The elements of ES
How do we create a sound scale?
Notes (in modular numbering) and sound intervals (iS) are the basic sound elements we need to create a sound scale (ES). All scales that we generate from the collection of chromatic notes based on the TET-12 tuning system must have a scalar register of iS (12).
To generate a scalar structure (eE) we have to choose a succession of iS. This succession defines the quantity of notes in the scale. For example, if we choose a succession of 7 iS, it means that we will obtain a collection of 7 notes. To know what specific notes the scale has, we define its transposition by choosing what we want to be the first note of the scale, and we apply the scalar structure to obtain the rest of the notes.
The notes of the scale receive a new numbering based on their scalar structure, and are renamed degrees (Nº), or degree notes.
The iS of the scalar structure also receive a new numbering and are called sound intervals of degree (iSº).
The vertical distance(Harmonic interval, iA) between two degrees is also renumbered and renamed Harmonic interval of degree (iAº).
Use the Nuzic app to practice changing the numbering of the different basic elements (Note, iS, iA) to scalar numbering (Nº, iSº, iAº).
The more abstract the definition of a musical element, the more possibilities we have to choose from. As we concretize a musical element, we lose potentialities and gain precision on the musical plane.
The degree (Nº) has 4 levels of abstraction. Let’s look at an example:
Level 1 | Level 2 | Level 3 |
Level 4 | |
grade (Nº) | 4 | 4 | 4 | 4 |
scale | diatonic | diatonic | diatonic | |
Scalar register | 3 | 3 | ||
transposition | Nº (0) = N (2) |
Therefore, the degree Nº (4) from which we start ends up materializing as the degree Nº (4) of the diatonic scale, in the Scalar register rE (3), and in a transposition of Nº (0) = N (2), which is equivalent to the Note in modular numbering N (9r3).
Notice how the iSº, as well as the degrees (Nº), are also elements of a high degree of abstraction since they not only vary according to their direction (ascending/descending), or the scale or scalar structure with which we are composing, but also vary within the same scale.
For example, the iSº between Nº (0) and Nº (1) is equivalent to an iS (2). On the other hand, the iSº between Nº (2) and Nº (3) is equivalent to an iS (1). Therefore, it is important to know in depth the scalar structure and the equivalences of the iSº with the iS, in order to be able to create successions of Nº and iSº.
Finally, the same abstraction as in the iSº occurs with the iAº. Considering that the iAº are vertical scalar distances between two simultaneous Nº, they are very useful for the creation of chords in scalar harmony.