99/64

Interval information

Ratio	99/64
Factorization	2-6 × 32 × 11
Monzo	[-6 2 0 0 1⟩
Size in cents	755.2279¢
Names	undecimal superfifth, undecimal major fifth, Alpharabian paramajor fifth, just paramajor fifth
Color name	1o5, ilo 5th
FJS name	[math]\displaystyle{ \text{P5}^{11} }[/math]
Special properties	reduced, reduced harmonic
Tenney height (log2 nd)	12.6294
Weil height (log2 max(n, d))	13.2587
Wilson height (sopfr(nd))	29
Harmonic entropy (Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])	~4.24979 bits
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In 11-limit just intonation, 99/64 is an undecimal superfifth of about 755.2 ¢. This interval is also known as the undecimal major fifth through analogy with 16/11 being the "minor fifth" as named by Ivan Wyschnegradsky, and can additionally be somewhat similarly dubbed the Alpharabian paramajor fifth or even the just paramajor fifth. It is distinguished from the simpler 17/11 by the twosquare comma (1089/1088).

Despite being relatively more complex, 99/64 is actually pretty useful as an interval for those who work more extensively with the 11-limit. For example, Margo Schulter has stated that it is useful in a Neo-Medieval European setting as a substitute for 14/9, and is closer to the likeliest interpretation- such as that of Jay Rahn- of Marcheto (or Marchettus or Marchetto) of Padua in 1318 than her own older septimal interpretation of the same interval.

Approximation

This interval is especially close to the 17th step of 27edo.

See also

• 128/99 – its octave complement
• Gallery of just intervals