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Pitches and Notes



Pitch Basics: Pitches and Notes


Pitch refers to the particular"highness" or "lowness" of a musical sound. A note is thesounding of a particular pitch for some time duration (i.e. a sound at aparticular pitch that lasts some particular amount of time).


The following excerpt from the aria"Ev'ry valley shall be exalted," from Handel's Messiah, illustratesthese two ideas. Listen and watch as the example plays.


Example 1. Handel, "Ev'ry valley shallbe exalted."


The singer of this passage sings seventeennotes, each of which is represented by a circle on the example. However,although there are seventeen notes, the excerpt makes use of only eight differentpitches. The pitch of each note is represented visually by the height of itscircle on the example: notes at higher pitches are placed higher up on thescreen, notes at lower pitches are placed lower on the screen. (Click on anycircle to hear its pitch and compare it to the others.)


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Intervals (Part I)



Pitch Basics: Intervals (Part I)


An interval is the distance, or differencein pitch height, between two notes. It is also the sound of two pitchesoccurring at that given distance.


Example 2 illustrates an interval betweentwo notes. A higher-pitched note is represented by a circle placed higher onthe screen, a lower-pitched note is represented by a circle placed lower on thescreen, and the interval between them is represented by the arrow between thecircles.


Example 2. An interval between two notes.


A given interval may ascend from the lowernote to the higher.


A given interval may descend from thehigher note to the lower.


 Or, a given interval may occur between twosimultaneously sounding notes.


Example 3, also from Handel's Messiah, istaken from the aria "Rejoice greatly, O daughters of Zion." Theexample identifies several intervals that occur between consecutive notes inthe passage: the three rising intervals sung on the repeated word"rejoice," and the falling interval on the final word"greatly." (Other intervals, of course, exist between other notes inthe passage--indeed they exist between all notes--but we shall be concernedhere only with the four bracketed intervals.)

3这个例子也来自亨德尔《弥赛亚》,“锡安的民哪,应当大大喜乐。”这个例子确定了几个出现在这个乐段的连续音符之间的音程:重复单词“高兴”上唱出的三个上升音程和最后一个单词“下降”的音程“很大”。(当然,在这段乐段中的其他音符之间,还存在着其他音程 - 事实上它们存在于所有音符之间 - 但我们在这里只涉及四个相等音程。)

Example 3. Handel, from "Rejoicegreatly, O daughters of Zion."

3. 亨德尔,“锡安的民哪,应当大大喜乐”。

The bracketed interval on the first"rejoice" is called a fourth. The bracketedinterval on the second "rejoice" is called a fifth .The bracketed interval on the third "rejoice" is called a sixth (PLAYTHE SIXTH). The bracketed interval on the final word "greatly" iscalled an octave, from the Latin octavus, meaning "eighth". Why these intervals have these names will become clear later. For themoment, the big points are (1) that the greater the difference in pitch heightbetween notes, the greater the interval formed between them and (2) that largerintervals are generally labeled by larger ordinal numbers (i.e. a fifth isgenerally larger than a fourth, a sixth is generally larger than a fifth,etc.). You may have surmised, correctly, that there are other intervals calledthirds, seconds, sevenths, ninths-- we will encounter and discuss these in alater section as well.

第一个“rejoice”的相等音程被称为四度。第二个“rejoice”的相等音程称为五度。第三个rejoice”的相等音程称为六度。最后一个单词“极大地”的相等音程被称为八度,由拉丁八度而来,意思是“第八”。为什么这些音程有这些名字,之后会清楚。目前,重点是(1)音符之间音调高度的差异越大,它们之间形成的音程就越大(2)较大的音程一般用较大的序号标记(即,五分之一一般比四分之一大,六分之一通常大于五分之一等)。你还可能正确地猜到,还有其他叫做三分之、二分之、七分之、九点之的音程 - 我们将在后面的章节中讨论这些问题。

Did you notice a relationship between thetext of the above passage and the intervals used in Handel's setting. Theincreasingly large intervals used for successive statements of word"rejoice" depict the increasing excitement or joy expressed by thetext--an excitement that culminates in the largest (i.e. greatest) interval ofthe passage on the word "greatly.

你有没有注意到上述乐段的内容与 Handel所用的时间音程之间的关系。用于连续陈述“高兴”一词的音程越来越大,它描绘了文本所表达的兴奋或喜悦的增加 - 这是一个令人兴奋的结果,在这个词的最大范围(即最大的)音程中达到高潮。


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Tones and Semitones



Pitch Basics: Tones and Semitones


Listen to the following example, whichpresents the dramatic opening to Franz Liszt's Concerto for Piano and Orchestrain Eb-major.


Example 4. Franz Liszt, opening from theConcerto for Piano and Orchestra in Eb-major.


The passage oscillates back and forthbetween two pitches, before slinking down to a third, slightly lower pitch. Thesmall intervals between adjacent notes in the passage are all examples ofsemitones. A semitone is the smallest interval used in traditional Westernclassical music--it defines the smallest possible distance between musicalpitches (although smaller intervals are used, for example, in Indian classicalmusic).

该乐段在两个音高之间来回摆动,然后下降到三度略低的音高。乐段中相邻音符之间的小音程都是半音的例子。半音是传统西方古典音乐中使用的最小音程 - 它定义了音高之间可能的最小距离(尽管在印度古典音乐中使用了更小的音程)。

As the prefix "semi" suggests, asemitone is half of something, namely the interval know as a tone, also calleda whole tone. Example 5 illustrates how two consecutive semitones fill the spanof a tone (i.e. how two semitones rise in pitch by an amount equivalent to awhole tone).


Example 5. Tone and Semitone.


Lower Semitone


Upper Semitone


Whole Tone


The interval between the highest and lowestnotes in the Liszt passage is a whole tone; one sings a whole tone (ascendingthen descending) to the words "happy birthday" when one performs thesong of the same name at a birthday party. Tones and semitones are ubiquitousintervals in music; we shall see later that they are also the building blocksof musical scales and of larger intervals.


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Note Names and the Keyboard


Pitch Basics: Note Names and the Keyboard


Until now we have simply referred toparticular notes and pitches in the examples as "the highest,""the lowest," or else according to particular words to which theywere sung. Presently, we shall see how musical notes and pitches are morecommonly referred to by letter names. Our introduction to note names will beaided visually through reference to a piano keyboard, a portion of which ispresented below as Example 6. Whereas a full piano keyboard has 88 keys, wehave here shown only 24. 


Example 6. A segment of a piano keyboard.


Pitches on the keyboard ascend by semitonefrom left to right. On the segment of the keyboard presented above, the seriesof ascending semitones follows the pattern (starting at the left): white key,black key, white, black, white, black, white, white, black, white, black,white, white, black, and so on.


The white keys (and the pitches they play)are named using the letters A through G. Ascending alphabetical order reflectsascending pitch; after G, the letters recycle, beginning again from A. Pitches(and and piano keys) an octave apart are given the same letter name. Forexample, the key and note labeled F in the middle of the example is an octavehigher than the key labeled F at the far left of the example. Adjacent whitekeys that have an intervening black key (i.e. A-B, C-D, D-E, F-G, G-A) aredistant by a whole tone. The white keys B-C and E-F by contrast have nointervening black key; the intervals between B-C and E-F are semitones.

白键(和它们所播放的音高)用字母AG来命名。按字母顺序排列反映了上升音高;G之后,字母从A重新开始循环。相距一个八度的音调(和钢琴键)被赋予相同的字母名称。例如,在示例中间标记为F的键和音符,比在示例最左侧标记为F的键高八度。具有中间黑键(即A-BC-DD-EF-GG-A)的相邻白键,远离一整个音调。相比之下,白键B-CE-F没有中间黑键; B-CE-F之间的音程是半音。

The symbol # (called the sharp sign ) addedto any note name raises the pitch of that note by a semitone. For example, thenote A# (read, "A-sharp") is a semitone higher than the note A. Theblack key just to the right of the white note A plays the note A# . Similarly,the note C#, which sounds a semitone higher than C, is played by the black keyjust to the right of C.


The symbol b (called the flat sign) addedto any note name lowers the pitch of that note by a semitone. For example, thenote Eb (read, "E-flat") is a semitone lower than the note E. Theblack key just to the left of E plays the note Eb. Similarly, the note Bb ,which sounds a semitone lower than B, is played by the black key just to theleft of B.


The alert reader will have noticed that wegave the same black piano key--and for that matter the same pitch--twodifferent names: the black key to the right of A and the left of B is called A#but also Bb. This is not a mistake. The same sound in music can have differentnames--a composer might use one name instead of the other to make the musiceasier for a performer to read, or else (as we will see shortly) to adhere tocertain conventions when writing music in a particular key. Other identicallysounding notes have different names: F# versus Gb, G# versus Ab. Differentlynamed notes that have the same sound are said to be enharmonically related.

有警觉的读者会注意到,我们给了相同的黑色琴键 - 就此而言,相同的音调 - 两个不同的名字:A右边和B左边的黑键叫做A#和Bb。这不是一个错误。音乐中的相同声音可以有不同的名称 - 作曲家可以使用一个名称而不是另一个来使音乐更易于演奏者阅读,或者(正如我们会很快发现)在特定的键写入音乐时会遵循某些约定。其他相同的音符有不同的名字:F#与GbG#与Ab。据说声音相同而命名不同的音符被称为是等音的。

NOTE: when one talks about all notes namedC, or all notes named F#, rather than any particular C or particular F#, onesometimes refers to the tone C or the tone F#. Observe that in this case, tonedoes not refer to the specific interval of whole tone, but to a class of notesor pitches. Tone is a word that unfortunately has accumulated many meaningsover its thousands of years in musical usage.


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The Octave



Pitch Basics: The Octave


The reader might well ask why it is thatnotes an octave apart are given the same name, even though their pitches aredifferent: one is an octave higher than the other. The octave is a specialinterval in music and pitches an octave apart have such a similar quality intheir sound that they receive the same name. (Notes an octave apart, though notidentical, are said to be equivalent.) Notes an octave apart are so similarsounding, they generally blend indistinguishably into one another. Listen againto the opening of the Liszt Piano concerto, given as Example 7.


Example 7. Franz Liszt, opening from theConcerto for Piano and Orchestra in Eb-major.


Although one hears a single melody playedby the string instruments in the orchestra, that melody is played at differentoctaves by different instruments.


The violins play the melody using thesepitches:


The violas and cellos play an octave lowerthan the violins:


The contrabasses play two octaves below theviolins:


When heard together, the equivalentmelodies merge into one:


Notes in different octaves (also callednotes in different registers) are often distinguished by their relation to thepitch called middle C--so called because it lies roughly in the middle of thepiano and is roughly the middle of the human vocal range (i.e. it lies about inthe middle between the highest notes singable by women and the lowest notessung by men). One can refer, for example to the pitch A above middle C, A belowmiddle C, the second A above middle C and so on.


Example 8 presents middle C and several Csabove and below.


Example 8. C in several octaves.


In the Liszt example, the violins play thenotes Eb, D and Db just above middle C, the violas and cellos play the notesEb, D and Db below middle C, and the contrabasses play the notes Eb, D and Dbin the second octave below middle C.


ANOTHER NOTE TO THE CURIOUS READER: Asmentioned in an earlier note to the reader, pitch is determined by vibrationalfrequency. Intervals consequently are determined by frequency ratios. Theoctave has a very special ratio: pitches an octave apart stand in a frequencyratio of 2:1. That is, the higher sound vibrates twice as fast as the lowersound.


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Pitch Notation



Pitch Basics: Pitch Notation


We have so far been using colored circlesplaced at high and low positions on the screen to represent high and lowpitches respectively. Musicians and composers use a similar principle when theywrite music down on paper. High and low pitches are represented by circularmarks placed at various locations on musical staves--systems of lines andspaces that run horizontally across pieces of music paper. High lines andspaces indicate relatively higher pitches; low lines and spaces representrelatively lower pitches. Various clefs (from the Latin clavis, meaning key, asin the key to a map) identify particular lines and spaces on the staff withparticular pitches.

到目前为止,我们一直使用屏幕上高低位置的彩色圆圈分别表示高低音调。音乐家和作曲家在写下音乐时使用类似的原则。高音和低音用圆形标记表示,放在音乐板上的各个位置 - 线条和空间系统在乐谱纸上水平展开。高的线条和空间表示相对较高的音高;低的线条和空间代表相对较低的音高。各种谱号(从拉丁文clavis,意思是关键,如在地图的关键)用特定的线条和空间去鉴别有特定音高的五线谱。

Figure 1. The G-clef.        

1. G-

Figure 1 illustrates a G-clef, a clef thatidentifies the second line of a five-lined staff with the pitch G above middleC (the line is marked red on the figure). Notice how the curl of the clefencircles the G-line. The space above the G-line represents the pitch A abovemiddle C, the line above the A-space (i.e. the middle line) represents thepitch B above middle C. Other letter names associated with lines of the G-clefare indicated on Figure 1.

1显示了一个G-clef,一个谱号,用于确定用中音C上方的音调G谱写(线条在图中标记为红色)的五线谱的第二行。注意谱号的卷曲如何环绕G线。 G线上方的空间表示中音C上方的间距AA空间上方的线(即中线)表示中音C上方的音高B.其他与G-谱的线相关联的其他字母名称在图1

Figure 2. Notes placed on a staff with aG-clef.


Figure 2 illustrates how circles (callednoteheads) are placed on the lines and spaces of the staff to notate particularpitches. A circle centered on the G-line represents the note G; a circlecentered on the F-space below the G-line represents the note F, and so on. Towrite notes lower or higher than those available on the lines and spaces of agiven staff, one can add small line segments (called ledger lines) below orabove the staff. For example, on Figure 2, a ledger line is added below thestaff to represent the pitch middle C.


Figure 3. The F-clef (also called Bassclef).     

3. F-谱(也称为低音谱号)

Music uses other clefs. Figure 3illustrates another common clef called the F-clef or Bass clef, because itlocates the pitch F below middle C on the fourth line (the line centeredbetween the clef's two dots). The F-line is marked in red and the pitches ofother lines are indicated on the figure.

音乐使用其他的谱号。图3显示了另一个称为F谱号或低音谱号的通用谱号,因为它在第四行(谱号两点之间的中心线)上定位中音C下方的音高F. F线标记为红色,其他线的间距标注在图上。

Figure 4. The Alto clef.    

4. Alto谱号

Less common are the C-clefs, one of whichis shown in Figure 4. Figure 4 illustrates the Alto clef--a clef that locatesmiddle C on the middle line of the staff. Other C-clefs identify middle C withother lines.

不太常见的是C-谱,其中之一如图4所示。图4显示了Alto谱号 - 位于五线谱中线的中音C谱号。其他的C-谱用其他线识别中音C.

The lines and spaces of the staff ordinarilyrepresent the pitches of white-note piano keys: A, B, C, D, E, F, G and theiroctave replicates (we will see later cases where this is not so). In order torepresent black-key notes--sharp and flat notes--accidentals can be placed infront of particular noteheads. Figure 5 illustrates how the note C# isrepresented by a notehead on the C-space with a sharp sign before it.Similarly, we can indicate a Db with a notehead on the D-line preceded by theflat sign.    


Figure 5. The notation of accidentals.


Music (especially piano music) is oftenwritten on the Grand staff: a pair of staves, the upper of which uses a G-clef,the lower of which uses an F-clef. The Grand staff permits the notation of awide range of pitches. Figure 6 shows a Grand staff with C's indicated overfour octaves. NOTE: middle C is both indicated by the ledger line below theG-clef and the ledger line above the bass clef.


Figure 6. The Grand staff.