19-comma: Difference between revisions
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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)<sup>19</sup>/2<sup>11</sup>. If used as an interval in its own right, it is the '''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>. 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 vals]]. | ||
== 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 | 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]]. | ||
== See also == | == See also == | ||
* [[Large comma]] | * [[Large comma]] | ||
Revision as of 12:36, 15 October 2024
| Interval information |
Pythagorean kleisma,
Pythagorean inverse double-diminished second
reduced harmonic
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. Treating it as a comma, tempering out this comma gives rise to graywood, which is supported by edos 19, 38, 57, and 76 in their patent vals.
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 (81/80), we get 19edo, which supports kleismic.