason. The third one is the sea, because it reminds me of a song by Antonio Vega (“azul, lineas en el mar” re re do, re do re mi mi). The arrows are the two tendencies of the triton: Fa-Mi (4th – 3rd), Si-Do (7th -1st ). The fifth one is red, and it has volume, so that we can jump to the tonic easier. The sixth in blue just because. The more detailed these notes are in your imagination the better, because you will remember them more clearly.

At this point, I realized I had an imaginary instrument that worked like Movable Do, which I could easily relate to the strings in my guitar.

However, the main problem remained unresolved: so what if I had an imaginary new instrument, if it was still disconnected from written music?

So I tried to solve this problem. I drew combinations of 12 elements (like the 12 notes) so that I could imagine the notes in a logical manner. I drew tables of 4×3, 3×4, 6×2. I also plotted the notes on a clock, like they were hours. I drew them aligned as on a guitar string, displayed in different ways: by thirds, fourths, seconds… But these new shapes were no good. I went back to my new imaginary instrument, and tried to plot it along every sound in a clear, logical way.

The Solution

Finally, I was able to solve the problem. The answer was right there, on the score. Literally. Simply place my new imaginary instrument on top of a staff! Everything started falling into place seamlessly.

My new imaginary instrument could be moved up and down the satff, so that the first note/the base would coincide with the real/absolute note you wanted to use. In other words, you could tune it so that it would fit any key. Since the new instrument followed rules that remain the same, the relationship between the notes remained the same, but all you had to do was to look down on the staff to easily spot the tendencies. Like a template.

However, I still needed to find a place for sharps and flats. So all I did was place two additional columns, and placed all sharps on the right column and all flats on the left columns. The result was a 7×3 matrix. This matrix supplicated sounds, but not notes (Do# and Reb sound the same, but are different notes).

In other words, I had just inveted a sort of instrument with a shape similar to a piano keyboard, only placed within a music staff, which instruction manual was written music. This means that what I play and what I see is the same. And all of this, in such a way that, for the first time ever, Fixed Do and Movable Do coexisted simultaneously and in harmony.

Matriz de 3 x 7 de Pentagrom, y su relación con el solfeo, el sistema absoluto y el sistema relativo.

I will never forget how I jumped from my bed as I realized this.

So this is how Pentagrom was born.

For many years I only used it for myself, until I realized that, perhaps, others could benefit from it too.