music theory

Major and minor thirds – so important to chords and scales. Sing and play this little ditty to help make them part of your experience. Major and Minor Triads and Scales.

Triads are nice to juggle. Sing this little tune as you do the juggling.

The difference between major and minor thirds is the cornerstone of music theory. How can you learn to tell them apart? One way is to apply the “Frere Jacques test”. Frere Jacques uses the major third. If you try this tune on a minor third it sounds a bit miserable. Here’s the tune first in F major, then our hero protests in Dm (the relative minor sharing the same key signature) then later in F minor (the parallel minor). Did he get out of bed to ring the bells? Follow Frere Jacques’ Lament and you might find out.

Only one major scale but all those minor scales! This song will help you hear the difference between five of them. Minors start the same… and end the same . For classical exams you can get by with the harmonic and melodic. For jazz exams you may also need the Dorian. Look for the relationship between this tune and the following chart. The 6th and 7th degrees of the minor scale, which both can be either low or high, are shown in the grey bubbles hanging below the minor keynotes.

You can download a pdf version of this chart by clicking Key signatures and the Cycle of Fifths.

How can we ever remember the order of the sharps and flats in the key signature? Here’s a catchy song that you will never forget (after you have sung it three hundred times) What’s Your Sign-ature? Print it out then sing along to this track. You can also sing along reading up the list of six flats on the left and six sharps on the right that you see in the diagram above. On this track I am joined by Ruby Hamill on vocals with dad Andy on glockenspiel and audio.

Musical intervals are confusing things. You can think of them as bus stops that sometimes get moved around by the bus company when there are road works etc. They don’t want too few stops or too many stops close together. Sometimes all you need to know is the number of stops. But sometimes you just need to know the exact distance between them. For that you need a fixed unit, such as a mile. Sometimes you need to know the number of stops and the exact distance. The bus stops are your elastic 7 notes, counted 1st , 2nd, 3rd and the distance is measured in guitar frets (aka half steps or semitones) counted from 0. Put them together e.g. a 7th with 10 frets is a minor 7th.

It’s interesting to make various scales on one string. Imagine the open string 0 to be the bus station and fret 12 to be your destination, the same note an octave higher. Now play the frets 0 2 4 5 7 9 11 12. Looking at where the the seven bus stops were placed 1st stop fret 0, 2nd stop fret2, 3rd stop fret 4, 4th stop fret 5, 5th stop fret 7, 6th stop fret 9, 7th stop fret 11, 8th stop (the 8ve) fret 12. This is of course the major scale getting its name from the 3rd with 4 frets , the major third. Using the diagram above find the full names for the other intervals that make up the major scale.

At one time you just needed C, Cm and G7. But chord symbols have gradually grown more elaborate. Reading Chord Symbols is a guide through the rules that musicians read or download.

Chord symbols started to develop around 1850. Before that composers since 1600 would indicate a chord by counting the intervals above the bass note, known as figured bass. It works well so long as you stay close to the key signature but gets very messy when you get more adventurous in your key changes which is what the new generations of composers wanted to do. Chord symbols, in contrast, are completely independent of key signatures.

A casualty in the changeover is the diminished triad – a delicate ambiguous sound which was originally shown as Bo meaning just B D F. In classical harmony books it still has that meaning. However if you write Bdim or Bo these days pop or jazz musicians  will play the full diminished 7th, that is B D F Ab. So for that rare occasion when the diminished triad occurs in pop and jazz we could write Bo5 meaning “just the triad, please, leave out the 7th” , a bit like how B5 means bare 5th, please: leave out the 3rd”. By taking the dim 7th as the default things look neater and simpler, e.g D-7 D#o E-7 C#o …

We could also give people a list with the understanding that if there are more than one symbol of which would normally be a root then none of them is a root. Underlining can also distinguish these note lists. The first is played lowest while the others can be juggled in any order e.g. in this typical Baroque chord sequence.

in letternames Gm ACF# Gm/Bb

in fixed solfa Sol- LaDoFa# Sol-/Sib

in movable solfa l trs# l-/u or u- rft u-/mb (ut=do)

in Nashville 6m 724# 6m/1 or 1m 247 1m/b3

The convention could be useful for other sounds which can’t easily be portrayed in chord symbols e.g. C Ab B, CFBb, CDB, CF# etc.

There are so many ways to arrange notes. How come these two scales, the major and minor, stand head and shoulders above the rest? I try to answer this question in a short essay The Ionian-Aeolian Duopoly.

Most popular songs have around seven notes per octave. More than that and the tunes becomes less memorable and spontaneously singable. Is this part of our biology? This essay discusses these issues Sharps and flats are quite natural.

The frets of the guitar shorten the string by around 1/18 each time. 12 frets shorten the string by exactly half producing a note an octave higher. But none of the notes on the way up are exactly in tune. This method is called Equal Temperament that is equal but impure. The piano and all of the instruments of the orchestra use the same method. This short essay How out of tune is Equal Temperament and how much do we care? demonstrates the arithmetic with the help of some cut out shapes.

Equal Temperament has a long history appearing in China two thousand years before it took hold in Europe and is now spread worldwide by radio, TV smart phones etc . Its progress is tracked in A Chronology of Equal Temperament and its Musical Exploration. Central to the history of Equal Temperament are the Lute Dances on Every Fret written by Gorzanis in 1567 which demonstrate that with equal frets whole pieces can be transposed. Each fret on a lute can be slid to be sharper or flatter. By experimentation lutenists found that by reducing the length of the remaining string by 1/18 twelve such frets would reach an octave and on the way get very close to all the intervals needed to make resonant major and minor chords. This is known by instrument makers as the rule of 18. I am pleased to say these lute dances have now been recorded by Michele Carreca and we have worked together to provide extensive commentary on the CD, see the gorzanis-1567 page. To celebrate the release of this CD and to celebrate the rule of 18 here is a poem Ugly Little Fretet.

Jazz musicians take the chords from a tune and say,” Lets do this as a bossa.. or a waltz or a swing?” This was also happening back in 1550 with the rhythms that were in fashion, e.g “Let’s do this as a Salterello”.  I asked Miyuki Tanaka to help me make a YouTube video to demonstrate using the jazz app iReal Pro with two popular dances of the time.

A Renaissance jam session.

These are the chord sequences that lutenist Gorzanis improvised on in every keythe first person to do so in Europe back in 1567. Here’s the CD of his explorations.

My dad was fond of peppering his speech with the odd Latin phrase. One that stuck with me is sine qua non – without which not – in other words something essential. The sine qua non of the luxurious harmonies we enjoy is the tuning system that originated around 1550 on the lute in the north of Italy. So for all the tuning nerds out there, its all explored in the calm presentation of a specialist on the topic, Chris Egerton

Melody and harmony are closely related but often people use different different writing systems when trying to understand what is going on , for example writing the melody as notes on the stave and chords as roman numerals, scale degree numbers or chord symbols. Lets see if writing these two aspects in the same script makes the relationships jump out. See if this analysis of Saint Seans’ The Swan can help us to understand the beauty of the relationship between the melody, its harmony and changes of key. This version uses a chromatic version a movable solfa written in lower case. An example of fixed solfa written in upper case is to be found on the for pianists page. Melody and harmony written in the same medium can be called melarmonic analysis.

The US uses fraction names for the symbols we use to write rhythms down e.g “quarter note”. There are other names , e.g crotchet, which are used in the UK but I prefer the fraction names as they are more straightforward and also relate directly to the time signatures. Gradually during lessons a way of singing the fraction names has evolved. Are there similar conventions in the US? If you know of any please drop me a line.

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