Theory. Some hate it, while others love it. Personally, I do not mind musical theory and I find it fun, and intriguing. Of course I say math is fun too, but math and music go hand in hand! We owe a lot of our modern musical theory to the Ancient Greeks, including scholars like Pythagoras, and Plato. Sure the Ancient Greeks may have used different scales and notation but its the same concept, that is the same. In the end it all adds up to a whole...! Haha
The Scale: Instrumental Versus Vocal...
In modern day when we think of the musical scale we know that there is only one scale, but they are different clefs, and key signatures that will enhance the scale. The main thing to know is that in today's world of western music when it comes to instrumental music versus vocal, there is only one scale- ABCDEFG. However, in Ancient Greek, they had two separate scales for vocalists and instrumentalists. So, what was the main difference between these two scales?
THE VOCAL SCALE:
The notation of the vocal scale is very alphabetical, and closely follows the Greek alphabet. These twenty four symbols are responsible for the central region of the pitch scale. Another twenty four symbols are continued down in the pitch scale, however, these have been altered in comparison to the central twenty four symbols. Then in the opposite direction (up the pitch scale) is another twenty one alphabet symbols that have been inverted this time.
THE INSTRUMENTAL SCALE:
The notation of the instrumental scale is considered to be obscure, with the main feature being the triadic nature of the symbols. Like the vocal scale, the lower end of the pitch scale uses the same symbols as the vocal scale, just rotated differently. "The ‘triads’ of the instrumental series play a pivotal role in the modern theory of how the notation system works. This theory views the signs as notes (with intervals between them) and suggests that the signs of each triad are used to divide the intervals of a diatonic scale into smaller intervals where required. This ‘note theory’ is rather problematic and it is understood that the theory is probably incomplete." (Ancient Greek Musical Notation).
It is believed that the original pitch scale was much less than the known 70 symbol scale that has been discovered today. Some have suggested that it was originally the central twenty four symbols. I can believe this, as being an octave consists of eight notes, then since 24/8 = 3; then that '3' could be seen as the whole tone, a semi tone up (sharp), and a semi tone down (flat). Just thought...
Note: Be sure to click on the images below for increased size and quality.
THE VOCAL SCALE:
The notation of the vocal scale is very alphabetical, and closely follows the Greek alphabet. These twenty four symbols are responsible for the central region of the pitch scale. Another twenty four symbols are continued down in the pitch scale, however, these have been altered in comparison to the central twenty four symbols. Then in the opposite direction (up the pitch scale) is another twenty one alphabet symbols that have been inverted this time.
THE INSTRUMENTAL SCALE:
The notation of the instrumental scale is considered to be obscure, with the main feature being the triadic nature of the symbols. Like the vocal scale, the lower end of the pitch scale uses the same symbols as the vocal scale, just rotated differently. "The ‘triads’ of the instrumental series play a pivotal role in the modern theory of how the notation system works. This theory views the signs as notes (with intervals between them) and suggests that the signs of each triad are used to divide the intervals of a diatonic scale into smaller intervals where required. This ‘note theory’ is rather problematic and it is understood that the theory is probably incomplete." (Ancient Greek Musical Notation).
It is believed that the original pitch scale was much less than the known 70 symbol scale that has been discovered today. Some have suggested that it was originally the central twenty four symbols. I can believe this, as being an octave consists of eight notes, then since 24/8 = 3; then that '3' could be seen as the whole tone, a semi tone up (sharp), and a semi tone down (flat). Just thought...
Note: Be sure to click on the images below for increased size and quality.
Pythagoras: Music is Math
In the time of the Ancient Greeks, music was not seen as an art, but rather as a quantitative science that was used as a mathematical and philosophical description of how the universe was perceived to be constructed. [Mess with music, and you're messing with the universe!]
Anyways, Pythagoras was born around 570BC, and grew up on the island of Samos. Throughout his life he traveled to vast lands, including |
Egypt. Eventually he returned to Greece and settled in Croton, in Magna Graecia (modern day Italy). Pythagoras is most well known for his contributions to both mathematics and music. For example, when I first hear his name I think of the Pythagorean Theorem which states when the two sides of a triangle that make a right angle, the values of each sides squared and added will equal the length of the hypotenuse squared. Likewise in music, Pythagoras is best known for his contribution in regards to intervals, specifically in association with the lengths of string; the octave scale; and a tuning system that he developed.
Intervals: It is believed that one day Pythagoras was walking by a blacksmith's shop, and heard different pitches coming from the anvil that had been hit with different weight hammers. This inspired Pythagoras to further research into the topic, through which he discovered intervals. In music an interval is the distance between two or more notes. Intervals are counted including the starting note and every note between that and the end note. He discovered this by playing different notes on both a lyre and mono chord, which was believed to be invented by him. He would play a single note without pressing down on the string, then play a note with the string pressed down in the middle and then the middle of that, so-on and so-forth. Pythagoras later even linked these intervals to the vibrations of the planets in the solar system.
The Octave Scale: By adding an eighth string to the lyre, Pythagoras was able to create a complete octave on the instrument. He also helped to prove that what could be "said of one octave could also be said for all octaves. For every octave, no matter what pitch range it encompasses, repeats itself without variation throughout the entire pitch range in music. For that reason, Pythagoras considered it sufficient to limit the study of music to the octave." (The Creation of the Musical Scale).
Tuning System: Pythagoras was able to create a method of tuning twelve tones based solely on the perfect fifths. This would produce a satisfactory sound, and more can be learned about it here. There is so much that could be explained and wrote about this topic. I suggest further research if truly interested.
Pythagoras was also the first person to realize the relationship between human emotion and music. This is explained in more detail in the video entitled "Pythagoras and Music (Part 2).
"Music was number and the cosmos was music." Pythagoras believed that music was a mathematical expression of the cosmic order.
If you want to learn more on Pythagoras' contribution to musical theory and math I recommend you check out this website. Halfway down the page under the heading "Western Music." Also, this website has immense detail about Pythagoras and his theories that have contributed to music. Amazing to see the connection between music and mathematics!
Intervals: It is believed that one day Pythagoras was walking by a blacksmith's shop, and heard different pitches coming from the anvil that had been hit with different weight hammers. This inspired Pythagoras to further research into the topic, through which he discovered intervals. In music an interval is the distance between two or more notes. Intervals are counted including the starting note and every note between that and the end note. He discovered this by playing different notes on both a lyre and mono chord, which was believed to be invented by him. He would play a single note without pressing down on the string, then play a note with the string pressed down in the middle and then the middle of that, so-on and so-forth. Pythagoras later even linked these intervals to the vibrations of the planets in the solar system.
The Octave Scale: By adding an eighth string to the lyre, Pythagoras was able to create a complete octave on the instrument. He also helped to prove that what could be "said of one octave could also be said for all octaves. For every octave, no matter what pitch range it encompasses, repeats itself without variation throughout the entire pitch range in music. For that reason, Pythagoras considered it sufficient to limit the study of music to the octave." (The Creation of the Musical Scale).
Tuning System: Pythagoras was able to create a method of tuning twelve tones based solely on the perfect fifths. This would produce a satisfactory sound, and more can be learned about it here. There is so much that could be explained and wrote about this topic. I suggest further research if truly interested.
Pythagoras was also the first person to realize the relationship between human emotion and music. This is explained in more detail in the video entitled "Pythagoras and Music (Part 2).
"Music was number and the cosmos was music." Pythagoras believed that music was a mathematical expression of the cosmic order.
If you want to learn more on Pythagoras' contribution to musical theory and math I recommend you check out this website. Halfway down the page under the heading "Western Music." Also, this website has immense detail about Pythagoras and his theories that have contributed to music. Amazing to see the connection between music and mathematics!
This video is excellent in explaining Pythagoras theory about the ratio of tones that helped to develop our modern day intervals. She also explains more on the means of diatonic. chromatic, and enharmonic tetra chords.
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Ancient Greek Modes:
In today's music the most common mode used is Ionian, which for example if in the key of C Major would be CDEFGAB. A mode is basically a scale that has been created by starting on a different note from a familiar scale (i.e. C Major) and adding sharps or flats. [This is when knowing the Circle of Fifths and Order of sharps and flats comes in handy! FCGDAEB (Order of Sharps) / BEADGCF (Order of Flats)]
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These are seven Ancient Greek Modes.
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Music Terms:
Music:
The word "music" has derived from the Greek word "mousike," which
originates from "Muse." Traditionally in Greek Mythology, the Nine Muses, daughters of Zeus were the goddesses of inspiration in literature, science and the arts.
Scale: The most common, simplistic scale is Concert C Major. With no sharps or flats, the C Major is commonly wrote in the form of an octave, which consists of eight notes. Starting on middle C and ending on C, it can be sung as, "Do, Ray, Mi, Fa, Sol, La, Te, Do." Our scales today are made up of two tetra chords. Tetra Chord: A musical fourth. A tetra chord is made up of four consecutive notes. Two tetra chords make an octave. Diatonic Scale: Is a scale composed of seven distinct pitches. T-T-S-T-T-T-S...Where T is a whole tone; and S is a semi, or half tone. For more in depth information about diatonic scales go here. Chromatic Scale: A scale that consists of 12 notes. Traditionally, on the way up the scale, the player will play every note, including all of the sharps. Then on the way down, every note including the flats are played. Enharmonic: Notes that sound the same, but are written differently. For example, A# is the same as Bb. |
Theory Now Versus Theory Then
As you can see, there have been no major changes to the theory used by the Ancient Greeks in comparison to the theory we use today. Rather, improvements have made. There has been influence on the system of consonance and dissonance (intervals) (consonant – pleasant, melodic) (dissonant – harsh, unpleasant). However, there is one thing that is interesting to note. While today we have the twelve note chromatic scale, in Ancient Greece, they actually had an eighteen note chromatic scale.