emuso

Music 101 (part 2)

Jerry

Last time, we looked at effective learning with directed practice and recall.

Now we must briefly explore how musical sounds are created by various instruments. This is because music is made up of sounds and silence, occurring over time. Fundamental to all music are the concepts of pitch, octave, and semitones, which we take a high-level look at here. When pitches are combined (played at the same time) the sound flavour we hear depends mostly on how many semitones apart these pitches are, which means if someone plays a chord on guitar, say, and then shifts that exact shape along the neck, we recognise these two sounds as the same sound flavour. As a result, this means we can discuss music theory in terms of the semitones between the pitches, rather than note names, and hence we can massively reduce how much needs to be remembered and recalled. Let’s get going.

Pitch

When a tuning fork is struck, it vibrates  backwards and forwards some number of times a second, known as the fundamental frequency).  These vibrations pass through the air, and arrive at our ears, which respond.  Our brain converts the vibrations into the sound we hear.  Our perception of a vibration of one frequency is known as pitch.  Unlike the tuning fork, when a single string on a guitar is plucked, it additionally creates many related frequencies. You needn’t remember this, but it helps the following discussion.  This mix of  vibrations pass through the guitar and travel through the air, and if pick-ups or a microphone are used, travel down a cable as an electric signal  (for amplification to send to loudspeakers to recreate these vibrations in the air).

The construction of the guitar affects the mix of vibrations . We perceive the fundamental frequency, and we perceive the other frequencies in the mix as the timbre of the instrument.  We can tell the resulting sound has been produced by a classical guitar with nylon strings, or by an acoustic guitar with steel strings, or by a heavily distorted electric guitar. We informally call this sound a pitch or a note or a tone. Similarly, other instruments (piano, synth, violin, brass, wind and so on) create vibrations in various ways, whose timbre we can recognise. Sound engineers refer to the sound as “having a (fundamental) frequency of some number of Hertz (Hz)“).  For example, “that is a pitch of 110 Hz from nylon guitar” or “110 Hz from a male singer”.  The purest tone (just one frequency) we hear is produced by a tuning fork or a test signal that sound engineers use, available in some DAW (Digital Audio Workstation) products (such as Steinberg’s Cubase).  The engineers use tone controls to affect the timbre (e.g. to remove some bass (low) frequencies in the sound when mixing a song).

Octave

We say two sound frequencies are an octave apart if one’s frequency is double the other. For example, 110 Hz and 220 Hz are an octave apart. As are 220 Hz and 440 Hz.  The sound of two pitches an octave apart is extremely stable … not clashy at all.

Semitone

The next image shows some frets on the fretboard of  guitar, and shows an arbitrary pattern using coloured circles, indicating a shape to use to create the sound of some chord.  You will encounter many such shapes, though not usually drawn on such a realistic image (see below).

 

International standards pick out twelve pitches within an octave (for example. within 110 Hz, but less than 220 Hz). It singles out pitches from 0 to 11 semitones above 110 Hz, say, or above 220 Hz, say. A semitone is a magic number, 1.059 (roughly). A semitone above 110 Hz is 1.059 times 110 Hz (116.49 Hz). A semitone above this is 1.059 times 116.49. Keep doing this, and 12 semitones above 110 Hz is 220 Hz, its octave.

Look at the above guitar. Adjacent frets are positioned on the fretboard so the two pitches produced by plucking adjacent frets on the same string are are a semitone apart. On guitar, this means fret 12 produces a pitch an octave higher than its open string, and frets 0 (the nut) to frets 11 produce pitches that are 0 to 11 semitones above fret 0. As another example, the pitch of the fifteenth fret is an octave above the pitch of the third fret, and frets 3 to frets 14 produce pitches that are 0 to 11 semitones above fret 3.

Here are visual representations on emuso, using coloured circles labelled 0 to 11 of the above, arbitrarily using the second string.  It all repeats from the 12th and 15th frets respectively, where the next octave begins.

 

 

Piano is particularly simple. Any block of twelve adjacent keys (regardless if they are black or white) produces pitches that are 0, 1, 2, …, 10, 11 semitones higher than the leftmost key in that block. It then starts all again at the very next key.

Here are two examples of seven pitches singled out at semitones 0 2 4 5 7 9 and 11 within an octave, each example starting at a different piano key (different pitch) …

 

 

Music theory gives names to these pitches, such as C, D sharp and G. You’ll often see a number attached, such as C4 above, when looking at computer software that supports MIDI. This indicates which octave the sound is in.  You can a few such names above, but don’t worry about these.  Do notice the labelling used on the circles, and that the starting pitch is shown as a solid red circle.

Here are the same two examples, this time shown along different guitar strings.

 

Interval

Our brains are very good at recognising how many semitones apart two pitches are, for example, three semitones apart. If we hear fret 0 followed by fret 3 on the same string (3 semitones apart), we recognise this has a particular sound flavour. If we hear fret 4 followed by fret 7 on that same string (3 semitones apart, again) we recognise the same sound flavour, just higher, even though the pitches involved are different. Try this for yourself. When just two pitches are involved, we call this combination an interval.

We can also create the same interval using more than one string.   The shape depends on the guitar tuning.  Here are examples of 3 and 4 semitones.  You’d learn about this when you begin to learn intervals.

       

 

Music theory assigns names to different sized intervals, such as major third for 4 semitones, and minor 3rd for 3 semitones.  You will need to learn these  There are only a handful.

Intervals with different semitone distances have their own unique sound flavour. This is crucial … an interval of 3 semitones say sounds completely different to an interval of 4 semitones. We can relate visual shapes to intervals, whose names we learn, and with ear training practice, to the sound of each. Intervals are the underpinning of all musical sounds.

Traditional music theory discusses different concepts using a set of pitches.  In reality, each pitch makes an interval made with one important pitch.  We are just singling out pitches relative to this , as we saw above (look back at the piano or guitar images).  When we come to create the set of pitches on-instument, we choose the start pitch, which then is used to locate all the others relative to it. On guitar, there are many ways to locate these, which we will look at later (not in this overview series). But regardless of what shape is used, if we want to use a different start note, we can just shift that shape.  We’ll look at the details when you learn about the guitar fretboard (not in this overview series).

For now, realise this means you have far less to learn using semitones compared to learning based on pitch names. This can literally reduce the learning effort by a 100 times or more. With pitch names, there is signifcant danger of overloading the brain, seriously impeding learning progress.

Summary

Informally, we think of the sound created by an instrument as having a pitch of some fundamental frequency (e.g. 110 Hz), with a mix of other frequencies that create the sound that lets us distinguish one type of instrument from another (timbre).  We’ve learned about the octave, where the frequency of one sound is double the other.  We’ve learned about the semitone, internationally standardised where two frequencies are a a semitone apart if one of these is 1.059 times the frequency of the other. This results in twelve different pitches being singled out in an octave, at semitone 0 to 11 above the start frequency of the octave.  We’ve learned about the interval, that intervals of different semitones have unique sound flavours, that are recognisable regardless which pitches are involved in the interval, and that these are the foundations of musical sounds like chords and scales.  We’ve learned that semitone intervals, in the range 0 – 11, can be used to describe musical concepts, rather than pitch names, thereby reducing the learning effort.

Next time, we’ll take a  high-level look at rhythm, melody, and phrasing.