Common Intervals, Chords and Scales and Their Jordan Chromatic System EquivalentsBy Stanley JordanAug 12, 2023
 First, some terminology and notation:
 The Jordan Chromatic System (JCS) is built on Integer Pitch Class Notation (IPCN) but extends it in unique ways. IPCN uses the numbers 0-11 to specify pitch classes and interval classes.
 A pitch class (pc) is a tone regardless of octave. For example F# is a pitch class. All the F#s in all possible octaves are different pitches but they're all members of the same pitch class. In conventional IPCN the note C is 0, C# is 1, and so on up to B which is 11. After 11 comes 0 again, and we get the same pcs in the next octave, and so on. JCS uses that same standard but calls these "absolute pitch classes." The word "absolute" is added to distinguish them from "relative pitch classes," which are described next.
 "Relative pitch classes" in JCS are tones that are referenced from an absolute pitch class root. Whereas in the absolute system C is always 0, in the relative system any tone can be 0. We then use the same numbers 0-11, starting from whatever our root is. So, for example, if E is the root then E is now 0, and then F would be 1. In every case if the root is 0, then absolute and relative become the same, so if C is the root then F would be 5 in both the absolute and the relative sense.
 Conventional IPCN has something called "interval classes" which correspond to relative pitch classes in JCS but they are not exactly the same. An interval class is an interval regardless of octave and direction. Interval class refers to the space between two tones whereas relative pitch class refers to the tone itself that exists at a given distance from the root. It's a subtle distinction but an important one.
 In JCS "chord type" refers to any set of relative pitch classes. It is typically notated by an ascending series of numbers. This conveniently groups together all chords and scales, as well as sets with only 1 or 2 tones. These are all relative, so we are not specifying a root. For example a major chord, or major triad, corresponds to the chord type 0 4 7. 0 4 7 is any major chord—it could be C major, G# major or whatever. A minor chord would be 0 3 7.
 A major scale would be 0 2 4 5 7 9 11. Even though it's a scale in conventional terms, in JCS it's called a chord type. Calling everything a chord type does away with the messy issue of determining what's a chord and what's a scale, since that often depends on the musical context.
 In JCS a "rooted chord type" is a root plus a chord type built on that root. Typically it is notated with a root followed by a colon followed by an ascending list of relative pcs. The root is an absolute pc, and for convenience it can be expressed either as a number or by using the conventional letter notation. For example an Em chord can be notated as 4: 0 3 7 or E: 0 3 7.
 Absolute Pitch Classes
 C = 0
 C#, D♭ = 1
 D = 2
 D#, E♭ = 3
 E = 4
 F = 5
 F#, G♭ = 6
 G = 7
 G#, A♭ = 8
 A = 9
 A#, B♭ = 10
 B = 11
 Intervals (No Root Specified)
 Simple Intervals (up to an octave)
 Unison = octave = 0
 Minor 2nd = 1
 Major 2nd = 2
 Augmented 2nd, Minor 3rd = 3
 Major 3rd = 4
 Perfect 4th = 5
 Augmented 4th, Diminished 5th = 6
 Perfect 5th = 7
 Augmented 5th, Minor 6th = 8
 Major 6th = 9
 Augmented 6th, Minor 7th = 10
 Major 7th = 11
 Compound Intervals (larger than an octave) still use the numbers 0-11:
 octave = 0
 Minor 9th = 1
 Major 9th = 2
 Augmented 9th, Minor 10th = 3
 Major 10th = 4
 Perfect 11th = 5
 Augmented 11th, Diminished 12th = 6
 Perfect 12th = 7
 Augmented 12th, Minor 13th = 8
 Major 13th = 9
 Augmented 13th, Minor 14th = 10
 Major 14th = 11
 Chords And Scales in C (Rooted Chord Types with Root = 0):
 1 TONE
 C Monotone = 0: 0
 2 TONES
 C5 = C Power Chord = 0: 0 7
 3 TONES
 CM = 0: 0 4 7
 Cm = 0: 0 3 7
 C dim. = 0: 0 3 6
 C+ = 0: 0 4 8
 C sus4 = 0: 0 5 7
 C sus2 = 0: 0 2 7
 4 TONES
 7th Chords
 CM7 = 0: 0 4 7 11
 CM7♭5 = 0: 0 4 6 11
 CM7#5 = 0: 0 4 8 11
 Cm7 = 0: 0 3 7 10
 Cm7♭5 = 0: 0 3 6 10
 CmM7 = 0: 0 3 7 11
 C7 = 0: 0 4 7 10
 C7♭5 = 0: 0 4 6 10
 C7#5 = 0: 0 4 8 10
 C dim. 7 = Cm6♭5 = 0: 0 3 6 9
 CM7 sus4 = 0: 0 5 7 11
 C7 sus4 = 0: 0 5 7 10
 6th Chords
 C6 = 0: 0 4 7 9
 Cm6 = 0: 0 3 7 9
 Cm6♭5 = C dim. 7 = 0: 0 3 6 9
 C add9 = 0: 0 2 4 7
 C add♭9 = 0: 0 1 4 7
 Cm add9 = 0: 0 2 3 7
 Cm add♭9 = 0: 0 1 3 7
 C add11 = 0: 0 4 5 7
 C add#11 = 0: 0 4 6 7
 Cm add11 = 0: 0 3 5 7
 Cm add#11 = 0: 0 3 6 7
 5 TONES
 6/9 Chords
 C6/9 = C major pentatonic = 0: 0 2 4 7 9
 Cm6/9 = 0: 0 2 3 7 9
 Cm♭6/9 = Japanese Minor = 0: 0 2 3 7 8
 9th Chords
 CM9 = 0: 0 2 4 7 11
 CM7#9 = 0: 0 3 4 7 11
 CM9♭5 = 0: 0 2 4 6 11
 CM9#5 = 0: 0 2 4 8 11
 Cm9 = 0: 0 2 3 7 10
 Cm9♭5 = 0: 0 2 3 6 10
 Cm♭9 = 0: 0 1 3 7 10
 Cm9♭5 = 0: 0 2 3 6 10
 C9 = 0: 0 2 4 7 10
 C7#9 = 0: 0 3 4 7 10
 C9♭5 = 0: 0 2 4 6 10
 C7♭5♭9 = 0: 0 1 4 6 10
 C7♭9 = 0: 0 1 4 7 10
 C7#5♭9 = 0: 0 1 4 8 10
 C9#5 = 0: 0 2 4 8 10
 C7♭5#9 = 0: 0 3 4 6 10
 C7#5#9 = 0: 0 3 4 8 10
 CmM♭9♭5 = 0: 0 1 3 6 11
 CmM♭9 = 0: 0 1 3 7 11
 CmM9 = 0: 0 2 3 7 11
 CmM9♭5 = 0: 0 2 3 6 11
 11th Chords (No 3rd)
 C11♭9 = 0: 0 2 5 7 10
 CmM11♭9 = 0: 0 1 5 7 10
 6 TONES
 CM11 = 0: 0 2 4 5 7 11
 CM11#9 = 0: 0 3 4 5 7 11
 CM11♭5#9 = 0: 0 3 4 5 6 11
 CM#11 = 0: 0 2 4 6 7 11
 CM#11♭5 = 0: 0 2 4 5 6 11
 CM#11#9 = 0: 0 3 4 6 7 11
 CM7#11♭9 = 0: 0 1 4 6 7 11
 Cm11 = 0: 0 2 3 5 7 10
 Cm11♭9 = 0: 0 1 3 5 7 10
 Cm11♭5 = 0: 0 2 3 5 6 10
 Cm#11♭9 = 0: 0 1 3 6 7 10
 Cm#11 = 0: 0 2 3 6 7 10
 C11 = 0: 0 2 4 5 7 10
 C11♭9 = 0: 0 1 4 5 7 10
 C11♭5#9 = 0: 0 3 4 5 6 10
 C11#9 = 0: 0 3 4 5 7 10
 C7#11 = 0: 0 2 4 6 7 10
 C7#11♭9 = 0: 0 1 4 6 7 10
 C7#11#5♭9 = 0: 0 1 4 6 8 10
 C Whole Tone = C7#5#11 = 0: 0 2 4 6 8 10
 C7#11#9 = 0: 0 3 4 6 7 10
 CmM11 = 0: 0 2 3 5 7 11
 CmM11♭9 = 0: 0 1 3 5 7 11
 CmM11♭9 = 0: 0 1 4 5 7 11
 CmM11♭5 = 0: 0 2 3 5 6 11
 CmM#11 = 0: 0 2 3 6 7 11
 CmM#11♭9 = 0: 0 1 3 6 7 11
 C Augmented Scale = 0: 0 3 4 7 8 11
 7 TONES
 Diatonic Modes
 C Major Scale (Ionian Mode) = 0: 0 2 4 5 7 9 11
 C Dorian Minor = 0: 0 2 3 5 7 9 10
 C Phrygian Minor = 0: 0 1 3 5 7 8 10
 C Lydian = 0: 0 2 4 6 7 9 11
 C Mixolydian = 0: 0 2 4 5 7 9 10
 C Aeolian (Natural) Minor = 0: 0 2 3 5 7 8 10
 C Locrian Minor = 0: 0 1 3 5 6 8 10
 Other Modes
 C Harmonic Minor = 0: 0 2 3 5 7 8 11
 C Melodic Minor Ascending = C Jazz Melodic Minor = 0: 0 2 3 5 7 9 11
 C Lydian Diminished = 0: 0 2 3 6 7 9 11
 C Lydian Dominant = C Acoustic scale = 0: 0 2 4 6 7 9 10
 C Lydian Augmented = 0: 0 2 4 6 8 9 11
 8 TONES
 C Diminished Scale = 0: 0 1 3 4 6 7 9 10
 C Auxiliary Diminished = 0: 0 2 3 5 6 8 9 11
 C Bebop Major = 0: 0 2 4 5 7 8 9 11
 C Bebop Melodic Major = 0: 0 2 3 5 7 8 9 11
 C Bebop Harmonic Minor = 0: 0 2 3 5 7 8 10 11
 C Bebop Dominant = 0: 0 2 4 5 7 9 10 11
 12 TONES
 C Chromatic Scale = 0: 0 1 2 3 4 5 6 7 8 9 10 11© 2023 Stanley Jordan