Guitar Scales
I found it hard to find a definition (let alone an explanation) of music scales for guitars. This is what I figured out. No need for the circle of fifths.
A scale is a set of notes. Songs composed with only these notes usually sound pleasant to humans. Including a note that is not in the scale will usually sound discordant, i.e., it will not fit into the tune. However, that misfitting note would sound fine in a song with a different scale.
The first note of the scale is the key, also known as the root note. The scale in the key of C Major will start with the C note. It ends with a C note that is one octave higher. This scale has 7 notes, i.e., it skips 5 of the 12 notes.
Scales can start with a sharp or flat note. The D# Major scale starts with the D# note, and ends with the D# note that is an octave higher.
The notes included in a major scale are determined as follows. Starting with the root note, we would include the 2nd, 4th, 5th, 7th, 9th, 11th and 12th note. The 12th note would also be the root note, but one octave higher. The scale can be extended to higher (and lower) octaves. This sequence applies to major scales of all notes.
The C Major scale is popular. It starts with C note and comprises the notes D, E, F, G, A, B and C. This scale does not have any sharp or flat notes. On a piano, this scale uses only white keys. The scales in other keys have sharps.
The Minor scale is conceptually similar, and includes the 2nd, 3rd, 5th, 7th, 8th, 10th and 12th notes.
There are many more scales, each has a different inclusion sequence. I remember them as follows. The numbers show how many frets to jump over to get the next note in the scale.
· Major: 2-2-1-2-2-2-1
· Minor: 2-1-2-2-1-2-2
· Pentatonic: 2-2-3-2-3
Most untrained human ears cannot identify an audible note. The frequency of a note could be off by 10% or more and we would not notice the difference. However, we are much more sensitive to scales. We would notice if one note was off relative to others. But we would not notice if all the notes in a tune were off by the same fraction, say 10% higher. Effectively, the tune would be in a different key, and it would be recognizable. Most songs are written to stay in one scale, but some songs switch back and forth between scales.
It would be great if someone built a guitar that highlighted the frets for the scale that was being played. If the song being played was in C Major, then all the fret positions for C, D, E, F, G, A, and B would light up. It would be great for beginners. The player could configure the desired scale, or the guitar could deduce the scale automagically.
Notes come before Scales, but everyone knows about notes, and this page is about scales.
A Note is a tone with a specific frequency. The range of audible sound is split into octaves. The starting frequency of an octave is double that of the preceding octave.
Each octave is split into 12 notes. A scale with 12 notes is called a Chromatic scale, though it has nothing to do with color. The 12 notes are split into 7 main "notes" plus 5 "sharp notes". The sharp notes are denoted by the # symbol. The 12 notes in sequence are C, C#, D, D#, E, F, F#, G, G#, A, A#, and B. I don't know why the scale starts with C, but the leftmost key on a piano is a C. There is no sharp note between E & F, or B & C, so there is no black key in a piano between these two pairs. E# is the same as F. I also could not find why each octave is split into 12 notes. I hear that some cultures have split it into 17, 19, 22 or 24 notes. It is whatever one gets used to.
The A note in the 0th octave is called A0. A0 is 27.5 Hz, A1 is 55Hz, A2 is 110Hz, A3 is 220Hz, A4 is 440Hz, etc. Note how the frequency of the A note is double that of the note in the previous octave. The human ear hears these notes as being similar. It has to do with the conical cross-section of the cochlea and the positioning of sensory cells in there.
The frequencies of all other notes in an octave are in a geometric progression. The frequency of each note is a fixed multiple of the preceding note. The fixed multiple is the 12th root of 2, or 1.05946309436. The note after A is A#, then B, then C, C#, … In the second octave, A2 is 110Hz, so A#2 will be 110x1.059, or 116.54Hz, and B2 will be 116.54x1.059, or 123.47Hz.
I picked the A note because it has nice round numbers for the frequency in each octave. However, there are notes lower than A0. The note G#0/Ab0 comes before A0, and its frequency is 27.5/1.0594 or 25.96. Continuing lower, we get G0 at 24.5Hz. Notes start with C0, at 16.35Hz, which is close to the limit of human hearing. I don’t know who picked these specific frequencies or why. Music would probably sound just fine with other frequencies as long as the geometric progression was maintained.
The note frequencies for all octaves are shown below. Note how the frequency for a note doubles in each successive octave, and the frequency of any note is a multiple of the previous note’s frequency and 1.059.
|
Note |
Octave |
||||||||||
|
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
|
|
C |
16.351598 |
32.703196 |
65.406391 |
130.81278 |
261.62557 |
523.25113 |
1046.5023 |
2093.0045 |
4186.009 |
8372.0181 |
16744.036 |
|
C# |
17.323914 |
34.647829 |
69.295658 |
138.59132 |
277.18263 |
554.36526 |
1108.7305 |
2217.461 |
4434.9221 |
8869.8442 |
17739.688 |
|
D |
18.354048 |
36.708096 |
73.416192 |
146.83238 |
293.66477 |
587.32954 |
1174.6591 |
2349.3181 |
4698.6363 |
9397.2726 |
18794.545 |
|
D# |
19.445436 |
38.890873 |
77.781746 |
155.56349 |
311.12698 |
622.25397 |
1244.5079 |
2489.0159 |
4978.0317 |
9956.0635 |
19912.127 |
|
E |
20.601722 |
41.203445 |
82.406889 |
164.81378 |
329.62756 |
659.25511 |
1318.5102 |
2637.0205 |
5274.0409 |
10548.082 |
21096.164 |
|
F |
21.826764 |
43.653529 |
87.307058 |
174.61412 |
349.22823 |
698.45646 |
1396.9129 |
2793.8259 |
5587.6517 |
11175.303 |
22350.607 |
|
F# |
23.124651 |
46.249303 |
92.498606 |
184.99721 |
369.99442 |
739.98885 |
1479.9777 |
2959.9554 |
5919.9108 |
11839.822 |
23679.643 |
|
G |
24.499715 |
48.999429 |
97.998859 |
195.99772 |
391.99544 |
783.99087 |
1567.9817 |
3135.9635 |
6271.927 |
12543.854 |
25087.708 |
|
G# |
25.956544 |
51.913087 |
103.82617 |
207.65235 |
415.3047 |
830.6094 |
1661.2188 |
3322.4376 |
6644.8752 |
13289.75 |
26579.501 |
|
A |
27.5 |
55 |
110 |
220 |
440 |
880 |
1760 |
3520 |
7040 |
14080 |
28160 |
|
A# |
29.135235 |
58.27047 |
116.54094 |
233.08188 |
466.16376 |
932.32752 |
1864.655 |
3729.3101 |
7458.6202 |
14917.24 |
29834.481 |
|
B |
30.867706 |
61.735413 |
123.47083 |
246.94165 |
493.8833 |
987.7666 |
1975.5332 |
3951.0664 |
7902.1328 |
15804.266 |
31608.531 |
All in fun
Oct 2023