r appearance vary, (3) the elegant shaping of the overtones and the intensity of each is so complex that no pair of sound sources could be possibly the same unless the artificial digital techniques are employed, and (4) many more reasons. As mentioned earlier, the fundamental is heard as the pitch and only this pitch; however, the overtones, though not affecting the sensation of this pitch, find their way inevitably to the hearing mechanism and affect one’s sensation of the timbre or tone quality. An analogue could be borrowed for describing it when one sees two copies of a picture which are printed from the same printing machine, due to a slight different color processing for printing the two copies, the factual colors imprinted onto them may differ though the differences of the properties are small. The general impression of the two copies is the same, but the different coloring is detected. The analogue applies to the sense of timbre well, that is, the different properties of overtones, or more technically the different wave forms, like the coloring, make our perception aware of them—as timbre or tone quality or romantically tone color though the sense of pitch is not altered, like the same general impression of the picture.  

【 】The implications of a knowledge in the scientific basics of sound:

If you are asked what should be the logical starting point of the study for music. What will your respond? Because of its complicated nature of music, it may function, like those anthropologist Merriam identified, as endeavors of human beings for emotional, aesthetical, communicational and educational purposes or just for entertainment, of societal and cultural inheritance, of tribal conventional uses, of industrial and commercial benefits, of reinforcing cohesion or conformity to social criteria. Viewed from different angles, the logical starting points for the studies of music vary. Despite these many functions music assumes, one thing is inevitably certain, that is, it uses sound. And the ultimate elements of sound are rooted in the four mental parameters that are reflections of the physical properties of vibration. These psycho-physical relationships should be made clear that the physical attributes of vibration are the causal resources on which the sense of sound is based; this is the objective side of the phenomenon in regard of the substance used for music, and the subjective side of mental sensations of sound is the reflection of the former. To reiterate the relationship between these two sides, the physical properties per se are not sound but the sound’s causal resources; they are there hylic, immune to subjective hearing. Based on these interrelationships, the elements of music are organized. We may consider, therefore, these four relations and their interactions as the logical starting points for the beginning study of music:

(1) From pitch-frequency to musical elements of names of pitches or steps, staffs, intervals, keys and related signatures, modes, tonalities, and, those larger elements of melody, harmony and counterpoint, etc..

(2) From duration-time to musical elements in lengths of notes and rests, beats and times as well as the time signatures, and the larger elements of rhythm and so on.

(3) From loudness-intensity to musical elements of dynamics embodied in the related terminologies and signs indicating the artistic rendering and shaping such as crescendo, pianissimo, and the interactive dynamic effects from the domain of rhythm and time, belonging mainly to the description above but exerting collaborated dynamic effects on music. Remember, music is an organized whole where the four elements can never be separately functioning.

(4) From timbre-waveform to the realm of tone quality or tone color, the crucial music element not only determined by one particular musical instrument pre se but also largely shaped through nuances in performing skills as well as the various thoughtful texturing and instrumentation via composing techniques.

Please keep in your mind the above four roots from which varieties of music concepts generate. For example, when you read the entries such as rhythm, tempo marks and notes in different lengths, discuss with yourself in your mind and decide which of the four categories these concepts belong to. This process would better organize your thinking for your learning.

【 】Temperament; Equal temperament; Just intonation:

Temperament is a general designation for various systems of tuning in which the intervals are “tempered”, i.e. they deviate from the acoustically correct intervals of the Pythagorean scale and of just intonation. Such adjustments are necessary since systems based on the pure intervals are limited, restricting choice of keys as well as harmonic progressions. During the 16^th and 17^th centuries various systems of tempered tuning were in use which provided for partial adjustments, so that a number of keys could be used. These are called unequal temperament, in contrast to equal temperament universally adopted during the 18 century. The piano uses the equal temperament.

【 】Pitch names: Pitch names are the designations used to indicate the various tones (pitches). The basic steps or tones within an octave, simply those white keys at risk of overgeneralization as we will see later, are called c, d, e, f, g, a, and b, starting from each c to b. To reiterate the idea, these tones, in the study of music theory, are called basic steps. With the accidentals (those signs of # －sharp , b－flat, ×－double-sharp, bb—double-flat  and 口－natural canceling the alternations; For a full description see below) added on, the original pitch names of the basic steps get the corresponding pitch names, e.g., c-sharp, because of chromatic alternations. As warned before, cautions should be taken not to take it for granted that the white keys are always basic or natural steps, for one might logically figure out that white keys could also stand for chromatic steps

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