Please elaborate on this "tetrachord theory". I'm pretty sure I can follow any explanation you think you can give for it.
Make sure you have read the previous post on a quick touch on cycle of 5ths and 4ths. This theory is classic music theory on the construction of scales and i teach it to reinforce the whole why sharps and flats work, keys, and cycle of 5ths.
when disagreements arise about the scalar approach over the chordal, i find that those who side on chordal have never heard of, so never studied tetrachord scale theory, yet they can say that one is better??? To truly understand scales you need to know this. Have fun and read it through bit by bit and write it down as you go.....
Each major scale can be split in the middle to form two four note scales, these are called tetrachords. It comes from the Greek Tetra, meaning four and has evolved along with the Greek names for modes, but more on that later. These can be identified as the upper tetrachord and the lower tetrachord. A tetrachord is formed with the interval, tone (T), tone (T), semitone (S). When two are joined together a tone is used in between them so a scale becomes T-T-S- T -T-T-S now we have the intervals of a Major scale. This scale or mode is called Ionian, more on that later. All Major scales can be divided into these two halves
The C is a perfect scale due to the fact that we add no accidentals (sharps, (#) and flats(b) ) to the scale in order to make it sound correct when using the intervals of T-T-S-T-T-T-S so lets start here. The C scale is C,D,E,F,G,A,B,C. it consists of eight notes, the first seven of the alphabet and one repeated, this is called a Diatonic scale as each note has a letter of the alphabet to describe it.
We only use seven letters of the alphabet to name the notes in music so your alphabetic (diatonic) sequence ascending , going up, or forward from C is ;
C,D,E,F,G,A,B,C,D,E,F,G,A,B,C,D,E,F,G,A,B,C
It is important you understand this and can recite it backwards and forwards and count along it backwards and forwards. It will help if you write this down, and use it as a reference to work out what is happening from this point forward.
Split a C scale in two and you have C,D,E,F the lower tetrachord and G,A,B,C the upper tetrachord. The first note of the upper tetrachord which is G, is now your root (starting note) of a new scale. Count out the eight notes in alphabetic sequence and you have G,A,B,C the upper tetrachord from C Major, and add D,E,F,G which follow on the alphabetic sequence to complete the new scale of eight notes, which is really a new mode, the one we call Mixolydian, but more on that later. We now need to apply to this scale the intervals of T-T-S-T-T-T-S and to do that we need to add accidentals. Now we have to alter the 7th note as it is a tone away from the Tonic , F-G is a tone. So we add a sharp to it to create G,A,B,C,D,E,F#,G as our scale. It was necessary to add a sharp to the F because in order for the scale to be considered major, one of the laws of theory states the interval between the 7th note and the key note ( the 8th, octave, unison last note) of a Major scale must be a semitone. So now we have added a sharp to the F to follow this law, and this is how and why sharps start to be ordered in the way they do. We now have a G major scale formed
..G,A,B,C,D,E,F#,G
.. Lets split the G Major scale in two... G,A,B,C D,E,F#,G and repeat the process of using the upper tetrachord as the start of a new scale which is D.
Starting with the upper tetrachord write out the notes so we would have D,E,F#,G which is the upper tetrachord of G and the new alphabetic sequence of,
..A,B,C,D
As you can now see the upper tetrachord of the previous scale becomes the lower tetrachord of the new scale it forms which in this case is D...
.D,E,F#,G,A,B,C,D
But for it to be considered a Major scale the interval between the 7th note and Tonic must be a semitone, which in this scale it is not. So we add a sharp to the C which now gives the scale with its intervals of T-T-S-T-T-T-S , and the notes of
D,E,F#,G,A,B,C#,D
.. and the scale is now D Major. If we had used no accidentals and it ran
.. D,E,F,G,A,B,C,D
.. this would give us the scale or mode of Dorian, but more on that later.
Now we can see a pattern starting to emerge here which is that each new scale that is created from the previous Major when it is split in half, and the upper part four notes of the scale are used as the lower part four notes of the new scale. When we add the next four alphabetic notes in creating this new scale we must add a sharp to the 7th note to keep it a semitone from the tonic, for it to be considered a Major scale, thus an order for sharps is emerging. The fact we are moving in a "Cycle of 5ths" to form each new scale should also be noted. Why is this so? Its because each new scale is formed with the 5th note of the previous scale, think how the tetrachords are formed
..think
and if each one consists of four notes, when you join them together to form an eight note scale the upper tetrachord which will become the new lower tetrachord of a scale, the new root is in the 5th of the scale it is taken from.
Lets split D major
. D,E,F#,G
A,B,C#,D
. and use A,B,C#,D as the new lower tetrachord and add the ,E,F,G,A as the new upper in keeping to the alphabetic sequence to create an A scale. The previous key we worked on had two sharps so they must be added. The C# is already in place in the lower part so it is only the F# in the upper part that needs adding at this point. So now we have A,B,C#,D,E,F#,G,A, as our new scale. But we know that the 7th note and the Tonic must be a semitone interval for it to be considered a Major scale, which G-A in this scale is not. Now we can't mix sharps and flats together in the same key, the confusion would be chaos, so we must raise the 7th again with a sharp so now the scale reads
.A,B,C#,D,E,F#,G#,A
..and can now be considered an A major scale.
Following these rules and laws will allow you to create the seven scales and keys that have sharps in them and this is how the "Cycle of 5ths is formed and decided. It is the need to keep a semitone between the 7th and the Tonic that will see each sharp added in sequence the give us the rhyme "Father Charles Goes Down And Enters Battle", the first letter of each word in the rhyme is the note to be sharpened and the rhyme give you the order they appear and must be written so it is F,C,G,D,A,E,B for the sequence of sharps. As there are only seven individual notes of the eight (the root is repeated again at the top as the tonic) notes used, there can be only seven sharps for maximum use in scales. Carry on the with this process and use these laws and rules to see for yourself how you end up with a scale and key signature of 7 sharps.
Now what happens to the lower tetrachord in all this? Lets go back to C major and have a look and start from the perfect scale
C,D,E,F,G,A,B,C
we split it in half to get two tetrachords which was
C,D,E,F.....G,A,B,C
.. of which the upper part we used to form new scales with sharps being added up to the maximum of seven, the "cycle of 5ths", so lets now look at the lower one in the same detail. As we went forward (ascending) or up in the alphabetic scale to find sharps,
.C,D,E,F,G,A,B,C
lets go back (descending) in the scale to see what we find,
.C,B,A,G,F,E,D,C
is the C major scale ascending, which we know is perfect, split it in half and it forms the two tetrachords
.C,B,A,G....F,E,D,C
using the upper part we have a new scale to work on, F major, and it notes will be
.. F,G,A,B,C,D,E,F,
... But for it to be considered a true major scale the 7th and the Tonic must be a semitone apart, which in this case they are, so no need to put an accidental on the 7th to keep the intervals T-T-S-T-T-T-S so the scale now reads
..F,G,A,B,C,D,E,F,
.. but the intervals on the scale are wrong so this cannot be truly F major. F-G is a tone, G-A is a tone, A-B is a tone, but we know that the interval at A-B should be a semitone if the law about major intervals is to be maintained. The A sharp has already being taken and used for the scale B major so that cannot be used again because we do not mix sharps and flats, so the only option is to flatten the B. Now we have
.F,G,A,Bb,C,D,E,F
. and the intervals are now correct T,T,S,T,T,T,S, now we have flattened the 4th to achieve this, we can consider this scale as F major. As with the other examples with no accidentals to this scale at all it becomes a new scale or mode which is called Lydian but more on that later.
Remember we are now ascending with our scales in effect going down or backwards so read the alphabetic (diatonic) sequence as such when working out the ascending sequence of notes to arrive at the new root before going forward(ascending) the new scale you are forming.
C,D,E,F,G,A,B,C,D,E,F,G,A,B,C,D,E,F,G,A,B,C
In effect by doing this, the two tetrachord are reversed in relation to the way the sharps were formed. Now when we when work on the lower part becomes the new upper part and we now
need to form a new lower tetrachord to go with this.........think about this...........When working out new sharps the upper tetrachord was used and a new lower one formed and added. Now we use the lower tetrachord to form new scales. To make this less confusing we will now talk about them as the first part and second part. You have to understand that even though we count back on the alphabetic scale to identify the new scale we are forming, must go forward once the new root is established.
So lets split F major, F,G,A,Bb ....C.D.E.F
..F,G,A,Bb is now the second part and we now have the last four note of the Bb scale. By following the alphabetic sequence we will get the first part of the scale which is B,C,D,E
and we know the B is flat so the new scale reads
. Bb,C,D,E,F,G,A,Bb
but as in the previous scale its intervals are wrong for it to be considered Major. Bb-C is a tone, C-D is a tone, D-E is a tone, but we know that the intervals for a Major scale are T-T-S so D-E cannot be a tone and must be altered into a semitone, so we have to flatten the 4th note which is E with a flat. So now we have Bb,C,D,Eb,F,G,A,Bb and the scale can now be considered Bb Major as it has T,T,S,T,T,T,S as its intervals.
So lets look at what is happening here each time we split the scale,.......... the first tetrachord becomes the second tetrachord of the new scale,....think..............as in the previous scale, that makes Bb the new tonic from F major, so the root must be Bb Major as the tonic and the root can be considered to be the same. Why? Well we have two notes with the same letter in the scale, the root which in the previous scale was Bb and the tonic which was Bb, but they have a different pitch. The tonic is eight notes or an octave (unison) above the root, so it helps to separate them in scale study this way. When we add the first part to give us our scale it is always the 4th that needs to be flattened, this is where "cycle of 4ths" comes from and is decided. All the flats will follow this sequence till we reach 7 flats and their order will follow
B,E,A,D,G,C,F
.and can be remembered as Battle Ends And Down Goes Charles's Father ( now see the similarities to the sharps, as it is this rhyme in reverse).
Once again you can follow these laws and rules to form Major scales and keys with 7 flats if you so wish to do so and understand why sharps and flats are produced and how to apply them correctly.
So if you understand the laws and rules of scale study and in particular tetrachords you will understand scales, how and why we have the cycle of 5ths, the cycle of 4ths, why chords work, why harmony works as it is all based on scales, single tones blended together.
Remember those Modes well it is now later so lets look at them. There are seven modes (scales) that have specific intervals to be considered, these are;
T=TONE, S=SEMITONE
Aeolian............T,S,T,T,S,T,T....just like all the white notes on a piano A-A
Locrian............S,T,T,S,T,T,T....just like all the white notes on a piano B-B
Ionian..............T,T,S,T,T,T,S....just like all the white notes on a piano C-C Our Major scale
Dorian.............T,S,T,T,T,S,T....just like all the white notes on a piano D-D
Phrygian......... S,T,T,T,S,T,T....just like all the whitenotes on a piano E-E
Lydian............ T,T,T,S,T,T,S....just like all the white notes on a piano F-F
Mixolydian.......T,T,S,T,T,S,T....just like all the white notes on a piano G-G
These Modes can be applied in many ways, it is this application that the student must work out on their own to define their own way of thinking. Scales when practised properly, rather than just running up and down them fast requires you to listen to what you are playing, hear the notes and more importantly the intervals between them. Hear the chord tones you can play. Play them in inversions or as a 9 note, 10 note scales. You can play them as relative Minor scales, triads, arpeggios, you are only limited by your imagination. All we have here is how to build major scales in the Ionian mode and this is a small part of the big picture but the most important part, as it give you the tools to break scale down and understand them and create new ones.. From here you can build Minor scales and learn about chord structure, and so much more
.but only if you want to. How much work you do depends on you and what you wish to achieve and how you apply it
have fun..
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