Tuning math tools - Revision history

Fizzwikiadmin: /* Difference between an interval and ratio in cents */

2026-07-26T21:26:51Z

Difference between an interval and ratio in cents

← Older revision		Revision as of 17:26, 26 July 2026
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	1200log ₂(3/2) = 701.96		1200log ₂(3/2) = 701.96

	== Difference between an interval and ratio in cents ==		== 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/edo-log ₂(ratio)		1200(semitones/edo-log ₂(ratio)

Fizzwikiadmin: /* Frequency ± cents */

2026-07-26T21:26:02Z

Frequency ± cents

← Older revision		Revision as of 17:26, 26 July 2026
Line 37:		Line 37:
	== Difference between an interval and ratio in cents ==		== Difference between an 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 ratio in cents, use this formula (works on Google). Make sure to write the ratio with "/" on a calculator instead of ":".
	1200(semitones/12-log ₂(ratio)		1200(semitones/edo-log ₂(ratio)

	=== Examples ===		=== Examples ===

Fizzwikiadmin at 21:23, 26 July 2026

2026-07-26T21:23:37Z

← Older revision		Revision as of 17:23, 26 July 2026
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	440(2^(-50/1200)) ≈ 427.47		440(2^(-50/1200)) ≈ 427.47

			[[Category:Music Theory]]

	== Ratio in cents ==		== Ratio in cents ==

Fizzwikiadmin at 21:23, 26 July 2026

2026-07-26T21:23:02Z

← Older revision		Revision as of 17:23, 26 July 2026
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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)

	~~To find the~~ difference between ~~frequencies in~~ cents~~, use this formula (works on Google)~~.		=== Example ===
	~~1200log ₂(hz/hz)~~		The difference between 440hz and 432hz is roughly 32 cents.

	~~For 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).
	hz(2^(±cents/1200))		frequency(2^(±cents/1200))

			=== Examples ===

			* 440hz + 50 cents is approximately 453hz

	~~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		== 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.

	~~For 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 an interval and ratio in cents		== Difference between an 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 ratio in cents, use this formula (works on Google). Make sure to write the ratio with "/" on a calculator instead of ":".
	1200(semitones/12-log ₂(ratio)		1200(semitones/12-log ₂(ratio)

			=== Examples ===

			* The difference between a perfect 5th in 12tet and a justly-tuned fifth (3:2) is approximately 2 cents.

	~~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 ~~that~~ western music ~~mostly~~ uses 12 notes per octave instead of 17, which would sound like absolute garbage. The mikes wouldn't mind such a reality though.
			* 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

Fizzwikiadmin: 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..."

2026-07-26T21:14:44Z

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..."

New page

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^(±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)

For example, the amount of cents in a 3:2 ratio is approximately 702 cents.
1200log ₂(3/2) = 701.96

Difference between an 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 ":".
1200(semitones/12-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 that western music mostly 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