Scale
The first scale discovered was by the philosopher Pythagoras. Pythagoras discovered
what is now called the diatonic scale, which is a scale consisting of seven notes
which are five whole tones and two semitones. Pythagoras had found that when
plucking a string, then dividing the string into half and plucking (ratio of 2:1), the
same note was made; except at a higher octave. Taking one of the originals halves
and dividing it by two and plucking (ratio of 3:2), then another half (4:3) and so
forth, the diatonic scale was built.
The greeks had named each ratio so that it may be applicable to their own musical
terms (what would have been 'a', 'b', 'c', and so forth for us); the ratio 2:1 was named
diapason, the ratio 3:2 was known to the Greeks as diapente, and the string ratio 4:3
was called diatessaron. The Greeks applied the prefix dia to their definitions, as it
was defined is between, through or across.
Each of these intervals are found through the strings with lengths relative to 2, 3 and
4, therefore causing the most harmonious intervals to have the numerical progression
of 1:2:3:4. Pythagoras did not leave a written record of his work, his pupil Philolaus
had Pythagoras's discoveries passed on. The first recorded use of an individual using
a monochord to demonstrate and prove Pythagoras's theory was by an individual
named Euclid, in approximately 300 B.C.
what is now called the diatonic scale, which is a scale consisting of seven notes
which are five whole tones and two semitones. Pythagoras had found that when
plucking a string, then dividing the string into half and plucking (ratio of 2:1), the
same note was made; except at a higher octave. Taking one of the originals halves
and dividing it by two and plucking (ratio of 3:2), then another half (4:3) and so
forth, the diatonic scale was built.
The greeks had named each ratio so that it may be applicable to their own musical
terms (what would have been 'a', 'b', 'c', and so forth for us); the ratio 2:1 was named
diapason, the ratio 3:2 was known to the Greeks as diapente, and the string ratio 4:3
was called diatessaron. The Greeks applied the prefix dia to their definitions, as it
was defined is between, through or across.
Each of these intervals are found through the strings with lengths relative to 2, 3 and
4, therefore causing the most harmonious intervals to have the numerical progression
of 1:2:3:4. Pythagoras did not leave a written record of his work, his pupil Philolaus
had Pythagoras's discoveries passed on. The first recorded use of an individual using
a monochord to demonstrate and prove Pythagoras's theory was by an individual
named Euclid, in approximately 300 B.C.
Tuning
The Greeks most basic scale unit used was practices on their Tetrachord (meaning
four strings). The first and fourth notes on the Tetrachord were tuned purposely to a
diatessaron tone (the ratio 4:3). The second and third strings were tuned according to
the mode and genus of the music. When tuning, the Greeks used a descending scale
with notes 1/1, 8/9, 27/32, 3/4, 2/3, 16/27, 9/16, 1/2[6]6. . Each of the descending notes
(ratios) are less than one. Also, it was found that all of the intervals included in
this tuning system could be created by multiplying intervals 8/9, which is called a
'tone' and 243/256 (which is called a 'hemitone', or more commonly 'semitone').
It is believed that Pythagoras created this scale for tuning by selecting a root note,
and produced either ascending or descending fifths, however transposing the tones at
the same time in order to keep them in the same octave. Pythagoras achieved this
by multiplying the fifths by either 2/1 (when transposing upwards) or dividing by 2/1
(transposing downwards). So that it would be like this:
Pythagoras's method of tuning survived for approximately 2000 years (which was
modified slightly from it's original format), until it was replaced by the Equal
Tempered Tuning, and the intonation tuning developed by Ptolemy (which was
forgotten but then discovered in the Renaissance period).
four strings). The first and fourth notes on the Tetrachord were tuned purposely to a
diatessaron tone (the ratio 4:3). The second and third strings were tuned according to
the mode and genus of the music. When tuning, the Greeks used a descending scale
with notes 1/1, 8/9, 27/32, 3/4, 2/3, 16/27, 9/16, 1/2[6]6. . Each of the descending notes
(ratios) are less than one. Also, it was found that all of the intervals included in
this tuning system could be created by multiplying intervals 8/9, which is called a
'tone' and 243/256 (which is called a 'hemitone', or more commonly 'semitone').
It is believed that Pythagoras created this scale for tuning by selecting a root note,
and produced either ascending or descending fifths, however transposing the tones at
the same time in order to keep them in the same octave. Pythagoras achieved this
by multiplying the fifths by either 2/1 (when transposing upwards) or dividing by 2/1
(transposing downwards). So that it would be like this:
Pythagoras's method of tuning survived for approximately 2000 years (which was
modified slightly from it's original format), until it was replaced by the Equal
Tempered Tuning, and the intonation tuning developed by Ptolemy (which was
forgotten but then discovered in the Renaissance period).
Mode
To the ancient Greeks, the term Mode stood in when to apply the term of a scale.
Each mode was a set of rotations of the intervals: 9/8, 9/8, 256/243, 9/8, 9/8,
256/243. As there are seven notes here, just one note could clearly be the definition
of the diatonic scale. The intervals in the scale would consist as follows: tone,
semitone, tone, tone, tone, semitone, tone.
Each mode was a set of rotations of the intervals: 9/8, 9/8, 256/243, 9/8, 9/8,
256/243. As there are seven notes here, just one note could clearly be the definition
of the diatonic scale. The intervals in the scale would consist as follows: tone,
semitone, tone, tone, tone, semitone, tone.