Goldis comma

Interval information

Ratio	549755813888/533935546875
Factorization	239 × 3-7 × 5-12
Monzo	[39 -7 -12⟩
Size in cents	50.55043¢
Name	Goldis comma
Color name	Trisa-quadtrigu comma
FJS name	[math]\displaystyle{ \text{8d5}_{5,5,5,5,5,5,5,5,5,5,5,5} }[/math]
Special properties	reduced, reduced subharmonic
Tenney height (log2 nd)	77.9579
Weil height (log2 max(n, d))	78
Wilson height (sopfr(nd))	159
Harmonic entropy (Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])	~4.46611 bits
Comma size	medium
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The goldis comma (ratio: 549755813888/533935546875, monzo: [39 -7 -12⟩) is a medium 5-limit comma which is the amount by which six classic augmented second intervals of 75/64 fall short of 8/3. It is the sum of the porcupine comma (a.k.a. maximal diesis) and the luna comma, the difference between the negri comma and the kwazy comma, and the difference between the passion comma and the semicomma. It is also the difference between 4 dieses and a pythagorean chromatic semitone, as well as the difference between a pythagorean whole tone and three negri commas.

Temperaments

Tempering out this comma leads to the goldis temperament. It is mostly supported by edos in the Fibonacci sequence. These are 21edo, 34edo, 55edo, and 89edo. (144edo does not temper out this comma in the patent val, though the 144c val supports it.)

Etymology

This comma was named by Userminusone as a contraction of golden diesis. The diesis part represents the fact that this comma is close to the size of a diesis. The golden part refers to that the temperament tempering out this comma has a generator which is extremely close to logarithmic phi, or 1200/phi cents.

See also

• Logarithmic phi
• Acoustic phi
• Golden ratio