{"id":1409,"date":"2013-07-27T09:26:49","date_gmt":"2013-07-27T16:26:49","guid":{"rendered":"http:\/\/www.garygarrett.me\/?p=1409"},"modified":"2017-08-25T07:42:35","modified_gmt":"2017-08-25T14:42:35","slug":"consonance-experiment","status":"publish","type":"post","link":"https:\/\/www.garygarrett.me\/?p=1409","title":{"rendered":"Consonance Experiment"},"content":{"rendered":"

In my last post<\/a> I raised the idea that the consonance of an interval<\/a> is not just one thing, but has two distinct parts:<\/p>\n

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  1. The sensation created by the sound of the two notes played together — smooth or rough, pleasant or unpleasant<\/li>\n
  2. The sense of stability of the note — does it feel restful, like it has arrived, or restless, unstable, like it “wants” to move?<\/li>\n<\/ol>\n

    I propose that #1 is correlated with the harmonic distance<\/a> between the two notes of the interval, that is, the length of the solid lines that connect them on the lattice<\/a>.<\/p>\n

    I think #2 is determined by the polarity<\/a> of those connections, whether they consist of multiplying (stable) or dividing (unstable), or a combination of the two.<\/p>\n

    This suggests some experiments.<\/p>\n

    A mostly good rule in experiments is to change one thing at a time. The prime factors used in an interval’s ratio<\/a> (3, 5 or 7) strongly affect the sound, so I’ll stick to one axis (x3), and only go in one direction (multiplying, overtonal, East<\/a>).<\/p>\n

    This will all happen on the backbone of the lattice, the infinite horizontal line of fifths. The notes on this line are in Pythagorean<\/a> tuning, which is any tuning that uses only 3 and 2 in its ratios. Pythagorean tuning<\/a> is used in music, but many of the intervals are sharply dissonant, as we shall see.<\/p>\n

    If I’m right, according to #1 the notes should get rougher or more unpleasant as I go further from the center, and according to #2 there should be a sense of stability, that gets weaker as the tonal gravity<\/a> field weakens with distance.<\/p>\n

    I’ll play all the notes against a drone, several octaves of the tonic<\/a>. The notes will all be played in a single octave, in between two drone notes. I will octave reduce<\/a> (divide by 2) as necessary, to put all the notes in this octave.<\/p>\n

    The first interval is a perfect fifth. To get this, you multiply the frequency of the tonic by 3.<\/p>\n