Intervals and Pitches

Pitches and intervals:

Half step is the same as a semitone. A whole step is the same as a tone.
For intervals, I will look at different kinds of intervals: unison, 2nds, 3rds, 4ths, 5ths, 6ths, 7ths and octaves.
An interval is a distance between 2 musical pitches. Both scales and chords are built from intervals. There are two types of intervals:
Harmonic interval- where 2 intervals are played at the same time (Bottom).
Melodic interval- where 2 intervals are played at different times (top).

The identity of an interval is determined by quality and quantity.
Quantity, or number size is based on the number of lines and spaces apart from the first pitch/note. You determine an interval's quantity by simply adding up the lines and spaces included in the interval. Accidentals and sharps do not matter for the quantity.

If an interval spans for more than an octave, it is called a compound interval. For this, you do exactly the same thing and just count the lines. For example, you can have 10ths (octave apart + 2) and 11ths (octave apart +3).

Quality of an interval (half steps)
This is based on the number of half steps from one note to another.Unlike quantity of an interval, accidentals and sharps do matter. This image shows all the harmonic intervals, major, minor, perfect, diminished and augmented.






Major (M): Consists of 2 semitones between notes.
Minor(m): Consists of 1 semitone apart.
Perfect(P): A harmonic quality of unison, 4ths and 5ths.
Diminished(dim): Contains a semitone less than a minor or perfect interval.
Augmented(aug): Contains a semitone less than a major or perfect interval.

Names of intervals

Every interval gets its name from a combination of the quantity and the quality of the interval (e.g. minor third). Here are the combinations:

Perfect (P); used for unisons, fourths, fifths and octaves.
Major (M) and minor (m): can only be used for with seconds, thirds, sixths, and sevenths.
Diminished (dim): can be used with any interval, with the exception of unisons.
Augmented (aug): can be used with any interval.

Unisons, Octaves, Fourths and Fifths:
They are similar in the way that they can all be perfect, augmented, diminished to determine their quality.
Perfect unison's
This is just playing the same note twice. A perfect harmonic unison can also occur when 2 or more people play the same note at the same time on different instruments.

Augmented unison's:
To make a perfect unison augmented, you just add a semitone between the notes. The interval between Ab and A is called an augmented unison. You can't have a diminished unison because it doesn't matter how you change the interval, you still end up with a semitone gap between the 2 pitches.

Octave: is when you have an interval quantity of eight lines and spaces. A perfect octave is like unison as it is the same note being played. The difference is that there is a gap of 12 semitones in between.

To make the octave augmented, you increase the distance by one semitone. For example, if it is C to C octave above, the augmented version would be C to C# or Cb to C 13 semitones apart.

To make an octave diminished, you decrease the distance between the notes by a semitone. E.g. C# to C the octave above or C to Cb.

Fourths:
These are 2 notes, separated by 4 lines and spaces (7 semitones apart). 4ths are always perfect in quality with 5 semitones distance except from F natural to b, which consists of six semitones (augmented 4th).

Fifths: notes separated by 5 lines and spaces. All fifths are perfect 5ths. However, the interval between B to
F is a diminished 5th which sounds the same as a augmented 4th.

Seconds, Thirds, Sixths, and Sevenths:
All share the same characteristic is that they all use the terms minor, major, augmented and diminished to identify their quality.
A major interval made smaller by one semitone makes it a minor interval.
A major interval made larger becomes augmented.
A minor interval made larger by a semitone becomes major.
A minor interval made smaller by one interval becomes diminished.

Here is a table I made to show what interval name is given in relation to the number of semitones:

Seconds

This is when you have an interval quantity of 2 lines and spaces. If it there is 1 semitone difference, this is a minor second. If the gap is 2 semitones, then the interval is a major second. The only place where half steps occur between white-key seconds is from E natural to F natural and B natural to C natural. These are the 2 spots on the keyboard where there are no black keys between 2 white keys.

An augmented second is a half step larger than a major second.

A diminished second is one semitone lower than a minor second therefore there are no steps between each note. They are the same note. It is the enharmonic equivalent to perfect unison its just the notation that is different.

Thirds

This contains 3 lines and spaces. It contains 4 half steps and is called a major third. 

Major thirds occur from C to E, F to A, and G to B. If it contains 3 semitones, it is called a minor third, these occur from D to F, E to G, A to C, and B to D.

A major third can be turned into a minor 3rd by decreasing its interval size by one semitone. 

A minor 3rd can be turned into a major 3rd by adding a semitone to the interval size.

An augmented 3rd is the enharmonic equivalent to a perfect 4th. Again, they are the same note, just different notation.

Sixths and sevenths

Sixth, when you have a interval quantity of six lines and spaces. 

Seventh, when you have an interval quantity of seven lines and spaces.

 Here is my analysis of the different intervals in the solo piece I am playing. (Czardas):

Harmony and Tonality

Tonality:

Tonality is the hierarchy of pitch relationships between on a key center (or home) or mode. This is in all music that has a key.

Atonal- is when there the music is not in a key or a mode.

Bi-tonal- is where the music has 2 different keys at the same time in different parts.

Poly-tonality- where the music has 2 or more keys simultaneously in the music.

Key signatures:

This is the group of sharps or flats located next to the time signature.

The circle of fifths:

There are 12 sections and each section has a pitch value.

The circle of fifths helps you figure out which sharps and flats occur in different keys. As you can see, you can also see how many flats or sharps are in each key by counting either direction. Clockwise, you can count sharps from C (the top), and count the flats from counting round anticlockwise. For example, C has a number value of 0, so it has no sharps. G is second going clockwise, so has 1 sharp-F. It is also helpful to use when you are moving through different keys within your composition. The keys go round in 5ths, for example C to G is a fifth apart, and then D is the key next to G and so on.

You can remember sharps by using the mnemonic- Father Christmas Gets Dad An Electric Blanket with the first letter of each word telling you what sharp it is.

You can remember all the flats by:
Blanket Explodes And Dad Gets Cold Feet.


Relative minors:

To find the relative minor of a key, all you have to do is go down 3 semitones from your tonic of the key. For example, if you are in the key of C, if you go down 3 semitones, it will go B, Bb, A. A is your relative minor. A relative minor also has the same key signature as the original major key, it just starts on a different note. C major and A relative/natural minor just use white keys and have no sharps and no flats.

Here is a list of all the relative/natural minors:

D major and B natural minor
A major and F sharp natural minor
E major and C sharp natural minor
B/C flat major and G sharp/A flat natural minor
F sharp/G flat major and D sharp/E flat natural minor
C sharp major/D flat and A sharp B flat natural minor
A flat major and F natural minor
E flat major and C natural minor
B flat major and G natural minor
F major and D natural minor





Here is my other score for pitch and intervals, tonality and chords/chord progressions:

The saxophones in this score are a mixture of tenors, altos and a baritone. These wind instruments have different sounding pitches to the way they are written.

Alto saxohone-  is an E♭ transposing instrumentt and is written on the treble clef. A written C-natural sounds a major sixth lower (E♭) when played. This means the first note that the alto saxophones play is written as a G, however, it has a sounding pitch of Bb because if you go down a major 6th, this is the note it lands on. The range is from concert D♭3 (the D♭ below middle C) to concert A♭5. You can see that the Db sounding pitch is written as a Bb in the picture below and that the high F written actually has a sounding pitch of an Ab (a major 6th below). In tuxedo junction, the altos are written in G major instead of Bb major, because if they are in G, then the key they sound when the play is a Bb because Bb is a major 6th lower than G.










Tenor Saxophone-  is a Bb. It is another transposing instrument in the treble clef, sounding an octave and a major second lower than the written pitch. Modern tenor saxophones which have a high F# key have a range from A♭2 to E5 (concert) and are therefore pitched one octave below the soprano saxophone.









Baritone Saxophone:

It is a transposing instrument in the key of E♭, pitched an octave plus a major sixth lower than written. It is the lowest-pitched saxophone out of the saxophone family. It comes in two sizes with one ranging to low A and the other to low B♭. It is one octave lower than the alto saxophone. Modern baritones with a low A key and high F♯ key have a range from C2 to A4.









Trumpets:

The trumpets in this score are also transposing instruments and are in the key of B♭, written in treble clef. They sound a major second lower than written.










Here is me looking at chords in tuxedo junction:

The tonality of the piece is in Bb major. You can tell this as it has 2 flats in its key signature. Bb and Eb. The penultimate flat of the key signature tells you what key we are in so its Bb major. The first chord is also a Bb major.

The main chord progression is Bb, Bb/D, Eb9, F9, E9, F9. The F9 then resolves back onto the Bb chord as it is the dominant of Bb.

Harmony is the simultaneous playing of two or more notes, which are found in chords.

Chords and Chord Progressions

Chords:

What is a chord?
3 or more notes played together, or one after another (arpeggiated chords).
In western music, this involves notes constructed in thirds apart. With notes a third apart from each other, they are going to be stacked on top of each other on either lines or spaces.

Creating triads with 3 pitches:

These will tend to be Major, Minor, Augmented or Diminished chords.

Triads are made of the root, the third and the fifth.
The first note is the root, the second note is the third, and the last note in the chord is the fifth.
The third in the chord is very important because it determines if you are in a major or minor key (the quality).

Building triads by counting semitones and scale degrees:

Major- Root position + 4 semitones + 3 semitones (7 semitones above the root)
1, 3, 5

Minor- Root position + 3 semitones + 4 semitones (7 semitones above the root)
1, b3, 5

Augmented- Root position + 4 semitones + 4 semitones (8 semitones above the root)
1, 3, #5

Diminished- Root position + 3 semitones + 3 semitones (6 semitones above the root)
1, b3, b5

Here is a major triad in Bb major.

Seventh chords:

This is when you add another third above the 5th of the triad. They are called 7ths because it is the 7th interval from the root.

You can get many types of sevenths:

Major

Minor

Dominant sevenths

Minor 7 flat 5 chords (half-diminished chords)

Diminished 7ths
Minor-major 7ths

Building 7ths by counting semitones:

Major-   Root + 4 semitones + 3 semitones + 4 semitones (11 semitones above the root)
1, 3, 5, 7


Minor-   Root + 3 semitones + 4 semitones + 3 semitones (10 semitones above root)
1, b3, 5, b7


Dominant-   Root + 4 semitones + 3 semitones + 3 semitones (10 semitones above)
1, 3, 5, b7


Minor 7 flat 5-   Root + 3 semitones + 3 semitones + 4 semitones (10 semitones above root)
1, b3, b5, b7


Diminished-   Root + 3 semitones + 3 semitones + 3 semitones (9 semitones above root)
1, b3, b5, bb7


Minor-major-   Root + 3 semitones + 4 semitones + 4 semitones (10 semitones above root)
1, b3, 5, 7

Inverted chords:

This is if the lowest sounding pitch is not the root. Here are the possible inversions:

First inversion:

If the third of the chord is lowest sounding. 

Second inversion:

When the fifth of the chord is the lowest sounding note.

Third Inversion:

When the seventh of the chord is the lowest sounding note. 

Chord Progressions:

Chords built on the seven notes of a major key signature are called diatonic chords. Chords that are built up on notes outside the key signature are called chromatic chords.

This is a bit different with minor scales, as you can get relative and harmonic minor scales too. This means there is actually 9 different 9 notes that can fit in a minor scale. You can think of there just being 1 minor scale, just that they have the flexibility of the 6th and 7th degrees of the scale.

Chord progressions are chords which are played in a succession.
Roman numerals can be used to represent the different scale degrees. Roman numerals in capitals represent major chords and lower case roman numerals represent minor chords. You can also get other signs to indicate whether the chord is diminished (o) or augmented (+).


Chord names within a C maj scale:                          Note:

1  Tonic                                                                  C
2  Supertonic                                                           D
3  Mediant                                                               E
4  Subdominant                                                        F
5 Dominant                                                             G
6 Submediant                                                          A
7 Leading tone                                                        B
8/1 Tonic                                                                C

The image above shows the triads contained within the key of C major.

Common Major Key Chord Progressions:

Chord                          Leads To

I                                  Can appear anywhere and lead anywhere
ii                                  I, V,  or viidim
iii                                 I, IV, vi
IV                               I, ii, V, or viidim
V                                I or vi
vi                                I, ii, iii, iii, IV, or V
viidim                          I


Chord progressions in minor keys:
Here, the 6th and 7th degrees of the scale are variable, depending on whether the natural, harmonic or melodic minor are used in the music. The possible chords within C minor are:

Cm- C, E, G             i
Ddim- D, F, Ab        iio
Dm- D, F, A             ii
EbM- Eb, G, Bb       III
Eb aug- Eb, G, B      III+
Fm- F, Ab, C           iv
FM- F, A, C            IV
Gm- G, Bb, D          v
GM- G, B, D           V
AbM- Ab, C, Eb     VI
A dim- A, C, Eb      #vio
BbM- Bb, D, F        VII
Bdim- B, D, F          #viio
Cm- C, Eb, G          i


Common Minor Key Chord Progressions:
Chord                                              Leads To
i                                                       Can appear anywhere and lead anywhere
iio                                                     i, V (v), or vii (VII)
III (III+)                                           i, iv, (IV), VI (#vio), or viio (VI)
iv (IV)                                              i, V (v), or viio (VII)
V(v)                                                 i or VI (#vio)
VI (#vio)                                          i, III (III+), iv (IV), V (v), or viio (VII)
viio (VII)                                          i

Here is the Czardas score with me looking at chords on it:

It uses a lot of dominant A7 chords so that it can then resolve onto D with a perfect cadence.

Modulating to a new key:

This is when a piece of music temporarily moves into a new key. The moving is the modulation.

Cadence:

A cadence is a place where it feels like an ending. It can be a strong stopping point.

There are 4 types of cadences:

-Authentic cadence
-Plagal cadence
-Deceptive cadence
-Half cadence

Authentic cadences:

There are 2 types of authentic cadences:  Perfect cadence and imperfect cadence

Perfect cadence- chord V to chord I in root position. At its strongest when the root is at the bottom and top of the stack of notes.

Imperfect cadence- A V-I chord progression made with inverted chords (where the root, the third, and the fifth aren't in the perfect stack of notes).


Plagal cadences (Amen cadence):

These cadences go from IV (iv) to chord I (i).

Possible plagal cadences would include IV-I, iv-i, iv-I, IV-i.

Deceptive/interrupted cadence:

Reaches the ultimate point of tension on a V chord like an authentic cadence but then it doesn't resolve on the tonic but resolves onto any other chord. It is interrupted because you think it is going to resolve on the tonic, but it doesn't.  It has the feeling of incompleteness.

The most common interrupted cadence is a chord V leading onto a VI chord.

Half cadence/imperfect:

This cadence ends at the point of tension (the V chord) and stops, resulting in the music feeling unfinished.

The mos common way that this happens is when chord I is in second inversion (when the fifth of the chord is the lowest sounding note). This produces different chords with the same bass note.

Rhythms and Time signatures

For this unit, I will look at pitches and intervals, chords and chord progressions, rhythms (simple and complex) and tonality. I will also incorporate this knowledge into scores.

Rhythms

Here is me practising my theory knowledge by going through the grade 6 Trinity Guildhall theory book.
Swung quavers. Here I had to write down the way the music should be played. The first page was adding the correct time signatures to the extracts of music. The second is adding the correct duplets in the marked places. The 3rd, I had to place brackets on the main beats to show where they change to create a hemiola effect. A hemiola means ratio of 3:2. The next page I did was writing key signatures. Here I had to write out one octave scales in rhythm to fit the given time signatures.

Here is the tree of notes so you can identify the note values:

Semibreve Notes (on the top of the tree diagram):

It has the longest note value of all the notes and is a hollow oval as you can see on the left. In 4/4 time, a semibreve lasts an entire 4 beats. You can also get a double semibreve note called a breve. These hold the value of 2 semibreves which means they last 8 beats in 4/4 time.

Minim Notes: (Half notes) These have half the note value of a semibreve. This means they are held for 2 beats in common 4/4 time. 2 minims=1semibreve.

Crotchet Notes: (Quarter notes) This is equal to 1/4th of a semibreve or 1/2 of a minim. It has a note value of 1 beat.

Quaver note: (Eighth note) Has he note value of half a crotchet. Lasts for half a beat in 4/4 time.

Semiquaver: (Sixteenth note) This has half the note value of a quaver note so lasts for quarter of a beat in 4/4 time.

Demisemiquavers: (32nd note) This has half the value of a semiquaver which means there are 8 in 1 beat. These are fairly rare.

Extending Notes with Dots and Ties:

Using dots to increase a note's value:
These dots are called augmentation dots and it indicates that the note value is increased by one half of its original value. The most common use of it is when a minim is made into 3 crotchets instead of 2.

Double dotted notes increase the time note by another quarter of the original note, on top of the half incresed as well. This is less common. A minim with a double dot = 3 and a half beats.

Using ties:
Tying to another note which connects notes of the same pitch together to create one sustained note instead of 2 seperate notes. For this, you just add the 2 note values together. E.g a crotchet tied to another crotchet is equal to 2 beats in common time.

Slurs are different, they are similar, except they connect 2 different notes of different pitches.

Rests:

These have all the same value as the notes do going down from semibreve, minim, crotchet, quaver and semiquaver rests.

Time signatures:

This is the pair of numbers at the beginning of the staff. It tells you 2 things:

The number of beats in each bar- The top number number tells you this.
Which note gets a beat- The bottom number tells you which type of note value equals one beat.

You can get 2 types of time signatures:

Simple: The beat can be broken down into 2-part rhythms. E.g. 4/4, 3/4, 2/4, 3/8, 2/2.

Compound: The beat is broken down into 3-part rhythms. Any time signature with a top nu,ber of 6, 9, 12, 15...

Irregular rhythms: Triplets and Duplets:

This involves dividing the beat differently from what is allowed by the time signature.
Triplets- 3 notes joined together played within the time of a crotchet.
Duplet- 2 notes which have the same value as 3. Duplets are the reverse of triplets.

Here is me analysing rhythms for the Czardas. The semiquavers in this piece give it a feel of great urgency when it gets into the allegro vivo and gives the piece of music contrast to the Con tenerozza, which is slower and the use of more rhythms like quavers and minims. This use of "rhythm and speed" change the feel of the different sections in this piece dramatically. Its written for xylophone. The xylophone I play on at home has a range of 3 and a half octaves. From the F an octave an a half below middle C to a C which is 2 octaves above middle C. This is a standard sized xylophone as they tend to have 3 and a half or 4 octaves.

Here is the other score I have studied to identify rhythms in. The piece is Tuxedo junction and is a jazz standard which contrasts with my other classical piece above. I choose a contrasting style as it is scored completely different and I also picked it as it had multiple parts compared to my other score which just for 1 part- xylophone.

Instrumentation
The parts/instruments in this piece is for a typical big/swing band. Wind section- 4 saxophones consisting of 2 alto saxophones, 2 tenor saxophones, and a baritone saxophone. Then the brass section which has 4 trumpets, and 4 trombones (the bassier of the brass). It then has the rhythm section which consists of guitar and piano which act as the chordal instruments. Then there is the bass and the drums and also auxiliary percussion, which is vibraphone.

There are many dotted rhythms so that the next beat lands off the beat for syncopation which is very common in jazz music. Another thing about this piece is that there are also many tied notes. This is often the case with quavers tied to crotchets with the quaver off the beat being accented to emphasis syncopation. This is a very commonly used rhythmic device and leaves the next note to land on the beat. This propels the music forward as accented anticipation and delay of the main beats of the bar are used. For example, on the score you see on the second page, in bar 14, where I have circled. The emphasis is on 2+ and then the next emphasised note is on beat 4. The bass part is a walking bass line, which is very common and gives the crotchet beat clearly throughout the whole piece of music.

"Swing style"- means swung quavers are used in this jazz piece. This means the beat is subdivided, not into 2 even quavers, which is common in classical music, like my other piece I have looked at (Czardas), but into long-short groupings called swung quavers. They are hard to write in notation form on a score, so instead, it is written as straight quavers, but you play it as swung instead in performance.