19-comma: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
Created page with "{{Infobox Interval | Monzo = -30 19 | Name = 19-comma, Pythagorean kleisma }} The '''19-comma''', otherwise known as the '''Pythagorean kleisma''' ({{monzo|legend=1| -30 19 }}..."
 
+alt name and clarify
Line 1: Line 1:
{{Infobox Interval
{{Infobox Interval
| Monzo = -30 19
| Monzo = -30 19
| Name = 19-comma, Pythagorean kleisma
| Name = 19-comma, Pythagorean kleisma, Pythagorean inverse double-diminished second
}}
}}
The '''19-comma''', otherwise known as the '''Pythagorean kleisma''' ({{monzo|legend=1| -30 19 }}, [[ratio]]: 1162261467/1073741824), is an interval of about 137.1{{cent}}. It is the amount by which nineteen [[3/2|perfect fifth]]s exceed eleven octaves, or (3/2)<sup>19</sup>/2<sup>11</sup>.
The '''19-comma''', otherwise known as the '''Pythagorean kleisma''' ({{monzo|legend=1| -30 19 }}, [[ratio]]: 1162261467/1073741824), is an interval of about 137.1{{cent}}. It is the amount by which nineteen [[3/2|perfect fifth]]s exceed eleven octaves, or (3/2)<sup>19</sup>/2<sup>11</sup>. If used as an interval in its own right, it is the '''Pythagorean inverse double-diminished second'''.  


== Terminology ==
== Terminology ==
The term ''Pythagorean kleisma'' seems to be first used by [[Flora Canou]] in 2024, for this is the [[kleisma]] of the [[Pythagorean tuning|Pythagorean]] [[5L 2s|diatonic scale]], where ''kleisma'' refers to the inverse double-diminished 1-step i.e. |2L - 3s|. It is equated with the 5-limit kleisma of [[15625/15552]] along with many other intervals in [[meantone]].  
The term ''Pythagorean kleisma'' seems to be first used by [[Flora Canou]] in 2024, for this is the [[kleisma]] of the [[Pythagorean tuning|Pythagorean]] [[5L 2s|diatonic scale]], where ''kleisma'' (adjective: ''kleismic'') refers to the inverse double-diminished 1-step i.e. |2L - 3s|. It is equated with the 5-limit kleisma of [[15625/15552]] along with many other intervals in [[meantone]].  


== See also ==
== See also ==
* [[Large comma]]
* [[Large comma]]

Revision as of 10:38, 25 July 2024

Interval information
Factorization 2-30 × 319
Monzo [-30 19
Size in cents 137.145¢
Names 19-comma,
Pythagorean kleisma,
Pythagorean inverse double-diminished second
FJS name [math]\displaystyle{ \text{dd}{-2} }[/math]
Special properties reduced,
reduced harmonic
Tenney norm (log2 nd) 60.1143
Weil norm (log2 max(n, d)) 60.2286
Wilson norm (sopfr(nd)) 117
Open this interval in xen-calc

The 19-comma, otherwise known as the Pythagorean kleisma (monzo[-30 19, ratio: 1162261467/1073741824), is an interval of about 137.1 ¢. It is the amount by which nineteen perfect fifths exceed eleven octaves, or (3/2)19/211. If used as an interval in its own right, it is the Pythagorean inverse double-diminished second.

Terminology

The term Pythagorean kleisma seems to be first used by Flora Canou in 2024, for this is the kleisma of the Pythagorean diatonic scale, where kleisma (adjective: kleismic) refers to the inverse double-diminished 1-step i.e. |2L - 3s|. It is equated with the 5-limit kleisma of 15625/15552 along with many other intervals in meantone.

See also