Kleisma on:
[Wikipedia]
[Google]
[Amazon]
In
Development of a 53-Tone Keyboard Layout
, ''Xenharmonikon XII''. independently discovered this interval which also manifested in a unique mapping using a generalized keyboard capable of accommodating all the above temperaments as well as just intonation constant structures (periodicity blocks) with these numbers of scale degrees The kleisma is also an interval important to the
In music theory
Music theory is the study of the practices and possibilities of music. ''The Oxford Companion to Music'' describes three interrelated uses of the term "music theory". The first is the "rudiments", that are needed to understand music notation (ke ...
and tuning
Tuning can refer to:
Common uses
* Tuning, the process of tuning a tuned amplifier or other electronic component
* Musical tuning, musical systems of tuning, and the act of tuning an instrument or voice
** Guitar tunings
** Piano tuning, adjusti ...
, the kleisma (κλείσμα), or semicomma majeur, is a minute and barely perceptible comma
The comma is a punctuation mark that appears in several variants in different languages. It has the same shape as an apostrophe or single closing quotation mark () in many typefaces, but it differs from them in being placed on the baseline ...
type interval important to musical temperaments
In psychology, temperament broadly refers to consistent individual differences in behavior that are biologically based and are relatively independent of learning, system of values and attitudes.
Some researchers point to association of temperam ...
. It is the difference between six justly tuned minor third
In music theory, a minor third is a musical interval that encompasses three half steps, or semitones. Staff notation represents the minor third as encompassing three staff positions (see: interval number). The minor third is one of two com ...
s (each with a frequency ratio of 6/5) and one justly tuned '' tritave'' or ''perfect twelfth'' (with a frequency ratio of 3/1, formed by a 2/1 octave
In music, an octave ( la, octavus: eighth) or perfect octave (sometimes called the diapason) is the interval between one musical pitch and another with double its frequency. The octave relationship is a natural phenomenon that has been refer ...
plus a 3/2 perfect fifth
In music theory, a perfect fifth is the Interval (music), musical interval corresponding to a pair of pitch (music), pitches with a frequency ratio of 3:2, or very nearly so.
In classical music from Western culture, a fifth is the interval fro ...
). It is equal to a frequency ratio of 15625/15552 = 2−6 3−5 56, or approximately 8.1 cent
Cent may refer to:
Currency
* Cent (currency), a one-hundredth subdivision of several units of currency
* Penny (Canadian coin), a Canadian coin removed from circulation in 2013
* 1 cent (Dutch coin), a Dutch coin minted between 1941 and 1944
* ...
s (). It can be also defined as the difference between five justly tuned minor third
In music theory, a minor third is a musical interval that encompasses three half steps, or semitones. Staff notation represents the minor third as encompassing three staff positions (see: interval number). The minor third is one of two com ...
s and one justly tuned major tenth
In music, the third factor of a chord is the note or pitch two scale degrees above the root or tonal center. When the third is the bass note, or lowest note, of the expressed triad, the chord is in first inversion.
Use
Conventionally, the t ...
(of size 5/2, formed by a 2/1 octave plus a 5/4 major third) or as the difference between a chromatic semitone
In modern Western tonal music theory an augmented unison or augmented prime is the interval between two notes on the same staff position, or denoted by the same note letter, whose alterations cause them, in ordinary equal temperament, to be one ...
(25/24) and a greater diesis
In classical music from Western culture, a diesis ( , plural dieses ( , "difference"; Ancient Greek, Greek: δίεσις "leak" or "escape"Benson, Dave (2006). ''Music: A Mathematical Offering'', p.171. . Based on the technique of playing the ...
(648/625).
The interval was named by Shohé Tanaka after the Greek for "closure",Just Intonation Network (1993). ''1/1: The Quarterly Journal of the Just Intonation Network, Volume 8'', p.19. who noted that it was tempered to a unison
In music, unison is two or more musical parts that sound either the same pitch or pitches separated by intervals of one or more octaves, usually at the same time. ''Rhythmic unison'' is another term for homorhythm.
Definition
Unison or per ...
by 53 equal temperament
In music, 53 equal temperament, called 53 TET, 53 EDO, or 53 ET, is the tempered scale derived by dividing the octave into 53 equal steps (equal frequency ratios). Each step represents a frequency ratio of 2, or 22.6415 ...
. It is also tempered out by 19 equal temperament
In music, 19 Tone Equal Temperament, called 19 TET, 19 EDO ("Equal Division of the Octave"), or 19 ET, is the tempered scale derived by dividing the octave into 19 equal steps (equal frequency ratios). Each step represent ...
, 34 equal temperament In musical theory, 34 equal temperament, also referred to as 34-TET, 34- EDO or 34-ET, is the tempered tuning derived by dividing the octave into 34 equal-sized steps (equal frequency ratios). Each step represents a frequency ratio of , or 35.29 ...
and 72 equal temperament
In music, 72 equal temperament, called twelfth-tone, 72-TET, 72- EDO, or 72-ET, is the tempered scale derived by dividing the octave into twelfth-tones, or in other words 72 equal steps (equal frequency ratios). Each step represents a frequency ...
, but it is ''not'' tempered out in 12 equal temperament
Twelve-tone equal temperament (12-TET) is the musical system that divides the octave into 12 parts, all of which are equally tempered (equally spaced) on a logarithmic scale, with a ratio equal to the 12th root of 2 ( ≈ 1.05946). That result ...
. Namely, in 12 equal temperament the difference between six minor thirds (18 semitones) and one perfect twelfth (19 semitones) is not a comma, but exaggerated to a semitone (100 cents). The same is true for the difference between five minor thirds (15 semitones) and one major tenth (16 semitones).
The interval was described but not used by Rameau
Jean-Philippe Rameau (; – ) was a French composer and music theorist. Regarded as one of the most important French composers and music theorists of the 18th century, he replaced Jean-Baptiste Lully as the dominant composer of French opera an ...
in 1726.
Larry HansonHanson, Larry (1989).Development of a 53-Tone Keyboard Layout
, ''Xenharmonikon XII''. independently discovered this interval which also manifested in a unique mapping using a generalized keyboard capable of accommodating all the above temperaments as well as just intonation constant structures (periodicity blocks) with these numbers of scale degrees The kleisma is also an interval important to the
Bohlen–Pierce scale
The Bohlen–Pierce scale (BP scale) is a musical tuning and scale, first described in the 1970s, that offers an alternative to the octave-repeating scales typical in Western and other musics, specifically the equal-tempered diatonic scale.
The ...
.
References