Thursday, June 11, 2009

Music of the Spheres/Celestial Music

"Music of the Spheres" is a phrase used by Pythagaros (ca.580-500BC),an early Greek mathematician and astronomer who was the first to discover a mathematical relationship in the frequencies of the various tones of the musical scales.

Material I could gather from various sources on Pythagaros and his contribution to music,and particularly ,celestial music:-

"Pythagaros and his followers believed that a Universal philosophy could be founded in numbers.According to him there were three forms of music:Music of instruments,music of human body and soul and Music of the Spheres (music of the cosmos).He was the first to establish the theory of strings as a tool for understanding the Universe.
When Pythagaros listened to a blacksmith's hammers pounding iron and producing a variety of reverbrations,he derived musical notes from the same.He analysed the hammers and realised that those that were harmonious with each other had a simple mathematical relationship-their masses were simple ratios or fractions of each other.That is to say that hammers half,two-thirds or three quarters the weight of a particular hammer would all generate harmonious sounds.He explained that if two strings in the same degree of tension were divided,one of them exactly in half,and when plucked,the pitch of the shorter string is exactly one octave higher than the longer string.He also discovered that if the length of the 2 strings in relation to each other are 2:3,the difference in pitch is called a fifth.He also taught that various musical notes had different effects on human beings and could also be used in healing people suffering from ailments.
In Astronomy Pythagaros taught that the Earth was a sphere at the centre of the Universe.He observed that the orbit of the moon was inclined to the equator of the earth.He taught that movements of planets travelling through the Universe created sounds that could be perceived by only those who were trained to hear them(this is the same anaahatha shabda that could be perceived only by yogis of high order at a very advanced stage of yoga).This music of the spheres could be replicated using a single string instrument called the monochord. The monochord was used for demonstration by Pythagaros to explain musical intervals and harmonics to his students."
Marsilio Ficino,(1433-1499),a humanist philosopher and astrologer observed that there was an essential congruity between the music of the spheres and the music of the human microcosm.When a person's soul is in tune with the Heavens it responds just as sensitively to the music of the spheres.
John Milton(1608-1674),the english poet said in his lyric poem"Arcades",Milton's genius of the Wood explains to an assembly of nymphs and shepherds how he listens to the music of the spheres at the end of the day."But else in deep of night,when drowsiness hath locked up mortal sense,then I listen to the celestial harmony."
Kircher ,a 17th century German Jesuit scholar said,"Tune the enneachord of my soul to Thy Divine will;play upon all the strings of my soul to the praise and glory of Thy name that I love Thee!"


Shabari said...

Hi Veena Gayathri Ji,

Honestly, I couldn't understand most of this article:-)
Especially the lines:-
"He explained that if two strings in the same degree of tension were divided,one of them exactly in half,and when plucked,the pitch of the shorter string is exactly one octave higher than the longer string."
Looks like one requires an in-depth knowledge of musical notes to understand this article in its entirety..

Mrs Mythili Srinivasan

Veenaagayathri said...

What I have presnted here are excerpts of the early investigations about the nature of sound of the Pythagoreans,based on the relationship between music-maths and physics.
An indepth analysis of the topic would require a lot more than a mere gist of what you had read in my article.Thank you.Gayathri

Robert said...

No, you only need the most elementary imaginable knowledge of music to understand that sentence. An octave is what encompasses the major scale. There are seven different notes in that scale. The eighth note is a repetition of the first, but an octave higher (the eighth, hence the octave from the Latin "octus" meaning eight as in octopus, which literally means eight-footed.)

Now all you need to add to this are two more very basic facts:

1. Musical pitches are physical vibrations. That means some physical movement back and forth at some rate per second, which we call frequency. For example, the international standard for the concert A an orchestra tunes to is 440 vibrations for second, hence the term A440.

2. Any note repeated an octave higher has double the frequency of its lower counterpart. In other words, if we sound the A an octave above A440, it will vibrate at a rate of 880 per second. An octave lower would vibrate at a frequency of 220 Hz, another way of saying vibrations per second, since Hz is an abbreviation for Hertz, which simply means cycles per second.

So when we touch a vibrating guitar string lightly at the exact midpoint, it will sound an octave above its normal frequency of vibration. That corresponds to the eighth note in the scale above the normal pitch of that string.

This is physically equivalent to having two identical strings half as long tuned by the same tension on the string. The tension is included simply because changing the tension of a string, for example tightening or loosening the tension of a string with the tuning pegs at the end of a guitar neck, changes its rate of vibration. Tighter strings vibrate at higher frequencies and correspondingly higher pitches, while looser strings vibrate at lower pitches.

The scientific part of this used to be junior high science in the 1950s. I don't know how much they teach at that level now. Not much, I would guess. But all of this is extremely basic musical knowledge; certainly not anything we could justifiably call "in-depth knowledge". Musicians who fail to understand these simple facts may know how to play, but that represents only mechanical ability to manipulate these factors without any understanding about how any of what they're doing actually works.


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