The Alterations

The harmonic connections between the various scales are important regarding both the construction of a song, and the melodic development during the improvisation.
You also need to remember that every scale is conceived through the construction of the scales, using the whole and half-step rule. It's therefore possible to establish a scale that has the typical alteration for that scale, at the beginning of the stave. From here come the various armatures of key that are mostly identified with a major scale, or its relative minor.
For example, if we wanted to write using the scale of D major, we need to identify this scale by writing the typical alterations immediately after the key of that scale, and therefore F# and C#. Attention: this system is subject to very precise rules.
- The armature in key identifies a scale, but doesn't obligate the use of only that scale. Any alterations and momentary scale changes are identified by their appropriate symbols. When the scale change is fixed, the new scale is identified in key.
- The position of the alterations in key is universal, in that each scale always has the alteration symbols in the same place, as we will see below.
There are two types of alterations: momentary and permanent.
The momentary alteration appears on a note in a bar, altering this note for the entire duration of the bar.
There are many examples that can be found in one or more musical measures. We will extract the rules from these examples, which are those normally used during the reading and writing of a musical piece on a stave.
1) On the stave, the alteration symbol is found in front of the note.
2) The alteration symbol is placed behind the note when it is part of a written text.
3) A momentary alteration has value from the point of the bar that its applied to the end of the bar.
In the example below, the A in the first movement is altered with the sharp. The alteration influences all the A notes (in whatever octave it is found) and continues to the end of the bar, without needing to be written again. Then also the A that is found in the fourth movement must be considered an A#.

In the case where the last A is not played as A#, you need to interrupt the value of the alteration using the natural symbol. This is used for eliminating an alteration (and therefore lowered by a half-step) from an altered note. In the example, the last A of the bar isn't influencee by the # placed on the A of the first movement due to the presence of the natural symbol.


4) Using alterations in key, the notes with the alteration symbols (that must be written between the key and the indication of time) are to be read as altered notes for the duration of the song or until there is another change in scale.
In the example below the altered notes in key are F#, C#, G# and D#, and they must be read (and played) as such, even if they are written in the score without the symbol before the note.


The natural sign, as written above, cancels any previous alterations. This rule is also obviously true if the alterations are in key. In the following example, the first C is read as C# (subject to the influence of the alteration in key), while the second is natural because it has the natural symbol before it. Also the following two C's are influenced by the natural, while the last one has the # symbol before it, and is read as C#.

The relationships between the scales

To completely understand the relationship betweem the various scales, you can use the system that we will analyze now. To do this we will use the tables of the scales.
Starting with the basic scale of C major, which is without altered notes, we find its V° (G note). Analyzing this scale we find an altered note, the F#. The difference between the scale of C major and G major is therefore only one note, the F#. The two scales are called near scales.
The V° of the G scale is the D note, whose major scale contains two alterations (the F# and the C#). The difference between the two scales is the C note, which becomes C# in the scale of D.
On the scale of D the V° is the A, which has the F#, C# and G# altered notes.
The G and D scales are therefore considered near scales, as well as the D and A scales, but the C and D and the A and G scales are not.
Continuing with the analysis of the near scales of E, B, F# and C# in succession. When looking at the scales in succession, starting with the C and always increasing a fifth, it's easy to see that an alteration is added to each of those already present. This can be seen in the chart and is more commonly called the circle of fifths. As you can see in the graph, the alterations in key are always in increasing order.
In the chart, continuing in a clockwise direction, the alterations are sharp. Moving in a counter-clockwise direction, the alterations are flat. This is similar to the previous system, except that it is developed for ascending fourths. Let's verify the construction.
Always starting with the C major scale, this time we raise to the IV°, where we find the F. Looking at the scale of F major, we find an altered note, the Bb, and we can see that the difference between the C and the F scales is only one note (the Bb). Therefore the scales of C and F are considered near scales.
The IV° of the F major scale is the Bb note. From this note we will build the new scale (Bb major), which differentiates itself from the scale of F by the addition of one new note, the Eb. Using the fourths system of construction, you can easily see that the IV° degree of the scale, besided being the root of the new scale, is also the different note between the two scales.
In succession the scales are these: C, F, Bb, Eb, Ab, Db, Bb. The C# and Db scales are consider inharmonic, in that they have the same notes, even if they have different names; the same is also true for the scales of F# and Gb.

In the armature in key you can make reference to the chart of the circle of Fifths, always remembering to maintain the same position of the alterations depending on the scale that you intend to use.
Using the table of the minor scale, and remembering that every major scale has its relative minor, we can also build the circle of fifths for the minor scale. The starting scale is the relative minor of C, A minor, composed of all natural notes. Raising a fifth above we find the E note, which will be the root of the near minor scale. We find an alteration in this scale, the F#, remembering that the scale of E minor is the relative minor of G.
From the scale of E minor, climbing to the V°, we find the B, root of the new minor scale that has two alterations (F# and C#). Making reference to the chart of the minor circle of the Fifths, continuing in a clockwise direction for the progression of the sharps.
In a counterclockwise direction, we find the progression of the flats, based on the construction of fourths. From A minor we go up to D minor, then to G minor, etc.
Also in this case we will have inharmonic scales.