[THEORY] Notes, pitches, semitones and octaves

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This topic contains 10 replies, has 6 voices, and was last updated by Sayonil Mitra Sayonil Mitra 8 months, 1 week ago.

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  • #179775
    Andrei Moraru
    Andrei Moraru
    Participant

    Hello one and all. Let’s begin our journey down music theory lane by talking about some core concepts (the ones in the title). Let’s begin.

    Notes are to music what letters are to the spoken language, in that they are the basic unit used to express yourself through a song. You have two common ways in which you can name your notes:

    • using letters: C, D, E, F, G, A, B
    • using latin names: Do, Re, Mi, Fa, Sol, La, Si

    I usually use letters, much easier. Notes differ from one another through their pitch.

    A note’s pitch reflects how high or low a note is perceived by the human ear. While it’s not exactly a scientific measuring unit, a note’s pitch can be quantified by the note’s frequency, which is measured in Hertz (Hz). In order to understand what a frequency is, we need to understand the fact that sound “travels” in waves. In other words, each and every sound you hear can be represented by using a sine wave, kind of like this:

    A sine wave

    A sound’s frequency is given by how many wave cycles its sine wave goes through in one second. The higher the frequency, the higher your ear will perceive these notes. A normal human ear is usually capable of hearing sounds between 20 Hz and 20 kHz, while some are capable of hearing sounds even beyong this interval.

    Frequencies are important because of octaves. In signal processing, an octave is the spot where the signal doubles or halves its frequency.

    In music, this translates to the places where we encounter the same note, but its pitch is either higher or lower. The simplest example is when you play your E string open and then on the 12th fret. Same note, but with a higher pitch.

    An octave spans a total of 12 different notes</b>, each separated from the next by what is called a semitone. A semitone is the lowest pitch distance two notes can have. On the guitar this translates to a 1 fret distance. A tone consists of 2 semitones, or two frets on your guitar.

    And since earlier I gave you an interval of audible frequncies, it’s only fair to tell you that in this interval there are I believe a total of 10 octaves. Ever notice that sometimes notes have a number after them, e.g. C4. E5 etc? That number designates the octave that that note is a part of. Most notably, octave number 4 is considered the middle octave. You can find a table of frequencies for notes here, if you’re into it: link.

    The tricky part I never fully understood is with regards to the middle octave on guitar. I’ve noticed that when transcribing music in Guitar Pro, the C on the 3rd fret of the A string is transcribed on the music sheet variant as C4, even though its pitch corresponds to C3 (an octave lower). If someone has any idea on why this is a thing, please enlighten me.

    There is a lot of stuff here, so take your time with everything. We’re probably going to slow down the pace in future posts.

    If you have any questions, let me know and hopefully I’ll have the answer. Also @aaronaldous and anyone who wants to add anything, feel free to do so, there may have been things that I have missed.

    #179777
    Vasrely Derian
    Vasrely Derian
    Participant

    This is very well written! 👍

    #179779
    James Thomas
    James Thomas
    Participant

    This is written excellently! Very excited for future posts 😀

    #179780
    Ids Schiere
    Ids Schiere
    Participant

    Cool!

    I love the way you explained frequency(it’s a very physical explanation). Could you also write something on the factors that can change the frequency?

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    #179783
    Andrei Moraru
    Andrei Moraru
    Participant

    Frequency is directly related to the cycle duration. Mathematically, frequency is equal to 1/T, where T is the duration of one wave cycle, measured in seconds (also known as the period of the signal).

    In other words, the smaller the period, the higher the frequency, and as a result the higher the pitch.

    In music, a pitch/frequency is usually altered by the use of accidentals (sharps and flats). We will discuss those as well.

     0 likes
    #179785
    Nadim Captan
    Nadim Captan
    Participant

    To add to that, frequency is also a function of wavelength. The shorter the wavelength, the higher the frequency. When you pluck a string, you cause vibrations in the string (which are transferred to sound waves). The string’s length can be thought of as the wavelength and when you press on a fret, you make the wavelength shorter. As i mentioned before, when wavelength decreases, frequency increases. A shorter wavelength results in a higher frequency and hence, a higher pitch.

    #179786
    Nadim Captan
    Nadim Captan
    Participant

    Another thing that increases pitch is an increase in tensioN. This isn’t the musical term but the physical term. Tension is the force acting on both ends of the string in a guitar. The higher the tension, the higher the pitch. This is why the notes get higher when you wind the tuning pegs more and more. Bending while playing also increases the tension in the string. This is exactly why bending will never make the notes lower, only higher.

    #179787
    Ids Schiere
    Ids Schiere
    Participant

    I think my question was misunderstood. I actually study applied physics so the whole frequency depending on the wavelength and 1/T I’m fully aware of that. What I would like to add to the whole wavelength thing is that the wavelength of the string is actually not the length(L) of the string but 2L.

    My question was more aimed at material properties that affect the frequency. As we are all aware(at least I think) the tension of a nylon string is a lot less than the tension in a steel string. If you would apply the same tension you use to tune your steel strings to a nylon stringed guitar you would get incredibly high notes(or it will just break). The reason this happens is because of two material properties called Young’s modulus(stiffness)(E) and poisson’s ratio(which describes how a material gets pulled or pressed)(v). Now let’s take these constants for Nylon and phospor Bronze(used in steel strings a lot). For Nylon E=2-4 GPa and v=0.39 for Phospor Bronze E=116 GPa and v=0.359. This means that to get the tension you need to tune a string is a lot higher for Phospor bronze (since it a lot stiffer so harder elongate).

    Another thing to take into account when you want to look at frequency is the string diameter. It’s clear that a bigger string will require more tension to achieve the same note compared to a smaller string. This is simply that if you would calculate the frequency mass per unit length is an important factor(mass per unit length can be readily derived from the density of the material)

    #179788
    Andrei Moraru
    Andrei Moraru
    Participant

    Dang, I used to know this stuff, or a part of it, when I studied engineering. It’s been a few years since I visited these topics.

     0 likes
    #179789
    Nadim Captan
    Nadim Captan
    Participant

    Yes definitely, Ids. The different materials have different properties and that’s why they require different tensions to achieve the same frequency. And I didn’t want to get into the concept of L and 2L I just wanted to explain the correlation between wavelength and frequency. Another thing to add that might be relevant to your question is that the neck and fretboard wood also affect the tone of the guitar, which is the set of frequencies heard when the note is played. When you play a note you don’t just hear that specific frequency, you also hear its multiples along with it. The different types of wood reflect different proportions of those multiples and that’s why they give different tones.

     0 likes
    #179800
    Sayonil Mitra
    Sayonil Mitra
    Participant

    So glad you started this thing Andrei. we need more like this.

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