Prosodic Structure - Speech Signal Block Coding

 tinyimin Nanjing China ; 18260060980@163.com

Do you like the music,and understand the relations between seven Nodes “CDEFGAB”. Ancient Greece Pythagoras said: Four degree five degree sounds are nature sounds under universe, therefore we study to this magical Prosodic Structure .

[Main Text]:

1. The Prosodic Structure

The Prosodic Structure is a data relation structural, called " PS "，and it is a block coding way for Speech Signal too.

1.1 The Prosodic Ratio and Prosodic Network (See Fig.1)

In the positive real number domain, assume: X1 is a any point ,then ,always have four point X2, X3, X4, X5, that to X1 ,the Ratio of their numerical values is [2/3, 3/4, 4/3, 3/2], that called "Prosodic Ratio" or  "Four_way Ratio", these four points are called "Four-way point" of X1. Between them is “Prosodic Relations” or called “Prosodic Correlation”, it is two-way (See Fig.1). Similarly, these four points respectively have four points that with it are Prosodic Relations too. Similarly ....It is easy to prove that, by the “Prosodic Ratio”, these Prosodic Relations points are convergence at the same Network, that called "Prosodic Network” or "pW ". 

In the field of positive real numbers, there are many pW's co-exist logically, and they are all similar.

1.2 Prosodic Area and Music (See Fig_2)

In the prosodic network naturally form prosodic Area one by one, that denoted as "pA" (as shown in the black dot area of Fig_2). The relationship of the nodes that in the Prosodic Area can be expressed by the following formula:

pA=[1,k,k*k,4/3,3/2,3/2*k,3/2*k*k]; (k=9/8)。

Among them, the "1" is the" base point ", denoted as "C1". When a sound Xi as the fundamental tone BF, that is C1=BF, it is called "Instantiation", and this pA is the musical point understood by humans that denoted as [CDEFGAB] (physiological reasons unknown). Therefore, pA is called the " Music Nodes Coefficient".

Human musical sense does not rely on the fundamental note C1. Sometimes, even without C1 in a piece of music, it can still recognize the musical sense of that section. From this, it can be seen that the sense of music mainly depends on the structure of the prosodic ratio between musical points.Fig.1 is a part of Fig.2.

[Description]: The short arc in the figure is expressing “Four_way Ratio” relationship (logical relationship).

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In Fig_2, there are two red arc, which are boundary line that made by F or B. Between two boundary line is main pA of X1. In a pW, on both sides of the main Prosodic Area(pA) are “Shadow Areas” .The Shadow Areas likes Shadow of the main pA that one by one. For example, the first of the left side is "Shadow Areas -1 " (in blue arc), the first of the right side is "Shadow Areas +1" (in green arc).... Any Prosodic Area (pA) has all properties of main pA, they are similar. The Ratio of Between the adjacent pA is 3^7/2^11.

1.3 VK System(vkSy):

The auditory sense can obtain the fundamental tone BF of the speech in a short time. But auditory more emphasis on the relative comparison between the subsequent sounds, which is the prosodic ratio pA. pA can be refined into 12 points that called " Volute Knot", or simply "VK" :

VK=[pA(2:3)*2^11/3^7，pA(1:3)，pA(4:7)，pA(4:6)*3^7/2^11];

The upward direction are the "VK coefficient", and after sorting they are [CdDeEFfGgAaB], Obviously, the music set (pA) is a subset of the VK.

The vkSy is called "VK System": vkSy=VK*2^n; (n is an integer, it is called "n-level"). vkSy divides the spectrum into many small regions, which can be understood as the frequency region between two VK points. It can also be understood as a frequency domain of a VK point, which called the " vkPD": The frequency region from this VK point (closed region) to the next VK point (open region).

1.4 The formants of speech are closely related to the VK point domain vkPD.

For example:  "Me1" is a Example of the Vowel's [e] , this is 12th time period of it. (goal peak >12.0. the max 1312 Hz(70.2) is in 9th time period): 

Analysis: In “ Me1” the main Formant is in close with vkPD.

IIn which, there are three main Formants: “896~928(F)”; “1072~1104(g)”; “1248~1296(B)”, that sampled by three vkPD that is F,g,B, that can writed “vkPD(F,g,B)”. In these vkPD the energy compared to their left and right sides, these vkPD are stronger a lot. In which: Three main Formant (their main part of energy) (Red) are respectively sent in the three vkPD(F,g,B)(blue); Three vkPD (F,g,B) respectively sampled the three Formants (their main part). 

In other, Formant "352~368~384" is jointly sampled by two adjacent vkPD (d,D) , that formed "left hillside", "right hillside"; the Formant “528~544~576” is jointly sampled by two adjacent vkPD (g, A) , that formed "left hillside", "right hillside" too.

These sampling facts, have provided two aspects information for us: 1)The pronunciation of this Formant is generated from this "vkPD" (frequency area), this vkPD is called "goal vkPD" of this Formant (its pronounce goal); 2)These 5 main Formants (its main part) are 7 vkPD of the VK System. (These has provided important clue for follow-up study).

1.5 "Characteristic VK Point Group" (vG) of the Speech unit

In the VK System (vkSy), there are "Characteristic VK Point Group" that denoted as "vG". Here, only two vowels [a] [ao] are used to explain this vG. (They only roughly indicate the direction and methods of the research. The data needs to be optimized and deepened)

1.5.1 Vowel [a]: First, let's look at its example one " za7". The next line extracts the main frequency-domain signals of its 57th and 59th time periods: (This article only analyzes the relationship among the first few stronger frequency points in the frequency domain signal. Using the autocorrelation BF=204Hz)