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How many notes are in a key?

There are 12 unique named tones in Western music; all pitches are one of these 12 tones. Thus, from a purely sonic perspective, there are only twelve starting notes for a key, and with major and minor scale qualities, there are 24 tonally unique keys.

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I am wondering about how many major and minor keys there are and why.

Here are some suggestions:

24 keys

One could argue that there should be one major and one relative minor key for each of the 12 equal tempered enharmonic notes, that is for each of

C; Db(/C#); D; Eb(/D#); E; F; F#/Gb; G; Ab(/G#); A; Bb(/A#); B

totalling 24 keys.

This would in some sense be supported by the mere idea of 24-key set compositions such as Bach's The Well Tempered Clavier and Chopin's 24 preludes (although the choice of enharmonic high-number sharps/flats key signatures vary in different composition sets).

26 keys

Sticking to the idea of enharmonic notes and the 24 keys but making a difference between the note names F# and Gb since they require an equal amount of sharp and flat symbols in their major and relative minor key signatures, and in that way seem equally relevant, yields 26 keys.

30 keys

If you count keys while you keep adding sharps or flats, until all seven natural notes (A to G) have a sharp or a flat symbol in the key signature, you end up with 30 keys.

That is the 15 keys

C; F; Bb; Eb; Ab; Db; Gb; Cb(!); G; D; A; E; B; F#; C#(!)

in majors and their relative minors.

42 keys

Counting all seven natural notes (A to G) on their own, as well as their respective flattened, and sharpened notes we get 21 note names as a basis for keys. That is Major and relative minor keys for each of these 21 gets you 42 keys (indeed with a lot of double sharps of flats in twelve of them).

Infinate number of keys

Albeit seemingly ridiculous someone might amuse himself/herself with for instance "transposing" 'Also Sprach Zarathustra' from C major to A### major1 ("A triple-sharp major" with 24 sharps in the key signature :-) or use any other super-sharp/-flat key. This is to say that you can invent pretty much as many keys as you please.

THE QUESTION

So, is there a consensus on or a standard answer to how many keys there are?

Or

When asked "How many major and minor musical keys are there?", what is the generally accepted correct answer?

Also

Why, and says who?

I am pretty sure I know what's considered the answer to how many keys there are, but I would like to know why and who settled for this. In case you find that it matters I'm referring to 12 tone equal temperament. I could otherwise perhaps further have suggested, say, nine (usable) keys for e.g. quarter-comma meantone temperament.

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What is it called when 5 people sing?

A quintet is a group containing five members. It is commonly associated with musical groups, such as a string quintet, or a group of five singers, but can be applied to any situation where five similar or related objects are considered a single unit.

en.wikipedia.org - Quintet - Wikipedia

This article is about a group of five members. For other uses, see Quintet (disambiguation) A quintet is a group containing five members. It is commonly associated with musical groups, such as a string quintet, or a group of five singers, but can be applied to any situation where five similar or related objects are considered a single unit.

Overview [ edit ]

In classical instrumental music, any additional instrument (such as a piano, clarinet, oboe, etc.) joined to the usual string quartet (two violins, a viola, and a cello), gives the resulting ensemble its name, such as "piano quintet", "clarinet quintet", etc. A piece of music written for such a group is similarly named. The standard wind quintet consists of one player each on flute, oboe, clarinet, bassoon, and horn, while the standard brass quintet has two trumpets, horn, trombone, and tuba. Other combinations are sometimes found, however. In jazz music, a quintet is group of five players, usually consisting of two of any of the following instruments, guitar, trumpet, saxophone, clarinet, flute or trombone, in addition to those of the traditional jazz trio – piano, double bass, drums.[citation needed] In some modern bands there are quintets formed from the same family of instruments with various voices, as an all-brass ensemble, or all saxophones, in soprano, alto, baritone, and bass, and sometimes contrabass.