Showing posts with label music theory. Show all posts
Showing posts with label music theory. Show all posts

Friday, April 24, 2015

Can Classical Music Make Us Smarter?


Mozart_Effect
Image credit:blog.lib.umn.edu
Classical Music Developed in 18th Century

Classical music is usually seen as a choice of the refined, music for clever people having stylish taste and since many tend to listen to classical music regularly to relax, there have been claims that listening and playing classical music could do more than entertaining. Research has recommended that the music of Mozart could boost the power of the brains enabling us to grow more intelligent. Suzy Klein, writer and broadcaster visits the Royal College of Music Museum to explain toher, power of classical music and find out if it has made her smarter.

Classical music developed in the 18th century due to a way of writing music down which was accepted all over Europe. It not only enabled complex musical instruction on what to play, how to play and who played it but also helped to preserve music for the future generations. Classical has its own term like symphony, sonata and concerto which baffles those who are untrained. Music tends to have its own language with strange symbols and musicians need to be able to read these musical notations prior to picking up an instrument to play a piece of music.

Classical Music Associated with Intelligence

Plenty of practice is essential in order to play classical music of good standard. The reason to think that classical music is associated with intelligence is due to a study dubbed the Mozart Effect. Researcher carried out an experiment in 1993 and volunteers were divided into two groups with each group asked to perform complex origami style tasks.

Each group, in the experiment were asked to listen to different music and had their speed and efficiency measured while carrying out the task. It was found that the group which had listened to Mozart’s music excelled in the task and their IQs boosted for the duration of time they had performed the task. The discovery was published by the researchers in the respected science journal – Nature which unexpected started a phenomenon.

The classical music soon unlocked the doors of untapped reserves of the mind and gave way to the Mozart Effect. There were several issues that came up when other researchers struggled to duplicate the Mozart Effectwith some who produced a similar effect but not with Mozart’s music.

The Mozart Effect 

The Mozart Effect could have been generally de-bunkedbut with science’s attraction with music together with its effect on the brain led to a sincerely fascinating encounter where playing music was at the forefront. Boosting our brains with music may not depend on listening to it but in learning to play it and learning a musical instrument had indication of sharpening the learning skills, improve our motor coordination as well as our memories.
Besides teaching new useful skills, playing a musical instrument could also permanently activate our brains. Scan done on professional musician’s brains have indicated that there has been great development in areas which involve sound processing, coordination and movement when compared to non-musicians.

Though there is no confirmation that musicians could be more intelligent due to playing an instrument or singing, it is clear that musicians’ brains have improved for the better by their dedication and love for music. Often people tend to enjoy listening and playing music which enables them to relax and discover more about themselves. Music does help to change the overall mind set.

Sunday, November 17, 2013

History mystery: Apollo’s Numbers – Part II



Apollo with Lyre
The special forms of lyre namely phorminx and the kithara were used more or less by professionals while the ordinary lyre was used for the social life due to its unsuitability of its softness for open air use. The strings of Hermes’ lyre vary but probably four strings were widely used originally and later on increased in number. The tetrachord or the four strings had to be tuned so that the first and the fourth strings could define the interval known as the fourth while the tuning of the other two strings seems uncertain. Towards 670 BC, the tetrachord got expanded with improvement by Terpander who added three strings to the original four strings while the last string of the original string acted as the double duty as well as the first string to the newly added strings together providing a new tetrachord. Mevsh or middle, being the common string, was considered the most important of all the seven strings. Based on standard pitch nowadays, A is considered as 440 vibrations per second and each lyre player tuned the strings to suit their own voice though whichever pitch was taken as fundamental for tonic or base note, the interval between the first and the fourth strings and between the fourth and seventh stings were called a fourth. The second, third, fifth and sixth strings were tuned according to the player and a number of varieties of tuning were used.


Phorminx
Performance was based solely on the ear and if the fourth and the fifth strings of tetrachord could conform to the interval of a fourth, the final results was the ear of the player that established it besides the fundamentals or tonic. Practitioners while committed to the interval of fourth as the basis for their instrument’s structure for performances had another larger interval demanding increased attention by way of octave. The string lengths were related to vibrations and shorter the string, greater was the number of vibrations resulting in higher tone. The Greeks had no means of measuring the vibrations of string but could measure its length and the common practice was to put the higher number first in a musical ratio though it was their custom to sing or play in descending scales while the custom presently is on ascending scales. Here the relationship between two tones is a ratio and the numbers are measured either on string length or vibrations, the ratio of which is called the interval between two tones. Intervals cannot be treated as string lengths and added but they may be combined. Combining ratio and intervals: When a numerical ratio is written as a:b, a, the first term is called the antecedent and b the second term is known as the consequent.

Kithara
Pythagoras’s general principle has given illustration which shows that the interval which we call octave was defined by ratio 2:1 which means that if a string length was doubled it would define the tone of the octave below or if it was halved it would define the tone above. For scientific purposes, Pythagoras established the octave as the predominant interval and defined that it was the simplest string divisions and multiplications through doubling or dividing and the discovery in the use of the first two integers, 1 & 2, were the results of the most consonant of intervals. The next most natural consonants, the fifth, was defined by the ratio 3:2, and if a given string length is divided into three similar parts, the interval between whole string length and length of two of its part can be known as a fifth. With an interval of octave, it is possible to produce from a higher tone of the octave to a descending fifth which leaves the interval of a fourth i.e. `doh to fah’ and it is observed that an octave has been made up of fifth and a fourth. For the Greeks, the octave and the fifth were natural with pleasing sound to the human ear. In consideration of the lyre, the term octave is used but we do not have the scale eight tones but only seven tones due to the last tone of one string which did double duty as the first tone of the other tetrachord. Pythagoras used intervals to provide steps in the scale and he called a whole tone or just a tone and it was this interval which was used to separate the two tetrachords. With the given array of numbers representing the divided octave: 6 8 9 12 where 6:8 is the fourth and 6:9 is the fifth and the difference between them is the interval of 8:9 being a numerical expression of the whole tone of Pythagoras. Each fourth proposed by him should be divided into whole tones though the fourth will not contain the exact number of the whole tones and it will hold only two whole tones with a smaller interval left being close to a semitone or a half a whole tone with a calculated value of 234:256.

For example:

Let x:y be the left over interval

9:8 compounded with 9:8 compounded with x:y :: 4:3

Or 81:64 cp with x:y :: 4:3

Or x:y:: 4:3cp with 64:81

So x:y :: 256:24

On combining intervals; by multiplying we get

9/8 x 9/8 x 256/243 = 20736/15552 = 4/3 tone  tone   semitone   fourth, and the Pythagorean scale of one octave was made of following intervals -> tone, tone, semitone, tone, tone, tone, semitone, 

(first tetrachord)    (middle)     (second tetrachord) 

Terpander
The arrangement was satisfactory with regards to the practical and ancient traditions of tetrachand though it was within the arithmetical musical division of the octave of Pythagoras. The division of tetrachand was in two whole tones as well as a semitone from which this system derived its name from those tones and was called the diatonic system. Scale or scales was the necessary base for tuning theory and diatonic scales were constructed mathematically or theoretically within the octave with the fifth and the fourth, while there was another method of constructing the scale with only the two intervals of an octave and a fifth, the method of which is known as the Spiral of Fifths. This had the advantage of being empirically tuned.

Wednesday, November 6, 2013

History mystery: Apollo’s Numbers – Part I



Many stories are told about the Greek scholar, Richard Porson who was born in 1759 and was educated at Eton and Trinity College, Cambridge and held the Regius Professorship of Greek till his death in the year 1809. He invited anecdotes and at times was ridiculed for his Dipsomaniacal conduct. Porson had a wonderful sense of humor which was invoked by the Trinity Combination Room which had the custom of permitting smoking during the twelve days of Christmas and one of the wittiest stories in connection with him was his habit of always taking toddy to bed.

Plato too enjoyed intellectual witticisms and Plato’s Ion dialogue is full of intellectual witticisms, with many references and allusions to Apollo, though his name is not mentioned. Ion in its eponymous term in connection to Ionians is related to Apollo. The dialogue Ion composed by Plato was about joke and riddle and in ancient Hellenic world it was assumed that every learned person would be familiar with the lyre and its basic theory and its tune. The rhapsode Ion had come from a festival of Asklepios, a city of Epidaurus which had a shrine of Apollo while Asklepios was another son and both were born out of wedlock. The festival had all the arts of music and Apollo presided over it.

Ion after winning the first prize in the competition got engaged with Socrates in a philosophical discussion where he admitted when asked by Socrates that his skill in performance recitation was limited to Homer and all other poets bore him. This puzzled Socrates which led him to solve the riddle of Ion’s limited expertise and informed him that art critics and judges of sculpture do not limit themselves to judge the work of single artist but criticize the art irrespective of the artist. To understand the dialogue Ion, one needs to read it which is a continual reminder of Apollo though he is not mentioned in it and the understanding is in the ancient tuning theory where the comprehension could probably be in the present acoustics or harmonics, though it is not concerned with composition or performance, on the contrary, it deals instead with arithmetical structure of the tones, scales and intervals connected in music.

Present musical instruments are made in terms of the historically developed tuning theory which is described with regards to the terms associated with it though the instrument does not explain the theory but embody and illustrate it. Modern musical terminology is the result of the long complicated history, details of which are not understandable. For those interested in tuning theory, the following brief preliminary details could be helpful. Platonist, Plutarch, who for twenty years of his life was a priest at Delphi and had taken an oath of secrecy, wrote with knowledge on what he could not reveal though he provided us with his helpful hints.


His most relevant hints are found in Isis and Osiris wherein he informs that sixty is the first of measures related to the heavenly bodies that is with science, astronomy and harmonics. Second being The E at Delphi, he goes on to tell us that Pythagoreans called five, the marriage number, stating that it is an attribute of the god Apollo and that it is confirmed by the importance of the number in music. He states that the right angled triangle – 3, 4, 5 is used in the Republic in formulating marriage number and 3 is the male number while 4 is the female number. The number 5 is in some ways like its father and mother since they are made up of 3 and 2 making 5 the human number.

The number sixty derived from the ancient Babylonian use of sexagesimals, is the base of all scientific work. The number five, an attribute of Apollo, an importance in music, together with sixty is the human number which is also designated with the letter E in the Greek alphabetized system of numerals and carved in wood, stone, metal in Apollo’s temple at Delphi. The combination of sixty and five results in 60 to the 5th power, 605 or 777,600,000, regarded as Apollo’s number, intimated by Plutarch though it is not certain and may have been known at Delphi.

This number is most important in tuning theory being the least number needed in tuning with spiral of fifths and coordinating the sexagesimal as well as decimal expression of tones involved and hence it is given the title of Apollo’s number. As per the ancient practice, the zeros have been omitted and we have 6 to the fifth power 65 or 7776.

The Ion has 7776 syllabus as per Plato’s joke and since Apollo being the whole of it, is not needed to be named in the dialogue and the joke is in the form of an enigma. People often became famous by solving and making up riddles which were obscene and Plato was obscure and could not be obscene. Apollo was thus connected with riddles while riddles were philosophy. Having musical knowledge, Plato knew the number 605 though it is not mentioned in the dialogues but 604 is mentioned in the Republic- Book VIII, the sovereign of better and worse births in the Critias – the foundation of the mathematical model of Atlantis. Dating back to ancient Greek tuning theory, the most clearly associated name is Pythagoras, born on the Ionian island of Samos, migrated to Crotona and later died in Metapotum in Magna Graecia (Italy) around 497.

 He was the first Greek who provided a scientific basis for music theory. Musical performers did not need the development of theory. Performers played either on aulos which were translated as flute, which was an impossibility, since it was a reed instrument and could be a single or a double reed or a form of the lyre. The greatly preferred instrument was the lyre by amateurs since it had the advantage over the aulos where the player could sing to one’s accompaniment and besides this it was also Apollo’s instrument who had accepted this as a gift from his younger brother, Hermes.

Monday, October 22, 2012

History Mystery: Music Theory of Pre Historic World

  The Sumerian not only developed the first cuneiform writings but all so they developed the new mathematical system with a base number of 60 (Every one of you aware, now we are following a decimal system of numbers based on 10). They have created a far-reaching acoustical theory with mathematical model for their universe. That was the laying stone for their musical system and they assigned each number to their god and their functions which is the basic ratio of music system. Here you have to keep in mind the Sumerians cuneiform writings and mathematical notations were fully exploited by the later period Babylonian who controlled them in the later period. If you are the regular reader of my blog then no need to say In Mesopotamia the myths and mythology took a firm place in their life. They have marked the important events of their gods in bricks in a matrix form they used few symbols and marks to notate them. The classical music tones were to be deciphered and it is waiting more than 2000 years.

    The musical theory is nothing but acoustic science about the notes and the distance between their pitches connecting with the ratios of integers and numbers. This kind of theory was first accredited by the famous mathematician of the 6th century BC the great Pythagoras. All the countries like India Greece, Egypt, and China of those days music was very important in cultural life and all of them have a same mythic values for the same numbers. Amazing isn’t it??? They played a greater role in mention the musical intervals. This similarity between the cultures raises our doubt that any of those people were expert in musical knowledge in other words Acoustics. The Mesopotamian used the word “Harp” which also referred the string length. You can correlate the pitch and the string length. Likely in prehistoric china people used the leg bones of the birds and they hole them accurately to give specific tones as flutes. These pairs of flutes were used in the rituals of the sacred burials. The expertise in making holes to the suitable note proves their knowledge in the music. The Sumerian tombs of fourth millennium BC gives a valuable proof for their music knowledge, harps, lyres and pipes and many literature with musical notes of hymns in clay tablet yet to be deciphered perfectly give evidence to their usage of 60 based number theory. The religious gods were assigned glyph a grooved notation or a symbol followed by a particular number named after that god himself. And the importance of these numbers can be ascertained from the triangular pebble counter.



The Sumerian mythology and cosmology is based upon the symbolic copulation of the male and female numerical number arrays. The head god of the Sumerians is the sky god “An” (A male god; I know my regular blog readers are familiar with this name) is assigned 60 written as one in cuneiform. Mathematically “An” is the geometrical mean and is the mean of any number and it’s reciprocal. Theologically An/ Anu is the central reference point, middle group of sky else it is the middle tone of reference. The Sumerian platonic harmonics are very simple to learn, why because even those can count the base ten can sing and play the scale constructively which resembles the cosmos. Since 60 are perfectly divisible by multiples of 2 and 3 it can be correlate with many subsystem which allows the handling of fractions. Amazingly this is the very early mastery of arithmetic. Most of the pitch ratios- string length calculations of ancient harps, length of the panpipes of those days which is similar to that of the flute, tone -Hole ratios of the Aulos are based on this mastery of the number theory.

Cont.