19-comma: Difference between revisions

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{{Infobox Interval

| 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)19/211.

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)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 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 ==

* [[Large comma]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
 | 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 ==
-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 ==
 * [[Large comma]]