From the terms of octaving and piano mode alone, the distance is indeed a bit far, one biased towards technology and the other towards entertainment. But distance doesn’t mean it doesn’t matter, so let’s give them a lesbian relationship.

Author: Liang Yi, ali Cloud technology expert, Ali Cloud audio and video communication QoS research and development

What is an octave

First of all, what is the octave? In Chinese, it means “the range of X times frequency”, which is a frequency band with the ratio of the end frequency to the start frequency multiplied. A corresponding concept is equal bandwidth, meaning a frequency band where the difference between the cutoff frequency and the start frequency is equal. Specific definitions are as follows:

Why use octave?

As we know, the frequency perception range of human ears ranges from 20Hz-20000Hz, which is very wide. During analysis, we need to divide this frequency range into different frequency bands (frequency bands) for analysis. How to divide them? Thus, there are the above two ways of partitioning. One is equal bandwidth, which means that the frequency band width of each partition is equal. The other is the octave, which means that the width of each partition corresponds to the width of the preceding adjacent band in a geometric sequence.

If the wide range, such as to show the voice of the low frequency to high frequency information need is a large amount of data, the efficiency is lower, and the degree of the human ear is sensitive to high and low frequency is not the same, usually the human ear is sensitive to the frequency of the low frequency part of change, and change the frequency of high frequency part is not too sensitive, so using octave conforms to the human ear hearing characteristics, Moreover, the efficiency of frequency band data analysis is improved.

Another concept related to the octave is the center frequency. The “geometric average” of the upper and lower frequencies of each band is called the center frequency f0 of the band. The specific center frequency F0 represents a specific frequency band, and F0 serves as the reference frequency. As long as the reference frequency is determined, the entire frequency range of 20HZ-2000Hz can be expanded in sections according to the definition of frequency octav. Octaves are usually displayed linearly spaced by the center frequency of their bandwidths. This is called octave format. This results in the octaves being equally spaced along the corresponding horizontal axis of the spectrum diagram, even if they are not evenly spaced. As shown in the figure below (citing the open test results on the network, see the data source below) :Photo data source:Community.sw.siemens.com/s/article/o…

The same white noise is represented in narrowband (blue) and octave (purple) formats, and the X-axis is octave format. Note that the octave band at the lower frequency has less data filled than the octave band at the higher frequency. As shown in the table above, this is because the octave band of the higher frequencies covers a wider frequency range than the octave band of the lower frequencies. If the x axis is drawn, the effect is as follows (citing the open test results on the network, see the data source below) :Photo data source:Community.sw.siemens.com/s/article/o…

Compared to the octave format, the figure above plots the same white noise data as before, but the X-axis is in a linear format. As can be seen, the power spectrum (blue) has the same density at all frequencies, but each octave band (purple) covers an increasingly larger frequency range.

In addition, because different base frequencies are selected, the final expanded frequency band format is also different, so how to select the base frequency? Standardization organizations provide standard definitions of different octaves according to different application scenarios. In acoustic measurement, 1/3 octave range is generally used to analyze the spectrum. In the National standard GB 3240-1982 Common Frequencies in acoustic Measurement, its standard frequency is defined as follows:

octave

And from there let’s see what the octave has to do with music. When we search for the English translation of “octave”, we will find the following results:Why is Octave the same as Octave? In fact, the octave is borrowed from the theory of the octave, because historically people’s knowledge of music predates the theory of signal spectrum analysis. According to human experience, when the pitch is raised an octave, the frequency is doubled, and with the advent of modern spectrum analysis technology, it is found that this just satisfies the law of frequency doubling. So we redefine the octave in terms of frequency. The octave actually predates the idea of frequency.

As we all know, an octave in simplified notation looks like this:There is an 8 degree difference between the low do and the high do. It is also known that girls’ voices are generally 8 degrees higher than boys’ voices.

Here we also need to talk about the concept of pitch, pitch is translated into pitch, and there is a function called pitch Detection in Opus encoder, translated into genetic testing, then what is the relationship between pitch and pitch? The sound produced by the vibration of an object contains many frequency components. The lowest frequency is called the fundamental frequency and the corresponding sound is called the pitch. The sound produced by the other harmonic frequency components is called the overtone. The pitch determines the pitch of the sound heard by the human ear, while the overtones form different timbre. Different instruments have different timbre because they produce different overtones. The divisions of frequency associated with the octave, and the pitches associated with the octave, refer to the frequencies of the pitch, not the overtones.

Law of twelve averages

Let’s look again at the characteristics of the octave.We will find a semitone relationship between mi and FA, si and high do, and a whole tone relationship between every other note. A semitone relationship means that the pitch of a semitone relationship is less than half that of a whole tone relationship. If you take an octave, and you spread it out to the width of a half step, you get a band of 12 half steps wide, and that’s called the twelve-tone temperament, or twelve-tone temperament, and that’s how pianos are tuned today. I finally have something to do with the piano. We also know that an octave corresponds to an octave with a low frequency and a high frequency separated by a factor of one, which is an octave range, and if the equal range is divided into 12 parts, that corresponds to 1/12 octave range. The standardization of music field has come again, the following is the international standard pitch and frequency comparison table:In this table, the frequency of A4 440Hz is specified as the reference frequency. The frequency spectrum is expanded according to the relationship of 1/12 octave range, and the corresponding pitch frequency of each standard piano key is obtained. Similarly, the center C on the piano corresponds to the key OF C4, which is 261.63Hz.

Call and roll

We see that the octave scale is 1234567 (do re mi fa sol la si), and here we have CDEFGAB, and anyone who has studied music knows that one is the name of the roll and the other is the name of the note. The song name is used for singing, while the song name is linked to a fixed frequency or pitch. The difference is that the same song name can be placed on different names and can be moved left and right on the piano keys, but different names are linked to a fixed frequency and do not move.

The piano mode.

With the whole note, the half note, the name of the note, the name of the roll, and the name of the roll can move on the key, there is the mode. First of all, the relationship between the whole note and the half note determines whether it is major or minor. All scales arranged in accordance with the [full, full, half, full, full, half] structure of the scale, is a major. Generally speaking, the main notes of a piece of music are 1, 3 and 5, and the music that ends on 1 is major music.All scales in accordance with the [full, half, full, full, half, full, full] structure of the scale, is a minor. Minor music usually starts with the first note at 6 or 3 and ends at 6.Of course there are many other subdivisions of major and minor notes according to different inflection rules, which I won’t go into here. Secondly, because the name can be moved on the key, when the do of the main note moves to C, then the major is called C major. Similarly, when the do of the main note moves to D, then the major is called D major, and the minor is defined in this way. Here, finally to these two seemingly unrelated nouns pull on the relationship, is it not a little interesting?

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