The world of mathematics.
It's noon and we are in the office of the British radio station 1.
This week, producer Gioff Smith and Mark Pudier receive hundreds of new albums from groups with a lot of popularity and others not so well known.
Of all the songs received, only a few are accepted and released.
We observed the radio 1 lists and decided to examine the music of the song called I Believe played by the group EMF.
And any new recording? Yes, here it is. In fact, it has just arrived. Let's listen to it. It's the one they recorded.
Would you believe this? They recorded it at the end of November. It would be good to have it on the program. Will we be the first to play it?
Yes, we will be the first to play it. Very well. Let's listen.
In the morning outside the recording studio located in the west of London, Gordy Allan Goldin arrives with a large number of electronic equipment that the EMF group will need for its recording session.
Electronic links music with mathematics, but music is not the only way in which mathematics can be used.
In the past, the relationship between mathematics and music was not so technical, but it was important.
For centuries, musicians have used numbers and sequences to compose and play music.
It is not uncommon that when we like a musical piece, we can take the rhythm with a kick. We acquired musical rhythm at a very early age.
So how does the EMF group use this association when it plays I Believe?
To answer this question, we need the group. They have not yet arrived because they are on a television program in Matutino.
Allan will have to place all the necessary instruments and equipment. This recording studio is located in the basement.
It was carefully isolated and tested so that no external noise could ruin the recording.
To achieve greater fidelity in recording, the sounds of the guitars, keyboards and drums must be separated.
Modern recording studios like this can handle up to 48 channels that separate the sounds, although most pop music recordings use only half.
The EMF group has finally arrived, but it has already been lost half of the day and not a single note has been recorded.
Hello friend, hello, how are you?
Hello.
All the music of the EMF group was separated into 24 different channels and recorded on a magnetic tape under the supervision of engineer Martin Foley.
He controls and mixes the sound of all the instruments to obtain the final sound of the song.
Everything is going to be fine.
Yes, I think it's fine.
Are there any adjustments?
Yes.
We probably have to do some modifications.
Small adjustments can make all the difference in the final sound.
Repeating the recording sessions due to previous errors can cause time and money loss.
Well Jack, let's see now everything we need.
Where do mathematics come in all this?
Most of us only see mathematics in books, but music allows us to listen to its sound sessions that are related to its numerical sessions.
200 years ago, Wolfgang Amadeus Mozart was a pop star of his time.
He was a master of the successful combination of mathematics and music.
Although music sounds different today, the notation of musical writing has not changed.
The notes are still written in lines and spaces.
With the aim of seeing the use of mathematics in music, we can do the following.
We can assign a different number to each of the notes.
We can rename the musical notes assigning a 1 to the first note, a 2 to the second note and in the same way we will do it with the rest.
So what happens with the last song of the group EMF?
Well, listen to this.
Let's pause and take a closer look at this phrase.
Everything we hear is a change of tone.
We could see it as a numerical sequence.
If we assign a number to each note, then we can change the notes by the corresponding numbers.
Tone.
Can you see the relationship between these two sets of numbers?
If the whole song changed in its tones, the disc of the group EMF could sound uninteresting.
Let's listen to other components of the song.
If we listen carefully, we can distinguish that music is divided into individual bars.
For the development of a musical structure, the bars are ordered into groups or patterns of ideas.
Some of these groups are the rhythmic pattern of the bars, the melodic pattern of the musical notes and the harmonic pattern of the strings.
Let's focus on one part of the song, the rhythm.
A rhythmic unit in I Believe consists of 10 notes, which are repeated in each 4 rhythmic units
during the time the song lasts.
If the whole song is made up of 300 rhythmic units, how many individual beats are there in the song?
How many rhythmic beats are there in total?
We have seen bars and bars, but how did EMF get to this particular song?
They could have played the notes in the order they wanted, but they didn't.
We can use mathematics to know the number of options they had.
The phrase I Believe was interpreted with four beats over two different notes,
but they could have been accommodated in many ways.
Options. How many different ways can you accommodate the four notes?
Using four beats with two notes, for example, 1 and 3, there are 16 different ways to accommodate the tune, although some of them don't sound very good.
But if we had 10 beats and 4 notes, let's say 1, 3, 5 and 7, how many tones could we get?
How many different ways could we accommodate the four notes?