Music analysis - Structures
Music systems
In general, an octave can be divided into more than 12 divisions, ie the so-called system order - HarmonicOrder. We consider evenly tempered tuning and the music creates a combinatorial (discrete) HarmonicSystem system - in the spirit of Modern Harmony by Karel Janeček (1903-1974). For order> 12 these are so-called microtonal systems, but we will pay minimal attention to them. Although some of their properties are similar to the 12-tone system and they can therefore be defined in general, however, the primary goal is to achieve satisfactory results first for order 12.
Similarly, it is also possible to access the rhythm component - RhythmicSystem is defined by the order RhythmicOrder, which represents the elementary rhythmic division of the beat - ie the timing layer of Leoš Janáček (1854-1928). The time location of the tone / pause in the measure is then determined by BitRange - bit slice (in the bit representation of the measure). A similar concept of division is defined in the MIDI interface, but here the number of "division" (division) is introduced, which indicates the number of "ticks" (bits) per quarter (not a clock). The order of the system is generally any number, but as it increases, the number of structures grows exponentially. Even so, among the rhythms of well-known compositions (apart from the simplest ones) there are often systems with higher orders than is the order (k) of the harmonic system (eg in the music of Antonín Dvořák we commonly meet in music notation with a beat division into 48 divisions or more). In addition, the number of combinations of different structures at rhythm (due to pauses) is proportional to 3k (not 2k as is the case with harmonic structures). This makes the rhythmic system - due to the algorithmic processing - much more complicated and demanding. In MIDI, the rhythm resolution is even more refined, which allows you to capture even small rhythmic nuances.
The musical composition is usually built of various structures - harmonic, rhythmic, melodic.
The harmonic system is determined by its order, ie the number of tones in an octave. The octave is distributed evenly (tempered tuning). Similarly, the rhythmic system is also determined by the order, ie the number of pieces into which the bar is divided (Janáček's timing layer).
Harmonic systemA regular k-tone system divides the octave (ie a 2: 1 resonance ratio on a logarithmic scale) to k straight parts. The order k is limited to such numbers (eg 12,19, ..), which also allow other resonances (eg 3: 2). The octave is distributed evenly (tempered tuning). The order of the system is generally any number, but numbers not exceeding the order of tens are usually used, because as the order increases, the number of structures grows exponentially.
The compositions are created in a regular (temperate) system (in the sense of Karel Janeček's Modern Harmony) - ie including microtonal systems (with an octave division other than 12 divisions). => Unresolved… (works only for 12-tone system)
Rhythmic systemThe elementary time period in a measure is called a "tick". A regular system of k-tics divides the beat on to the same parts. The order k is usually limited to numbers that are multiples of 2 or 3 (2 ^ a * 3 ^ b), which allows students to better distinguish time relationships.
The harmonic and rhythmic system is freely complemented by the melodic MelodicSystem (This concept is not yet fully resolved).
Metric
The meter of the song [MusicalMetric) is determined by two numbers Beat (b) and Base (s), while Base (s) indicates the exponent in the power of 2. We call the value 2s Ground (g). E.g. for Metrum 3/4, Beat = 3, Base = 2, Ground = 4. The musical naming of notes according to Ground (g) is determined by MusicalDenominator.
The whole measure has 4 quarter times and its division is therefore 4 * D (where D is the division of quarter times, division). A measure determined by a meter other than 4/4 then has a division proportional to this fraction, ie: C = b / g * 4 * D. Rhythmic order does not necessarily have to be equal to this division, we usually choose (for the reasons stated above) its some integer divisor to C (this may lose some minor nuances, but the system is simpler). The midi duration of a tone of length d within a system of order k is then C * d / k.
Musical structures
Summary of all musical (harmonic, rhythmic and melodic) structures that are available before composing we call it music material. Individual musical styles (styles) usually have a stable musical material - ie a set of chords, rhythmic patterns or. and melodic procedures.
Tone groupings are generally horizontal, vertical or combined. In the first case, we use to save HarmonicStructure, in the second RhythmicStructure or RhythmicShape and in the last MelodicStructure. The difference between RhythmicStructure and RhythmicShape is that the first (ternary) takes into account pauses and the second (binary) does not. The binary / ternary resolution determines RhythmicDegree. The structures generally have some properties in common. The core for binary (harmonic or shape) structures are BinaryStructure and BinarySchema, the core for more complex (rhythmic and melodic) structures are FiguralStructure and FiguralSchema.
General structures
Binary structures
Figural structures
Musical modalities
HarmonicModality is a selection of system tones. The level indicates how many tones the modality has (pentatonic: level = 5). HarmonicInterval RhythmicModality TonalityGenus
It is similar for the rhythm, with the fact that "1" in the modality means that the given tick (eighth,…) will be followed by the wording, "0", that there will be no (Janáček's timing layer ...).
Harmonic modalityThe natural (7-tone) modality (CDEFGAB) can be written as a binary number [010101101011], i.e., a decimal number 1387. This modality has 12 transpositions, eg C # DEF # GAH (110101101010) and 7-rotations, eg DEFGABC. The level indicates how many tones the modality has (eg heptatonics: level = 7).
In the case of the rhythm "1" in the modality, it means that the word will start on the given tick (eighth,…), "0" that it will not be (timing layer of Leoš Janáček). Rhythm systems, including pauses, require the use of ternary numbers.
The melodic modality limits the list of tones, eg the melody cfdfffcc has the modality cdf. Then, when entering a given melodic line, the modality is selected first and then a figure from it (necessary to limit the length of the figure).
Musical tonalities
Structures
It is similar for the rhythm, with the fact that "1" means that the given tick (eighth,…) will be followed by the wording, "0", that there will be no (Janáček's timing layer ...).
Structure generators
Harmonic variety
The harmonic variety consists of all such chords (of material) that exist in a given modality and meet the given qualifier. E.g. constraint with harmonic minor modality and qualifier of consonant triads the whole harmonic material is reduced to a few chords (Ami, Dmi, E, C5 +,…). Based on these chords, harmonic functions are determined.
The harmonic current (subtext) is determined by the rhythmic and harmonic course and the individual melodic lines by their rhythmic, harmonious and melodic course. Harmonious course (inspired by the principles of Karel Risinger's functional relationships) consists of cycles of continuity, impulse, variability and potential, rhythmic course of cycles of mobility and variability, melodic course from cycles of wording and dynamics.
The harmonic qualifier is used to select from all possible structures (modalities or chords) only some (eg pentatonics or consonant triads). The harmonic variety consists of all such chords of material that exist in a given modality and satisfy a given qualifier. E.g. by constraint with harmonic minor modality and qualifier of consonant triads, the whole harmonic material is reduced to a few chords (Ami, Dmi, E, C5 +,…) => Unresolved… (need to figure out the qualifiers - ie conditions for chords, etc.) The harmonic variety is all chords that will be available in a given modality for a given qualifier. Ie. when I limit the harmonic minor modality by the qualifier of consonant triads, for example, Ami, Dmi, E, C5 +,… (some of these chords form harmonic functions). The whole complex forms a key (some modalities have 2 equal tonics… !? => Unresolved
The rhythm variety consists of all such rhythmic patterns (from the material) that exist in the given modality and meet the given qualifier. In a certain part of the song, the tones can only start at certain times - eg only on 0., 1., 3., 4. and 6th eighth (numbered from zero) - ie syncope + two quarter notes.
The rhythm qualifier selects only some of all possible rhythm patterns (for example, only 2 beats for a beat, or just the simple ones - dotted rhythms…).
I use the rhythmic simple variety for the rhythm of the harmonic current and for the rhythm (which has no duration), ie. where no pauses are needed.
The rhythm variety includes pauses. (This is mainly different due to the generation speed - where there are no pauses, they would unnecessarily delay - there are many more rhythms with pauses ...). Similarly, the rhythmic variety can be limited by the values of mobility, tension…, etc.
List of selected melodic patterns ...
Music material
The sum of all used structures (in composition, musical style, etc.) is called "material". Used to store these lists: HarmonicMaterial, RhythmicMaterial a MelodicMaterial. Summary of all musical (harmonic, rhythmic and melodic) structures, which are available before composing begins is called musical material. Individual musical styles usually have stable musical material - ie a set of chords, rhythmic patterns or and melodic procedures.
StructuralVarietyFactory is used to generate new material, the enumeration of options is determined by the StructuralVarietyType ( Instances, BinaryClasses, BinarySubstructuresOfModality, FiguralSubstructuresOfModality, MelodicStructuresOfModality, RhythmicModalityClasses, RhythmicMetricClasses, Classes) Pro podporu výběru rytmických vzorů byl zaveden RhythmicContainer.
Properties of structures
Structures have certain properties - eg harmonic structures consonance / dissonance, rhythmic structures mobility and tension. The continuity of harmonic structures is evaluated by the characteristics of continuity and impulse. Used to store these properties HarmonicBehavior, RhythmicBehavior a BindingBehavior.
Chord
Harmony - the actual distribution of tones is contained in the HarmonicCluster class. The area (narrow, medium, wide) is determined by HarmonicClusterExtent (TightExtent, MiddleExtent, WideExtent).