Engineers learn music theory (II) scale and tendency

Preface

Before reading this article , Please read first 《 Music theory for science and engineering students 》.

This article mainly talks about scale . Details that can be found elsewhere , We won't say much here . This article focuses on sorting out the logic behind the scale , Try to string up the technical points .
We engineers hate things without logic , Any natural 、 Beautiful things , There must be logic behind it , Master the logic before you learn , To learn thoroughly .

Scale

A scale is a pitch , That is, the sound of a certain frequency . The frequency is continuous , Continuous things are inconvenient to use , We need to discretize . After frequency discretization , It's called a scale .

How to divide the scales ？ You can't divide it like this , I divide it that way , That would be a mess .

Such as IT The industry is the same , There are various standards in every field , Standards must be followed in any industry , If there are no standards, we should formulate standards .

Internationally unified scale division method , It's called the international scale . Everyone creates according to the standard scale , communication , This can greatly promote the development of the music industry .

Standard scale division method

The following is a brief description of the division process of the international standard scale ：

• from 440Hz Start , To double it 880Hz until , Intermediate according to Geometric series Divided into 12 Share , The calculation shows that , The common ratio is 2^(1/12)=1.06. Now? , Add two sounds at the beginning and end , Altogether 13 A note .

• 13 Too many sounds , The following will 13 A note , become 8 A note .8 One note should be divided into 7 branch , If the original 12 Share 7 Share , That's definitely not even , You can take it out first 10 Share equally 5 Share , be left over 2 Parts directly constitute 2 Share .

• Give it away 8 Name each sound , Use letters to indicate , namely ：A B C D E F G A, This is the sound name . A phoneme is just a code for a scale , Easy to record 、 Communication and communication .

• The positions of two tones are subtracted and added 1 It's interval , The unit of interval is degree , for example ,C - A = 3 - 1 + 1= 3 degree , It is better to write in capital letters , Because of the prevention and digital marking of this 8 The sound is confused , The numbers mark below or say . Because the interval is calculated by adding 1 了 , So interval is not what we think , The distance between two notes , But between two notes , Including two tones , Number of tones .

• this 8 A note , It can also be numbered as 6 7 1 2 3 4 5 6.

There are some problems in scale division , We need to think about .

Scale FAQ

One 、 Why is every section on the piano from C At the beginning , Why not from A Start ？

According to our above division , The sound name should be from A Start talking about . So why do people usually start from C Let's start , And on the piano, every zone starts from C To start? ？

This issue has been discussed online , You can take a look at this first ： Why is the sound name from C Start , instead of A？

The main idea is , Because major is very common ,C It is the beginning and end of the major , therefore C Very often , Put it in the first place . So explain , We just use the unknown to explain the unknown . therefore , To put it another way, just say , Namely C Too often , So it was put in the first place . When we talk about scales , Basically from C Start talking about .do、re、mi、fa、sol、la、si, among do All means C.

Two 、 Number mark 6 7 1 2 3 4 5 6 in , Why? A yes 6,C yes 1？A Why not 1？

From question 1, we know , Generally we say scale , from C Start talking about . But from C Start ,C D E F G A B, from G Jump to the A Isn't that hard ？ It really hurts .

To solve this problem , Make the scale look more comfortable , Easier to use and remember , We put the most commonly used one , That is to say C, Make it 1. In this way ,do、re、mi、fa、sol、la、si = 1、2、3、4、5、6、7, No more from C Here we go , I won't feel so bad anymore . I recommend this scale notation . You just need to know ,1 Corresponding C, Everything else is in natural order , Simple and easy to use .

3、 ... and 、 How can I remember the letters, numbers and pronunciation of the scale ？
We can use the above-mentioned method of marking letters and numbers to remember .
namely ：

do、re、mi、fa、sol、la、si = 1、2、3、4、5、6、7.
1 = C

Of course, it is difficult to map numbers to letters , You can even remember ：

1C 2D 3E 4F 5G 6A 7B

Some can be associated with memory ： Such as 2D Of the movie 2D,3 Billions of 3E,F4,5G Mobile phone 5G.

Propensity to

What we studied earlier is an individual scale , Now we are going to study the relationship between scale individuals .

A single sound is emotionless , There is no good or bad . Don't believe it , You can try it yourself , Sound to sound should be played completely separately .

however , The sound is connected with the sound , Or it can be engraved and superimposed together at the same time , Will express feelings , Sometimes sad , Sometimes happy , Sometimes magnificent , Sometimes crazy . You can play several notes in succession , Feel the , At this time, the emotion will burst out from the music unconsciously , Why is that ？ The answer is tendentiousness .

Propensity to , Is harmony . It is an attribute that describes the relationship between scales , It measures the tendency of one sound to another 、 Degree of harmony . Tendentiousness is the most important link between sounds , Only by understanding the tendency , You can write “ Not bad ” The music of .

Next, we will explain the mathematical logic contained in tendentiousness , After understanding the logic , You can listen 、 verification . Most of the students should have no piano on hand like me , We can download a piano software to use , Don't ask for good or bad , For beginners , Just use it. .

Okay , Now let's start with the mathematical logic and quantitative methods of tendentiousness . Most of the following is subject to 《 Music theory for science and engineering students 》 Enlightening .

Tendentious mathematical logic

We know the sine wave superposition of two frequencies , It may be periodic , It may also be aperiodic .

What about this part , stay 《 Signals and systems 》 There are explanations in this course . You can refer to ： Signals and systems （ For postgraduate entrance examination ） One （2） Do you really know the period of the signal ？. Just get a rough idea of it , There is no need to do problem calculation .

Throw away the mathematical symbols , Understand in an intuitive way . The following is the scene of the bridge swaying in the wind .

When the wind blows across the bridge, it will cause the bridge to shake , And may cause violent resonance phenomenon .

among , The core word is resonance . When waves of two or more frequencies , Superimposed together according to a certain phase , If the superimposed wave is also periodic , And the period of the wave after stacking is closer to that of the wave before stacking , The stronger the resonance , The energy of the original wave produces superposition . By contraries , The greater the difference between the period of the post stack wave and that of the pre stack wave , The smaller the resonance , Most of the energy of the two waves will cancel each other out . When the period after superposition is infinite , It means that there will be no resonance .

Yes, of course , The scale is superimposed on the scale , It must be periodic , Because the frequency values of the scale are rational numbers , So the period of the scale is also Rational number , Superimposed waves , Is their minimum common integer period . The difference lies in , When different scales are played together , The ability to resonate is different .

The picture below is from 《 Music theory for science and engineering students 》. The least common multiple in the figure is the quantitative index of resonance degree , The smaller the least common multiple , It means that the stronger the resonance ; On the contrary, it means that the resonance is weaker .

Sum up , The degree of resonance is the physical expression of tendentiousness . When two tones resonate more strongly , The more harmonious our brain feels , The more stable （ Form a stable period ）. The worse the resonance , The weaker the brain feels , The less stable . Our mood swings when we listen to music 、 Emotional changes are also inspired by this .

Tendency form

The above describes the mathematical logic of the tendency between scales , Next, let's talk about the specific forms of tendentiousness .

Because the phase or time of scale superposition is different , The inclined forms of scales can be divided into two types ：

The first form is to start playing the next note before the last one ends , One sound after another , Form a sequence of scales , This tendency to form is called melody . The melody is characterized by ： The sound is simple and clear , But it's too simple , Although it can cause resonance , But resonance can also be enhanced .

The second form is two or more sounds , Play at the same time , This tendency is called chord . Melody can be seen as a scale in the horizontal direction , That is, the superposition in the direction of time , Chords can be seen as the superposition of scales in the vertical direction . The function of chords is , It can enhance the resonance ability of music , Enriching the sense of musical hierarchy . Generally speaking , Chords are used as a foil to melody , That is, the background exists , Melody is always the main character . When the melody is accompanied by chords , Vertical stacking will make the music fuller , Horizontal stacking takes advantage of tendentiousness , Push the music forward .

verification

The task of verification is left to the students to do by themselves , You can talk about single tones 、 Melody and chords , Feel the difference .

Conclusion

After writing for a long time, I finally finished , Relatively hasty , Please point out any mistakes , It will be revised in time . In the next article, we will study chords .

​ This is the official account Qt Original release by future engineers , Please indicate the author and source of reprint .