19-comma: Difference between revisions

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| Color name = L3w-2, trilawa negative 2nd

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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'''. Treating it as a comma, [[tempering out]] this comma gives rise to [[graywood]], which is supported by edos 19, [[38edo|38]], [[57edo|57]], and [[76edo|76]] in their [[patent val]]s.

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'''.

== Temperaments ==

Treating it as a comma, [[tempering out]] this comma gives rise to [[graywood]], which is supported by edos 19, [[38edo|38]], [[57edo|57]], and [[76edo|76]] in their [[patent val]]s.

== 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 out this comma alongside the meantone comma ([[81/80]]), we get [[19edo]], which [[support]]s [[~~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 ([[81/80]]), we get [[19edo]], which [[support]]s [[kleismic]].

== See also ==

* [[Large comma]]

@@ Line 4: / Line 4: @@
 | Color name = L<sup>3</sup>w-2, trilawa negative 2nd
 }}
-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'''. Treating it as a comma, [[tempering out]] this comma gives rise to [[graywood]], which is supported by edos 19, [[38edo|38]], [[57edo|57]], and [[76edo|76]] in their [[patent val]]s.
+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'''.
+== Temperaments ==
+Treating it as a comma, [[tempering out]] this comma gives rise to [[graywood]], which is supported by edos 19, [[38edo|38]], [[57edo|57]], and [[76edo|76]] in their [[patent val]]s.
 == 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 out this comma alongside the meantone comma ([[81/80]]), we get [[19edo]], which [[support]]s [[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 ([[81/80]]), we get [[19edo]], which [[support]]s [[kleismic]].
 == See also ==
 * [[Large comma]]