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Statements

Subject Item
dbr:List_of_meantone_intervals
rdfs:label
List of meantone intervals
rdfs:comment
The following is a list of intervals of extended meantone temperament. These intervals constitute the standard vocabulary of intervals for the Western common practice era. Here 12-EDO refers to the size of the interval in 12 equal divisions of the octave temperament, which is the most common meantone temperament of the modern era, 19-EDO to 19 equal temperament, 31-EDO to 31 equal temperament, and 50-EDO to 50 equal temperament. Note that several of the intervals for 31-EDO and 50-EDO are absent from the table.
dcterms:subject
dbc:Music_theory_lists dbc:Linear_temperaments dbc:Intervals_(music)
dbo:wikiPageID
5515942
dbo:wikiPageRevisionID
1076431022
dbo:wikiPageWikiLink
dbr:Minor_sixth dbr:Whole_tone dbr:19_equal_temperament dbr:Submediant dbr:Augmented_sixth dbr:Chromatic_semitone dbr:Augmented_third dbr:Octave dbr:Septimal_minor_third dbr:Diminished_fifth dbr:Septimal_quarter_tone dbr:C_(musical_note) dbc:Music_theory_lists dbr:Perfect_fourth dbr:Interval_(music) dbr:Diminished_second dbr:Common_practice dbr:Diminished_fourth dbr:31_equal_temperament dbr:Diminished_octave dbr:Tonic_(music) dbr:B_(musical_note) dbr:Diminished_seventh dbr:Diminished_sixth dbr:Septimal_major_second dbc:Linear_temperaments dbr:Diminished_third dbr:Septimal_diatonic_semitone dbr:Meantone_temperament dbr:Septimal_major_third dbr:Major_seventh dbr:Major_sixth dbr:Septimal_chromatic_semitone dbr:Quarter-comma_meantone dbr:Perfect_fifth dbr:Minor_third dbr:Septimal_meantone_temperament dbr:Minor_second dbr:Major_third dbr:List_of_pitch_intervals dbc:Intervals_(music) dbr:Augmented_fifth dbr:Augmented_fourth dbr:Augmented_second dbr:Unison dbr:Equal_temperament dbr:Augmented_seventh dbr:Harmonic_seventh dbr:Minor_seventh
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dbo:abstract
The following is a list of intervals of extended meantone temperament. These intervals constitute the standard vocabulary of intervals for the Western common practice era. Here 12-EDO refers to the size of the interval in 12 equal divisions of the octave temperament, which is the most common meantone temperament of the modern era, 19-EDO to 19 equal temperament, 31-EDO to 31 equal temperament, and 50-EDO to 50 equal temperament. Note that several of the intervals for 31-EDO and 50-EDO are absent from the table. In How Equal Temperament Ruined Harmony (and Why You Should Care), pp. 91–92, Ross W. Duffin states: "specifying that the major semitone should be 3/2 the minor semitone [a 3:2 ratio] creates a 31-note division of the octave, which, in turn, closely corresponds to extended-quarter-comma meantone... the 5:4 ratio [whose] extended-sixth-comma meantone corresponds to the 55-division... extended-fifth-comma meantone [corresponds to] the 43-division of the octave [in which the] ratio of the major to minor semitone is 4:3." The other meantone correspondencies: a 1:1 ratio producing a 12-division (1/11-comma meantone)... "2:1 [which] results in a 19-division (1/3-comma meantone)... 5:3, which results in a 50-division" (2/7-comma meantone) are derived from these statements. [Brackets added for readability.] The column of ratios gives a ratio or ratios approximated by the interval in septimal meantone temperament. An augmented interval is increased by a chromatic semitone, and a diminished interval decreased.
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