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An arrangement of just intonation pitches in a diamond shape, invented by Harry Partch to show the relationships between the pitches and the tonalities that they form. The otonalities or "major" tonalities go from lower left to upper right like a slash: / , while the utonalities or "minor" tonalities go from lower right to upper left like a backslash: \ . This means that each ratio is a part of at least one otonality and one utonality, and indeed the tonic 1/1 is a part of every tonality of either kind. Here is a 5-limit (no odd factors greater than 5) Tonality Diamond on "G":

    5/3     6/5
    "E"     "Bb"
4/3     5/5     3/2
"C"     "G"     "D"
    8/5     5/4
    "Eb"    "B"
Note that 3/3 and 5/5 are just different ways of saying 1/1. They are left unreduced to show how they relate to the other ratios by sharing a numerator or denominator.

The Tonality Diamond is not just an abstract musical idea like the circle of fifths: Partch actually built an instrument, the Diamond Marimba, to play the tones of an 11-limit Tonality Diamond, arranged in the same shape, albeit turned 90 degrees for ease of playing. You can play a really neat Java demo of the Diamond Marimba online at http://members.home.net/prodgers13/DiamondMarimba.html.

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