Theory primer 1: Notes

Discussion in 'Beginner's Q&A Forum' started by srakshit, Aug 9, 2007.

  1. srakshit

    srakshit New Member

    During the process of learning the guitar, a lot of us come upon a stumbling block called theory.

    I'll try and share what limited knowledge I have, in three parts: Notes, intervals (which will also cover some basic thoery on scales) and chords.

    I will not complicate the postings with references of how to find those notes or chords on the guitar fretboard - there are hundreds of web resources that will help you get those.

    Please give feedback on the post - is it too heavy/too stupid/could not understand and I'll work on the next piece accordingly.

    Remember that some of the world's best players knew little to know theory. Howling Wolf and Blind Willie Mctell probably knew very little of conventional theory, but the music they produced was undescribably beautiful and emotional. Would they have produced better music if they knew theory? I don't know - but musicians like them are rare indeed, and a lot of us have to work hard at it. I'm one of those with very little natural talent, so I had to learn a bit of theory to get myself going.

    With all that said, let's get moving, shall we?

    1. What are notes?

    Notes are quite simply, a sound emitted from any source, that causes a vibration in the air which reaches our eardrums. It can be visually represented by a waveform. Depending on the source emitting the waveform, it can be a simple graph (called a 'pure tone') or a complex one with harmonics and irregularities. Generally, computers (when programmed), tuning forks, pitch pipes etc will generate pure tones. Musical instruments, cars, animals and people will generate complex tones that are a combination of multiple notes, harmonics and distortion.

    Notice the difference betwen note and tone. Note is a pure frequency pitch, and since most sources don't have a pure single frequency coming off it, the resultant sound is known as tone. In fact, a note does not really exist in the context of musical instruments, it's only a representative of the main frequency (called the fundamental) that the instrument should emit.

    Look at this graph:

    Notice the difference between the note coming off a computer, guitar and piano. The guitar is the most harmonically rich of the three, though that may not be always the case, depending on the instruments.

    All musical instruments have a harmonically rich structure, yet we play notes, right? Then what is this 'Tone' all about? Basically 'Note' is what you play, and 'tone' is what comes out of the instrument! Fundamentally though, they mean the same thing, and will be interchangeably used. Scientists like to refer to tones and frequency, musicians call them notes and pitch.

    2. Notes, why are they needed?

    The same reason you need a liter, or a kilo, or a meter - it's a measure of the pitch of a note. For the moment we'll abandon the concept of 'Tone', and stay with notes. The human ear has an approximate range of 20 Hz - 20,000 Hz. That is, there are 19,980 possible pure frequencies that can exist. Can the human ear hear all them differently?

    As it turns out, no. Human hearing is much more sensitive to direction and timing of sound (for example, if that wild beast was coming to eat it) than its frequency (to judge whether said animal was happy or sad). So we can only detect incremental differences in sound, and our perception gets better as the intervals get bigger. If you play a pure tone at 20Hz and the next one at 20,000 Hz (assuming the listener can hear it, as most people's hearing tapers off to about 10 Khz by the time they're 40), you'll be able to immediately tell the difference. If the same two tones are at 5000 and 5001 Hz, it's pretty certain nobody will know a difference. The surprising thing is that if you play them at the same time, you will immediately hear a pulsation about once a second, and you can tell there are two different tones.

    Every double of frequency is heard by the ear to be exactly the same thing. Play a G on the open string and on the 12th fret of the 3rd string, the relationship between them sounds the same. They are not the same pitch/frequency, but the ear hears them as the same 'note'.

    Therefore, every time the frequency doubles, it's known as an 'octave', and the frequencies an octave apart are given the same name. Put a finger on this, we'll return to it later.

    On unfretted instruments such as the violin, you have an infinite number of notes - the player moves their finger by a millimeter, and the pitch changes. Since music upto the end of the 16th century used only modes (no, we won't get into that), this worked just fine. But for more modern music, we needed different instruments to play with each other (the 'scales' concept). So, we came up with what is known as equal temperament tuning.

    3. Temperament, intervals and other musical compromises. Heavy going, please skip if desired.

    What is temperament? It is the progression and timber that defines the music as heard by the human ear. There are many kinds of temperaments, and the Indian system and the western system are different from each other in their temperament and tuning, though the concepts of notes, scales and intervals are common.

    Pythagoras found that the ear finds certain frequency ratios very appealing. The most appealing is 1:2 (the octave mentioned earlier), or double the frequency. The next most pleasing was the fifth (2:3) and then the 3rd (3:5). These intervals were known as 'Pythagorean' intervals, and for a long time were the defacto standard (and still are the basis) of most 'western' music.

    When the piano was being designed initially, it was with the pythagorean system. But if you had an instrument which played in strict pythagorean intervals, you would not be able to play the same melody across different keys. This was limiting instruments like piano from becoming an ensemble instrument. Music was moving from solo to multiple instruments, and composers needed to be able to write for multiple instruments across keys.

    A bit of explanation here of range. Each musical instrument (including the human voice) has a bottom note and a top note beyond which it cannot comfortably reach - at the right volume and intonation. Construction of musical instruments dictates their 'range', so a cello and a violin reach different ranges of the spectrum. It is necessary for instruments to be able to play with each other, and if the old intervals were followed the music would be limited.

    Therefore, equal temperament tuning emerged. It is a tuning for fretted, wind and percussive instruments that divide the musical spectrum between octaves into equally compromised intervals, so that scales can be played in 'unison'. The old systems, because of their concentration on the absolute frequency, had some tonally perfect intervals and some horrible intervals to dump the frequency errors into (and therefore unusable). I'm not going to go deeper into it - though we can do that separately if people are interested.

    Using this tuning system, we end up with 12 tones with equally spaced frequencies, with the 'tonal center' at A, or 440 Hz.

    Note there is nothing new to this - the basis of the system had existed from 350BC, it's now the most modern way (not nessecarily the 'best') of tuning instruments so everybody can just get along.
  2. srakshit

    srakshit New Member

    4. Whew, so I still haven't learnt anything except history - where is this going?

    Actually nowhere, so let's get going. I'll steamroller through here.

    Remember we had put our finger on octaves, take it off. We divide the octave and end up with 12 notes from C to B, defined as C, C#, D, D#, E, F, F#, G, G#, A, A#, B. Each interval is known as a semitone or half-step. When we get to C all the notes repeat again, and you get to the next octave. The A is 440Hz, which is obtained from a pitch pipe. There are no sharps between E and F, and between B and C. There's a sticky here that details why - it's due to the relationships between the notes in terms of pure pitch.

    A quick sidestep: There are more than one way to split the octave, there are 19-step and 43-step tunings. Because music is art, there are no 'right' answers to most things. This is just one way of doing things and the most conventional, but there are others.

    The # after a note denotes a 'sharp'. When we discuss the circle of fifths and intervals, we'll see how the sharps and flats come into play.

    By the way, there are also flat notes, which are 'enharmonic' (sound the same as) with the sharps. These are Db=C#, Eb=D#, Gb=F#, Ab=G#, Bb=A#.

    In the piano all the notes are arranged in a line, with the sharps (flats) in the little black keys and the pure notes in the white keys. C major scale on the piano is simply all the white keys in a line.

    Next instalment we will talk about intervals and the circle of fiths, and begin to apply these to our playing.

    What you can do is learn your way around the fretboard.

    Basically pick a note and play it on any string. So think of a note, and then play it on each of the 6 strings where it occurs. Ask a friend to call out the notes. Try and get the smallest gaps between your notes.

    For example, call A, and play the high E string 5th fret, b string 10th fret, G 2nd fret...

    you get the idea. This will also help when we get to chords two instalments later, and enable you to quickly pick up basic chords.

    Use this image to help you at first:

    Guitarnoise is a great resource for lessons, do stop over there and have a look. I've learnt a lot of concepts and songs there, very good if you like folk and standards.

    5. Bonus section: Tuning your guitar.

    Every lesson has to give you something useful, so here it is:

    A lot of people ask the question "How do I tune the guitar" and get all sort of answers. The truth is you can tune your guitar any way you want, but it may or may not sound good. It is possible to tune a guitar such that you can play a single pentatonic scale across the open strings, but it may be boring. OK for one song or two, but boring.

    So a guitar is most commonly tuned in standard tuning, which is (starting from the thinnest string) e, b, G, D, A and E, with the heavier strings going lower in pitch. You can use a reference pitch from a piano, PC program, pitch pipe or tuning fork, for the note A. The best way to tune is to match the reference note to the same note on each string. This also will help you find your way around the fretboard quickly.

    A good way to tune when you're just starting out, is to sing the reference note and the guitar note, to know whether it's high or low. When I started I was tone deaf (not that I've improved much) so I would find other ways to tune the guitar, mostly to my voice, and sometimes to harmonics. It would never play in tune with other instruments, but I found myself learning many songs quickly that way. I do not advise this, it's better to tune up to reference notes.

    Once frequencies get close, you will be able to hear 'beats', or the differences between frequencies. It will pulse and the sound will sound like it's literally 'beating'. Once the beating stops, you're either dead tuned, or way too high or low. Use this aural trick to tune up quickly.

    6. Further reading

    If you want to get into temperaments and historical tunings in-depth, the wikipedia page on equal temperament has a decent explanation but the links are outstanding, do drop in and take a look. There's history, maths and music all together in it.

    7. Feedback and questions

    Do let me know if there's something you felt was missing or unexplained and I'll try my best to answer.

    Also if this is a good idea at all, because I see most of you guys just want to play songs - yeh theory sheory kya hai?

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