Integer Name- Pitch Class Content 12/0 B#,C, Dbb 1 C#, Db 2 C‹, D, Ebb 3 D#, Eb 4 D‹, E, Fb 5 E#, F, Gbb 6 F#, Gb 7 F‹, G, Abb 8 G#, Ab 9 G‹, A, Bbb 10 A#, Bb 11 A‹, B, Cb
Twelve is called the modulus/octave, and we will frequently use arithmetic modulo 12, for which mod 12 is an abbreviation. In a mod 12 system, –12 = 0 = 12 = 24, and so on. Similarly, –13, –1, 23, and 35 are all equivalent to 11 (and to each other) because they are related to 11 (and to each other) by adding or subtracting 12. It is easiest to understand these mod 12 relationships by envisioning a circular face like clock
Scale(raaga) =A scale in music is a set of musical notes arranged in ascending or descending order by pitch. It's essentially a ladder of musical notes that provides the foundation for melodies, harmonies, and chords in a piece of music. Different scales have distinct arrangements of notes, resulting in unique sounds and characteristics.It is usually in diatonic(heptachodral scale) contains 7 music notes
Diatonic scale degrees are the numbered names given to each note within a diatonic scale. There are seven diatonic scale degrees in total, each with a specific function and name. These names are used to describe the note's relationship to the tonic (the root or first note) of the scale. Here's a breakdown of the diatonic scale degrees: * Tonic (I): The root note of the scale, the foundation.(Sa) * Supertonic (II): The second note of the scale.(Ri) * Mediant (III): The third note of the scale.(Ga) * Subdominant (IV): The fourth note of the scale.(Ma) * Dominant (V): The fifth note of the scale, creates a sense of tension and pull towards the tonic.(Pa) * Submediant (VI): The sixth note of the scale.(Da) * Leading tone (VII): The seventh note of the scale, creates a strong pull towards the tonic.(Ni)
Intervals are calculated in semitones, not in diatonic steps
I can't display diagrams here, but I can describe how a piano keyboard can illustrate 16 semitones. Imagine a piano keyboard. Each white key represents a natural note, and the black keys represent sharps and flats between them. * Start on first white key (e.g., C). * Count 16 keys, including both white and black keys (C, C#, D, D#, E, F, F#, G, G#, A, A#, B, C, C#, D). This span of 16 keys showcases 16 semitones. It goes beyond one octave (C to C) and reaches into the next octave (D). The specific interval name (e.g., major thirteenth, minor fourteenth) depends on how you arrange those 16 semitones within a scale.
No. of Semitones-Traditional Name.
0-unison
1-minor 2nd
2-major 2nd, diminished 3rd
3-minor 3rd, augmented 2nd
4-major 3rd, diminished 4th
5-augmented 3rd, perfect 4th
6-augmented 4th, diminished 5th
7-perfect 5th, diminished 6th
8-augmented 5th, minor 6th
9-major 6th, diminished 7th
10-augmented 6th, minor 7th
11-major 7th
12-octave
13-minor 9th
14-major 9th
15-minor 10th
16-major 10th
The table contains music intervals * Simple Intervals (Unison to Perfect Fourth): These intervals have a straightforward relationship between their name and the number of semitones. A unison has 0 semitones (same pitch), a perfect fourth has 5 semitones, and so on. * Composite Intervals (Augmented and Diminished): As you move down the table, things get more complex. Intervals can be "augmented" (widened) or "diminished" (narrowed) by one semitone. For example, a major third is 4 semitones, but an augmented second is only 2 semitones (like a squeezed-in major third). * Quality Matters: The "perfect," "major," and "minor" designations indicate the quality of the interval within a scale. Perfect intervals (like the perfect fifth) have a specific and pleasing sound within the tonal system. Major and minor intervals create different moods and tensions. Key Points: * This table is a helpful reference, but keep in mind that the specific sound of an interval depends on its context within a piece of music. * Intervals can be named based on the number of scale degrees they span (e.g., a major third spans three scale degrees). * While the table shows intervals up to a major 10th (16 semitones), larger intervals exist and are built upon these foundations. In essence, this table is a cheat sheet to understanding the building blocks of melodies and harmonies in music!
Intervals¶
There are four different ways of talking about intervals: (1) ordered pitch interval; (2) unordered pitch interval; (3) ordered pitch-class interval; (4) unordered pitch-class interval (also called interval class).
A pitch interval (pi) is the distance between two pitches, measured by the number of semitones between them. A pitch interval is created when we move from pitch to pitch in pitch space. It can be as large as the range of our hearing or as small as a semitone.Intervals with a plus or minus sign are called directed or ordered pitch intervals (opi). At other times, we will be concerned only with the absolute space between two pitches. For such unordered pitch intervals (upi), we will just provide the number of semitones between the pitches.
A pitch-class interval (pci) is the distance between two pitch classes. A pitch-class interval is created when we move from pitch class to pitch class in modular pitch-class space. It can never be larger than eleven semitones, because no two pitch classes can be more than eleven semitones apart. As with pitch intervals, we will sometimes be concerned with ordered pitch-class intervals (opci) and sometimes with unordered pitch-class intervals (upci).
(1) ordered pitch interval
(2)unordered pitch interval
The ordered pitch intervals focus attention on the contour of the line, its balance of rising and falling motion. The unordered pitch intervals ignore contour and concentrate on the spaces between the pitches.
(3)Ordered Pitch-Class Intervals
To state this as a formula, we can say that the ordered interval from pitch-class x to pitch-class y is: y – x (mod 12)
0 and 12 1 and 11 (or –1) 2 and 10 (or –2) 3 and 9 (or –3) 4 and 8 (or –4) 5 and 7 (or –5) 6 and 6
(4)Unordered Pitch-Class Intervals/interval class
The formula for an unordered pitch-class interval is: x – y (mod 12) or y – x (mod 12), whichever is smaller
interval class-pitch intervals 0 - 0, 12, 24 1 - 1, 11, 13 2 - 2, 10, 14 3 - 3, 9, 15 4 - 4, 8, 16 5 - 5, 7, 17 6 - 6, 18
Instead of using the formula, however, you will probably find it faster just to envision a musical staff, keyboard, or clockface. From the first pitch class, just count semitones up or down to the nearest instance of the second pitch class. Including the unison (0), there are only seven different unordered pitch-class intervals, because to get from one pitch class to any other, one never has to travel farther than six semi-tones. Thus 6 is the largest unordered pitch-class interval.
Example- Four ways of describing an interval.
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Interval-Class Content
No. of Pitch Classes-No. of Interval Classes 1-0 2-1 3-3 4-6 5-10 6-15 7-21 8-28 9-36 10-45 11-55 12-66
Interval-Class Vector