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Frequency ratios are a fundamental concept in music theory, used to determine how two musical notes relate to each other in terms of their pitch. The frequency of a note is the number of vibrations per second, usually measured in hertz (Hz).
To find the frequency ratio of two notes, you divide the higher frequency by the lower frequency. For example, if you have a note with a frequency of 370 Hz and another at 261.63 Hz, the ratio is \( \frac{370}{261.63} \approx 1.41 \). This calculation gives insight into the relationship between the notes.
A frequency ratio reveals whether notes tend to sound harmonious or not. Simple ratios like 1:1 (unison) or 2:1 (octave) are found where the wave patterns of the notes align more closely. This alignment is key to achieving harmony, which leads us next to the concept of consonance and dissonance.

Consonance and dissonance describe how combinations of musical notes relate in terms of pleasantness or tension.
Consonance is the harmonious relationship of notes, typically generated by simple frequency ratios such as 1:1, 2:1 (octaves), or 3:2 (perfect fifths). These intervals produce a stable sound, often perceived as pleasant.
On the other hand, dissonance arises from more complex frequency ratios. For instance, a ratio of around 1.41 might suggest a tritone, known for its tense and unstable nature, which often requires resolution to a consonant interval. Dissonant sounds add tension or expression to music, often driving the musical narrative forward.

• Consonant intervals: unison, octave, fifth
• Dissonant intervals: tritone, seconds, sevenths

Consonance and dissonance are not universally fixed but can vary slightly with context, including cultural and historical influences.

Musical intervals represent the difference in pitch between two notes, and they're essential for understanding Western music. They can be classified as harmonic (if played together) or melodic (if played in sequence).
Intervals are labeled by counting note names inclusively (like G-C encompasses G, A, B, C – a fourth) and can have various qualities such as perfect, major, minor, augmented, or diminished.
Simple intervals include:

• Perfect intervals (unison, fourth, fifth, octave): These are often consonant.
• Major intervals (second, third, sixth, seventh): Generally, more complex with varying consonance.

Compound intervals, like ninth or thirteenth, extend beyond the octave and have their own characteristics.
In our example with G-flat at 370 Hz and C at 261.63 Hz, the resulting interval has an approximate frequency ratio of 1.41, which correlates with a dissonant tritone rather than a simple consonant interval. Understanding these intervals allows musicians to create the desired mood or emotion in their compositions.