Editing Harmony (section)

== Intervals ==
An [[interval (music)|interval]] is the relationship between two separate musical pitches. For example, in the melody "[[Twinkle Twinkle Little Star]]", between the first two notes (the first "twinkle") and the second two notes (the second "twinkle") is the interval of a fifth. What this means is that if the first two notes were the pitch '''C''', the second two notes would be the pitch '''G'''—four scale notes, or seven chromatic notes (a perfect fifth), above it.

The following are common intervals:

{| class="wikitable"
|-
! Root
! [[Major third]]
! [[Minor third]]
! Fifth
|-
| C
| E
| E{{music|b}}
| G
|-
| D{{music|b}}
| F
| F{{music|b}}
| A{{music|b}}
|-
| D
| F{{music|#}}
| F
| A
|-
| E{{music|b}}
| G
| G{{music|b}}
| B{{music|b}}
|-
| E
| G{{music|#}}
| G
| B
|-
| F
| A
| A{{music|b}}
| C
|-
| F{{music|#}}
| A{{music|#}}
| A
| C{{music|#}}
|-
| G
| B
| B{{music|b}}
| D
|-
| A{{music|b}}
| C
| C{{music|b}}
| E{{music|b}}
|-
| A
| C{{music|#}}
| C
| E
|-
| B{{music|b}}
| D
| D{{music|b}}
| F
|-
| B
| D{{music|#}}
| D
| F{{music|#}}
|}

When tuning notes using an equal temperament, such as the [[12-tone equal temperament]] that has become ubiquitous in Western music, each interval is created using steps of the same size, producing harmonic relations marginally 'out of tune' from pure frequency ratios as explored by the ancient Greeks. 12-tone equal temperament evolved as a compromise from earlier systems where all intervals were calculated relative to a chosen root frequency, such as [[just intonation]] and [[well temperament]]. In those systems, a major third constructed up from C did not produce the same frequency as a minor third constructed up from D♭. Many keyboard and fretted instruments were constructed with the ability to play, for example, both of G♯ ''and'' A♭ without retuning. The notes of these pairs (even those where one lacks an accidental, such as E and F♭) were not the 'same' note in any sense.

Using the [[diatonic scale]], constructing the major and minor keys with each of the 12 notes as the tonic can be achieved using only flats ''or'' sharps to spell notes within said key, never both. This is often visualized as traveling around the [[circle of fifths]], with each step only involving a change in one note's accidental. As such, additional accidentals are free to convey more nuanced information in the context of a passage of music and the other notes that make it up. Even when working outside diatonic contexts, it is convention, if possible, to use each letter in the alphabet only once in describing a scale.

A note spelled as F♭ conveys different harmonic information to the reader versus a note spelled as E. In a tuning system where two notes spelled differently are tuned to the same frequency, those notes are said to be [[enharmonic]]. Even if identical in isolation, different spellings of enharmonic notes provide meaningful context when reading and analyzing music. For example, even though E and F♭ are enharmonic, the former is considered to be a major third up from C, while F♭ is considered to be a [[diminished fourth]] up from C. In the context of a C major tonality, the former is the third of the scale, while the latter could (as one of numerous possible justifications) be serving the harmonic function of the third of a D♭ minor chord, a [[borrowed chord]] within the scale.

Therefore, the combination of notes with their specific intervals—a chord—creates harmony.<ref name=Jamini>Jamini, Deborah (2005). ''Harmony and Composition: Basics to Intermediate'', p. 147. {{ISBN|1-4120-3333-0}}.</ref> For example, in a C chord, there are three notes: C, E, and G. The note '''C''' is the root. The notes '''E''' and '''G''' provide harmony, and in a G7 (G dominant 7th) chord, the root G with each subsequent note (in this case B, D and F) provide the harmony.<ref name="Jamini" />

<!-- I will leave the following below for the moment, but is it really relevant to this article?? (Please see talk page)-->
In the musical scale, there are twelve pitches. Each pitch is referred to as a "degree" of the scale. The names A, B, C, D, E, F, and G are insignificant.<ref>{{cite web|last=Ghani|first=Nour Abd |title=The 12 Golden notes is all it takes... |website=Skytopia |url=https://www.skytopia.com/project/scale.html|access-date=2021-10-02}}</ref> The intervals, however, are not. Here is an example:

{| class="wikitable"
|-
! 1°
! 2°
! 3°
! 4°
! 5°
! 6°
! 7°
! 8°
|-
| C
| D
| E
| F
| G
| A
| B
| C
|-
| D
| E
| F{{music|sharp}}
| G
| A
| B
| C{{music|sharp}}
| D
|}

As can be seen, no note will always be the same scale degree. The ''tonic'', or first-degree note, can be any of the 12 notes (pitch classes) of the chromatic scale. All the other notes fall into place. For example, when C is the tonic, the fourth degree or subdominant is F. When D is the tonic, the fourth degree is G. While the note names remain constant, they may refer to different scale degrees, implying different intervals with respect to the tonic. The great power of this fact is that any musical work can be played or sung in any key. It is the same piece of music, as long as the intervals are the same—thus transposing the melody into the corresponding key. When the intervals surpass the perfect Octave (12 semitones), these intervals are called ''compound intervals'', which include particularly the 9th, 11th, and 13th Intervals—widely used in [[jazz]] and [[blues]] Music.<ref>{{Cite book |last=STEFANUK|first=MISHA V. |url=https://books.google.com/books?id=JolkN10wM78C&q=Compound+intervals&pg=PA9|title=Jazz Piano Chords |date=2010-10-07|publisher=Mel Bay Publications|isbn=978-1-60974-315-4}}</ref>

Compound Intervals are formed and named as follows:
*2nd + Octave = 9th
*3rd + Octave = 10th
*4th + Octave = 11th
*5th + Octave = 12th
*6th + Octave = 13th
*7th + Octave = 14th

These numbers don't "add" together because intervals are numbered inclusive of the root note (e.g. one tone up is a 2nd), so the root is counted twice by adding them. Apart from this categorization, intervals can also be divided into consonant and dissonant. As explained in the following paragraphs, consonant intervals produce a sensation of relaxation and dissonant intervals a sensation of tension. In tonal music, the term consonant also means "brings resolution" (to some degree at least, whereas dissonance "requires resolution").{{Citation needed|date=January 2020}}

The consonant intervals are considered the perfect [[unison]], [[octave]], [[Perfect fifth|fifth]], [[Perfect fourth|fourth]] and major and minor third and sixth, and their compound forms. An interval is referred to as "perfect" when the harmonic relationship is found in the natural overtone series (namely, the unison 1:1, octave 2:1, fifth 3:2, and fourth 4:3). The other basic intervals (second, third, sixth, and seventh) are called "imperfect" because the harmonic relationships are not found mathematically exact in the overtone series. In classical music the perfect fourth above the bass may be considered dissonant when its function is [[contrapuntal]]. Other intervals, the second and the seventh (and their compound forms) are considered Dissonant and require resolution (of the produced tension) and usually preparation (depending on the music style<ref>{{Cite web|title=Music and the Making of Modern Science|author=Peter Pesic|url=https://issuu.com/376746/docs/music_and_the_making_of_modern_-_pesic__peter_5685|access-date=2021-10-02|website=Issuu|archive-date=2 October 2021|archive-url=https://web.archive.org/web/20211002180942/https://issuu.com/376746/docs/music_and_the_making_of_modern_-_pesic__peter_5685|url-status=dead}}</ref>).

The effect of dissonance is perceived relatively within musical context: for example, a major seventh interval alone (i.e., C up to B) may be perceived as dissonant, but the same interval as part of a major seventh chord may sound relatively consonant. A tritone (the interval of the fourth step to the seventh step of the major scale, i.e., F to B) sounds very dissonant alone, but less so within the context of a dominant seventh chord (G7 or D{{music|b}}7 in that example).<ref>{{Cite web|title=Intervals {{!}} Music Appreciation|url=https://courses.lumenlearning.com/musicappreciation_with_theory/chapter/interacting-with-intervals-and-scales/|access-date=2021-10-02|website=courses.lumenlearning.com}}</ref>