99/80

Interval information

Ratio	99/80
Factorization	2-4 × 32 × 5-1 × 11
Monzo	[-4 2 -1 0 1⟩
Size in cents	368.9142¢
Names	undecimal submajor third, cake third
Color name	logu 3rd, 1og3
FJS name	[math]\text{m3}^{11}_{5}[/math]
Special properties	reduced
Tenney height (log2 nd)	12.9513
Weil height (log2 max(n, d))	13.2587
Wilson height (sopfr(nd))	30
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~4.21059 bits
open this interval in xen-calc

99/80, the undecimal submajor third, also known as the cake third, is 45/44 flat of the Pythagorean major third (81/64), and also 100/99 flat of the classical major third (5/4), while being 8019/8000 sharp of the grave major third (100/81). The alternate name, cake third, refers to the fact that tempering out 45/44, the cake comma, leads to a temperament that slices 99/80 exactly in half (into two 11/10's). It arises in just intonation as the sum of a 9/8 whole tone and an 11/10 submajor second.

Approximation

This interval is exactly 8/7 flat of the very accurate half-octave of 99/70, and so is accurately represented in any even edo with a good 7, such as 26edo.

See also

• 160/99 – its octave complement
• 40/33 – its fifth complement
• 320/297 – its fourth complement
• Gallery of just intervals