3.1.1.1.3 Measurement

Let's first discuss periodic vibrations. It is possible to simply count the number of periods in a second. This number is a vibration's frequency and is measured in "Hertz" (Hz); frequency in this context always means how often something repeats in one second (expressed mathematically: 1/second).

우선 주기적인 소리에 대해..

일초에 몇번 하나의 주기가 반복되는지 셀수잇다.

이 숫자가 진동의 프리퀀시이고 헤르츠라는 단위로 잰다.

A tone's frequency determines its pitch. A440 (also called A4, the standard pitch that orchestras use for tuning) means that the air vibrates periodically at a rate of 440 times per second; C5 vibrates 523 times per second; the low G on a cello vibrates about 100 times per second.

톤의 프리퀀시는 피치를 정한다. a440은 a4 음을 말하고, 기본 피치이다. 오케스트라들이 튜닝할때 쓰는 음.

일초에 440번 주기를 보이는 진동이란 말이지 c5는 523번 진동된다. 낮은 G톤 첼로는 일초에 100번..

Here you can already see: the slower the frequency, the lower the pitch appears to our ear. In fact, humans - depending on age - hear pitches between 20 Hz and 15000 Hz. Children can hear up to 20000 Hz; elderly people can often only hear up to 10000 Hz. Dogs and bats can hear well over 20000 Hz. This range is referred to as ultrasonic. In contrast to this is the infrasonic range, which is lower than the bottom of the audible threshold - i.e., between 0 and 20 Hz. This range is perceived by us as rhythm. You can use Pd to experience this for yourself with the following experiment:

낮은 프리퀀시는 낮은 피치값으로 구현.

사실 사람들 나이에 따라 다르지만, 20헤리츠에서 15000헤르츠를 들을 수 애들을 20000헤르츠 더 듣고

나이 많은 사람들 10000헤르츠까지

개랑 박쥐는 20000헤르츠 넘게 들을 수 있고, 그 범위를 넘으면 울트라 소닉 초음파,

반대로 들을 수 있는 저주파범위는 한계점은 0~20 헤르츠. 이 범위는 우리가 주로 리듬으로 인식하는 범위이다.

You hear a rhythm of clicks (that's the sound of a sawtooth wave) that gradually gets faster. After a certain speed (over 20 clicks per second), our perception 'shifts gears' and begins to hear a low pitch. For the air (and for the computer), this is still a "rhythm". But for the human ear (ca. 20 Hz) it's a pitch! The faster this rhythm becomes, the higher the pitch we hear.

Another defining characteristic of the human ear is that it hears pitcheslogarithmically. This means when a given frequency is doubled, we perceive this as an octave leap. If you change from A4 (440 Hz) to its double (880 Hz), you hear A5, which is exactly one octave higher:

인간의 듣는다는 것의 다른 특징을 말해보자면, 로그적으로(대수학적으로) 피치들을 듣는다는 것이다.

이 말은 주어진 프리퀀시가 두배가 되었을때, 우리는 한옥타브 높아진 음으로 인식하게 된다.

만약 A4(440)에서 그것의 두배 880은 A5인 것이다. 한 옥타브 높은 음

If we want to hear an octave above 880 Hz, we have to double it again. 880 + 880 = 1760:

Just to be clear: from 30 Hz to 60 Hz, we hear an octave but from 1030 Hz to 1060 Hz, we hear just a small step. In fact, the jump from 10000 Hz to 20000 Hz is only an octave!

Another important concept: let's add the same amount to a fundamental frequency, say 100 Hz - which is roughly the frequency of the open G-string on a cello - to which we'll add 100 Hz successively:

우선 100헤르츠를 100부터 더해보면, 이건 러프하게 첼로의 G 스트링이다

You hear an octave from 100 to 200, a fifth from 200 to 300, a fourth from 300 to 400, etc. In mathematics, this is an additive process in which the same amount is added each time. Our ears, however, perceive that this amount gets smaller and smaller with every step:

우리는 100에서 200 옥타브를 들을 수 있고 다섯번째(오부) 200에서 300, 네번째(4부) 300에서 400. 수학적으로는 이것은 가산적 과정인데, 같은 양을 한번에 더하는 것이다. 우리의 귀는 그러나 이 양을 조금조금씩 매 단계에서 인식하게 된다.

The graph on the left shows the mathematical function - a linear function. The right side shows what we hear - a logarithmic function.

If you want to hear a linear progression - i.e., a process by which the same interval is added, for example the octave - the mathematical function has to be exponential:

만약 등가적으로 피치가 올라가는 선적인 소리를 듣고 싶다면, 수학적인 방법으로는 지수함수다.

The conversion from linear to logarithmic progressions in Pd is accomplished by using MIDI numbers and frequencies. MIDI numbers reflect the way we hear in that the intervals we hear correspond to an equivalent interval in MIDI numbers: one whole number per half-step. You can convert entries in frequencies and MIDI numbers in Pd:

이런 선적인 방식에서 로그적으로의 진행의 변환은 피디에서 미디 넘버와 프리퀀시를 사용함으로서 가능한데,

A small table of MIDI numbers, frequencies, and their traditional names:

N.B.: Oscillators like "osc~" or "phasor~" have to receive their input in Hertz.

3.1.1.4.3 Converting MIDI numbers into frequencies

The "mtof" object converts MIDI numbers to frequencies. The formula for this calculation is:

mtof오브젝트는 미디 숫자를 프리퀀시로 바꿔주는 것이다.

To calculate the frequency of a pitch in equal temperament that is a certain distance away from a given frequency, use this formula:

'f' is the frequency you want to know, 'g' the frequency of the given pitch, 'a' the interval in half-steps.

For instance, if you want to calculate the frequency of C5 and know that A4 has a frequency of 440 Hz:

위에 수식에서g는 주어지는 헤르츠440이고,a는 내가 변환하려는 미디노트와 A4사이의 간격을 나타내는 숫자다

예를들면, C5의 주파수를 알고자 할때, C5는 A4와 3단계 격자가 있다. +3 그래서 a = 3

In Pd:

For the inverse operation - converting a frequency into MIDI - the formula is:

However, in Pd we have only the natural logarithm based on Euler's number (the mathematic constant 'e'); so we need this formula as well:

Programmed in Pd:

3.1.1.4.4 Noise periodicity

We've covered the fact that noises are not periodic. You could, however, imagine a noise that lasts 10 seconds and then repeats precisely as before. Such a noise would theoretically have a periodic frequency of 0.1 Hz. So a noise can be more precisely defined as a sound that is aperiodic or has a period of less than 20 Hz. Furthermore, one could also say that the frequencies of noise may have a common fundamental tone that is lower than 20 Hz.+

Many exciting experiments have been conducted in the field of acoustics, for example involving the Doppler effect or calculating the length of sound waves. Please consult leading acoustics textbooks for more information.

노이즈는 주기적이지 않다고 알았지만, 10초 정도 진행되는 노이즈를 상상해보고 그것이 계속 반복되는 거라고 생각해볼 수 있다. 이론적으로 노이즈는 0.1 헤르츠의 주기를 가졌다고 보면되는데, 그래서 노이즈는 정확하게 20헤르츠 미만의 주기를 가지는 것이거나 혹은 비주기적인 것이라고 정의 할 수 있겠다.