Tuning math tools: Difference between revisions
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Created page with "The following is a list of basic tools to find the exact differences between frequencies, ratios, and cents. Difference between frequencies in cents To find the difference between frequencies in cents, use this formula (works on Google). 1200log ₂(hz/hz) For example, the difference between 440hz and 432hz is roughly 32 cents. 1200log ₂(440/432) ≈ 31.77 Frequency ± cents To add or subtract cents from a frequency, use this formula (works on Google). hz(2^(±cent..." |
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The following is a list of basic tools to find the exact differences between frequencies, ratios, and cents. | The following is a list of basic, accessible tools to find the exact differences between frequencies (440hz, 432), ratios (3:2, 7:4), and cents. | ||
Difference between frequencies in cents | == Difference between frequencies in cents == | ||
To find the difference between frequencies in cents, use this formula (works on Google). | |||
1200log ₂(hz/hz) | |||
=== Example === | |||
The difference between 440hz and 432hz is roughly 32 cents. | |||
1200log ₂(440/432) ≈ 31.77 | 1200log ₂(440/432) ≈ 31.77 | ||
Frequency ± cents | == Frequency ± cents == | ||
To add or subtract cents from a frequency, use this formula (works on Google). | To add or subtract cents from a frequency, use this formula (works on Google). | ||
frequency(2^(±cents/1200)) | |||
=== Examples === | |||
* 440hz + 50 cents is approximately 453hz | |||
440(2^(50/1200)) ≈ 452.89 | 440(2^(50/1200)) ≈ 452.89 | ||
440hz - 50 cents is approximately 427hz | * 440hz - 50 cents is approximately 427hz | ||
440(2^(-50/1200)) ≈ 427.47 | 440(2^(-50/1200)) ≈ 427.47 | ||
Ratio in cents | [[Category:Music Theory]] | ||
== Ratio in cents == | |||
To find the amount of cents in a ratio, use this formula (works on Google). Make sure to write the ratio with "/" on a calculator instead of ":". | To find the amount of cents in a ratio, use this formula (works on Google). Make sure to write the ratio with "/" on a calculator instead of ":". | ||
1200log ₂(ratio) | 1200log ₂(ratio) | ||
=== Example === | |||
The amount of cents in a 3:2 ratio is approximately 702 cents. | |||
1200log ₂(3/2) = 701.96 | 1200log ₂(3/2) = 701.96 | ||
Difference between | == Difference between interval and ratio in cents == | ||
To find the difference between an interval and ratio in cents, use this formula (works on Google). Make sure to write the ratio with "/" on a calculator instead of ":". | To find the difference between an interval and a ratio in cents, use this formula (works on Google). Make sure to write the ratio with "/" on a calculator instead of ":". | ||
1200(semitones/ | 1200(semitones/edo-log ₂(ratio) | ||
=== Examples === | |||
* The difference between a perfect 5th in 12tet and a justly-tuned fifth (3:2) is approximately 2 cents. | |||
1200(7/12-log ₂(3/2) ≈ -1.96 | 1200(7/12-log ₂(3/2) ≈ -1.96 | ||
The difference between a major third in 17tet and a justly-tuned major third (5:4) is approximately 37 cents. Thank goodness | |||
* The difference between a major third in 17tet and a justly-tuned major third (5:4) is approximately 37 cents. Thank goodness most western music uses 12 notes per octave instead of 17, which would sound like absolute garbage. The [[Mike|mikes]] wouldn't mind such a reality though. | |||
1200(6/17-log ₂(5/4) ≈ 37.22 | 1200(6/17-log ₂(5/4) ≈ 37.22 | ||
Latest revision as of 17:26, 26 July 2026
The following is a list of basic, accessible tools to find the exact differences between frequencies (440hz, 432), ratios (3:2, 7:4), and cents.
Difference between frequencies in cents
To find the difference between frequencies in cents, use this formula (works on Google).
1200log ₂(hz/hz)
Example
The difference between 440hz and 432hz is roughly 32 cents.
1200log ₂(440/432) ≈ 31.77
Frequency ± cents
To add or subtract cents from a frequency, use this formula (works on Google).
frequency(2^(±cents/1200))
Examples
- 440hz + 50 cents is approximately 453hz
440(2^(50/1200)) ≈ 452.89
- 440hz - 50 cents is approximately 427hz
440(2^(-50/1200)) ≈ 427.47
Ratio in cents
To find the amount of cents in a ratio, use this formula (works on Google). Make sure to write the ratio with "/" on a calculator instead of ":".
1200log ₂(ratio)
Example
The amount of cents in a 3:2 ratio is approximately 702 cents.
1200log ₂(3/2) = 701.96
Difference between interval and ratio in cents
To find the difference between an interval and a ratio in cents, use this formula (works on Google). Make sure to write the ratio with "/" on a calculator instead of ":".
1200(semitones/edo-log ₂(ratio)
Examples
- The difference between a perfect 5th in 12tet and a justly-tuned fifth (3:2) is approximately 2 cents.
1200(7/12-log ₂(3/2) ≈ -1.96
- The difference between a major third in 17tet and a justly-tuned major third (5:4) is approximately 37 cents. Thank goodness most western music uses 12 notes per octave instead of 17, which would sound like absolute garbage. The mikes wouldn't mind such a reality though.
1200(6/17-log ₂(5/4) ≈ 37.22