19-comma: Difference between revisions

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== Terminology ==
== Terminology ==
The term ''Pythagorean kleisma'' seems to be first used by [[Flora Canou]] in 2024, for this is the [[kleisma|moskleisma]] 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]]. It can also be reasoned as a fitting name as by tempering it and the meantone comma, we get [[19edo]], which supports [[hanson and cata|kleismic]].
The term ''Pythagorean kleisma'' seems to be first used by [[Flora Canou]] in 2024, for this is the [[kleisma|moskleisma]] 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]]. It can also be reasoned as a fitting name as by [[tempering out]] this comma alongside the [[meantone comma]], we get [[19edo]], which [[support]]s [[hanson and cata|kleismic]].


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

Revision as of 12:08, 15 October 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
Color name L3w-2, trilawa negative 2nd
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 moskleisma 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. It can also be reasoned as a fitting name as by tempering out this comma alongside the meantone comma, we get 19edo, which supports kleismic.

See also