TonalityGUIDE - Tonal music basic theory for Undergraduates
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Tuning and Temperament
This is too large a subject for a quick definition, but here are a few points that are worth noting for the purposes of this web site:

  • if you tuned a set of strings in ascending perfect fifths starting in C you would never arrive back at C after 7 octaves like you do on the piano - the resulting B# would in fact be considerably sharper
  • in the days when music did not modulate much or cover a particularly wide range this was not a problem
  • as music has ranged more widely over the last half millenium, a standard system has gradually evolved in which fifths have been made slightly smaller or tempered so that 12 fifths fit within the 7 octaves (the same applies to all the other intervals)
  • this system is called equal temperament and it closes the circle so that, in the example above, C# = Db and Gb = F#
  • part of the controversy arises over which composers would have been familiar with which tuning systems or temperaments, because equal temperament is one of many competing systems that have been used over the centuries
  • there are many books and web sites that discuss this issue in detail