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Synthesizers, Music & Television © T. Yahaya Abdullah
The speed of oscillation or vibration is called "Frequency". Frequency is measured in Hertz (Hz), which is oscillations per second. If the hollow tube vibrates at 200 cycles per second, the frequency is 200 Hz.
When you hit a hollow tube, the shock-wave is actually travelling at a constant speed. What determines the frequency is the length of the hollow tube. The longer the tube, the further the shock-wave has to travel, hence, the lower the frequency... and vice versa.
"Octaves" of a note are just multiples of the original frequency. Let's say that a length of hollow tube has a frequency of 264 Hz and we'll call it "C".
Tube Length | Note | Octave | Frequency | |
---|---|---|---|---|
Original | C | Original | 264 Hz | 264 Hz |
Half | C | Up 1 | 264 x 2 | 528 Hz |
Quarter | C | Up 2 | 264 x 4 | 1,056 Hz |
Double | C | Down 1 | 264 / 2 | 132 Hz |
For simplicity, let's call 132 Hz = "C2", 264 Hz = "C3", 528 Hz = "C4" and 1,056 Hz = "C5". By convention, the first note in a numbered octave is "A" (ie G#3 is followed by A4).
If we use fractions where the numerator and denominator are whole numbers, we are creating the "just intonation" sysem of tuning. The fractions are listed in the table below and are referenced to "C".
Tube Length | Frequency | Note | |
---|---|---|---|
Original | 264 x 1 | 264 Hz | C3 |
3 / 4 | 264 x 4 / 3 | 352 Hz | F3 |
2 / 3 | 264 x 3 / 2 | 396 Hz | G3 |
3 / 5 | 264 x 5 / 3 | 440 Hz | A4 |
4 / 5 | 264 x 5 / 4 | 330 Hz | E3 |
For most cultures, the "just intonation" tuning has been in use for thousands of years. This makes sense because we are using multiples of the original length (and then normalising them to the octave) to create notes.
The just-intonation tuning system works fine and sounds beautiful. However, it has only one drawback... you cannot transpose a song (ie you can only play songs in any key but "C"). When you play in another key (eg "D"), the tuning sounds wrong.
The "equal-tempered" tuning was developed to overcome this problem.
This is how it's worked out... "A4" (the note "A" at the fourth octave) is deemed to be at 440 Hz and, therefore, "A5" will be at 880 Hz. We then take logarithms (base 2) of A4 and A5 frequencies. Next, we mark in 11 equally spaced points between log(A4) and log(A5). On the logarithmic scale, this is the same as having 12 equally spaced notes per octave. We then apply arc-logarithms to those points and arrive the equal-tempered tuning.
Hertz | Octave=1 | Octave=2 | Octave=3 | Octave=4 | Octave=5 | Octave=6 | |
---|---|---|---|---|---|---|---|
0 | A | 55.000 | 110.000 | 220.000 | 440.000 | 880.000 | 1,760.000 |
1 | A#/Bb | 58.270 | 116.541 | 233.082 | 466.164 | 932.328 | 1,864.655 |
2 | B | 61.735 | 123.471 | 246.942 | 493.883 | 987.767 | 1,975.533 |
3 | C | 65.406 | 130.813 | 261.626 | 523.251 | 1,046.502 | 2,093.005 |
4 | C#/Db | 69.296 | 138.591 | 277.183 | 554.365 | 1,108.731 | 2,217.461 |
5 | D | 73.416 | 146.832 | 293.665 | 587.330 | 1,174.659 | 2,349.318 |
6 | D#/Eb | 77.782 | 155.563 | 311.127 | 622.254 | 1,244.508 | 2,489.016 |
7 | E | 82.407 | 164.814 | 329.628 | 659.255 | 1,318.510 | 2,637.020 |
8 | F | 87.307 | 174.614 | 349.228 | 698.456 | 1,396.913 | 2,793.826 |
9 | F#/Gb | 92.499 | 184.997 | 369.994 | 739.989 | 1,479.978 | 2,959.955 |
10 | G | 97.999 | 195.998 | 391.995 | 783.991 | 1,567.982 | 3,135.963 |
11 | G#/Ab | 103.826 | 207.652 | 415.305 | 830.609 | 1,661.219 | 3,322.438 |
12 | A | 110.000 | 220.000 | 440.000 | 880.000 | 1,760.000 | 3,520.000 |
Since this tuning is mathematically derived, a song will sound "correct" when played in a different key.
Special note - The decision to use A4 = 440 Hz, 12 notes per octave and naming them A to G was due to historical circumstances. Any other combination would also be valid. However, the equal-tempered tuning is now the de facto system.
A Scale is usually referenced to a "root" note (eg C). Typically, we use notes from the "equal-tempered" tuning comprising 12 notes per octave; C, C#, D, D#, E, F, F#, G, G#, A, A# and B.
For most of us, we will only probably need to know 2 scales: the Major scale; and, the Minor scale. Using a root of "C", the Major scale comprises C, D, E, F, G, A, B while the Minor scale comprises A, B, C, D, E ,F, G. Both of these scales have 7 notes per octave.
Name | C | Db | D | Eb | E | F | Gb | G | Ab | A | Bb | B | C |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Major | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 1 | |||||
Minor (natural) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 1 | |||||
Harmonic Minor | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 1 | |||||
Melodic Minor (Asc) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 1 | |||||
Melodic Minor (Desc) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 1 | |||||
Enigmatic | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 1 | |||||
Chromatic | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 1 |
Diminished | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 1 | ||||
Whole Tone | 1 | 2 | 3 | 4 | 5 | 6 | 1 | ||||||
Augmented | 1 | 2 | 3 | 4 | 5 | 6 | 1 | ||||||
Pentatonic Major | 1 | 2 | 3 | 4 | 5 | 1 | |||||||
Pentatonic Minor | 1 | 2 | 3 | 4 | 5 | 1 | |||||||
3 semitone | 1 | 2 | 3 | 4 | 1 | ||||||||
4 semitone | 1 | 2 | 3 | 1 | |||||||||
Bluesy R&R* | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 1 | |||||
Indian-ish* | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 1 |
As you can see, there are many scales and there is nothing to stop you from creating your own. After all, scales are just a series of notes. Different cultures have developed different scales because they find some series of notes more pleasing than others.
The Major scale will always have semitone jumps of 2 2 1 2 2 2 1 while a Minor scale has semitone jumps of 2 1 2 2 1 2 2. Semitone means the next note so one semitone up from "C" is "C#". In any major scale, the 6th note will be the equivalent minor scale. Similarly, in any minor scale, the 3rd note will be the equivalent major scale.
By a process called "transposition", we can workout the major or minor scale for every key (ie root). Transposition is basically starting from another key but still maintaining the separation of notes by following the same sequence of semitone jumps. In other words, we are shifting the scale to a different starting note. We can calculate the "Db Major" scale as being Db, Eb, F, Gb, Ab, Bb and C. The concurring minor for the "Db major" scale will be "Bb minor".
Key | C | C# | D | D# | E | F | F# | G | G# | A | A# | B | C |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
C | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 1 | |||||
D | 7 | 1 | 2 | 3 | 4 | 5 | 6 | ||||||
E | 6 | 7 | 1 | 2 | 3 | 4 | 5 | ||||||
F | 5 | 6 | 7 | 1 | 2 | 3 | 4 | 5 | |||||
G | 4 | 5 | 6 | 7 | 1 | 2 | 3 | 4 | |||||
A | 3 | 4 | 5 | 6 | 7 | 1 | 2 | ||||||
B | 2 | 3 | 4 | 5 | 6 | 7 | 1 |
I have not included the Major scales for Db, Eb, F#, Ab and Bb but that should be easy for you to work out.
This document will concentrate on one-note transforms. If you have a song in C Major, then converting every occurrance of F to F# will transform it into G Major. Similarly, converting every B to A#/Bb will give you F Major.
The table below highlights the one-note transforms for the major scale. These particular transforms only involve Key changes (not scale).
Key | C | C# | D | D# | E | F | F# | G | G# | A | A# | B | C |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
F | 5 | 6 | 7 | 1 | 2 | 3 | 4 | 5 | |||||
C | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 1 | |||||
G | 4 | 5 | 6 | 7 | 1 | 2 | 3 | 4 | |||||
D | 7 | 1 | 2 | 3 | 4 | 5 | 6 | ||||||
A | 3 | 4 | 5 | 6 | 7 | 1 | 2 | ||||||
E | 6 | 7 | 1 | 2 | 3 | 4 | 5 | ||||||
B | 2 | 3 | 4 | 5 | 6 | 7 | 1 |
When would you use a transform? Let's say you have a nice sequenced pattern running throughout a song. You have to accommodate a big key change but transposing it doesn't sound right. Then try transforming it instead. Transforming only a few notes will not detract too much from the original pattern and can sound more natural.
The table below shows the modal scales for the white notes on a piano.
MODES | C | D | E | F | G | A | B | C | Semitone Jumps | ||
---|---|---|---|---|---|---|---|---|---|---|---|
mC | Ionian | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 1 | 2 2 1 2 2 2 1 | |
mD | Dorian | 7 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 2 1 2 2 2 1 2 | |
mE | Phrygian | 6 | 7 | 1 | 2 | 3 | 4 | 5 | 6 | 1 2 2 2 1 2 2 | |
mF | Lydian | 5 | 6 | 7 | 1 | 2 | 3 | 4 | 5 | 2 2 2 1 2 2 1 | |
mG | Mixolydian | 4 | 5 | 6 | 7 | 1 | 2 | 3 | 4 | 2 2 1 2 2 1 2 | |
mA | Aeolian | 3 | 4 | 5 | 6 | 7 | 1 | 2 | 3 | 2 1 2 2 1 2 2 | |
mB | Locrian | 2 | 3 | 4 | 5 | 6 | 7 | 1 | 2 | 1 2 2 1 2 2 2 |
The table below shows the same modal scales with a "C" root:-
MODES | C | Db | D | Eb | E | F | Gb | G | Ab | A | Bb | B | C | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
mC | Ionian | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | |||||
mD | Dorian | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | |||||
mE | Phrygian | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | |||||
mF | Lydian | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | |||||
mG | Mixolydian | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | |||||
mA | Aeolian | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | |||||
mB | Locrian | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
What do they sound like? Well, Ionian mode is the same as the Major scale and Aeolian mode is the same as Minor scale. The rest sound strangely familiar but not quite right. For example, Dorian mode sounds like the band is playing in "D" but you're doing the melody in "C" instead.
If you have a song in C Major (ie Ionian), then converting every occurrance of B to A# (Bb) will give you Mixolydian. Similarly, converting every F to F# will give you Lydian.
Modes | C | Db | D | Eb | E | F | Gb | G | Ab | A | Bb | B | C | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
mF | Lydian | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 1 | |||||
mC | Ionian | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 1 | |||||
mG | Mixolydian | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 1 | |||||
mD | Dorian | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 1 | |||||
mA | Aeolian | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 1 | |||||
mE | Phrygian | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 1 | |||||
mB | Locrian | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 1 | |||||
mF^-1 | Lydian | 2 | 3 | 4 | 5 | 6 | 7 | 1 |
A Major pentatonic in "C" comprises C, D, E, G and A... which is a common scale used by most cultures in the world. This is achieved by removing the 4th and 7th notes.
What is interesting is that if we remove the 4th and 7th notes from the modal scales, we get quite remarkable results. The table below illustrates the modal pentatonics. This time I'm using the "black" notes on the piano.
Name | from | F# | G | G# | A | A# | B | C | C# | D | D# | E | F | F# | Semitone Jumps | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
pC | Ionian | 1 | 2 | 3 | - | 4 | 5 | - | 1 | 2 2 3 2 3 | ||||||
pD | Dorian | 1 | 2 | 3 | - | 4 | 5 | - | 1 | 2 1 4 2 3 | ||||||
pE | Phrygian | 1 | 2 | 3 | - | 4 | 5 | - | 1 | 1 2 4 1 4 | ||||||
pF | Lydian | 1 | 2 | 3 | - | 4 | 5 | - | 1 | 2 2 3 2 3 | ||||||
pG | Mixolydian | 1 | 2 | 3 | - | 4 | 5 | - | 1 | 2 2 3 2 3 | ||||||
pA | Aeolian | 1 | 2 | 3 | - | 4 | 5 | - | 1 | 2 1 4 1 4 | ||||||
pB | Locrian | 1 | 2 | 3 | - | 4 | 5 | - | 1 | 1 2 3 2 4 |
What do they sound like (my interpretation)?
"pF, pC & pG" are exactly the same and as they are all the Major pentatonic. The major pentatonic is the mainstay of most Folk music.
"pA" is used mainly in Japanese and Balinese music.
"pE" is a popular scale in music from India (also used in Bali).
"pB" sounds like a mix of arab and indian music (or somewhere from Asia minor). You'll have to judge this one yourself.
"pD" sounds very serious indeed. You'll have to judge this one yourself too.
Notes | E | F | F# | G | G# | A | A# | B | C | C# | D | D# | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
pF | Folk | 1 | 2 | 3 | 4 | 5 | |||||||
pC | Folk | 1 | 2 | 3 | 4 | 5 | |||||||
pG | Folk | 1 | 2 | 3 | 4 | 5 | |||||||
pD | AsiaMin | 1 | 2 | 3 | 4 | 5 | |||||||
pA | JapBali | 1 | 2 | 3 | 4 | 5 | |||||||
pE | Indian | 1 | 2 | 3 | 4 | 5 | |||||||
pB | Serious | 1 | 2 | 3 | 4 | 5 | |||||||
pF^-1 | Folk | 1 | 2 | 3 | 4 | 5 |
In addition to the above transforms, there are a further set of transforms for the modal-pentatonics. The table below is slightly different as it groups the possible transforms by each pentatonic. These particular transforms involve scale changes ans well as key changes.
Name | E | F | F# | G | G# | A | A# | B | C | C# | D | D# | ||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
pFCG | Folk | - | - | 1 | - | 2 | - | 3 | - | - | 4 | - | 5 | |
pFCG^+7 | 3 | 4 | 5 | 1 | 2 | |||||||||
pFCG^+5 | 4 | 5 | 1 | 2 | 3 | |||||||||
pB^+1 | 1 | 2 | 3 | 4 | 5 | |||||||||
pD^+7 | 3 | 4 | 5 | 1 | 2 | |||||||||
pB^+6 | 4 | 5 | 1 | 2 | 3 | |||||||||
pD | AsiaMin | - | - | 1 | - | 2 | 3 | - | - | - | 4 | - | 5 | |
pA^+7 | 3 | 4 | 5 | 1 | 2 | |||||||||
pFCG^+5 | 4 | 5 | 1 | 2 | 3 | |||||||||
pB^+6 | 4 | 5 | 1 | 2 | 3 | |||||||||
pA | JapBali | - | - | 1 | - | 2 | 3 | - | - | - | 4 | 5 | - | |
pE^+7 | 3 | 4 | 5 | 1 | 2 | |||||||||
pD^+5 | 4 | 5 | 1 | 2 | 3 | |||||||||
pE | Indian | - | - | 1 | 2 | - | 3 | - | - | - | 4 | 5 | - | |
pB^+7 | 3 | 4 | 5 | 1 | 2 | |||||||||
pA^+5 | 4 | 5 | 1 | 2 | 3 | |||||||||
pB | Serious | - | - | 1 | 2 | - | 3 | - | - | 4 | - | 5 | - | |
pD^+6 | 4 | 5 | 1 | 2 | 3 | |||||||||
pFCG^+6 | 3 | 4 | 5 | 1 | 2 | |||||||||
pE^+5 | 4 | 5 | 1 | 2 | 3 |
Well, there you have it... all the posible one-note transforms for the pentatonics. If wish to transform from one pentatonic to another but no direct one-note transform is available, then you will have to do it in two or more steps.
If you have a sequencer, try this modal pentatonic experiment:
- Write a short pattern using only the black notes... name it "pFCG".
- Using "pFCG", convert every "A#" into "A"... name it "pD".
- Using "pD", convert every "D#" into "D"... name it "pA".
- Using "pA", convert every "G#" into "G"... name it "pE".
- Using "pE", convert every "C#" into "C"... name it "pB".
- Using "pFCG" again, convert every "F#" into "E"... name it "pD^+7".
- Using "pD^+7", convert every "C#" into "B"... name it "pA^+2".
- Using "pFCG" again, convert every "F#" into "G"... name it "pB^+1".
- Using "pB^+1", convert every "A#" into "C"... name it "pE^+6".
- Then delete "pFCG".
You now have 7 pentatonic patterns: 2 AsiaMins, 2 JapBalis, 2 Indians and 1 Serious. Arrange the patterns in any order you like... you've now made one seriously ethnic-sounding new tune.
NAME | C | - | D | - | E | F | - | G | - | A | - | B | C | ALTERNATIVE |
Chromatic | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 1 | - |
Spanish 8 Tone | 1 | 2 | - | 3 | 4 | 5 | 6 | - | 7 | - | 8 | - | 1 | - |
Flamenco | 1 | 2 | - | 3 | 4 | 5 | - | 6 | 7 | - | 8 | - | 1 | - |
Symmetrical | 1 | 2 | - | 3 | 4 | - | 5 | 6 | - | 7 | 8 | - | 1 | Inverted Diminished |
Diminished | 1 | - | 2 | 3 | - | 4 | 5 | - | 6 | 7 | - | 8 | 1 | - |
Whole Tone | 1 | - | 2 | - | 3 | - | 4 | - | 5 | - | 6 | - | 1 | - |
Augmented | 1 | - | - | 2 | 3 | - | - | 4 | 5 | - | - | 6 | 1 | - |
3 semitone | 1 | - | - | 2 | - | - | 3 | - | - | 4 | - | - | 1 | - |
4 semitone | 1 | - | - | - | 2 | - | - | - | 3 | - | - | - | 1 | - |
NAME | C | - | D | - | E | F | - | G | - | A | - | B | C | ALTERNATIVE |
Ultra Locrian | 1 | 2 | - | 3 | 4 | - | 5 | - | 6 | 7 | - | - | 1 | - |
Super Locrian | 1 | 2 | - | 3 | 4 | - | 5 | - | 6 | - | 7 | - | 1 | Ravel |
Indian-ish* | 1 | 2 | - | 3 | 4 | - | - | 5 | 6 | - | 7 | - | 1 | - |
Locrian | 1 | 2 | - | 3 | - | 4 | 5 | - | 6 | - | 7 | - | 1 | - |
Phrygian | 1 | 2 | - | 3 | - | 4 | - | 5 | 6 | - | 7 | - | 1 | - |
Neapolitan Minor | 1 | 2 | - | 3 | - | 4 | - | 5 | 6 | - | - | 7 | 1 | - |
Javanese | 1 | 2 | - | 3 | - | 4 | - | 5 | - | 6 | 7 | - | 1 | - |
Neapolitan Major | 1 | 2 | - | 3 | - | 4 | - | 5 | - | 6 | - | 7 | 1 | - |
Todi (Indian) | 1 | 2 | - | 3 | - | - | 4 | 5 | 6 | - | - | 7 | 1 | - |
Persian | 1 | 2 | - | - | 3 | 4 | 5 | - | 6 | - | - | 7 | 1 | - |
Oriental | 1 | 2 | - | - | 3 | 4 | 5 | - | - | 6 | 7 | - | 1 | - |
Maj.Phrygian (Dom) | 1 | 2 | - | - | 3 | 4 | - | 5 | 6 | - | 7 | - | 1 | Spanish/ Jewish |
Double Harmonic | 1 | 2 | - | - | 3 | 4 | - | 5 | 6 | - | - | 7 | 1 | Gypsy/ Byzantine/ Charhargah |
Marva (Indian) | 1 | 2 | - | - | 3 | - | 4 | 5 | - | 6 | - | 7 | 1 | - |
Enigmatic | 1 | 2 | - | - | 3 | - | 4 | - | 5 | - | 6 | 7 | 1 | - |
NAME | C | - | D | - | E | F | - | G | - | A | - | B | C | ALTERNATIVE |
Locrian Natural 2nd | 1 | - | 2 | 3 | - | 4 | 5 | - | 6 | - | 7 | - | 1 | - |
Minor (natural) | 1 | - | 2 | 3 | - | 4 | - | 5 | 6 | - | 7 | - | 1 | Aeolian/ Algerian (oct2) |
Harmonic Minor | 1 | - | 2 | 3 | - | 4 | - | 5 | 6 | - | - | 7 | 1 | Mohammedan |
Dorian | 1 | - | 2 | 3 | - | 4 | - | 5 | - | 6 | 7 | - | 1 | - |
Melodic Minor (Asc) | 1 | - | 2 | 3 | - | 4 | - | 5 | - | 6 | - | 7 | 1 | Hawaiian |
Hungarian Gypsy | 1 | - | 2 | 3 | - | - | 4 | 5 | 6 | - | 7 | - | 1 | - |
Hungarian Minor | 1 | - | 2 | 3 | - | - | 4 | 5 | 6 | - | - | 7 | 1 | Algerian (oct1) |
Romanian | 1 | - | 2 | 3 | - | - | 4 | 5 | - | 6 | 7 | - | 1 | - |
NAME | C | - | D | - | E | F | - | G | - | A | - | B | C | ALTERNATIVE |
Maj. Locrian | 1 | - | 2 | - | 3 | 4 | 5 | - | 6 | - | 7 | - | 1 | Arabian |
Hindu | 1 | - | 2 | - | 3 | 4 | - | 5 | 6 | - | 7 | - | 1 | - |
Ethiopian 1 | 1 | - | 2 | - | 3 | 4 | - | 5 | 6 | - | - | 7 | 1 | - |
Mixolydian | 1 | - | 2 | - | 3 | 4 | - | 5 | - | 6 | 7 | - | 1 | - |
Major | 1 | - | 2 | - | 3 | 4 | - | 5 | - | 6 | - | 7 | 1 | Ionian |
Mixolydian Aug. | 1 | - | 2 | - | 3 | 4 | - | - | 5 | 6 | 7 | - | 1 | - |
Harmonic Major | 1 | - | 2 | - | 3 | 4 | - | - | 5 | 6 | - | 7 | 1 | - |
Lydian Min. | 1 | - | 2 | - | 3 | - | 4 | 5 | 6 | - | 7 | - | 1 | - |
Lydian Dominant | 1 | - | 2 | - | 3 | - | 4 | 5 | - | 6 | 7 | - | 1 | Overtone |
Lydian | 1 | - | 2 | - | 3 | - | 4 | 5 | - | 6 | - | 7 | 1 | - |
Lydian Aug. | 1 | - | 2 | - | 3 | - | 4 | - | 5 | 6 | 7 | - | 1 | - |
Leading Whole Tone | 1 | - | 2 | - | 3 | - | 4 | - | 5 | - | 6 | 7 | 1 | - |
Bluesy R&R* | 1 | - | - | 2 | 3 | 4 | - | 5 | - | 6 | 7 | - | 1 | - |
Hungarian Major | 1 | - | - | 2 | 3 | - | 4 | 5 | - | 6 | 7 | - | 1 | Lydian sharp2nd |
NAME | C | - | D | - | E | F | - | G | - | A | - | B | C | ALTERNATIVE |
"pB" | 1 | 2 | - | 3 | - | - | 4 | - | 5 | - | - | - | 1 | - |
Balinese 1 | 1 | 2 | - | 3 | - | - | - | 4 | 5 | - | - | - | 1 | "pE" |
Pelog (Balinese) | 1 | 2 | - | 3 | - | - | - | 4 | - | - | 5 | - | 1 | - |
Iwato (Japanese) | 1 | 2 | - | - | - | 3 | 4 | - | - | - | 5 | - | 1 | - |
Japanese 1 | 1 | 2 | - | - | - | 3 | - | 4 | 5 | - | - | - | 1 | Kumoi |
Hirajoshi (Japanese) | 1 | - | 2 | 3 | - | - | - | 4 | 5 | - | - | - | 1 | "pA" |
"pD" | 1 | - | 2 | 3 | - | - | - | 4 | - | 5 | - | - | 1 | - |
Pentatonic Major | 1 | - | 2 | - | 3 | - | - | 4 | - | 5 | - | - | 1 | Chinese 1/ Mongolian/ "pFCG" |
Egyptian | 1 | - | 2 | - | - | 3 | - | 4 | - | - | 5 | - | 1 | - |
Pentatonic Minor | 1 | - | - | 2 | - | 3 | - | 4 | - | - | 5 | - | 1 | - |
Chinese 2 | 1 | - | - | - | 2 | - | 3 | 4 | - | - | - | 5 | 1 | - |
The classical notation system is well suited for instruments which are "pre-fingered" for the major scale (eg keyboards) but, for "linear" instruments (eg guitar, violin), it requires more familiarisation.
With classical notation, problems arises because the Staff represents notes by their "letter". This means that every note in the scale should have a different letter. For example, the scale of F major is F, G, A, Bb, C, D, E. You should not use A# instead of Bb, otherwise the "A#" will have to share the same line or space as "A" (and the "B" line or space will not be used at all). This will cause problems with the Key-Signature.
The table below gives Major and Minor Scales which conform to classical notation. Note - as you count the notes in the scale, you are also counting "letters" (ie In E major, the 6th note is "C#"... so counting 1, 2, 3, 4, 5, 6 is counting E, F, G, A, B, C... and "C" is letter no.6 from "E").
MAJOR SCALE R - 2 - 3 4 - 5 - 6 - 7 C maj.: C - D - E F - G - A - B Db maj.: Db - Eb - F Gb - Ab - Bb - C D maj.: D - E - F# G - A - B - C# Eb maj.: Eb - F - G Ab - Bb - C - D E maj.: E - F# - G# A - B - C# - D# F maj.: F - G - A Bb - C - D - E F# maj.: F# - G# - A# B - C# - D# - (E#) G maj.: G - A - B C - D - E - F# Ab maj.: Ab - Bb - C Db - Eb - F - G A maj.: A - B - C# D - E - F# - G# Bb maj.: Bb - C - D Eb - F - G - A B maj.: B - C# - D# E - F# - G# - A# MINOR SCALE R - 2 b3 - 4 - 5 b6 - b7 - A min.: A - B C - D - E F - G - Bb min.: Bb - Cb Db - Eb - F Gb - Ab - B min.: B - C# D - E - F# G - A - C min.: C - D Eb - F - G Ab - Bb - C# min.: C# - D# E - F# - G# A - B - D min.: D - E F - G - A Bb - C - Eb min.: Eb - F Gb - Ab - Bb (Cb) - Db - E min.: E - F# G - A - B C - D - F min.: F - G Ab - Bb - C Db - Eb - F# min.: F# - G# A - B - C# D - E - G min.: G - A Bb - C - D Eb - F - G# min.: G# - A# B - C# - D# E - F# -Note - F# major contains "E#" (which is "F") and that Eb minor contains "Cb" (which is "B"). This is a small discrepancy in the system.
The table below illustrates the "letter" problems of using the non-conforming keys. Notes in brackets () indicate small discrepancies. Notes in square brackets [] indicate serious problems.
C# maj.: C# D# (E#) F# G# A# (B#) D# maj.: D# (E#) [F##] G# A# (B#) [C##] Gb maj.: Gb Ab Bb (Cb) Db Eb F G# maj.: G# A# (B#) C# D# (E#) [F##] A# maj.: A# (B#) [C##] D# (E#) [F##] [G##] Ab min.: Ab Bb (Cb) Db Eb (Fb) Gb A# min.: A# (B#) C# D# (E#) F# G# Db min.: Db Eb (Fb) Gb Ab [Bbb] (Cb) D# min.: D# (E#) F# G# A# B C# Gb min.: Gb Ab [Bbb] (Cb) Db [Ebb] (Fb)These problems do not exist physically, scientifically or mathematically. The problems arise from the system itself. However, the classical notation system is the de facto "language" of music. Plus the system is fairly compact and concise. So perhaps this extra "learning" is not too bad.
The table below shows the Scales of the Major and Minor Keys which conform to classical notation. This may be easier to visualise and remember.
Major only Db Ab both Major & Minor C D Eb E F F# G A Bb B C Minor only C# G#
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