*Thanks to the existence of overtones we have an orderly system of flageolets on every string. Actually, overtones elicited from the string are called flageolets (from the Old French "flageolet" - a flute, because of the similarity of a sounding). We will not delve deeply into the "physics" of processes, will mark only that a great Greek philosopher Pythagoras discovered all modern music structure studying positions of flageolets or overtones on a single string. Let's view it on the example of the D-string:*

*1 - the whole string, a D-note, **I - the first mode degree**;*

*2 - half-and-half, a note D one octave higher, **I - the first mode degree**;*

*3 - one third, a note A, **V - the fifth mode degree**;*

*4 - a half in two, a note D two octaves higher then the initial one, **I - the first mode degree**;*

*5 - one fifth of the string gives a note F#, **III - the third mode degree**;*

*6 - one sixth repeats a division into three, a note A again one octave higher, **V - the fifth degree of the mode**; *

*7 - one seventh, a note C, a lowered **VII seventh degree** in the key of D Major;*

*8 - a division into eight gives us a note D again three octaves higher then the initial one, **I - the first mode degree**;*

*9 - one ninth gives E note, this is the ninth or **II - the second mode degree**; *

*10 - repeats one fifth one octave higher, a note F#, **III - the third mode degree**;*

*11 - one eleventh, in this case the risen eleventh or fourth (triton), a note G#, **the risen** **fourth mode degree**;*

*12 - is the note A again, one octave higher then one sixth, **V - the fifth mode degree**;*

*13 - a division into thirteen gives us an altered thirteenth chord degree, a note Bb, **the** **lowered** **VI - the sixth mode degree**;*

*14 - a division into fourteen repeats the division into seven, we get a note C, **the** **lowered** **seventh mode degree**;*

*15 - one fifteenth part gives the natural seventh degree in the key of D Major, a note C# is **the** **natural** **VII seventh degree of the mode**;*

*16 - and at last, one sixteenth part repeats the tonic D but it is four octaves higher then the initial one, **I - the first mode degree**. *

*Theoretically, we can continue the division of a string into all sequence of natural numbers; that is to infinity. But in practice, try to find all the viewed above flageolets (overtones, harmonics) on the guitar and you will see, the father we move, the higher in frequency and lower in sound flageolets become, and it gets harder to elicit them. So the elicitation of flageolets become problematic after the twelfth division (the fifth degree), let alone a division into 17, 18, 19 and so on. If we produce the sound from the opened D string, its tone will be limited for our ear to the single note - D one-line octave. This is the main tone, the nucleus of this sound. But simultaneously with the D note a great number of other tones sound, which we call overtones or harmonics. Thus mostly overtones are indiscernible by ear, every adds individual inflexion to the common color or sound timbre. All instruments produce different overtones. Overtones explain the timbre color of certain tones and the uniqueness of an instrument's sounding.*

* *