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How are whole tones and semitones sized in Pythagorean tuning?
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In Pythagorean tuning, the sizes of whole tones and semitones are defined as follows:
- Whole tones: All five whole tones, which represent the larger steps in the diatonic scale, are equal in size at a ratio of 9:8 (204 cents).1
- Semitones: The two semitones, representing the smaller steps, are equal in size at a ratio of 256:243 (90 cents).1
In this system, the semitones are significantly smaller than half the size of the whole tones. This specific Pythagorean semitone is also known as a limma. While this tuning system is considered melodically satisfactory, it is noted for making major thirds and sixths sharp, which can result in dissonance when notes are sounded simultaneously.12