Wikipedia

A countertenor is a type of classical male singing voice whose vocal range is equivalent to that of the female contralto or mezzo-soprano voice types. The countertenor range is generally equivalent to a contralto range, extending from around G3 to D5 or E5, although a sopranist (a specific kind of countertenor) may match the soprano’s range of around C4 to C6. Countertenors often are natural baritones or tenors, but rarely use this vocal range in performance.

Merriam-Webster Dictionary

A tenor with an unusually high range (as an alto range)

Oxford English Dictionary: A part higher in pitch than the tenor, sung by a high male voice; the alto.

Voice Science

A man who sings regularly in the C3-C6 range. Countertenors are often associated with castrati of the baroque era and many countertenors sing music composed for castrati. Countertenor bodies greatly differ from those of castrati–countertenors do not achieve their vocal ranges through pre-pubescent castration.

Grove Music Online

A male high voice, originally and still most commonly of alto range, though the title is increasingly employed generically to describe any adult male voice higher than tenor. Historically, it derived in England from the contratenor line in late medieval and Renaissance polyphony, via contratenor altus (‘high contratenor’), which – used interchangeably – became ‘countertenor’ and ‘altus’, then alto (as in Italian nomenclature) and, later still, even ‘male’ alto.

Wikipedia

(\fȯl-ˈse-(ˌ)tō\ Italian: diminutive of “false”) is the vocal register occupying the frequency range just above the modal voice register and overlapping with it by approximately one octave. It is produced by the vibration of the ligamentous edges of the vocal cords, in whole or in part. Commonly cited in the context of singing, falsetto, a characteristic of phonation by both men and women, is also one of four main spoken vocal registers recognized by speech pathology.

Merriam-Webster Dictionary

An artificially high voice; especially: an artificially produced singing voice that overlaps and extends above the range of the full voice especially of a tenor

Oxford English Dictionary: A forced voice of a range or register above the natural; the head voice.

Voice Science

Especially in males, phonation that vibrates primarily the inner portions of the vocal folds rather than the entirety of the vocal folds.

Grove Music Online

The alto or higher range available to most adult male singers through a technique whereby the vocal folds vibrate/undulate in a length shorter than usual, known as the second mode of phonation. Falsetto is usually associated exclusively with the male voice, though it is available to and employed in that of the female. This phonatory mode has been equated with ‘unnatural’ as opposed to ‘natural’ (partly through misleading philological usage) even though falsetto can be achieved and employed by almost everyone at will. Therefore, the correct term, second-mode phonation (or pure ‘head’-register) is preferred here to ‘falsetto’, except in the interests of convenient brevity.