Just intonation
Just intonation is like playing with blocks. Imagine you have a bunch of blocks with different sizes, colors, and shapes. When you stack two blocks with the same shape and size on top of each other, they fit perfectly and make a smooth and stable tower. That's what just intonation does with music notes.
Every musical note has its own size, or frequency, which determines the pitch or how high or low it sounds. In just intonation, we match the frequencies of different notes using simple ratios. For example, if we have a note that vibrates at 440 Hz, we can stack another note that vibrates at 880 Hz on top of it to make a perfect octave. This ratio is 1:2, which means the second note vibrates at twice the frequency of the first note.
But it's not always that simple. Some notes don't fit well with each other when we use just intonation. This happens because the intervals between some notes are not simple ratios. For instance, the interval between a major third and a perfect fifth is not a simple ratio, which means it's difficult to stack two blocks with these shapes on top of each other and make them fit perfectly.
To solve this problem, we use a different kind of intonation called temperaments. Temperaments modify the frequencies of some notes to make all intervals sound good, even if they are not simple ratios. This allows us to play music in different keys and still sound pleasant to our ears.
In summary, just intonation is like stacking blocks with simple ratios, while temperaments are like adjusting the blocks to make all intervals sound good. Both methods are used in music to create beautiful melodies and harmonies.
Every musical note has its own size, or frequency, which determines the pitch or how high or low it sounds. In just intonation, we match the frequencies of different notes using simple ratios. For example, if we have a note that vibrates at 440 Hz, we can stack another note that vibrates at 880 Hz on top of it to make a perfect octave. This ratio is 1:2, which means the second note vibrates at twice the frequency of the first note.
But it's not always that simple. Some notes don't fit well with each other when we use just intonation. This happens because the intervals between some notes are not simple ratios. For instance, the interval between a major third and a perfect fifth is not a simple ratio, which means it's difficult to stack two blocks with these shapes on top of each other and make them fit perfectly.
To solve this problem, we use a different kind of intonation called temperaments. Temperaments modify the frequencies of some notes to make all intervals sound good, even if they are not simple ratios. This allows us to play music in different keys and still sound pleasant to our ears.
In summary, just intonation is like stacking blocks with simple ratios, while temperaments are like adjusting the blocks to make all intervals sound good. Both methods are used in music to create beautiful melodies and harmonies.
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