A chord can be altered in many ways, but not all alterations make a chord an "altered" chord. Which alterations actually make a chord an altered chord? Do altered chords have special notation?
In Jazz usage "altered" refers to chords where the 5th or 9th (or both) are raised or lowered. Often a chord will have both raised and lowered notes simultaneously.
There are various ways to notate the alterations: either with +/- or #/♭
C(alt) refers to a chord with both raised and lowered 5th and 9th.
A chord with a raised 11th can also be regarded as an alternative notation for a ♭5 as the real 5th is mostly omitted.
The term 'altered chord' is sometimes used to label an extended dominant 7th shape where only the 3rd and 7th remain unaltered. The 5th is both raised and lowered, likewise the 9th and 11th.
In classical theory, an "altered chord" usually refers to a chord that contains non-diatonic notes, which are chromatically raised or lowered by a semitone from the usual notes of the scale. This encompasses a wide variety of possible chords, and many would even speak of altering the root of a chord, if it is a non-diatonic note within the local key/scale.
The term "altered chord" is not frequently used, however, in classical theory when speaking of basic secondary/applied dominants or leading tone chords. (For example, a D major chord with an F-sharp appearing in C major is often just called an applied dominant when it resolves to G, rather than an altered chord.) Note also that in the minor mode, the raised leading tone is generally not considered an "alteration" in dominant function chords, even though it is written with an accidental. Furthermore, when a chord is common to the parallel mode (that is, a typical chord from the parallel minor appearing in a major key or vice versa), it is often referred to as borrowed rather than altered, though this usage is not universal. (For example, an F minor chord in a C major context could be considered borrowed from C minor, even though it involves chromatic alteration of A to A-flat.)
Note that technically the chords in the previous paragraph are "altered chords" in the sense that they involve chromatic alteration from the diatonic notes of the key, but they aren't typically what one means in classical theory when using the phrase "altered chords." Rather, the term "altered chords" tends to be used to refer to more exotic chords with chromatic alterations beyond applied dominants and "borrowing" from another mode.
In jazz theory, notes with chromatic alterations other than the third or seventh of a chord can be considered "altered." The usual template for a chord in jazz theory is assumed to be an extended dominant structure, i.e., with perfect fifth, major ninth, perfect eleventh, and major thirteenth. If any of those notes is lowered or raised by a semitone, they can be referred to as "alterations." (Thirds and sevenths in jazz are usually considered to determine the chord identity: major or minor third, with major or minor or diminished seventh. These semitone changes are used to name the basic chord structure, and thus are usually not thought of as "alterations." The other exception in jazz theory is typically diminished sevenths and half-diminished sevenths, which are not usually called "altered chords" even though they contain a lowered fifth.)
not all alterations make a chord an "altered" chord ...
So which alterations don't make an altered chord?
The German Wiki-page is different from the English version:
It says altering the prime will be a different chord as the chord is named by the root note: e.g. Bb in C is a borrowed chord.
Altering the 3rd will change the mode from major to minor and vice versa.
The fifth is the most frequently altered tone.
For more explanations and examples look up the following links:
For more explanations and examples you may look up the following link:
An altered chord is a diatonic triad or seventh chord that has had one or more pitches lowered or raised by a half step. By lowering or raising (altering) the chord tone you change the character and color of the chord. Depending on what pitches you change, you can even change its function.
Wikipedia explains even more extended:
Altered seventh chord:
An altered dominant seventh chord arising from voice leading in the first movement of Chopin's Piano Sonata No. 2, Op. 35 An altered seventh chord is a seventh chord with one, or all, of its factors raised or lowered by a semitone
and includes also the altered third:
An altered dominant chord is, "a dominant triad of a 7th chord that contains a raised or lowered fifth and sometimes a lowered 3rd."
Also it makes a difference of classical terminology and altered chords in Jazz:
In jazz, the term altered chord, notated as an alt chord (e.g. G7alt), refers to a dominant chord, in which neither the fifth nor the ninth is unaltered—namely, where the 5th and the 9th are raised or lowered by a single semitone, or omitted. Altered chords are thus constructed using the following notes, some of which may be omitted.
But it will be enlightening to study all the examples!
If you want to study more about Alteration you could also look up the German page of Wîkipedia translating it by google. It is not quite identical with the English version.