Editing Interval (music) (section)

=== Deducing component intervals from chord names and symbols ===
The main rules to decode chord ''names or symbols'' are summarized below. Further details are given at [[Chord names and symbols (jazz and pop music)#Rules to decode chord names and symbols|Rules to decode chord names and symbols]].
# For 3-note chords ([[Triad (music)|triads]]), [[Major third|major]] or [[Minor third|minor]] always refer to the interval of the third above the [[root (chord)|root note]], while [[Augmented fifth|augmented]] and [[Diminished fifth|diminished]] always refer to the interval of the fifth above root. The same is true for the corresponding symbols (e.g., Cm means C<sup>m3</sup>, and C+ means C<sup>+5</sup>). Thus, the terms third and [[perfect fifth|fifth]] and the corresponding symbols 3 and 5 are typically omitted. This rule can be generalized to all kinds of chords,{{efn|name=rule1|General rule 1 achieves consistency in the interpretation of symbols such as CM<sup>7</sup>, Cm<sup>6</sup>, and C+<sup>7</sup>. Some musicians legitimately prefer to think that, in CM<sup>7</sup>, M refers to the seventh, rather than to the third. This alternative approach is legitimate, as both the third and seventh are major, yet it is inconsistent, as a similar interpretation is impossible for Cm<sup>6</sup> and C+<sup>7</sup> (in Cm<sup>6</sup>, m cannot possibly refer to the sixth, which is major by definition, and in C+<sup>7</sup>, + cannot refer to the seventh, which is minor). Both approaches reveal only one of the intervals (M3 or M7), and require other rules to complete the task. Whatever is the decoding method, the result is the same (e.g., CM<sup>7</sup> is always conventionally decoded as C–E–G–B, implying M3, P5, M7). The advantage of rule 1 is that it has no exceptions, which makes it the simplest possible approach to decode chord quality. {{pb}}
According to the two approaches, some may format the major seventh chord as CM<sup>7</sup> (general rule 1: M refers to M3), and others as C<sup>M7</sup> (alternative approach: M refers to M7). Fortunately, even C<sup>M7</sup> becomes compatible with rule 1 if it is considered an abbreviation of CM<sup>M7</sup>, in which the first M is omitted. The omitted M is the quality of the third, and is deduced according to rule 2 (see above), consistently with the interpretation of the plain symbol C, which by the same rule stands for CM.
}} provided the above-mentioned qualities appear immediately after the root note, or at the beginning of the chord name or symbol. For instance, in the chord symbols Cm and Cm<sup>7</sup>, m refers to the interval m3, and 3 is omitted. When these qualities do not appear immediately after the root note, or at the beginning of the name or symbol, they should be considered [[#Quality|interval qualities]], rather than chord qualities. For instance, in Cm<sup>M7</sup> ([[minor major seventh chord]]), m is the chord quality and refers to the m3 interval, while M refers to the M7 interval. When the [[#Number|number]] of an extra interval is specified immediately after chord quality, the quality of that interval may coincide with chord quality (e.g., CM<sup>7</sup> = CM<sup>M7</sup>). However, this is not always true (e.g., Cm<sup>6</sup> = Cm<sup>M6</sup>, C+<sup>7</sup> = C+<sup>m7</sup>, CM<sup>11</sup> = CM<sup>P11</sup>).{{efn|name=rule1}} See [[Chord names and symbols (jazz and pop music)#Rules to decode chord names and symbols|main article]] for further details.
# Without contrary information, a [[major third]] interval and a [[perfect fifth]] interval ([[major triad]]) are implied. For instance, a C chord is a C major triad, and the name C minor seventh (Cm<sup>7</sup>) implies a minor 3rd by rule 1, a perfect 5th by this rule, and a [[Minor seventh|minor 7th]] by definition (see below). This rule has one exception (see next rule).
# When the fifth interval is [[Diminished fifth|diminished]], the third must be minor.{{efn|name=rule4|All triads are [[Chord (music)#Secundal, tertian, and quartal chords|tertian]] chords (chords defined by sequences of thirds), and a major third would produce in this case a non-tertian chord. Namely, the diminished fifth spans 6 semitones from root, thus it may be decomposed into a sequence of two [[minor third]]s, each spanning 3 semitones (m3 + m3), compatible with the definition of tertian chord. If a major third were used (4 semitones), this would entail a sequence containing a major second (M3 + M2 {{=}} 4 + 2 semitones {{=}} 6 semitones), which would not meet the definition of tertian chord.}} This rule overrides rule 2. For instance, Cdim<sup>7</sup> implies a diminished 5th by rule 1, a minor 3rd by this rule, and a diminished 7th by definition (see below).
#Names and symbols that contain only a plain [[#Number|interval number]] (e.g., "seventh chord") or the [[root (chord)|chord root]] and a number (e.g., "C seventh", or C<sup>7</sup>) are interpreted as follows:
#*If the number is 2, 4, 6, etc., the chord is a major [[added tone chord]] (e.g., C<sup>6</sup> = C<sup>M6</sup> = C<sup>add6</sup>) and contains, together with the implied major triad, an extra [[Major second|major 2nd]], [[Perfect fourth|perfect 4th]], or [[Major sixth|major 6th]] (see [[Chord names and symbols (jazz and pop music)#Added tone chords|names and symbols for added tone chords]]).
#*If the number is 7, 9, 11, 13, etc., the chord is [[Dominant chord|dominant]] (e.g., C<sup>7</sup> = C<sup>dom7</sup>) and contains, together with the implied major triad, one or more of the following extra intervals: minor 7th, major 9th, perfect 11th, and major 13th (see names and symbols for [[Chord names and symbols (jazz and pop music)#Seventh chords|seventh]] and [[Chord names and symbols (jazz and pop music)#Extended chords|extended chords]]).
#*If the number is 5, the chord (technically not a chord in the traditional sense, but a [[dyad (music)|dyad]]) is a [[power chord]]. Only the root, a perfect fifth and usually an octave are played.

The table shows the intervals contained in some of the main chords ('''component intervals'''), and some of the symbols used to denote them. The interval qualities or numbers in '''[[boldface]]''' font can be deduced from chord name or symbol by applying rule 1. In symbol examples, C is used as chord root.

{|class="wikitable"
|-
!colspan="2"| Main [[Chord (music)|chords]]
!colspan="3"| Component intervals
|-
!Name
![[Chord symbol|Symbol]] examples
!Third
!Fifth
!Seventh
|-
| rowspan="2" | [[Major triad]] || C || M3 || P5 ||
|-
| CM, or Cmaj || '''M'''3 || P5 ||
|-
| [[Minor triad]] || Cm, or Cmin || '''m'''3 || P5 ||
|-
| [[Augmented triad]] || C+, or Caug || M3 || '''A'''5 ||
|-
| [[Diminished triad]] || C{{music|dimdeg}}, or Cdim || m3 || '''d'''5 ||
|-
| [[Dominant seventh chord]] || C<sup>7</sup>, or C<sup>dom7</sup> || M3 || P5 || m'''7'''
|-
| [[Minor seventh chord]] || Cm<sup>7</sup>, or Cmin<sup>7</sup> || '''m'''3 || P5 || m'''7'''
|-
| [[Major seventh chord]] || CM<sup>7</sup>, or Cmaj<sup>7</sup> || '''M'''3 || P5 || M'''7'''
|-
|[[Augmented seventh chord]]|| C+<sup>7</sup>, Caug<sup>7</sup>,<br/> C<sup>7{{Music|sharp}}5</sup>, or C<sup>7aug5</sup> || M3 || '''A'''5 || m'''7'''
|-
| [[Diminished seventh chord]] || C{{music|dimdeg}}<sup>7</sup>, or Cdim<sup>7</sup> || m3 || '''d'''5 || d'''7'''
|-
| [[Half-diminished seventh chord]] || C{{music|halfdim}}<sup>7</sup>, Cm<sup>7{{Music|flat}}5</sup>, or Cm<sup>7dim5</sup> || m3 || '''d'''5 || m'''7'''
|}