26-comma: Difference between revisions
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{{Mathematical interest}} | |||
{{Infobox Interval | {{Infobox Interval | ||
| Name = 26-comma | | Name = 26-comma, Pythagorean inverse triple-diminished second | ||
| Ratio = 2541865828329/2199023255552 | | Ratio = 2541865828329/2199023255552 | ||
| Color name = Wa-26, L<sup>4</sup>w-2 | | Color name = Wa-26, L<sup>4</sup>w-2 | ||
| Comma = | | Comma = true | ||
}} | }} | ||
The '''26-comma''' is a [[3-limit]] [[semifourth]] that acts as a comma in certain temperaments. It is the difference between 26 perfect fifths and 15 octaves, as well as being two [[Pythagorean | The '''26-comma''' is a [[3-limit]] [[semifourth]] that acts as a comma in certain temperaments. It is the difference between 26 perfect fifths and 15 octaves, as well as being two [[Pythagorean comma|Pythagorean commas]] sharp of [[9/8]]. | ||
While it is exceptionally large for a comma (two of them make a near-perfect fourth, off by the small [[53-comma]]), it is tempered out in [[26edo]], because of that temperament's narrow fifths. | While it is exceptionally large for a comma (two of them make a near-perfect fourth, off by the small [[53-comma]]), it is tempered out in [[26edo]], because of that temperament's narrow fifths. | ||
Used as an interval in its own right, it is the '''Pythagorean inverse triple-diminished second'''. It approximates intervals like [[15/13]], and is the simplest Pythagorean interval of this size. As such, it could also be known as the ''Pythagorean semifourth''. | |||
[[Category:Commas named systematically]] | |||
Latest revision as of 07:47, 2 December 2025
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This page presents a topic of primarily mathematical interest.
While it is derived from sound mathematical principles, its applications in terms of utility for actual music may be limited, highly contrived, or as yet unknown. |
| Interval information |
Pythagorean inverse triple-diminished second
reduced harmonic
The 26-comma is a 3-limit semifourth that acts as a comma in certain temperaments. It is the difference between 26 perfect fifths and 15 octaves, as well as being two Pythagorean commas sharp of 9/8.
While it is exceptionally large for a comma (two of them make a near-perfect fourth, off by the small 53-comma), it is tempered out in 26edo, because of that temperament's narrow fifths.
Used as an interval in its own right, it is the Pythagorean inverse triple-diminished second. It approximates intervals like 15/13, and is the simplest Pythagorean interval of this size. As such, it could also be known as the Pythagorean semifourth.