Why are the frequency ratios of notes in the Pythagorean scales 9/8 and 256/243?

Why are the frequency ratios of notes in the Pythagorean scales 9/8 and 256/243? In Pythagorean tuning, for every 7th semitones the frequency would increase by a factor of 3/2 (to get that harmonious perfect fifth). If the frequency of C4 is set to 256Hz, the frequency of G4 can be calculated by 256 * 3/2 = 384Hz .

1. What is the size in cents of the interval between the frequencies 256 and 243?
2. What ratio is associated with Pythagorean tuning?
3. What are some common ratios used by Pythagoras to establish the relationship between pitch and string?
4. How do you calculate Pythagorean tuning?

What is the size in cents of the interval between the frequencies 256 and 243?

One of these parts is our diatonic semitone of 256:243, or 90 cents, at a-bb - the same size as at b-c' or e-f'. This interval is equal to the difference between the fourth f-bb and the major third f-a, i.e. (498 - 408) or 90 cents.

What ratio is associated with Pythagorean tuning?

Pythagorean tuning is a system of musical tuning in which the frequency ratios of all intervals are based on the ratio 3:2. This ratio, also known as the "pure" perfect fifth, is chosen because it is one of the most consonant and easiest to tune by ear and because of importance attributed to the integer 3.

What are some common ratios used by Pythagoras to establish the relationship between pitch and string?

Pythagoras called the relationship between two notes an interval. For example, as mentioned above, when two strings have the same length, they have the same pitch, and the relationship, or interval, between the notes is called a unison.
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3.2 Pythagorean Intervals.

How do you calculate Pythagorean tuning?

From a C, we will build a major scale according to the Pythagorean tuning. We first calculate the fifth by multiplying the frequency of C by 3/2 (fifth size): To multiply a number by a fraction we multiply by the numerator (top number) and then divide by the denominator (bottom number). G = 261 x 3 / 2.