Quinticular comma

Interval information

Ratio	1419857/1417176
Subgroup monzo	2.3.17 [-3 -11 5⟩
Size in cents	3.272038¢
Name	quinticular comma
Color name	s17o54, saquinso 4th
FJS name	[math]\displaystyle{ \text{5d4}^{17,17,17,17,17} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	40.8719
Weil norm (log2 max(n, d))	40.8746
Wilson norm (sopfr(nd))	124
Comma size	unnoticeable
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The quinticular comma is a 2.3.17 subgroup comma of measuring 3.27 cents, with frequency ratio of 1419857/1417176. It forms the difference between five semitones of 18/17 and a perfect fourth, 4/3.

Temperaments

Tempering out this comma in the 2.3.17 subgroup leads to the quinticular temperament, which is related to a number of cluster temperaments, such as quintaleap, quindromeda, and quintaschis.

This comma is tempered out in following EDOs:

• 12n family: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 2772, 2784
• 12n+1 family: between 109 and 337
• 12n+2 family: between 326 and 554
• 12n+3 family: between 555 and 783
• 12n+4 family: between 772 and 1000
• 12n+5 family: between 1001 and 1229
• 12n+6 family: between 1230 and 1446
• 12n+7 family: between 1495 and 1663
• 12n+8 family: between 1748 and 1892
• 12n+9 family: between 2001 and 2109
• 12n+10 family: between 2254 and 2338
• 12n+11 family: between 2507 and 2555

Etymology

The word quinticular was introduced by Xenllium in 2025.