F C G D A E H 0 0 0 -SC 0 0 Note) 0: Perfect fifth +-: Difference of Perfect fifth SC: Syntonic Comma->[How to calculate Just temperament]It is said that the temperament was devised by ``???Aristcsenous???'' in Greek era. Through Roman era to the end of 15th century, the temperament had been forgotten. However, the temperament was re-devised by Ramis who is musicologist in Renaissance era. The temperament was great influenced to the whole Europe in those days because people in Renaissance era was willing to use major third as consonance and the temperament matched the request.
The only merit of the temperament is that main triad (C,F,G) is Just tone.
At first, if the phrase moves step by step, the phrase sounds awkward. This is caused by the 2 types of whole tone named major whole tone and minor whole tone. In stepwise motion of the scale, E and A sound considerably lower.
In addition, the fifth between D and A is very narrow (the difference scale is SC), the fifth is hard to use in actual.
Theorically, it is impossible to modulate. ( means it needs to exchange the tune itself.)
Generally speaking, the temperament is not useful in actual performance.
C G D A E H Fis Cis Gis Es B F C 0 0 0 0 0 0 0 0 -PC 0 0 0 note) 0: Perfect fifth +-: Difference of Perfect fifth PC: Pytagorean comma->[How to calculate Pytagorian Temperament]It is said that This temperament was devised from Greek theorist Pytagoras. Until the end of 15th century the temperament was used as standard temperament in whole Europe.
The merit is that perfect fifth is the perfect fifth of Just Temperament. In addition, the difference between semitone and whole tone is wider, then adopting the temperament to monophony music like Gregorian chant makes impressive emotions.
The demerit is that major third sounds dissonance. In the temperament, it is able to use the third as major triad but the third sounds very high tension and makes solid sounds rather than major third of Just Temperament. That is why using the temperament in good echoing place like cathedral, the major third which cause the harmonic vibration is conspicuous.
C G D A E H Fis Cis Gis Es B F C
-SC/4 -SC/4 -SC/4 -SC/4 -SC/4 -SC/4 -SC/4 -SC/4 wolf -SC/4 -SC/4 -SC/4
Note) 0: Perfect fifth
+-: Difference of Perfect fifth
SC: Syntonic Comma
wolf: (5th wider than Perfect fifth: see below)
Aron devised the temperament in 1523. The temperament was made to create major third
of Just Temperament.
To create pure major third, each fifth is slightly lower than the perfect fifth. The merit
is that a triad sounds good rather than Pythagorean temperment. In fact the fifth
is a little bit lower than the perfect fifth, however the harmony only occur a little beat
that is why if the harmony sounds with major third, the beat may not noticeable.
However narrower the fifth makes the wider fifth named ``Wolf'' remained then in case of
modulation, there is an limitation.
C G D .... B F C -PC/12 -PC/12 .... -PC/12 -PC/12 Note) 0: Perfect fifth +-: Difference of Perfect fifth PC: Pythagoras CommaThe temperament is the most standard temperament in this century and each scale is derived from twelfth root of two between octave. It was announced in 1636 by Mersenne, but the same kind of the theory was announced in previous. The temperament was used in the early stage with fret instruments, but it is said that the addoptation to keyboard instruments was end of 19th century.(Miyauchi)