METHODS OF TEACHING MUSICAL SCALE, UPPER TONES, NATURAL SCALE AND OCTAVE TOPICS IN THE MUSIC EDUCATION PROGRAM

SCIENCE AND INNOVATION INTERNATIONAL SCIENTIFIC JOURNAL VOLUME 4 ISSUE 11 NOVEMBER 2025 ISSN: 2181-3337 | SCIENTISTS.UZ 231 METHODS OF TEACHING MUSICAL SCALE, UPPER TONES, NATURAL SCALE AND OCTAVE TOPICS IN THE MUSIC EDUCATION PROGRAM G.A. Ibrokhimjonova Senior Lecturer, “Music Education” Department, International Nordic University https://doi.org/10.5281/zenodo.17861744 Abstract. This article presents some considerations on the methodology of teaching the musical scale, upper tones, natural scale, and octave topics in the music education program. Keywords: music, octave, tone, scale, musical system, education, pedagogical approach, scale, overtone, tonality. Introduction It is known to everyone that a musical system consists of a series of sounds that have certain relationships in terms of pitch. The sequential arrangement of sounds in ascending or descending order of pitch is called a musical scale. Each sound of the scale is called a step (its number is indicated with Roman numerals). When a vibrating body of various thicknesses, such as a string, vibrates and divides into equal segments, a complex form of sound waves is produced. During the overall vibration of the body, these equal segments vibrate separately, generating additional waves corresponding to their length. Thus, upper tones (overtones) are produced as a result of additional simple vibrations. The pitch of upper tones varies because the frequency of the vibrations producing them differs. For example, when only the fundamental tone is heard on a stringed instrument, its waveform would correspond to the following graphic representation: The second overtone produced from half of the string has a wavelength that is half the length of the fundamental tone’s wave, and its frequency (speed of vibration) is twice as fast, and so on. Wave produced from half of the string (twice as fast): Wave produced from one-third of the string (three times as fast): Wave produced from one-fourth of the string (four times as fast): SCIENCE AND INNOVATION INTERNATIONAL SCIENTIFIC JOURNAL VOLUME 4 ISSUE 11 NOVEMBER 2025 ISSN: 2181-3337 | SCIENTISTS.UZ 232 If we take the number of vibrations of the initial tone (fundamental tone) of a string as one unit, the vibration numbers of the upper tones can be represented by the following simple numbers: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, and so on. A series of sounds related by a certain pitch is called a musical structure. The arrangement of the structure’s sounds according to their pitch is called a scale, and each sound is called a step. The complete scale of a musical structure contains 88 different sounds, ranging from the lowest to the highest, with vibration frequencies from 16 Hz to 4176 Hz. These pitches correspond to sounds that the human ear can comfortably perceive. The human vocal range, approximately from 60 Hz to 1000 Hz, falls within this frequency range, so many musical instruments produce sounds primarily within this range. Upper tones (overtones) arise from the complex form of sound waves. Elementary music theory does not study timbre characteristics in detail; this topic is discussed within the fields of organology and orchestration. The pitch of a sound depends on its vibration frequency. The higher the frequency, the higher the pitch; conversely, the lower the frequency, the lower the pitch. Therefore, sounds are divided into two main groups: 1. Sounds with a clearly defined pitch - musical sounds 2. Sounds with an indefinite pitch - noisy sounds The strength of vibrations is expressed in vibration amplitude, which determines the loudness (forte-piano) of the sound. The greater the amplitude, the louder the sound. The duration of vibrations is related to the length of the sound. The wider the amplitude, the longer the sound resonates. The composition of the vibrations of a sound source should be understood as follows: the source vibrates not only as a whole but also in segments. The whole vibration produces the fundamental tone, which is the most audible sound. Each segment (half, one-third, one-fourth, one-fifth of the string, etc.) produces vibrations corresponding to its length. These additional tones are heard two or three times higher than the fundamental. The shorter the segment, the faster its vibration, and the higher the resulting pitch. These additional component tones are called overtones or harmonics. In short, the overtones in the sound contribute to the richness of the tone, i.e., its timbre, which defines the individual quality of the sound and distinguishes it from others. These four characteristics are present in every musical sound. Sounds are named by syllables and letters. The main steps of the musical scale are given seven independent names: With syllable Do Re Mi Fa Sol La Si With letter C D E F G A H These names assigned to the main steps were formed during the Middle Ages. These main steps correspond to the white keys of the piano, which consist of 52 main keys SCIENCE AND INNOVATION INTERNATIONAL SCIENTIFIC JOURNAL VOLUME 4 ISSUE 11 NOVEMBER 2025 ISSN: 2181-3337 | SCIENTISTS.UZ 233 The letter-based system is widely used in our country and many foreign countries due to its simplicity and brevity for indicating keys, while for representing sounds it is mainly used in scientific and musical literature. In some European countries, such as Germany, Great Britain, and the Netherlands, the letter-based system remains the primary system even today. The names of the seven main steps in the musical scale repeat periodically, covering all main pitches. Each eighth note, produced on the white keys of the piano, results from a vibration twice as fast as the first note, forming the next higher tone, which corresponds harmonically to the fundamental tone. The closest interval between notes of the same name is called an octave. Each part of the scale containing the seven main steps is called an octave. The entire scale is divided into several octaves. In practice, the first note of each octave is considered the C note. In the elementary theory of music, the full scale studied consists of seven complete octaves, with the two ends of the scale on the piano keyboard forming two incomplete octaves, each consisting of four notes. The octaves are named from the lowest to the highest as follows: sub-contra octave, contra octave, great octave, small octave, first octave, second octave, third octave, fourth octave, and fifth octave. Among these, the complete octaves are: contra, great, small, first, second, third, and fourth octaves; the incomplete octaves are: sub-contra (three notes) and fifth octave (one note). The Art of Music and Its Specific Characteristics. Main Expressive Means of Music. Artistic Image. The content of art is life, the reality around us, and the inner world of humans their thoughts and feelings. Art assimilates reality through the creation of artistic images, unlike other types of human activity. It recreates the world in a way that directly affects human emotions and consciousness. However, an artist does not simply copy life, events, or objects. Instead, the artist selects the most general and typical characteristics of a given image, fully understands them, transforms the image, and then embodies it in the form of a painting, poem, or musical work. Naturally, any work of art retains traces of the author’s personality, because the objective material of the external world is reprocessed in the artist’s mind, becoming original and unique creative work. At the same time, each creative work can also be considered a product of public consciousness, as it is connected to specific social psychology, country, and historical context. The social aspect of artistic creation is evident when a person experiences a connection with contemporaries, the past of their people, and humanity through artistic images. True art creates eternal artistic values, thereby maintaining the continuous link between generations. Thus, works of art are a reflection of both life and creativity. However, different types of art cannot equally depict all aspects of life. Each art form is distinguished by its own means and principles of expression. So, what is the art of music? What are its goals and functions? Music (the art of inspiration) is the art of intonation, the artistic reflection of reality expressed in sounds. It represents and enriches existence in its own way, helping humans to understand and transform it. Music plays a significant role in society. It participates in human life, social activity, work, and leisure, serving as a unique means to elevate people to spiritual values. Music is rightly considered an effective tool for aesthetic education, shaping the spiritual world and moral goals of individuals. Music itself, along with its creators, performers, and listeners, forms musical culture, which is an essential part of a society’s overall culture. Music undoubtedly has close relations with other art forms. Its living connections are seen in its intonational basis (similarity to literature), rhythmic coherence (resemblance to poetry and dance), and the SCIENCE AND INNOVATION INTERNATIONAL SCIENTIFIC JOURNAL VOLUME 4 ISSUE 11 NOVEMBER 2025 ISSN: 2181-3337 | SCIENTISTS.UZ 234 proportional structure of works (similarity to architectural forms). Additionally, literature, visual arts, and sculpture often serve as foundations for musical compositions. This Course on Music: Grammar, Basic Elements, and Melody Study This course aims to teach music grammar, the main elements of music, and especially the study of melody. Within this subject, the following topics are studied analytically: the characteristics of musical sounds, their representation in notation, the main expressive means of music such as meter and rhythm, modes, harmony; the relationship between two sounds (intervals), the relationship of three or more sounds (chords) and the musical meanings they express; as well as the possibilities of modes and tonalities to convey musical content. An artistic image in music works is manifested in a unique way, that is, as a synthesis of certain sounds and tones. In musical works, form and content are mutually complementary and are of primary importance. Music conveys meaning through musical imagery. This content may represent natural landscapes, events and situations in social life, or a person’s inner spiritual world. Music is capable of expressing human emotions and mood. It also has the ability to depict nature scenes, portray movement, and imitate the authentic sounds of life, such as birdsong or thunder. Sound is a physical phenomenon. The concept of “sound” also includes several interrelated phenomena. The source of sound is the vibration of any object (e.g., a string of a musical instrument). Such vibrations produce wave-like oscillations in the air, which are sound waves. These waves affect the auditory organ, transmitting signals through the auditory nerve to the brain, thereby producing the perception of sound. In the elementary theory of music, the term sound has two meanings: 1. Sound as a physical phenomenon. 2. Sound as a perceptual phenomenon. For example, when a flexible object, such as a string of a musical instrument, vibrates, it produces longitudinal waves in the air. These vibrations constitute sound waves, which propagate in all directions from the sound source. The process can be summarized as follows: sound source → sound waves → effect on the auditory organ → excitation transmitted to the brain via auditory analyzers. From a physical perspective, the frequency of vibrations of a vibrating object per second is measured in hertz (Hz). 2. When the produced sound waves reach the auditory organ, they stimulate it, and the nervous system (auditory analyzer) transmits the signal to the brain, creating the perception of sound. In nature, the range of sounds perceptible to humans is infinite. These sounds can be divided into:  Noise sounds: natural sounds such as clattering, rustling, hissing, and buzzing.  Musical sounds: human singing, sounds of musical instruments, and other artificial sounds. Musical sounds are the primary means of music, serving to reflect reality. Throughout centuries of development, musical sounds have been selected and organized into specific systems. The foundation of musical expressiveness lies in the specific characteristics of musical sounds. These characteristics depend on the vibration frequency, amplitude, duration, and the number and quality of constituent parts of the vibrating object. In daily life, we hear a great variety of sounds, but not all of these sounds are used in music. Our auditory system can distinguish musical sounds from noise. Noise sounds, such as clattering, rumbling, hissing, whispering, or rattling, do not have a definite pitch, which is why they are not suitable for musical use. The Four Physical Properties of Musical Sound SCIENCE AND INNOVATION INTERNATIONAL SCIENTIFIC JOURNAL VOLUME 4 ISSUE 11 NOVEMBER 2025 ISSN: 2181-3337 | SCIENTISTS.UZ 235 From a theoretical standpoint, a musical sound has four physical characteristics: pitch, duration, intensity (loudness), and timbre (tone color). In foreign literature, these are also described as the basic elements of music: pitch, duration, timbre, and dynamics (sound intensity). Some authors additionally include speed (the rapidity of physical vibration that produces sound) and structure. The pitch of a sounding note depends on the vibration frequency of the vibrating elastic body. The faster the vibrations, the higher the pitch; conversely, slower vibrations produce a lower pitch. The duration of a sound depends on the amplitude of vibration of the source. While the length of the sound does not change its physical nature, from a musical perspective, duration is an important characteristic. The duration of a sound depends on how long the source continues to vibrate. For example, when a sound begins, the wider the initial vibration of the source, the longer it will take for the sound to fade away. It is important that the vibrating object be free to vibrate. The intensity (loudness) of a sound depends on the force of vibration, that is, the amplitude of the vibration of the source. The range over which the vibration occurs in space is called the amplitude of vibration. The greater the amplitude, the louder the sound is perceived. Fig-1. Conclusion. The greater the amplitude of vibration, the louder the sound is perceived, and conversely. Timbre refers to the quality of a sound, its colorfulness and richness. To describe timbre, various expressive terms related to emotions are used, such as soft, sharp, thick, resonant, melodic sound, and so on. It is well known that each musical instrument or human voice has a unique timbre. Sounds of the same pitch produced by different instruments differ in their color and richness. The distinctiveness of timbre depends on the composition of overtones (natural harmonics) present in each sound. REFERENCES 1. Vakhromeyev, V.A. Elementary Theory of Music. Tashkent: 1980. P.224. 2. Vakhromeyeva, T.A. 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