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Pitch Structure: Scales


A musical scale is a collection of notesordered by ascending or descending pitch (also called a stepwise ordering).Listen to the following example from the opening of Monteverdi's Orfeo.


Example 15. Opening Toccata fromMonteverdi's Orfeo.


The opening flourish uses a five-note scalethat ascends quickly and then descends through those same pitches more slowly.Listen to the notes of the same scale played more evenly on a piano.


Music uses a variety of scales, which aredistinguished by the specific intervals (called steps) between notes. Two verycommon musical scales are called the major and minor scales, our next topics.


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The Major Scale


Pitch Structure: The Major Scale


The major scale is a collection of notes spanning an octave that follows thestepwise ascending interval pattern: Tone, Tone,semitone, Tone, Tone, Tone, semitone (T-T-s-T-T-T-s). Because the steps of thescale are tones and semitones, the intervals between adjacent notes of thescale are called whole steps and half steps respectively. Example 16illustrates a major scale graphically.


Example 16. The major scale.

16. 主要音阶

Thenotes that make up the major scale are called scaledegrees, and are numbered 1 through 7 ascending. The highest note, an octaveabove scale degree 1 is also scale degree 1 (again, because of octaveequivalence). Notes of the scale can continue above and below those shown here,repeating the pattern T-T-s-T-T-T-s in different octaves (i.e. there is a scaledegree 2 a whole tone above the highest note on the figure, a scale degree 3 awhole tone above that, a scale degree 7 a semitone below the lowest note on thefigure, and so on). The scale degrees are also referred to by other names.Scale degree 1 is also called the tonic. Scale degree 2 is also called thesupertonic (meaning "above the tonic"). Scale degree 5 is called thedominant. Scale degree 4 is called the subdominant (because it is as far belowthe tonic--four steps down--as the dominant is above). Scale degree 3 is calledthe mediant (because it "mediates" or lies in the middle between thetonic and the dominant). Degree 6 is the submediant (mediating between tonicand subdominant), and so on.

构成大调音阶的音符称为音阶,并被编号为17。最高的音符,音阶1度以上的八度音阶也是音阶1度(同样是八度)。音阶的音符可以继续在这里所示的上和下,在不同的八度中重复TTsTTTs模式(即在音高最高的音符之上有一个整音调的音阶2度,音阶3度以上的音调,比图中最低音符低7个半音,等等)。音阶度也被称为其他名称。音阶1度也称为主音。音阶2度也被称为超音速(意思是“超主音”)。 5级称为主音。 4级称为次主音(因为它远远低于主音 - 四级降低 - 因为在上面占优势)。 3级称为中音(因为它“介入”或位于主音和占主导地位的中间)。 6级是下中音(介于主调音和次属音之间),等等。

Once again using the piano keyboard,Example 17 illustrates how the step pattern of the major scale coincidesexactly with the notes of the white keys from C to C: C to D is a whole tone orwhole step, D to E is a whole step, E to F is a semitone or half step, F to Gis a whole step, G to A is a whole step, A to B is a whole step, and B to C isa half step. The collection of notes C-D-E-F-G-A-B-C is thus called a C-majorscale, because it starts on C and follows the interval pattern of the majorscale.

17再次使用钢琴键盘说明了主音阶的阶梯模式如何与从CC与白键的音符完全重合:CD是整个音调或整个步骤,DE是整个步骤,EF是半音或半音阶,FG是整个音阶,GA是整个音阶,AB是整个音阶,BC是半音阶。 C-D-E-F-G-A-B-C音符的集合因此被称为C大调音阶,因为它从C开始并遵循主音阶的音程模式。

Example 17.


Major scales can occur, however, on anystarting pitch. For example, if we start on the pitch D, we ascend by wholetone to E, by whole tone from E to F#, by semitone from F# to G, by whole tonefrom G to A, by whole tone from A to B, by whole tone from B to C#, and bysemitone from C# to D. The collection D-E-F#-G-A-B-C#-D forms the D-majorscale. Note that each scale degree of the D-major scale is exactly one wholetone higher than the corresponding scale degree of the C-major scale. Such ashifting (up or down) of notes (be they a notes of a scale or an entire passageof music) is called a transposition.

但是,任何起始点都可能出现大的音阶。例如,如果我们从音调D开始,我们用整个音调上升到E,从EF#的整个音调,从F#到G的半音,从GA的整个音调,从AB的整个音调,从BC#的整个音调,以及从C#到半音的半音。集合DEF-GABC-D形成D大调。请注意,d -大音阶的每一个音阶都比c大音阶的相应音阶度高一个整音。音符的这种移位(向上或向下)(称为音阶或整个音乐段落)被称为转位。

Many musical works that use the notes of amajor scale do not necessarily use those notes in stepwise order. Scales may beviewed as abstract ordered collections of pitches; actual pieces may or may notexhibit that abstract ordering. In this sense, scales are more like palettes ofpitches from which composers can create musical works. Example 18 illustrateshow Handel uses notes from an E-major scale (E-F#-G#-A-B-C#-D#-E) in the aria"Ev'ry valley shall be exalted."


Example 18. Handel, "Ev'ry valleyshall be exalted."

18 亨德尔:“埃夫里山谷将被崇高。”

Notice how the singer skips around thenotes of the scale going up, before coming down the scale by step.


NOTE: Are you curious why we write thenotes of the D-major scale, for example, with F# and C# rather than with Gb andDb? Obviously, the scale would sound the same regardless of the spelling.However, it is conventional to write the notes of a major scale such that theycycle through some form of all seven letters of the note names, A through G,consecutively. For example, if in D-major we wrote D-E-Gb-G... and so on, wewould have skipped from E to a note whose name is a modified form of G (i.e.there would no form of F represented). We would also end up with two notesnamed G, albeit one a modified form of the other. By using F# and C# in theD-major scale, every of the seven letters is represented.

注意:你是否好奇我们为什么用F#和C#而不是GbDb来编写D大调的音符?显然,不管拼写是什么,音阶都是一样的。然而,传统的做法是写出一个主要音阶的音符,使得它们可以连续循环音符名称AG的所有七个字母的某种形式。例如,如果在D大调中,我们写了D-E-Gb-G ...等等,我们将从E跳到一个名字是G的修饰形式的音符(也就是说没有表示F的形式)。我们最后还会得到两个叫做G的音符,尽管一个是另一个音符的修改形式。通过使用D大小的F#和C#,七个字母中的每一个都被表示出来。

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The Minor Scale


Pitch Structure: The Minor Scale


The minor scale (also called the naturalminor scale) is a collection of notes spanning an octave that follows thestepwise ascending interval pattern: Tone, semitone, Tone, Tone, semitone,Tone, Tone (T-s-T-T-s-T-T). The minor scale is illustrated graphically inExample 19.


Example 19. The (natural) minor scale.


The minor scale, just like the major scale,labels its notes using scale degrees. The other names are similar, too, (tonic,supertonic, etc.) with the exception of scale degree 7, which is given the namesubtonic. (The name leading tone is reserved for degree 7 only when it is asemitone below the tonic.) The big difference between major and minor scales issimply the pattern of intervals each exhibits relative to their tonics.


Example 20 illustrates how the naturalminor pattern of whole steps and half steps occurs among the white keys of apiano keyboard from A to A, thus forming the A-minor scale.


Example 20.




Of course, the minor scale can be built onany starting note. For example, if C is the tonic, then the c-minor scalecomprises the notes C-D-Eb-F-G-Ab-Bb-C. Example 20 also plays the c-minorscale. One can compare the sound of the c-minor scale to that of the C-majorscale.


In musical practice, variations of thenatural minor scale minor scale are often used. Such forms involve modificationsof scale degrees 6 and 7. The harmonic minor scale raises the seventh degree ofthe scale by a semitone (i.e. it turns scale degree 7 into a leading tone);A-harmonic-minor comprises the notes A-B-C-D-E-F-G#-A. The A-melodic minorscale raises scale degrees 6 and 7 by a semitone when ascending (thusA-B-C-D-E-F#-G#-A ascending) but reverts to natural minor (all white notes)descending. All three kinds of minor scale are still referred to as A-minor.

在音乐练习中,经常使用自然小调的变化。这种形式涉及音阶6度和7度的修改。和声小调通过半音提高了音阶的七度(即它把音阶7变成领音)。和声小调包括音符A-B-C-D-E-F-G-A A旋律小音阶以半音为单位提高音阶67(因此A-B-C-D-E-F-G-A上升),但是恢复为自然小调(所有白音)下降。所有这三种小音阶仍然被称为A-小调。

The different interval patterns of majorand minor scales--the relatively lower forms, in particular, of scale degreesthree and six in minor--create different sounds and characters for major andminor scales and the music that uses them. The different sounds are bestappreciated by comparing the same music played alternately using degrees fromthe major and minor scales. For example, listen to the familiar tuneTwinkle-twinkle little star in major . Compare this to the same tune,transformed into minor. Historically in Western culture, the sound of the minorscale and of music written using the minor scale has often come to beassociated with somber, sad or melancholy feelings. Of course, many factorsdetermine the particular ethos of a musical work and it would be anoversimplification (and incorrect) to say all minor music is sad or that allsad music is minor.

大音阶和小音阶的不同音程模式 - 特别是三到六次音阶的较低形式 - 为小要和小音阶以及使用它们的音乐创造不同的声音和角色。通过比较使用大小音阶交替播放的相同音乐,可以更好地理解不同的声音。例如,听熟悉的大调《一闪一闪亮晶晶》,并比较同样的曲调变成了小调的效果。历史上在西方文化中,小音阶的音乐和小音阶作的音乐往往伴随着忧郁,悲伤或难过的感觉。当然,许多因素决定了音乐作品的特殊气质,如果说所有的小音乐都是悲伤的,或者所有悲伤的音乐都是微不足道的,那么这过于简单化了(而且是不正确的)。



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Pitch Structure: Intervals (Part II)


Pitch Structure: Intervals (Part II)


Earlier, we discussed intervals in generalterms, as the distance between pitches. We also saw that intervals had nameslike fourth, fifth, sixth, etc. that corresponded to their relative size (i.e.larger intervals had larger numbers). Now that we have discussed scales, we areable to talk with greater precision about intervals and see how their namesarise.


The numerical name of an intervalcorresponds to the number of consecutive letter-note-names it spans from thelower to the upper note. For example, the interval from C up to E is third,because it spans three different letters: C-D-E. The interval from C to Eb isalso a third, because it also spans three different letters C-D-Eb. NOTE: itdoes not matter what note(s) we imagine filling the span (e.g. D versusDb)--all that matters is that the interval alphabetically spans three letters.D-F is a third, D-F# is a third, E-G, F-A are thirds and so on. (Remember, wewrap around back to the letter A after G.)

音程的数字名称对应于从低音到高音连续的字母音符名称的数量。例如,从CE的音程是三度,因为它跨越三个不同的字母:C-D-E。从CEb的音程也是三度,因为它也跨越三个不同的字母C-D-Eb。注意:我们想象填充跨度的音符(例如DDb)无关紧要 - 重要的是音程按字母顺序跨越三个字母。 D-F是第三,D-F#是第三,E-GF-A是第三等。(请记住,我们回到G.之后的字母A

 All steps of the major and minor scales areseconds because they span consecutive letters in the alphabet. The intervalfrom C to F is a fourth (C-D-E-F). So is the interval from G# to C#(G#-A-B-C#). This method of naming intervals arose because intervals werehistorically measured from their spans in major and minor scales, which, as wesaw earlier, have alphabetically named and ordered notes.


However, not all intervals with the samenumerical name are the same size. We already saw how intervals of the secondoccur in two different sizes: seconds like B-C and E-F are semitones whileseconds like A-B, C-D, D-E, etc. are whole tones. We distinguish the two kindsof seconds with the modifiers major (Latin for "large") and minor(Latin for "small"). That is, the smaller second between B and C iscalled a minor second; the larger second between C and D is a major second.

Other intervals with the same numericalname come in different sizes. Example 21 illustrates two kinds of third: aminor third between D and F, and a major third between D and F#.

但是,并非所有具有相同数字名称的音程都是相同的大小。我们已经看到了第二拍的音程是如何以两种不同的大小出现的:像B-CE-F这样的拍是半音,而像A-BC-DD-E这样的拍是整个音。我们用修饰符major(拉丁语为“large”)和minor(拉丁语为“small”)区分两种拍。也就是说,BC之间的较小拍被称为次拍; CD之间的较大拍是主拍。具有相同数字名称的其他音程具有不同的大小。例21说明了1/3里面的两种:DF之间的次1/3,以及DF#之间的主1/3

Example 21. Major versus minor third.




Observe that the minor third is smallerbecause it spans a whole tone plus a semitone (T+s). The major third, bycontrast, is larger because it spans two whole tones (T+T). Other intervalswith the same numerical name come in different sizes. These are given onExample 15, which compares thirteen common musical intervals, from the unison(the interval between notes of the same pitch) to the octave (the intervalspanning eight letters). The example lists the size of the interval insemitones and illustrates the intervals.

注意次1/3,因为它跨越了整个音调加半音(T + s)。相比之下,主1/3更大,因为它跨越了两个整个音调(T + T)。具有相同数字名称的其他音程具有不同的大小。这个在例15中给出,它比较来自同一音调(相同音高的音符之间的音程)与八度(跨越八个字母的音程)之间的十三个普通音程。该示例以半音列出音程的大小并说明音程。

Example 15. Intervals from the unison tothe octave


Perfect Unison0 半音C#-C#, G-G, etc.
minor second1 半音C-Db, B-C, E-F, etc.
Major second2 半音C-D, A-B, F-G, etc.
minor third3 半音C-Eb, D-F, F#-A, etc.
Major third4 半音C-E, A-C#, Eb-G, etc.
Perfect fourth5 半音C-F, Db-Gb, F#-B, etc.
Augmented fourth
diminished fifth
6 半音C-F#, F-B, Eb-A, etc.
C-Gb, B-F, D#-A, etc.
Perfect fifth7 半音C-G, Eb-Bb, D#-A#, etc.
Minor sixth8 半音C-Ab, F-Db, A-F, etc.
Major sixth9 半音C-A, F-D, A-F#, etc.
minor seventh10 半音C-Bb, D-C, G#-F#, etc.
Major seventh11 半音C-B, F-E, G-F#, etc.
(Perfect) Octave12 半音C-C, D-D, F-F, etc.

Note that intervals of the second, third,sixth and seventh are divided into major and minor varieties. Intervals of thefourth and fifth (and also octave and unison) are ordinarily called perfect,but are called augmented and diminished respectively when they appear in largeror smaller varieties (i.e. one does not call them major fourths or minorfifths, etc.). Note also that the interval of the diminished fifth (i.e. theinterval a semitone smaller than the perfect fifth) is the same size insemitones as the interval of the augmented fourth (the interval a semitonelarger than the perfect fourth). The intervals differ in the pitches they span:C-Gb, spanning five letter names, is a diminished fifth whereas C-F#, spanningfour letter names, is an augmented fourth.


What about intervals larger than theoctave? Again, because of octave equivalence, intervals of the ninth, tenth,and so on, are considered equivalent to seconds, thirds, and so on, expanded byan octave (i.e. a ninth is a second plus and octave, a tenth is a third plus anoctave, etc.). The major ninth sounds similar to the major second, the minorthird sounds similar to the minor tenth, and so on (click on the examplesabove).


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Consonance and Dissonance



Pitch Structure: Consonance and Dissonance


When two different notes sound together,those sounds may blend into one another almost indistinguishably--something wealready observed with notes distant by an octave. By contrast, notes soundingtogether at other intervals do not blend so well, or may even clash with oneanother. For example, notes distant by a major seventh clash when soundedtogether (click on sounds in table below).

当两个不同的音符合在一起时,这些声音混合在一起,可能几乎无法区分 - 我们已经用远离八度的音符观察到了。相比之下,其他时段的音符混合不好,甚至可能相互冲突。例如,当一起响起时,远离大七度的音符碰撞在一起(点击下表中的声音)。

Intervals whose notes blend or else soundpleasing when heard simultaneously are called consonances. Intervals whosenotes clash or sound unpleasant when heard together are called dissonances. Iemphazize, however, that the distinction between consonance and dissonance isnot based on objective criteria, but rather is a subjective,culturally-conditioned distinction--what is pleasing to one person may becacophonous to another and vice-versa. For hundreds of years in Western musicalculture (from as far back as 14th century), the following division of intervalswas observed:


到时,很悦耳的音程被称为和谐音。一起听到时音符冲突或不愉快的音程称为不和谐音。然而,我强调,和谐音与不和谐音之间的区别并不是基于客观的标准,而是一种主观的,文化上的区别– 有些对于一个人来说是喜悦的,可能对另一个人来讲是不开心的,反之亦然。在西方音乐文化(从十四世纪起)的数百年中,观察到了以下的音程:                                        

  Consonant Intervals  和谐音程    Dissonant Intervals 不和谐音程 
  Unison  一度   minor  second  小二度 
  Octave 八度   Major  second 大二度 
  Perfect  fifth 纯五度  Augmented  fourth 增四度 
  Major  third 大三度   Diminished  fifth 减五度 
  minor  third 小三度   Major  seventh  大七度 
  Major  sixth  大六度 Minor  seventh  小七度
  minor  sixth  小六度

                                         Perfect  fourth  纯四度 

These distinctions hold true for octaveexpansions of each interval (i.e. minor ninths are dissonant, Major tenths areconsonant, etc.). NOTE: The Perfect fourth (see table above) is sometimesconsidered consonant and sometimes dissonant, depending on the context in whichit occurs. A full explanation of the fourth and its usage is beyond the scopeof the present tutorial.

Larger collections of simultaneouslysounding notes (called chords) are deemed consonant or dissonant depending uponwhether or not they contain dissonant intervals. Listen, for example, to thethumping chords that open Stravinsky's "The Augurs of Spring (Dances ofthe Young Girls)" from the Rite of Spring.


 Example 22.


Listen to the entire chord played on thepiano:


Did you hear the "crunchiness" ofthe sound? That crunch or clash arises from serveral dissonant intervals formedamong the pitches of the chord. For example, the chord includes a major seventhbetween Cb and Bb:


a major seventh between Fb and Eb:


an Augmented fourth between G and Db:


an Augmented fourth between Fb and Bb:


and a Major second between Db and Eb:


In the next section, we will look at someconsonant chords--chords that contain no dissonant intervals. These are themajor and minor triads.


Dissonant intervals (and chords) wereconsidered to be unstable by composers of Western classical music before thetwentieth century; such sounds created musical tension that requiredresolution. Consonant intervals and chords, by contrast, were consideredstable; they were more restful and provided the resolution demanded bydissonant intervals and chords. In the twentieth century, composers likeStravinsky began to explore the beauty of dissonant intervals and chords (likethe one in Example 22), and used them for their own sake without their needingto resolve anywhere. The way composers used and treated dissonances in thetwentieth century marked one of the big changes in musical style that definedmodern classical music.


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Pitch Structure: Triads


A triad is a chord containing three notes:a lowest note (called the root), a note in the middle (called the third) whichlies at the interval of a third above the root, and a higest note (called thefifth) which lies at the interval of the fifth above the root. Example 23illustrates two particular kinds of triads: the Major triad (consisting of aMajor third and a perfect fifth above the root) and the minor triad (consistingof a minor third and a perfect fifth above the root).


Example 23. Major and minor triads.




Particular triads are named for theirroots. Thus a C-major triad consists of the notes C-E-G: C is the root, thethird is E and the fifth is G. A c-minor triad consists of the root C, thethird Eb and the fifth G. A D-major triad consists of the notes D-F#-A, ad-minor triad consists of the notes D-F-A and so on.


The way in which triads are defined aboveis abstract in the way scales are abstract. Just as composers uses notes of thescale as they wish (and are not confined to their stepwise order), so too arecomposers free to employ triads in arrangements other than those shown inFigure 23. The intervals between notes of a chord may be expanded by octaves(e.g. with tenths or twelfths instead of thirds and fifths), notes of the chordmay be duplicated in different octaves, notes may be left out, the root neednot be the lowest note in the chord, and so on.


Example 24. Minor triad, from Handel,"He trusted in God," conclusion.


For example, Handel's "He trusted inGod" ends with the chorus singing a minor triad (on the word"Him" N.B. it is not the only triad in the passage!). Example 24illustrates the pitches from the final chord


The sopranos double the root two octavesabove the basses.


The altos sing the next higher fifth.


The tenors sing the third in a higheroctave.


The bases sing the root of the triad


Listen again to the entire chord, played ona piano.


Often, instead of playing all the notes ofa triad as a chord, a composer might choose to string the notes out one at atime. Such an arrangement is called an arpeggio.


Example 25.Major triad, from Handel,"Why do the Nations so Furiously Rage Together."

25. 亨德尔的大三和弦:“为什么民族如此疯狂地一起暴动”。

Example 25 presents Handel's aria "Whydo the Nations so Furiously Rage Together," also from the Messiah. Thesinger of the excerpt begins by arpeggiating the notes of major triad, singingfirst the root, then the third, then the fifth, then the root an octave higher,then the third above that. (Did you also notice that the singer concludes the passageby singing down the notes of a major scale?)


As mentioned in the last page, major andminor triads are special in that they are the only consonant three note chordsin music--no matter how one arranges the notes that make up either a major orminor triad, the intervals between all pairs of notes will be consonant.Further, one cannot add any new notes to a triad without creating dissonantintervals in the enlarged collection.

正如最后一页所述,大小三和弦的特殊之处在于它们是音乐中唯一的和谐三和弦 - 无论如何排列组合大小三和弦的音符,在成对的音符之间的音程是不和谐的。此外,在不增加不和谐的音程的前提下,我们不能在扩大的集合中创建新的音符到三和弦中。

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Scales and Keys


Pitch Structure: Scales and Keys


The major and minor scales are more thansimply collections of notes. In Western classical music, the scale degreespossess various degrees of tension that seek their resolution in the tonicnote. The ability of the tonic to exhibit a "gravitational pull" onthe other notes of the scale--to be the gravitational center of a scale--is oneof the most profound aspects of Western classical music. This weighty idea canbe illustrated by even so simple an example as chopsticks.

大小音阶不仅仅是音符的集合。在西方古典音乐中,音阶具有不同程度的张力,在音调中寻求解决。主音在音阶的其他音符上表现出“引力拉”的能力 - 成为音阶的引力中心 - 是西方古典音乐最深刻的一个方面。甚至可以用筷子这样简单的例子来说明这个重要的想法。

Example 26 illustrates schematically thechopsticks progression using notes from a C-major scale.


Example 26. The chopsticks progression.


On the example scale degrees 5 through 7ascend to scale degree 1 in the upper part, while scale degrees 4 through 2descend to scale degree 1 in the lower part. To someone immersed in Westernclassical music (as well as much popular music), the penultimate sonority has agreat deal of tension, not because the interval between the notes is dissonant(it is a consonant major sixth between D and B), but rather because theindividual scale degrees have a strong tendencies to move: scale degree 7, theleading tone, has a need to resolve up to the tonic (and thus the name leadingtone); scale degree 2 has a similar need to resolve down to the tonic. Thefinal sonority , the doubled tonic, is by contrast stable and at rest--again,not because of the interval of the octave, but because the tonic note is themost stable degree of the scale; it is a goal attained.

This phenomenon, that the tonic of a scaleis the point of repose and the tone to which all other tones of the scalerelate and refer, is known as tonality. Music that exhibits this phenomenon iscalled tonal music. Tonality is one of the most difficult concepts in music,and all of its aspects cannot be detailed in this tutorial--it is a conceptthat one comes to understand over time, from experiencing many tonal pieces.While the pages that follow will try to shed more light on tonality and what itmeans, it is expected that these pages will be a mere starting point that willopen up a dialogue between you, your TF and the other students.

在例子中,57级上升到1级,而42级下降到1级。对于沉浸在西方古典音乐(以及流行音乐)中的人来说,倒数二度音乐会有很大的紧张感,不是因为音符之间的音程是不和谐的(这是DB之间的辅音大六度),而是因为个体音阶有强烈的移动趋势:导音音阶7度有解决主音的需要(因此命名为导音);音阶度2有类似的需要解决的主音。最后的声音,双重主音,相比之下是稳定的和静止的 - 再次,不是因为八度的音程,而是因为主音音符是最稳定的音阶;这是一个目标达成。

这种现象,即音阶的主音是静止的,而音阶的所有其他音调所关联和引用的音符被称为音调。表现这种现象的音乐被称为音调音乐。音调是音乐中最困难的概念之一,所有的方面都不能在本教程中详细说明 -随着时间的推移,体验许多音调片断,以加深理解。虽然接下来的页面会试图说明音调及其意义,但这些页面预计只是一个开始,将会和你有个对话,你的任务小组和其他学生之间的对话。

When a major or minor scale is understoodnot simply as a stepwise ordering of notes, but as a collection of notes thatrevolve around and seek resolution in a tonic note, then those scales defineparticular musical keys. A key (not to be confused with keys that are depressedon keyboard instruments, like pianos) is a collection of notes that all relatedto, and gravitate toward, a central, tonic note. In the example above, the noteC is the tonic note of the C-major scale, and the progression of Example 26 isa tonal progression in the key of C-major. A piece of music that uses notes ofthe G-major scale in a way that gravitates around and resolves to G is said tobe in the key of G-major. A piece of music that uses notes of the E-minor scaleand whose notes gravitate around and resolve to the tone E is said to be in thekey of E-minor, and so on.


Figure 13.        


A NOTE ABOUT NOTATION: Since musical worksin a particular key predominantly use the notes of the major or minor scaleassociated with that key, one avoids writing hundreds of accidentals byaffixing a key signature to the musical staff. The key signature allows one tosay at the beginning of the work, which accidentals will be used throughout.For example, we observed earlier that the D-major scale consists of the notesD-E-F#-G-A-B-C#-D. Figure 13 illustrates the key signature for D-major: twosharp signs are placed on the F-line and C-space of the staff. The signatureindicates to the reader of the music that all Fs and all Cs are sharp unlessotherwise noted.


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The Chromatic Scale


Pitch Structure: The Chromatic Scale


We earlier saw how the keys on pianokeyboard are arranged by semitone. When those keys are played up or down inorder, the resulting scale of ascending or descending semitones is known as thechromatic scale. Example 27 again illustrates an ascending chromatic scale on apiano keyboard.


Example 27. The chromatic scale.


Observe that we say "The"chromatic scale. Although one can begin or end a chromatic scale on any note,there is no tonic note in a chromatic scale--no predetermined boundary note.This is because all notes of the scale are equidistant--one cannot orientoneself or distinguish one note from another intervallically. Thus althoughthere are C-major scales, F-major scales, g-minor scales, etc., the chromaticscale is simply called the chromatic scale, and composers choose to usewhatever portions of it they choose. sometimes a composer will use notes of thechromatic scale to make a passage of music more expressive. Watch the keyboardand listen to the following excerpt from Mozart's Rondo in A-minor (KV 511),which uses an expressive ascending chromatic scale from A to E.

观察我们说的“半音音阶”。虽然可以在任何音符上开始或结束半音音阶,但在半音音阶中没有音调 - 没有预定的边界音符。这是因为所有的音符都是等距的音符不能自己定位,也不能把一个音符与另一个音符相互区分。因此,尽管存在C大调,F大调,g小调等,但是半音音阶仅被称为半音音阶,并且作曲者选择使用它的任何部分。有时候一个作曲家会使用半音音符来使音乐更具表现力。观看键盘,听听莫扎特的A-minorKV 511)中的Rondo的摘录,它使用从AE的表现性递增半音音阶。

The passage illustrates an important aspectof tonality: even though the passage uses notes outside of the white-noteA-minor scale, the key of A-minor is not lost--A is still the center of gravityin the passage. (Mozart in fact ends the excerpt with a descending a-minorscale that concludes on the leading tone G#. One could not experience this noteas a leading tone were A not still exerting its tonal supremacy.) Thus,tonality and the sense of key have the ability to transcend the notes of ascale. Yet because all the intervals between notes of the chromatic scale arethe same size, chromatic scales or chromatic notes used in abundance, can, likea hall of mirrors, create disorientation, suspending one's awareness of thetonal center.

这片乐段说明了音调的一个重要方面:即使这片乐段使用的是白音A小调音阶以外的音符,A小调的琴键都不会丢失 - A仍然是这片乐段中的重心。(莫扎特事实上以下降的小音阶结尾,结束于G#的主音音调,没有人能体验到这个音符,因为主音不是仍然在发挥其音调优势。)因此,调性和关键感有能力超越规模的音符。然而,因为半音音符之间的所有音程都是相同的大小,所以大量使用的半音阶或色调音符可能像镜子大厅一样造成迷失方向,阻碍对音调中心的认识。

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Harmony and Counterpoint


Pitch Structure: Harmony and Counterpoint


The term harmony has two meanings in music.A harmony can refer to an individual chord or triad that occurs in a work ofmusic ("harmony" in this sense refers to the togetherness of disparatenotes when they join together to make a triad or chord). Harmony also refers tothe "logical" way chords or harmonies progress in tonal music. Thefollowing example, from the chorale "Du Lebensfuerst , Herr JesuChrist" from J. S. Bach's Cantata Gott faehret auf mit Jauchzen, willillustrate these two ideas.

和谐这个词在音乐中有两个意思。和声可以指音乐作品中出现的个人和弦或三和弦(在这个意义上的“和谐”是指不同音符联合起来形成三和弦或和弦时的统一性)。和声也是指和声或和声在和声音乐中的“逻辑”方式。下面的例子,来自J. S. Bach的“Cantata Gott faehret auf mit Jauchzen”的合唱团“Du LebensfuerstHerr JesuChrist”将会说明这两个观点。



The passage is made up of a series ofchords (if you have not done so already, try listening to the passage played ona piano--the piano version may make the individual chords easier to hear). Thefirst chord of the passage is a G-major triad; the second chord of the passageis an e-minor triad; the third chord is a D-major triad; the fourth chord isanother G-major triad, and so on. One sometimes refers to these as "aG-major harmony," "an e-minor harmony," and so forth. However,the chorale is a tonal piece of music, written in the key of G-major (i.e. it usesthe tones of a G-major scale, G-A-B-C-D-E-F#-G, and G is the gravitationalcenter). One therefore often uses different names for the triads. Since G isscale degree 1, the triad built on G (i.e. whose root is G) is called theI-chord in the key of G-major (N.B. one uses the Roman numeral instead of theArabic when describing the triad). Simlarly, the triad built on E (scale degree6 in G-major) is called the vi-chord (we use small Roman numerals because thetriad is minor). The triad built on D (scale degree 5 in G-major) is called theV-chord. One therefore also refers to "the harmony on I," "theharmony on ii," etc. when talking about individual chords in the contextof a key.

这片乐段是由一系列的和弦构成的(如果你还没有这样做,试听一下钢琴演奏的乐段 - 钢琴版本可能会使得和弦更容易听到)。这片乐段的第一个和弦是G大调三和弦;这片乐段的二度和弦是一个电子小调三和弦;第三和弦是D大调三和弦;第四个和弦是另一个G大调黑三和弦,等等。人们有时把它们称为“G大调和音”,“e小调和音”等等。然而,合唱是用G-大调(即使用G-G-A-B-C-D-E-F-GG是引力中心)的音调写成的音调。因此,经常对三和弦使用不同的名字。由于G是音阶度为1,所以建立在G上的三和弦(即其根是G)在G-大调(N.B.在描述三和弦时使用罗马数字而不是阿拉伯数字)的调被称为I-和弦。同样地,建立在E(在G大调的第6级)的三和弦被称为vi和弦(我们使用小罗马数字,因为三和弦是轻微的)。以D为基础的三和弦(G-5级)被称为V弦。因此,在一个关键词的背景下谈论个别和弦时,也就是指“和谐I”,“和谐II”等等。

Harmony in the more abstract sense refersto the progression of individual chords (or harmonies) in a work. In thechorale example, the opening progression of triads, I-vi-V-I, is a harmonicprogression that departs from and returns to the triad build on the tonic G(also called the tonic triad).


The passage illustrates another feature oftonality. The asterisk above the staff marks the appearance in the highestvoice of the note C#, a note that does not belong to the key of G-major.Rather, the A-major triad to which that C# belongs is not a harmony in the keyof G-major, but a V-chord in the key of D-major that resolves to the I-chord inD-major (remember the D-major scale consists the notes D-E-F#-G-A-B-C#-D). Inother words, by introducing the leading tone of a different key, Bachtemporarily changes the key center, making D a new tonic. This change of tonicis called a modulation. Bach returns to G-major, concluding the passage in theoriginal key, confirming that key with a V-I progression in G-major (alsocalled a cadential progression or cadence because it "falls"--L.cadere--back to the tonic). Modulations in larger works of music can last muchlonger, or works may modulate to many different keys before returning to theirhome key. Your TF can discuss modulation in greater detail. The big point isthat tonality is hierarchical: just as notes progress to other notes, andchords progress to other chords, so too can keys progress to other keys.


Counterpoint refers to the joining togetherof individual melodic lines to create a work of music.


Listen to the opening of "And with hisstripes" from Handel's Messiah


The passage begins with the sopranossinging the following melody by themselves:


Shortly thereafter, the altos begin singinga melody whose opening echoes what the sopranos just sang:


Yet while the altos are singing, thesopranos begin to sing a different melody against the alto part:


In other words, the sopranos are singing atune that "counters" the tune in the alto part. (NOTE: "And withhis stripes" is an example of imitative counterpoint--the altos imitatewhat the sopranos sang. Not all counterpoint involves imitation, althoughimitation is a common contrapuntal device because it helps the listenerrecognize and hear the individual melodic lines.)

Counterpoint is often considered to be theopposite of harmony: whereas harmony views music "vertically," as asuccession of chords, counterpoint looks at music "horizontally," asthe simultaneous joining of melodies. This distinction is somewhat misleadingif it suggests to us that some works are "harmonic" whereas othersare "contrapuntal." Rather, elements of both harmony and counterpointplay a role in most classical music, although our attention may be directedmore to one or the other. Consider, for example the Bach chorale above.Although we looked at the work from the perspective of its triads and theirprogression, the work is also contrapuntal: it combines four individual melodiclines sung by different parts of the chorus. Listen to each of the individual melodiesthat make up the chorale, then listen the the chorale as a whole:



Soprano part 女高音部分 

Alto Part 中音部分 

Tenor Part 男高音部分 

Bass Part 基音部分 

All Parts (piano) 所有部分(钢琴)

All Parts (chorus)  所有部分(合唱)

Similarily the contrapuntal joining ofmelodic lines in "And with his stripes" is done in such a way as tocreate harmonies and harmonic progressions. Listen first to the combinedmelodies of the alto and soprano lines, then listen to the progression ofcomplete triads those individual lines imply.


Play the lines


Play the the implied harmonies


A nice metaphor to describe therelationship of harmony and counterpoint is consider the relation of horizontaland vertical design in an ornately patterened woven rug. The pattern arisesfrom many parallel strands of multi-colored wool. Yet without some guidingprinciple to control the alignment of those individual strands, the patternwould quickly fall into chaos.