Shohé Tanaka
Encyclopedia
was a Japanese physicist, music theorist, and inventor. He graduated from Tokyo University in 1882 as a science student. On an imperial scholarship, he was sent to Germany for doctoral studies in 1884, together with Mori Ōgai
. His dissertation concerned just intonation
and practical means to its implementation.
Tanaka was an early advocate of 53 equal temperament
as a means of closely approximating 5-limit
just intonation
. He was the first to obtain a clear understanding of the temperament, noticing that it tempered out both the schisma
, 32805/32768, but also the kleisma
, an interval of size 15625/15552 = 2-6 3-5 5 6, which is the interval by which five just minor third
s of size 6/5 exactly differs from a just tenth of size 5/2 exactly. Tanaka was the first to take note of this interval and gave it its name. Tanaka realized that the 53 equal temperament was completely characterized as a five limit temperament by the fact that it tempers out both the schisma and the kleisma.
Tanaka was also an early advocate of the use of the hexagonal lattice
for representing the pitch class
es of 5-limit just intonation. First proposed in the 18th Century by Leonhard Euler
, this model was also used by Hugo Riemann
in his theory of harmony. Tanaka also suggested what would now be called a Fokker block
as a way of viewing the pitch classes of 53 equal temperament.
Tanaka proposed a set of harmonic cadences designed to reflect a traditional Japanese aesthetic, acknowledging pentatonic scales and incorporating suspended tones in the manner of the chords played by the shō. Tanaka's suggestion was taken up by a number of 20th century Japanese composers and theorists.
Tanaka was an inventor as well as a theoretician. He designed and patented a just intonation Enharmonium with 20 keys and 26 pitches in an octave. He had Johannes Kewitsch, of Berlin, construct a 5-octave version and in 1891 he demonstrated it to Anton Bruckner
in Vienna, who was impressed with its potential. He also constructed an early calculating machine.
Mori Ogai
was a Japanese physician, translator, novelist and poet. is considered his major work.- Early life :Mori was born as Mori Rintarō in Tsuwano, Iwami province . His family were hereditary physicians to the daimyō of the Tsuwano Domain...
. His dissertation concerned just intonation
Just intonation
In music, just intonation is any musical tuning in which the frequencies of notes are related by ratios of small whole numbers. Any interval tuned in this way is called a just interval. The two notes in any just interval are members of the same harmonic series...
and practical means to its implementation.
Tanaka was an early advocate of 53 equal temperament
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 . Each step represents a frequency ratio of 21/53, or 22.6415 cents , an interval sometimes called the Holdrian comma.- History :Theoretical interest in this...
as a means of closely approximating 5-limit
Limit (music)
In music theory, limit or harmonic limit is a way of characterizing the harmony found in a piece or genre of music, or the harmonies that can be made using a particular scale. The term was introduced by Harry Partch, who used it to give an upper bound on the complexity of harmony; hence the name...
just intonation
Just intonation
In music, just intonation is any musical tuning in which the frequencies of notes are related by ratios of small whole numbers. Any interval tuned in this way is called a just interval. The two notes in any just interval are members of the same harmonic series...
. He was the first to obtain a clear understanding of the temperament, noticing that it tempered out both the schisma
Schisma
In music, the schisma is the ratio between a Pythagorean comma and a syntonic comma and equals 32805:32768, which is 1.9537 cents...
, 32805/32768, but also the kleisma
Kleisma
In music theory and tuning, the kleisma, or semicomma majeur, is a minute and barely perceptible comma type interval important to musical temperaments. It is the difference between six justly tuned minor thirds and one justly tuned tritave or perfect twelfth...
, an interval of size 15625/15552 = 2-6 3-5 5 6, which is the interval by which five just minor third
Minor third
In classical music from Western culture, a third is a musical interval encompassing three staff positions , and the minor third is one of two commonly occurring thirds. The minor quality specification identifies it as being the smallest of the two: the minor third spans three semitones, the major...
s of size 6/5 exactly differs from a just tenth of size 5/2 exactly. Tanaka was the first to take note of this interval and gave it its name. Tanaka realized that the 53 equal temperament was completely characterized as a five limit temperament by the fact that it tempers out both the schisma and the kleisma.
Tanaka was also an early advocate of the use of the hexagonal lattice
Hexagonal lattice
The hexagonal lattice or equilateral triangular lattice is one of the five 2D lattice types.Three nearby points form an equilateral triangle. In images four orientations of such a triangle are by far the most common...
for representing the pitch class
Pitch class
In music, a pitch class is a set of all pitches that are a whole number of octaves apart, e.g., the pitch class C consists of the Cs in all octaves...
es of 5-limit just intonation. First proposed in the 18th Century by Leonhard Euler
Leonhard Euler
Leonhard Euler was a pioneering Swiss mathematician and physicist. He made important discoveries in fields as diverse as infinitesimal calculus and graph theory. He also introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion...
, this model was also used by Hugo Riemann
Hugo Riemann
Karl Wilhelm Julius Hugo Riemann was a German music theorist.-Biography:Riemann was born at Grossmehlra, Schwarzburg-Sondershausen. He was educated in theory by Frankenberger, studied the piano with Barthel and Ratzenberger, studied law, and finally philosophy and history at Berlin and Tübingen...
in his theory of harmony. Tanaka also suggested what would now be called a Fokker block
Fokker periodicity blocks
Fokker periodicity blocks are a concept in tuning theory used to mathematically relate musical intervals in just intonation to those in equal tuning. They are named after Adriaan Daniël Fokker...
as a way of viewing the pitch classes of 53 equal temperament.
Tanaka proposed a set of harmonic cadences designed to reflect a traditional Japanese aesthetic, acknowledging pentatonic scales and incorporating suspended tones in the manner of the chords played by the shō. Tanaka's suggestion was taken up by a number of 20th century Japanese composers and theorists.
Tanaka was an inventor as well as a theoretician. He designed and patented a just intonation Enharmonium with 20 keys and 26 pitches in an octave. He had Johannes Kewitsch, of Berlin, construct a 5-octave version and in 1891 he demonstrated it to Anton Bruckner
Anton Bruckner
Anton Bruckner was an Austrian composer known for his symphonies, masses, and motets. The first are considered emblematic of the final stage of Austro-German Romanticism because of their rich harmonic language, complex polyphony, and considerable length...
in Vienna, who was impressed with its potential. He also constructed an early calculating machine.
External links
- S. Tanaka. Musical Instrument. United States Patent 443,305. December 23, 1890 (pdf version)
- Anonymous. Testimonials, Etc. (Translations) Relating to the "Enharmonium," Invented by Shohé Tanaka. London, 1891.
- Item 0194 4443215 Enharmonium (Junseicho orugan) Japan, Shizuoka Pref., Hamamatsu Nippon Gakki 1936 G1 - c4 Invented by Shohei Tanaka, 1931. Gakkigaku Shiryôkan (Collection for Organology), Kunitachi College of Music