page_title: Equal temperament
section_title: 5 and 7 tone temperaments in ethnomusicology
hierarchical_section_title: Equal temperament / Other equal temperaments / 5 and 7 tone temperaments in ethnomusicology
caption_attribution_description: English: 7-tone equal tempered scale represented in traditional notation. + and - indicates approximate distance above and below notated pitch.
context_page_description: An equal temperament is a musical temperament or tuning system, which approximates just intervals by dividing an octave into equal steps. This means the ratio of the frequencies of any adjacent pair of notes is the same, which gives an equal perceived step size as pitch is perceived roughly as the logarithm of frequency.
  In classical music and Western music in general, the most common tuning system since the 18th century has been twelve-tone equal temperament, which divides the octave into 12 parts, all of which are equal on a logarithmic scale, with a ratio equal to the 12th root of 2. That resulting smallest interval, ​¹⁄₁₂ the width of an octave, is called a semitone or half step.
  In Western countries the term equal temperament, without qualification, generally means 12-TET.
  In modern times, 12-TET is usually tuned relative to a standard pitch of 440 Hz, called A440, meaning one note, A, is tuned to 440 hertz and all other notes are defined as some multiple of semitones apart from it, either higher or lower in frequency. The standard pitch has not always been 440 Hz. It has varied and generally risen over the past few hundred years.
context_section_description: Five and seven tone equal temperament (5-TET Play  and 7-TETPlay  ), with 240 Play  and 171 Play  cent steps respectively, are fairly common.
  5-TET and 7-TET mark the endpoints of the syntonic temperament's valid tuning range, as shown in Figure 1.
  In 5-TET the tempered perfect fifth is 720 cents wide (at the top of the tuning continuum), and marks the endpoint on the tuning continuum at which the width of the minor second shrinks to a width of 0 cents.
  In 7-TET the tempered perfect fifth is 686 cents wide (at the bottom of the tuning continuum), and marks the endpoint on the tuning continuum, at which the minor second expands to be as wide as the major second (at 171 cents each).
caption: Approximation of 7-tet
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