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Being the next most perfect perfect consonance after the octave, the twelfth is difficult to alter from the tritaveand and use as the base of a tuning of a scale. Here is a chart of why it is more logical to call the half octave an augmented fourth than a diminished fifth:
Octave | 1 | 2 | 4 | 8 | 16 | 32 | 64 | 128 | 256 | 512 | 1024 | 2048 | 4096 | 8192 | … | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Fifth | 3 | 6
3/2 |
12 | 24 | 48 | 96 | 192 | 384 | 768 | 1536 | 3072 | 6144 | 12288 | |||||||||||||||
Fourth | 4/3 | 8/3 | 16/3 | 32/3 | 64/3 | 128/3 | 256/3 | 512/3 | 1024/3 | 2048/3 | 4096/3 |