. For example, the tone of C could be either B# or D_bb and these tones or notes, identical in sound but written differently according to the context in which they appear, are called enharmonic. Could you count how many pitch names, if the basic and chromatic steps are all included and the idea of enharmonic is under consideration, an octave possess? And then please think about this on the actual keyboard of piano or an imagined keyboard: there are twelve keys, white and black within an octave, but thirty-five pitch names, natural and chromatic. Which key, the black key of course, then has less than three names? And why?    

【 】Octave and grouping of pitches:

As we know it, a same pitch name is not used for only one single tone but applies to any tone an octave or octaves higher or lower than a given pitch, say, a pitch within the middle group on the keyboard. Therefore, the basic steps (pitches of c, d, e, f, g, a and b) as well as the chromatic steps alternated by accidentals, must have several groups of them on the keyboard because a standard piano has 88 keys, white and black. Each group of the basic steps starts from c and ends with b within a certain group. On the keyboard of a standard piano, therefore, there are nine such groups of pitches (note that there are two incomplete “groups” on the keyboard of piano－the lowest having three keys and highest only one. To name the pitch related to the affiliated group, take the pitch c for example counted from the lowest high up, names of contra C₁, great C, small c, one line c’, two line c’’, three line c’’’, four line c’’’’, and five line c’’’’’ are called. Another way is to write them as, take pitch a for instance, A₂, A₁, A, a, a¹, a², a³, and a⁴ . To name a group of pitches or an octave, we may say contra octave, great octave, unaccented octave, one-line octave, two-line octave, three-line octave and four-line octave.

【 】Accidentals: The signs of accidentals are used to indicate chromatic alternations or to cancel them. The five signs are # (sharp), which raises the tone indicated by a semi-tone, b (flat) which lowers by a semi-tone, ×(double-sharp) which raises by two semi-tones, bb(double-flat) which lowers by two semi-tones, and口(natural) which cancels a previous alternation. These accidentals apply to the note before each they appear, as well as all the notes of the same pitch on the same line or space within the same measure. Please remember this but also warn yourself that it is easier remembered than actually played correctly. Sometimes, one plays the first alternated note correctly but forgets to keep alternating the following ones on the same line or space within that measure because the sign is placed earlier and no such sign placed afterwards. Did you ever have such an experience? Yes? Good! Making errors is a necessary part of learning.

【 】Whole tone and half-tone or semi-tone: The interval relation between each adjoining pair of two white keys on the keyboard is not identical. The interval between e-f and b-c is called half tone or semi-tone—the smallest interval－while other adjoining pairs of white keys are of an interval of whole tone. A whole tone is，naturally, composed of two additive half tones. A half tone or semi-tone also occurs, of course, between a black key and the adjoining white key.    

【 】Notation; Staff; Lines and space; Ledge lines: Generally, any system of symbols designed for the recording of music in written form is called musical notation. The basic components of the traditional system, as used in our class, contain a staff of five lines and other signs. The lines and spaces of the staff, defined by a clef, indicate the pitches where notes, rests and other signs should be placed. Because the pitch range of a staff per se is not wide enough for music beyond the range, short lines drawn underneath or above the staff called ledge lines are thus useful to record pitches higher or lower than that of the fourth or the first line of the staff. Other symbols include key signature if the music is not in the key of C and a time signature,. Furthermore, bar lines, accidentals, ties, dots, etc., are needed for indicating the basic music rendering. There are, however, many other systems, older or modern, where music is written down for its particular composing and performing purposes. You are encouraged to search on the web by putting words like music notation and music notation modernization into www.google.com to find newer descriptions.

【 】Clefs: There are three types of clefs, signs written at the beginning of each staff that designate the pitches of the lines and spaces, representing tones g’ using G clef, c’ and f with C clef and F clef. The clefs used for piano are G and F. The G clef, also called treble clef, is placed on the second line of the staff and indicates that the note on that line is g’. The F clef, placed on the fourth line of the staff, is called bass clef indicating that the note on that line is f. With reference to these two notes indicated by the two clefs, notes on other lines and spaces could then be correspondingly read in regard of their names of pitch or steps. The C clef is generally used in two positions, on the third line (alto clef) or on the fourth line (tenor clef) and indicate respectively either former or latter as c’. As concerned by a piano learner, the G clef is employed in the upper staff and the F clef in the lower staff for piano music. However, it is not surprising to see that in certain pieces of piano, the G and F clefs are not used in the usual way as aforementioned so that the unnecessary ledger lines are then wisely avoided as demanded by the music’s needs.

【 】Notes and Rests.

Conceptualized earlier, one logical starting point in music study is the category of duration-time concerned with values and proportions of temporal lengths in the progression of music. Notes and rests are signs and names indicating various relative lengths of tones and

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