Basic Definition: The circle of fifths is a visual representation of the relationships among the 12 tones of the chromatic scale(1), their corresponding keys signatures(2), and the associated major and minor keys. Below, you see the geometrical representation of relationships among the 12 pitch classes of the chromatic scale in pitch class space(3).
Digging Deeper
Going around the circle, each pitch is 7 semitones(half steps) higher than the last. At the top you see C Major and it has no sharps or flats at the bottom 6 flats/6 sharps.
Clockwise - As you move clockwise by ascending fifths you gain 1 sharp until you reach the bottom for 6 sharps at F Sharp/G Flat.
Counterclockwise - In the opposite direction you are descending fifths and instead of sharps they're flats. To pass twelve tones in this direction you have to ascend by perfect fourths(5 semitones) rather than fifths(7 semitones). You will find this comparison more often in Jazz music while the ascending fifths is often used to analyze classical music.
Enharmonic key signature(equivalent notes) - At the bottom of the circle, the sharp and flat keys overlap giving you pairs of enharmonic key signatures.
The circle and diatonic key signatures:
The circle can be used to represent the relationship between diatonic scales(4) where each letter represents the major scale with that note as tonic. In example, the major scale of D has 2 sharps. Minor scales as noted in the example above are rotated 3 letters counterclockwise to calculate sharps/flats. For any major key, a scale can be built beginning on the sixth degree(relative minor key) containing the same notes.
Example: G-Major scale(G-A-B-C-E-F#-G) is enharmonic to the e-minor scale(E-F#-G-A-B-C-D-E)
When playing remember that the major key you are in is one half-step above the last sharp you see in the key signature. Since diatonic scales contain seven pitch classes they share six of their seven notes so it's easy to move between scales(modulation). C Major -> G Major = F-C-G-D-A-E-B -> C-G-D-A-E-B-F#
Instrumental Examples: Start at any key on the piano and count seven keys to the right. Those 7 keys are equal to 7 semitones or half steps and also equal to 5 steps within a major or minor scale.
Tones in all keys:
(1) Chromatic Scale
(2) Key Signature: A set of sharp or flat symbols placed together on the staff. They designate the notes that are to be played high or lower than the corresponding natural notes and applies through to the end of the piece or up to the next key signature.
(3) Pitch class space: is the circular space representing all the notes or pitch classes in a musical octave. The different pitches are represented by a single letter in class space(ex: C = C4,C5,C6).
(4) Diatonic Scales: the diatonic scale is composed of seven pitches and a repeated octave. It includes five whole steps and two half steps for each octave. The two half steps are separated from each other by either two or three whole steps, depending on their position in the scale. The 7 pitches of any diatonic scale can be obtained by using a chain of six perfect fifths. C-major example: F-C-G-D-A-E-B
Chapter One: How to Build a Universe
The Facts:
- 1 light-year(distance light travels in 1 year) = 9460730472580800 metres (exactly) ≈ 5.878625 trillion miles ≈ 63241.077 astronomical units ≈ 0.306601 parsecs
- During the big bang temperatures were at 10 billion degrees
- Main initial ingredients: hydrogen and helium with a hint of lithium
- After 3 minutes of the initial bang 98% of all matter was produced
- Universe is 13.8 billion years old
- The visible end of the universe is 90 billion trillion miles away(~100 billion light years across)
- The Universe doubled every 10^-34 seconds under the inflation theory proposed by Alan Guth
Summary:
The Universe started as a infinitely small singularity with space only inside and nothing outside of it, space is created as it expands. In a single second it expanded massively and after a few minutes it is billions of miles wide.
Ancient cosmic radiation exists from the beginning of the universe and was discovered by two scientists testing equipment for bell with a large communications antenna. They were attempting to receive a clear signal but would always get noise, what they didn't realize was they were intercepting cosmic radiation in the form of microwaves from the beginning of the universe postulated by George Gamow(Russian scientists).
The chances that the universe turned out correctly for life are slim. If gravity had been slightly stronger or weaker then elements and conditions created would have been different and may not have been able to support life. Therefore, scientists agree that universes occur often if not infinitely and there are multiple universes in history even though we understand only one time and one t=0.
Scientists predict 3 possibilities for future of the universe:
- Closed: Gravity will end up being too strong and the universe will collapse on itself and shrink back to a singularity.
- Open: Universe will continue to expand until everything is so far apart reactions no longer occur and everything becomes stagnant and "dead".
- Flat: The "Goldilocks effect", everything is just right and the Universe will eventually stop expanding allowing things to exists to no end.
The Universe is endless in that a person who believes the Earth is flat would end up walking around the Earth and arriving in the same place.
Hello, I'm going to be reading Bill Bryson's A Short History of Nearly Everything. Each chapter will be a separate post with basic facts of the chapter displayed at the top then a summary of what I think is important below.
