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# You know pythagorean tuning-system?

I got a task at school where we need to tune a tone-scale based on the pythagorean tuning system.

1. 2:3 up from a tone equals one fifth up
2. 1:2 up from a tone equals one octave up

Now, how can I find chromatic notes based on this? I need to find Fiss and Ciss based on the knowledge of the lenght (string) of G.

The trick is to add two fifths. It is equal to one octave plus a major second.
Substract the octave, you get the major second alone.

In a greek scale, you need five major seconds, and two minor seconds. Substract five major seconds from an octave, and divide the result by two, you get the minor second that you need.

Now, remember that addition becomes multiplication, subtraction becomes division, thus division becomes root extraction.
Two fifths from a G is an A. Now, if I transpond that one octave down, it will still be an A !!!
Quote:
 Originally Posted by alexpea Two fifths from a G is an A. Now, if I transpond that one octave down, it will still be an A !!!
Exactly. You start from, say, G1, you get to A3, that is a ninth higher. Go down one octave, that's A2, which is a major second above your starting point G1.

The major second value is more convenient than the major ninth one, even if, from the scale point of view, they are equivalent.
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• You know pythagorean tuning-system?