Modes, Scale Degrees, and Ratios in Western Music
Pythagoras, an ancient greek philosopher and mathematician, discovered that music could be expressed in perfect numerical ratios. He believed music could unlock the unseen order and harmony existing in nature through the use of these perfect ratios. He is known as the Father of Mathematics, of Geometry, of Music, and of Philosophy. Important guy I think!
1.) Modes: In Western Music, a mode is a a type of scale with a certain set pattern. It is inspired by Pythagoras’ theory. For example: there are 5 major modes named after Ancient Greek subgroups: Ionian, Dorian, Phrygian, Lydian, Mixolydian. I may explain these in more detail later, but for now, just know they are each a set pattern of 7 notes including 5 whole steps and 2 half steps, called diatonic scales. Each one is a different pattern. The Ionian mode is very familiar to us: it is the scale from The Sound of Music- Do Re Mi Fa Sol La Ti Do , a Major Scale.
2.) Scale degrees:To establish order and understand theory, names and numbers are given to each note in these diatonic scales.
7- leading tone (sometimes subtonic)
So continuing with The Sound of Music:
Do-tonic, Re-super tonic, Mi-mediant, Fa-sub dominant, Sol-dominant, La-sub mediant, Ti- leading tone (sometimes subtonic), and 8(1)-tonic again.
*Octave (Do to Do, 1-8) has a ratio of 2:1
*Perfect 5th (Do to Sol, 1-5) 3:2
*Perfect 4th (Do to Fa, 1-4) 4:3
Very thought provoking, isn't it? Math is everywhere, there is order amidst what may seem to be chaos, and music has the ability to unlock the harmony in this world.
The vibrations of sound are measured in cycles per second. The unit to measure sound is called Hertz (Hz). This has no relation to Hertz car rental by the way... ;)
The human ear can register 20 to 20,000 Hz. This changes as we age. The violin's range is about 220 Hz to around 3,500 Hz. In orchestra, we tune to A 440 Hz. The image below shows a sine wave of A 440 Hz and then the A an octave above it.
Below are some interesting videos you should check out. More proof for how much of an impact sound, music, and this form of energy have on our daily lives. Music can move you! Literally.
**Ferrets have one of the lowest Hz wave frequency ranges of hearing (as low as 10 Hz). They have a strong ability to sense and map the direction of where a sound came from. Bottlenose dolphins have some of the highest frequency ranges of hearing (going above 150,000 Hzs. That is 7 times more sensitive than the human ear). These animals can hear things humans are incapable of. That is pretty cool!
**The term Hertz was named after Heinrich Hertz, a German physicist who proved the existence of electromagnetic waves.
Below is a link that illustrates different instrument ranges. Can you find the violin?
What to learn even more about the physics of sound?
Have fun exploring the science of sound waves!
'What will people think?'
'What if I miss that note?'
'What if I forget that passage?'
'Is what I do really important?'
These are all questions that may come to mind due to performance anxiety and the fear of failure. Not just restricted to the music profession or the violin, these feelings bleed into everyone's lives and in any profession. I still struggle with the fear of performing.
Below is a Ted Talk by Charlie Siem, a British concert violinist who really inspires me. Watch this video for his thoughts on performance anxiety and how playing the violin has brought meaning to every area of his life. As Charlie states in his talk, "Performance is a risk, you never know what is going to happen...But, expectation of how people perceive you, is a negative thing...it holds you back from possibly greater opportunities."
I love his boldness and dedication to his music. These concepts and his insights can be applied to anything you are fearful of. That upcoming recital, or that presentation in your science class you are dreading. Just remember that life is a journey of learning. We are all learning, we all make mistakes. The important thing is to learn from your mistakes, to get up and keep going. Embrace the process. Find beauty in-between reaching your goals.
Thanks to Charlie for his thoughts!
Remember to love yourself even when things don't go well.
"Your life isn't defined by the few successes you have, but the bits in between." -Charlie Siem
Have you ever wondered what the intricate symbols in front of music are? You have probably seen them. There are actually a few different symbols. They are called Clefs.
-Clef is a French term for ‘key’.
-A clef indicates the pitch of the note heads on the Staff (the 5 ledger lines on your sheet music).
In the picture below I have included the three clefs used in string orchestras.
So why are there different clefs you may ask....
I am glad you asked! It is for different ranges. The violin for instance is tuned in a higher range, the viola is in a middle range, and the cello and double bass are in lower ranges.
-The Treble Clef is also called the G Clef:
its circular swirl encircles the G above middle C on the piano.
-The Alto Clef is also called the C Clef:
its two curves meet at middle C.
-The Bass Cleff is also called the F Clef:
its two dots encircle F below middle C.
The different clefs help the notation to remain more centralized within the staff.
Middle C or C4 in scientific pitch notation is the 4th C on a standard 88 key piano keyboard.
On the piano, two clefs are used on every page of sheet music. This is called the grand staff.
The Treble Clef and the Bass Cleff are combined with a brace. The Treble Clef indicates all of the notes the right hand plays and the Bass Cleff indicates all of the left hand notes.
This was a lot of information. But don't be overwhelmed.
If you are a violinist, all you need to know is the Treble Clef.
Lucky you! Remember that the swirl encircles the G and you are all set!
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