在英语环境中学乐理

A Self-Checklist for Basic Music Concepts

 

Prepared for those who want to be facilitated for their communication with people interested in music in this global-village environment

刘沛

By Liu pei

This checklist is developed to encourage the students to check periodically whether the music concepts they know are understood in English.

Simply go through the following. Ask yourself, from the standpoint of an evaluator, the questions and give your responses such as:

1.Yes, I fully understand the meaning of it and I can even get the sense out of it while playing certain pieces where the concept stands a salient feature arousing much meaning in my emotion, thinking and aesthetic imagination.

2.Yes, but not quite sure. Then I might review the concept and at least get some implications or hints based on reading the descriptions provided, and then think about what I possibly could even through my intuition.

Please remember that this task does not mean to impose an extra burden on you but to provide a self-governed and self-study based opportunity for you to review and better organize what you have exposed to, pertaining to your doing, thinking and feeling in the realm of music. Having yourself equipped with the knowledge in English of music-related ideas will facilitate your communication with music interested people in this global village where talks in any topic using English is becoming a routine practice.

【 】Concepts about sound, the basic substance used in the art of music:

(1) Vibration vs. Sound: Please note that the former refers to a phenomenon in the realm of objectivity and the latter is with what we experience in the hearing mechanism being subjective in its nature. There are four physical attributes or properties considered essential in vibration―frequency, intensity, time and wave form―that determine, respectively, what we hear as sensations of pitch, loudness, duration and timbre or tone quality―the four corresponding mental parameters. These terminologies are included in the field of psychoacoustics, not normally in the study of music. However, it is necessary for music students to be acquainted with these concepts because they might be useful when your communication occurs with people out of the circle of musicians, but those such as psychologists.

 (2) A tentative definition of sound:

【 】Sound is mental reflection of vibration within a certain range of its acoustic properties. The definition given is based, among other things, on the following facts: (a) Range of frequencies that humans could possibly perceive is from the lowest possible frequency of 12 Hz to the highest 20,000Hz roughly. The higher vibrations beyond this range of frequency could be heard by, maybe, puppies. (b) If the vibration is, in terms of its intensity, too weak, then humans would not able to sense it as a sound.

(3) Considerations of tones employed in music:

【 】Music tone vs. Noise; Pure tone vs. Composite tone; Fundamental tone and overtones, partials; Relationship with timbre:  

Musical tones, or simply tones, fall into two categories when evaluated by the criteria whether the tone has a definite pitch: musical tone has but noise does not. You may conduct a quick experiment with two different sound sources. You could easily sing back, within your voice range of course, a tone produced from the piano but it is difficult even impossible for you to imitate exactly the sound emitted by clapping your hands. It is so because the former (a musical tone) is pitched but the latter (a noise) not. However it does not mean that noise makes no contributions to the art of music. In fact, it does and is so significant that African drumming and ethno-music in China resort much to the percussion instruments and many of the percussions are noise-based.

Pure tone is rarely used in music but is most often used in pychoacoustic research where it is crucial that unnecessary variables be eliminated to avoid interference of the influential elements, other than the defined independent variable, with the effect of an experiment so that the finding of the research may be secured as a function of independent variable only. The tone produced by a tuning fork, the small fork-shaped metal device as a pitch standard for helping tuning the musical instruments, is supposed to be pure tone. It is safe to claim that all the musical tones rendered by pitched music making media belong to the category of composite tones. Composite tone, simply put as the name suggests, is composed of the fundamental tone and overtones, that is, it is a blend of them. To better understand this phenomenon, you might imagine that a string of the piano is vibrating where the fundamental tone is heard most salient as its pitch that is produced by a “whole string in motion” vibration. Simultaneously, however, parts of the string at the lengths in ratios of 1/2, 1/3, 1/4, 1/5 etc. in an ideal situation, are also vibrating, thus emitting the frequencies as partials, the lowest of which is what was described above as fundamental viz. the first partial; the other partials are called overtones or harmonics. The significant role overtones play is in the perception of timbre. Before we go further to approach this marvel, note that wide differences exist among the overtone series produced by different as well as the same music media as vibrators. Rigorously, no one could possibly imitate exactly one sound produced by others. If you ever had the opportunity to view the scene of the wave form presented on the monitor of a spectrum detector, you would be convinced totally－complex! These descriptions tell us a fact that overtones vary according to types of vibrators or even the same vibrator under different conditions. The variances of overtones embody in the fact (1) the actual numbers of the overtones appearing vary; for example, the tones produced by the flute that sound “hollow” contain much fewer overtones than those by the cello (2) the sequences of their 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. 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 silences (silences are meaningful means of expression). In today’s practice, the common use of notes and rests, form the longest to the shortest, are designated by differently shaped signs and named accordingly in American English and British English as follows:

For the early music from mid 13^th century to about 1600, longer notes were used in the form of Mensural notation. These older notes include breve , long, large with the corresponding old names being called brevis, longa and maxims. A breve is twice as long as a whole note as its English

name semibreve for the latter suggests. The reader is reminded here that

Table 1.Common Signs of Notes and Rests and Their Names

Notes(Rests)AEBE  whole note semibreve  half noteMinim  quarter  notecrotchet  eighth  notequaver  sixteenth notesemiquaver    thirty-second notedemisemiquaver  sixty-fourth

note

Hemidemisemi- quaver  

the word note normally refers to a written symbol but the tone indicated is often implicated, though the word tone mainly means a musical sound or a whole tone. 

【 】Head, Stem, and Hook (Tail):

They are components to form the written shapes of notes. The head is necessary for notes of any time values. A whole note uses a head only that is written as a small hollow-circle ellipse or a “white head” so called by musicians. The head for a half note is similar but facing the opposite direction with a stem added on the left or right rim of the head. A solid printed or “black” head is used for notes whose time values are shorter than the half note for which a stem applied to the quarter note and a certain type of hook added on the notes shorter than the quarter note where a one-tailed hook is attached to the tip of the stem, for the eighth note, and a two-tailed hook for the sixteenth note. More tails are added to notes of shorter notes of the time values as illustrated in the table listed earlier. Referenced with the numeral notation, the number of the tails used for notes in the “five-line” staff is exactly the same as those used for notes in the numeral notation system indicating in the proportion of their values. 

According to musical notation that is an independent field of study, a note with a stem should be written side up when placed below the third line on the staff and upside down when the note is above the third line. It is so in principle to maintain a balanced sense of space in writing or printing the staff.

【 】 Dot and double dot; Dotted note and dotted rest; Tie; Pause or hold or fermata:

All of them are supplementary signs for prolonging time values of notes or rests. A dot following a note or occasionally a rest prolongs half value of the note or rest indicated. The second dot in the double dot prolongs half value further of the first dot. When more than two notes of the same pitch is to sustain without interruption between them, a tie or more ties, using the arching line “⌒” similar to that of legato, could be applied to connect them so that the notes are performed sustaining the sum of time values added up by the notes covered under the sign of tie. As an art, music does not want to restrict itself within the proportioned time values for notes and rests; a fermata thus functions well to meet the purpose which simply means to hold on the notes to the performer’s taste.

【 】Irregular grouping of notes for time values; Duplet, Triplet, Quadruplet, Quintuplet, Sextuplet, Septuplet:

To emancipate music from rigidly proportioned grouping of notes, irregular groupings are employed which effectively break the ordinary organizations for time values so that varieties are obtained. Alternations take place where the duplet substitutes for three-notes grouping, the triplet for two-notes grouping, and quadruplet, quintuplet, sextuplet, septuplet for groupings of four-notes or so. A good example can be found in the third and fifth measures of our National Anthem. The triplets produce a stirring and agitating bugling that can never be created by evenly grouped notes of eighths or sixteenths. The aesthetical principle of variety is perfectly reflected herein.

【 】Absolute pitch and relative pitch (sense of): Sight-singing, fixed-do and movable-do:

Absolute pitch, or perfect pitch, is an ability to name any musical tones immediately on hearing them or singing them without reference to hints of hearing or seeing the notes played on an instrument. This ability is in most cases achieved through early learning of musical instruments or deliberate training, but not necessarily a constituent part of traits found in musicality for musicians. It is suggested that a sense of absolute pitch, though admired by many, may sometimes become a hindrance in thinking process of key transposing. Contrary to absolute pitch, relative pitch is an ability to differentiate among intervallic tonal relationships. Though unable to name the exact (absolute) pitches heard, a person possessing the sense of relative pitch recognizes and identifies the tonal relations in the Gestaltist thinking, namely, in a way of organized perception which is, as being postulated by cognitivists－those cognition-oriented psychologists, more congruent with actual process for music in human mind. Relative pitch is a crucial trait indispensable for music learning and doing,

【 】Rhythm; Rhythmic pattern; Accent; Syncopation:

It is romantically conceived that rhythm is the skeleton of music. It is true to an extent because music is an art belonging to temporal phenomenon. Rhythm is the motion in a way of organized temporal sparse-dense structure with expressive purposes. Rhythm, structured for certain styles of expression, is oftentimes presented as a pattern called rhythmic pattern, rooted in this or that cultural and/or human causes throughout history, repeating itself through a passage or a whole piece of music, like what we know as Waltz developed from about 1800 whose rhythm is characterized most saliently by its accompaniment consisting of a low bass note on the first accented beat and the chords on the second and third beats moderately weak in the middle register. Rhythm is closely associated with the idea of accent that emphasizes or stresses on one tone or chord normally falling on the first beat of a measure for the simple time, with a secondary accent or accents on other particular beats of a measure for the compound time. Irregular accents are frequently found on weak beats to meet musical expressive needs, and syncopation is a good example that realizes its special rhythmic effect by shifting the ought-to-be accent in a way of tying (using a tie) a weak beat with the following strong beat or placing a rest on the strong beat or simply imposing an accent sign on the weak beat.

【 】Meter, time; Bar and bar line; Measure; Common meter; Simple meter(s); Compound meter(s); Time signature; Multi-meter; Irregular meter; Duple meter(s); Triple meter(s); Quadruple meter(s):

Meter is the basic way for organizing beats and accents. The various ways of such grouping are indicated by the time signature presented right after the key signature at the beginning of a composition on the staff that is written like a fraction. Of the signature, the upper numeral indicates how many beats exist in each measure (measures or bars are divided by bar lines meaning only accent on the first beat following that bar line), and the lower numeral indicates what kind of note is in length for one beat. For example, the time signature 3/4 means that there are three beats in each measure and each beat is valued a quarter note. All the meters fall mainly into two categories depending on whether each measure possesses one single accent or compounded accents. The former is called simple meter and the latter compound meter. Thus, duple meters including 2/2, 2/4, 2/8 and triple meters 3/2, 3/4, 3/8 belong to simple meters. Quadruple meters 4/2, 4/4 and 4/8 are considered by some as simple meters, but 4/4 are more frequently called common meter. Opposed to simple meters, compound meters, as the term suggests, are grouped together by multiplying the simple meters introduced earlier by three, whereupon compound duple, which is three times of duple, includes 6/2, 6/4 and 6/8, compound triple 9/4 and 9/8, and compound quadruple 12/4, 12/8 and 12/16. The meters mentioned so far are all regular ones. Irregular meters refer to those that contain, in each measure, more than one type of simple meters. For example, meter of 7/4 is possibly an irregular compound of (2+2+3)/4. The principle applies to, according to this writer but not necessarily agreed by others, quintuple meter 5/4 that is actually the sum of 3/4+2/4 or 2/4+3/4 for each measure. Still another concept concerns with multi-meter that simply means that more than one meter are employed throughout a musical piece. In such a case, the time signatures are either placed where the time signature normally is or placed where the alternatives take place.

【 】Tempo and tempo term(s); Metronome:

Some Italian terms are universally used to mark the tempo: how fast or slow a piece of music should go. From the slowest to the fastest, the frequently used terms include:

　

Larghissimo: very broad

Largo: broad

Lento: slow

Adagio: slow and gentle

Andante: walking

Andantino: quickened walking

Moderato: moderate

Allegretto: rather fast

Allegro: fast

Presto: very fast

Prestissimo: extremely fast

Accelerando: quickening

Ritardando: slackening

Ritenuto: holding back

　

The above terms suggest relative speed for a composition. To indicate accurate speed, Mälzel’s Metronome, abbreviated as M.M. is listed to guide the performer how many beats per minute should be played. Metronome was invented by J. N. Mälzel in 1816 which is an apparatus employing a swinging rod moving back and forth with the number to indicate how many times of oscillating go in a minute, and the sound of clicks secures a reference with which the performer might sustain the speed steadily.

【 】Dynamics and dynamic terms or mark(s):

Nuances of dynamics are an essential way to render music expressively. Dynamic terms or marks are thus directing the changes of loudness of the music played and related emotional fluctuation. The most commonly used dynamic terms or marks are:

　

Pianissimo (pp): Very soft

Piano (p): soft

Mezzo piano (mp): half soft

Mezzo forte (mf): half loud

Forte (f): loud Fortissimo (ff): very loud

Crescendo (cresc. or ＜): increasing loudness

Diminuendo (dim. or ＞): decreasing loudness

Decrescendo (decr, or ＞): decreasing loudness

　

【 】Interval; Melodic interval and harmonic interval; Root; Simple interval and Compound interval; Enharmonic intervals; Inversion or Complement; Major and Minor, Perfect, Augmented; Diminished; Double-augmented; Double-diminished; Unison（prime）; Second; Third; Fourth; Fifth; Sixth; Seventh; Octave; Ninth; Tenth; Eleventh; Twelfth; Tri-tone; Diatonic interval; Chromatic interval; Consonant and dissonant: 

An interval is the distance in pitch between two notes. If the notes are sounded successively, it is a melodic interval; if it is sounded simultaneously, it is a harmonic interval. The smallest or narrowest interval of the traditional western music system is the half tone or semi-tone, of which there are twelve within an octave. The distance of two half tones is called a whole tone or simply tone of which there are six within an octave. The major scale contains five whole tones (w) and two half tones (h) in the sequence of, for example, c-d (w), d-e (w), e-f (h), f-g (w), g-a (w), a-b (w) and b-c ’(h).

The names for intervals, first of all, refer simply to the number of scale steps from lower to the higher notes; the intervals contain, for example, unison or prime (c-c), second (c-d), third (c-e), fourth (c-f), fifth (c-g), sixth (c-a), seventh (c-b), octave (c-c’), ninth (c-d’), tenth (c-e’), eleventh (c-f’), and twelfth (c-g’). Please note that the intervals within an octave, not exceeding an octave in range, are called simple intervals. In contradiction to simple intervals, those larger than an octave are called compound intervals. For example, a ninth is a compound interval for it is compounded of an octave and a second: a combination of two simple intervals. This interval is named either as ninth or compound second.

When one of the two notes of an interval is placed an octave upside down or contrariwise, they are called the implement or the inversion to each other. That is, when two intervals sum up to an interval (d-a, a-d’), each of them is said to be the complement or inversion. So a third is the complement or inversion of the sixth, the fifth is the complement or inversion of fourth, and the seventh is that of the second. An interesting and simple math lies in such a counting that the inversion for the two tones is a sum of nine. Thus, to ask what the inversion of a second should be, just have it subtracted from nine (9-2=7), and the answer is the seventh.

When the same names are applied to intervals whose distances differ from each other, more detailed descriptions are added to define them. For instance, a second could be either d-e (w) or e-f (h) where the former is half-tone larger than the latter. Other comparisons might be that: the thirds of c-e, f―a, g-b are half-tone larger than those of d-f, e-g, a-c’, b-d’; the fourth of f-b is half-tone larger than those of c-f, d-g, e-a, g-c’ and a-d’; the fifth of b-f’ is half-tone smaller than those of c-g, d-a, e-b, f-c’ g-d and a-e’; the sixths of c-a, d-b, f-d’ and g-e’ are half tone larger than those of e-c’, a-f’ and b-g’; for the same reason, d-c’ and f-e’ are half tone larger than those having seven steps found on the, for example, white keys though all of them are named seventh.

The above descriptions are not embracive to include all the possible intervals presented alternatively in many ways. To sum up the laws for differentiating the intervals having the same ordinal numeral names but containing different number of half tone(s) and /or whole tone(s), the intervals in common use could probably be further classified into four or six types. They are, in the sequences from the fewer to more whole-tone-and/or-half-tone for the same ordinal-numeral-names, diminished→minor→major (or → perfect in the case of unison, fourth, fifth and octave) →augmented. Those intervals containing “one” half tone fewer than a diminished and “one” more half tone than an augmented are classified respectively double diminished and double augmented. In fact, the linguistic meanings of the terminologies used here explain these seemingly complicated distances between notes perfectly if they are checked up in an ordinary English dictionary.

Intervals of major, minor, perfect and tri-tone (diminished fifth and augmented fourth) belong to diatonic intervals, whereas chromatic intervals include those of diminished and augmented and their doubled. Being consonant or dissonant is a significant feature of intervals in musical expression. Intervals of perfect, major or minor third and sixth are consonant, leaving other intervals being dissonant. Your perception easily perceives the difference between the two. Enharmonic intervals, like enharmonic tones, refer to two intervals that are identical in pitch but written in different forms, having different names and appearing under different contexts. To understand the concept of enharmonic is to understand the idea of context. An augmented fifth appearing in the minor scale, for instance c- # g in A minor, sounds dissonant whereas its enharmonic the minor sixth, c- b a in C minor for example, sounds beautifully consonant. The importance of “context” is sufficiently reflected.

【 】Key and key signature; Mode; Scale; Major and minor; Natural, melodic and harmonic:

Please note that the explanation for the concept of key here differs from what might be found in other music dictionaries or other literatures written in English. The writer, based on an experience of teaching, did so with the purpose in mind to avoid possible confusions between key and the related ideas of mode and tonality.

A key simply signifies the pitch name, natural or chromatically alternated, where the singing name “do” stands in a musical piece using the movable-do system of music reading. There are fifteen keys in which three pairs of enharmonic keys exist. Therefore, enharmonically, there are twelve keys each of which starts from a white or black key within an octave on the piano. Different keys employ different key signatures. For key of C, there is no particular signature placed on the staff. Other keys use either sharp(s) or flat(s) to indicate which tone(s) of basic steps should be performed half tone higher or lower so that a correct series of “do, re, mi, fa, sol, la, si,” or, as stated earlier, a grouping relationship of “w, w, h, w, w, w, and h” is structured in the performance. For example, the key of G must have the tone of F half tone sharpened so that the pitch relationship of  “w, w, h, w, w, w, and h” is played sequentially correct as: g, a, b, c’, d’, e’, # f ’ and g’ and, of course, the same as in other octaves.

Table 2. illustrates the keys and their signatures as well as the enharmonic relations between the three pair of keys, and table 3 presents the sequence for adding the sharps and flats for the signatures.

Table2. Key Signatures and the Signified Keys

Sharp(s)

Key

Flat(s)

Key

0

C

 

 

1

G

 

 

2

D

 

 

3

A

 

 

4

E

 

 

5

B        =

7

C-flat

6

F-sharp   =

6

G-flat

7

C-sharp   =

5

D-flat

 

 

4

A-flat

 

 

3

E-flat

 

 

2

B-flat

 

 

1

F

 

 

0

C

 

Table 3. A Matrix for the Sequence of Sharps and Flats Added

Sharps or

Flats (Key indicated)  Added on:

The Notes Sharpened and Flattened Sequentially

1-sharp (G)

2-sharps (D)

3-sharps (A)

4-sharps (E)

5-sharps (B)

6-sharps (#F)

7-sharps (#C)

7-flats  (^bC)

6-flats  (^bG)

5-flats  (^bD)

4-flats  (^bA)

3-flats  ^(bE)

2-flats  (^bB)

1-flat   (F) 

F

F C

F C G

F C G D

F C G D A

F C G D A E

F C G D A E B

B E A D G C F

B E A D G C

B E A D G

B E A D

B E A

B E

B

Could you detect an invariant rule embodied in the sequence of the sharps and flats added and a certain intervallic relation existing between each adjoining pair of the keys in the above order? It might be interesting to skim over the sequence and you will surely find them out. 

【 】Mode; Scale; Major and minor; Natural, melodic and harmonic:

In a general sense, a mode refers to a type of structured tonal system in which a note functions as the center called “tonic” and other notes in the system function in a particular relation to the tonic. For the music during mediaeval times, however, the word is narrowly used with reference to a so-called church mode, such as Dorian mode, Phrygian mode etc,. To avoid possible confusions considering the fact that it has been out fashion, the description of “church mode ” is omitted here.

The term scale, derived from Latin “scala” meaning ladder, visualizes its salient manner that notes are arranged in ascending or descending order with the tonic as either the starting or ending note.

Modes cannot exist without specific organization, and the modes in most common use are major and minor in traditional western music. To illustrate the organizational structure for a mode, the scale in a specific way may be presented, for example, major scale is structured c, d , e, f, g, a, b, c’; minor scale a, b, c’, d’, e’, f’, g’, a’.

There are three forms for major and minor mode and/or scale. They are natural, harmonic and melodic. Here are comparisons between these two modes, both of which take C as the tonic, in the three different forms (see table 4).

Table 4. Major and Minor and the Scale Structure

Modes (forms)        The structural organization of the scale

Major

Natural    c      d      e   f      g      a      b   c’

  Harmonic  c      d      e   f      g  _b a         b   c’

Melod ic   c      d      e   f      g      a      b   c’

c      d      e   f      g  _b a     _b b      c’

Minor

  Natura l     c      d  _b e      f      g  _b a     b b       c’

  Harmonic.  c      d  _b e      f      g  _b a            b   c’

Melodic    c      d  _b e      f      g      a      b   c’

      .    c      d  _b e      f      g  _b a    b b       c’

Note: (1): ascending; : descending, read in reverse order.

     (2) The different width and length between notes denote w and h.

By the comparisons above, one can easily conclude that the ultimate difference between the modes/scales of major and minor lies in the intervallic relation between the tonic and third note if the three variant forms of the same mode/scale are under consideration. The interval between the tonic and the third note in the major mode/scale is a major third, and a minor third for the minor mode/scale as their names properly implies.

【 】Pentatonic, modes and scales of:

Being Chinese, one must know that our music, particularly music created by Han majority, has been pentatonic based in regard of modes and scales. Linguistically, the prefix penta- means “five”. The five notes in Chinese music are Gong, Shang, Jiao, Zhi and Yu. Each could be used, in the western sense of music theory borrowed, as the tonic forming a peculiar mode or scale and as the name for that mode or scale. Thus, a mode with Gong as its tonic in C is presented in the scale of c, d, e, g, a and c’. To say that Chinese music is pentatonic based does not mean that Chinese music employs only these five scale degrees and the style must be meager. The fact is that these five notes are regarded basic and more notes are used than those in traditional western art music.

【 】Degrees in scales and/or modes: Tonic(I), Supertonic(II); Mediant (III), Subdominant(IV), Dominant(V), Submediant(VI), Leading tone(VII):

The notes in a mode and/or scale are meaningful according to their relations to each other. Particular names and roman numerals are signed to these notes or degrees. As the tonal center for a mode, the first or starting note of a scale/mode is called tonic with the roman numeral I being written to indicate it within that certain mode/scale. For instance, the tonic of the major in the key of C is c, leaving other notes or degrees being called and signed with the roman numerals, in the ascending order respectively, supertonic II, mediant III, subdominant IV, dominant V, submediant VI, and leading tone VII. The tonic of the minor in the key of C is a, and the other notes or degrees being called and signed with the roman numerals, in the ascending order respectively, supertonic II,mediant III, subdominant IV, dominant V, submediant VI, and leading tone VII.

【 】Relative keys; Parallel keys:

To know something about key relations is important because the key related elements play an imperative role in the musical thinking. A pair of modes using the same key signature, of which one is a major and the other is minor, is considered relative keys mutually. For example, C major is the relative major of A minor, and vice versa. A more straightforward label for relative keys is “relative major/minor keys”.  Parallel keys, of which one is a major and the other is minor, refer to such two modes that use different key signatures but the tonic of them is the same. For example, C major and C minor are of parallel keys. In fact that the name per se provides a good hint for you to be certainly able to notice via comparisons that the ultimate difference of the two lies only in the intervals between the tonic and the third if enharmonic elements are considered. Parallel keys are also called keys “in common tonic”.

【 】Tonality; Atonality, bitonality and polytonality:

There are several meanings for the term tonality, specific and ambiguous. One of the vague connotations applies to the opposite side to modality where tonality refers to the whole system of all major and minor keys, and modality denotes the system of earlier church modes. It is the essential feature for tonality music to be loyalty to the tonic or the tonal center based on which a mode is then organized. Contrary to tonality, atonality denies this tonic centered practice using anti-traditional ways of composing to avoid forming any sense of tonal center, whereas bitonality and polytonality go all the more “modernized” as distinctive to traditional tonality music by adding on one or more tonalities simultaneously in a composition.

A narrow but practical usage of the idea “tonality” for music students is to combine the pitch name of the tonic in a mode with the specific type of that mode in expressing one’s understanding of “tonality” regarding a particular composition or a section of music. For instance, to answer a question such as “What is the key of this piece of music?” instead of replying the question as “It is in the key of C and its mode belongs to the minor,” you might simply say: “It’s A minor” to refer the “tonality” of that piece of music. It is more workable doing so to clarify among the interrelationships involved in key, mode and tonality.

【 】Monophonic music; Homophonic and polyphonic music; Harmony vs. Counterpoint:

Music may consist of either one part or multi-parts vertically. Music consisting of only one melodic line is called monophonic like those genres of folk songs sung and heard in the fields or conventional occasions. Music consisting of more than one part sounding simultaneously is called homophonic or polyphonic. Homophonic music holds a single melody accompanied by chords or other subordinate materials while polyphonic music possesses several melodic lines that interact one another based on the logic of counterpoint. Most music we encounter today belongs to homophonic category for which a study of harmony is needed to understand the laws of chords’ progression and expressive meaning embodied. A study of counterpoint is needed to understand the interactive relationships amid various parts in polyphonic music.

【 】Chord; Triad, major, minor, diminished and augmented; Seventh chord, dominant seventh chord; Fundamental position, first inversion, second inversion, and third inversion, sixth chord, sixth-four chord, consonant and dissonant:

A chord is the combination of three or more tones of which a triad consists of three tones and a seventh consists of four tones. Both of them are built up by superimposing intervals of a third, two for the triad and three for the seventh. The tones used in building a triad are called, from the lowest to the highest, the root, the third and the fifth. For a chord of seventh, a tone that is an interval of seventh to the root is added, and the name for the chord is then gained as such.

There are four main species of triad: major, minor, diminished and augmented. When considered as superposition of two intervals, a major triad is made of a major third plus a minor third, a minor triad is of a minor third plus a major third; a diminished triad consists of two minor thirds, and an augmented triad consists of two major thirds. As with intervals of the same nature, the former two triads sound consonant and the latter two are dissonant because either of them contains a dissonant interval: a diminished or an augmented fifth respectively. 

A chord may stand in the root position or be inverted depending on which note of the chord is placed lowest. When root note is placed lowest, the chord is in its root position. When the third or the fifth note is lowest, the triad is in its first or second inversion called respectively sixth chord or six-four chord.

【 】Chords in the context of mode:

As with steps or notes in the particular modes, the chords function and are named in the modes of major and minor. The names and Roman numerals signed to them are as follows: tonic (I), supertonic(II); mediant (III), subdominant(IV), dominant(V), submediant(VI), leading (VII). The most important chords in functional harmony include tonic, the center of the mode, with dominant and subdominant supporting the tonic. Other chords belong to these three forming three functional groups of chords, see figure 1. for detailed description.

Tonic(I with III and VI)

Figure 1.

Functional groups

                     ←

Dominant            Subdominant

 (V with III and VII)          (IV with II and VI)

The arrowheads indicate the direction of chordal progression typically found in the traditional western art music.

Armed with the knowledge of chords and the logical progression using these chords, the reader might be able to understand western traditional art music and music written by Chinese composers borrowing this logic reflected in functional harmony in a deeper and thoughtful level.

  

Note:

A small part of the content above refers to some entries of Harvard Handbook of Music

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