# data[].attributes.body
Western mathematics proceeds by increasing abstraction and generalization. In the Renaissance the Italian architect Filippo Brunelleschi invented linear perspective, a method to project geometric objects onto a “picture plane” from a given viewpoint. Three centuries later the French mathematician Jean-Victor Poncelet generalized perspective into projective geometry for planes that are tipped or rotated. Then in the early twentieth century the Dutchman L.E.J. Brouwer generalized Poncelet’s projective geometry to projections onto surfaces that are stretched or distorted into any shape—so-called rubber-sheet geometry—provided that the plane remains continuous (with no holes or tears), which is the subject of this photograph. The contemporary artist Jim Sanborn created it by projecting a pattern of concentric circles onto a large rock formation at night from about 1/2 mile away.

# data[].attributes.body
Music is also geometry.

# data[].attributes.body
Starting from the mathematical properties of music structure, scientists went even further and built complex computing algorithms, obtaining computer programs that transform music into kaleidoscopic images or geometrical structures in constant motion.

# data[].attributes.body
Musical instruments are geometric shapes, the lines must be perfect ...

# data[].attributes.body
Musical ranges and intervals can be helpful in understanding basic mathematical notions such as strings, intervals, or sets. If we think about the keyboard of a piano, we notice that the notes of the white keys are repeated from 7 to 7. If we replace in order each note with a number from 1 to 7, we obtain a number of numbers whose elements are repeated from 7 to 7.

# data[].attributes.body
Matching mathematics with music has a variety of applications. In the teaching of mathematics the concepts of rhythm and measure can be used to highlight the connection between multiplication, division and operations with fractions. For example, in a song that has measure 3/4, the sum of the note durations in each measure should be three quarters (the measures are separated by vertical bars):

# data[].attributes.body
The tempo and the measure play an important role: the tempo determines how alert the song should be played, and the measure gives the music a certain pulse (indicating how many times they are in a measure and which of them are accentuated). Thus, it can be 2/4 (two-quarters), 3/4 (three-quarters), 4/4 (four-quarters) or other even more complicated measures.

# data[].attributes.body
The most important features of the music are the rhythm and the tone. It is the rhythm that causes us to swing from one leg to another or shake when we listen to a song we like.

# data[].attributes.body
Have you ever wondered why the piano has white and black keys whose order is repeated every 7 white keys?

# data[].attributes.body
Mathematics is the science of numbers and forms, a science that arose from people's desire to understand and express the world around them. And since sound is part of this world, it is no wonder that mathematics can be used to describe or build this harmony of sounds called music.

# data[].attributes.body
It is said that listening to classical music leads to the improvement of mathematical skills, but also that mastering some basic notions of mathematics helps to understand musical theory.

# data[].attributes.body
A famous quote states that "Mathematics is the reason of music."

# data[].attributes.body
Prodan Selena, Huși, Romania

Music Theory has no axiomatic foundation in modern mathematics, although some interesting work has recently been done in this direction, yet the basis of musical sound can be described mathematically (in acoustics) and exhibits "a remarkable array of number properties". Elements of music such as its form, rhytm and metre, the pitches of its notes and the tempo of its pulse can be related to the measurement of time and frequency, offering ready analogies in geometry.

# data[].attributes.body
Ioannis Aioanei
I hope you enjoy my presentation.

# data[].attributes.headline
Jessica Mandiuc, Lațcu Vodă Siret, Romania

# data[].attributes.subject
Jessica Mandiuc, Lațcu Vodă Siret, Romania

# data[].attributes.body
Izabela Naida/Siret,Romania

# data[].attributes.body
Arife ÖZEY / Rumeysa BAŞARAN
In this way, Do, re, mi, fa, sol, la, si, do sounds are expressed with 1, 8/9, 64/81,¾, 2/3, 16/27, 128/243 and 1/2 ratios respectively.

Pythagoras achieved 1 full tone with 8/9 u of the string, but almost the octave of that note was achieved when 6 times the full tone was added to a note, which is called “Pythagorean coma”.

# data[].attributes.body
MATH IN MUSIC
Our mission in March is mathematics in music. Feyza AYDOĞAN, Şeyma ALTINKAYNAK, Sueda ÖZER, Arife ÖZEY and me matched the string of Fibonacci Numbers with notes. The Fibonacci series is a number sequence created by summing each term with the previous term. The first two terms are one. By adding up the first two terms, the sum is 2.  By adding up 2 and 1, we get 3. By adding up 2 and 3, we get 5... This sequence of numbers continues forever. We also matched the notes with the string of Fibonacci Numbers. We wrote up the seven notes. And then we wrote the  Fibonacci Series. Since there are seven notes; we divided the terms of the fibonacci numbers by 7. Since the numbers from 1 to 5 are not divided by 7, we wrote themselves. When 8 is divided by7, the remainder is 1. When 13 is divided by 7, the remainder is 6... İt continues until 987 like this. We matched the remainders to the notes. We wrote 'do' when the remainder is 1. We wrote 're' when the remainder is 2. We wrote 'mi' when the remainder is 3... We continued like this and we saw that the cycle was repeated after 987. Which shows us that the string of Fibonacci Numbers is melody of 16 notes! And we tried tı play this melody with my friens.You can watch our video on the materials page. You can play this melody too!!!

# data[].attributes.body
Music theory has no axiomatic foundation in modern mathematics, although some interesting work has recently been done in this direction , yet the basis of musical sound can be described mathematically (in acoustics) and exhibits "a remarkable array of number properties. Elements of music such as its form, rhythm and metre, the pitches of its notes and the tempo of its pulse can be related to the measurement of time and frequency, offering ready analogies in geometry.

The attempt to structure and communicate new ways of composing and hearing music has led to musical applications of set theory, abstract algebra and number theory. Some composers have incorporated the golden ratio and Fibonacci numbers into their work

# data[].attributes.body
Musical pieces are read much like you would read math symbols.  The symbols represent some bit of information about the piece.  Musical pieces are divided into sections called measures or bars.  Each measure embodies an equal amount of time.  Furthermore, each measure is divided into equal portions called beats.  These are all mathematical divisions of time.
Fractions are used in music to indicate lengths of notes.  In a musical piece, the time signature tells the musician information about the rhythm of the piece.  A time signature is generally written as two integers, one above the other.  The number on the bottom tells the musician which note in the piece gets a single beat (count).  The top number tells the musician how many of this note is in each measure.  Numbers can tell us a lot about musical pieces.

# data[].attributes.body
Math and music are usually organized into two separate categories, without obvious overlap.  It tends to be that people are good at math and science or art and music, as if the two elements could not be placed together logically.  In actuality, math and music are indeed related and we commonly use numbers and math to describe and teach music.

Musical pieces are read much like you would read math symbols.  The symbols represent some bit of information about the piece.  Musical pieces are divided into sections called measures or bars.  Each measure embodies an equal amount of time.  Furthermore, each measure is divided into equal portions called beats.  These are all mathematical divisions of time.

Fractions are used in music to indicate lengths of notes.  In a musical piece, the time signature tells the musician information about the rhythm of the piece.  A time signature is generally written as two integers, one above the other.  The number on the bottom tells the musician which note in the piece gets a single beat (count).  The top number tells the musician how many of this note is in each measure.  Numbers can tell us a lot about musical pieces.

Each note has a different shape to indicate its beat length or time.  Notes are classified in terms of numbers as well.  There are whole notes (one note per measure), half notes (two notes per measure), quarter notes (four notes per measure), eighth notes (eight notes per measure), and sixteenth notes (sixteen notes per measure).

These numbers signify how long the notes last.  That is, a whole note would last through the entire measure whereas a quarter note would only last ¼ of the measure and thus there is enough time for four quarter notes in one measure.  This can be expressed mathematically since 4 x 1/4 = 1.  A note with a dot after it lengthens the note by half.  For example, a quarter note with a dot after it would be held for 3/8 of a measure, since three eigths of a measure is midway between a quarter note and a half note.  It is important for musicians to understand the relationships and values of fractions in order to correctly hold a note.

Fibonacci

The Fibonacci sequence is a famous and well-known sequence that follows as: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, … and so on, adding each term to the one before it to create the next term.  That is, 5 + 8 = 13, 8 + 13 = 21, 13 + 21 = 34, and continuing infinitely.  In music, the Fibonacci sequence can be seen in piano scales.  For example, the C scale on the piano consists of 13 keys from C to C; eight white keys and five black keys, with black keys arranged in groups of three and two.

In the Fibonacci sequence, the ratio between each term is very close to 0.618, which is known as the golden ratio.

# data[].attributes.body
We can see math in every part of our world. We can see this in the video. Fazıl Say is a famous pianist and this video from his concert. Piano make a sound which we can only explain it with math. Piano strings make vibrate. Sound from piano through vibration.
Rojda Güneş Doğan -Turkey-

# data[].attributes.body
There is a long history of connection between the world of music and the world of mathematics.

A squared plus B squared equals C squared; that is of course the Pythagorean theorem from basic geometry, named for the Greek philosopher and religious teacher from 5th century BCE, Pythagoras.  Pythagoras taught the belief that numbers were a guide to the interpretation of the universe. Mathematics could explain everything, including music.

Legend states that one day Pythagoras was walking past a smithy’s workshop, listening to the sound of the blacksmith’s hammers on the anvil. He turned his attention to the percussive sound that was produced and noted that some strikes sounded much higher than others. He was certain that there was a mathematical explanation for the different pitches he was hearing. So he entered the smithy’s shop and observed that they were using different sized hammers. Some of the hammers were large and others smaller, but they were ratios of each other: one being twice the size of another one, one being two-thirds the size of the last. Pythagoras declared these relationships as absolute intervals of music.

It’s a great story, but completely false. That’s not how these ratios actually work. But if we apply the story to lengths of string rather than hammers, we have something much more plausible.

Pythagoras is attributed with discovering that a string exactly half the length of another will play a pitch that is exactly an octave higher when struck or plucked. Split a string into thirds and you raise the pitch an octave and a fifth. Spilt it into fourths and you go even higher – you get the idea. This concept is known as the overtone series or harmonic series and it is a feature of physics, affecting waves and frequencies in ways we can see and hear and ways we can’t.

Pythagoras believed that the planets themselves, all heavenly bodies, rang out notes of vibration based on their orbit and distance to each other. We humans simply lack the ability to hear this music of the spheres.

These mathematical ratios helped to define every system of intonation throughout history. In other words, we tune our modern day instruments using the mathematics that Pythagoras discovered almost 2,500 years ago.

Enes Buğra Ersoy / Turkey