Pythagorean Tuning - The Circle of Fifths, Note Ratios, The Pythagorean Comma and The Wolf Interval

Why do scales contain specific notes in a specific order? It was all down to a man named Pythagoras (yes, the same Pythagoras who developed his theorum in mathematics!) He developed a system which enabled him to create the correct tuning of every note on a scale through a mathematical approach of string ratios. If you place your finger on a string at a certain point, mathematically it will produce a particular note. After calculating the string ratio of an octave, pure fifth and pure fourth, he used these calculations to create the interval required to produce every other note on the scale. The tuning which this system created as used right until the early Renaissance, and therefore for approximately 2000 years! In fact, it is thought that Pythagoras developed the first system which made the Circle of Fifths mathematically possible. It had to be tweaked slightly to work perfectly but the string ratios Pythagoras had calculated made it possible. ⏰ Timecodes ⏰ 00:00 - Background information on Pythagoras and the beginnings of his findings 2:10 - How Pythagoras calculated the strings ratios needed to create the interval of a pure 4th, pure fifth and octave 6:10 - Background to the Circle of Fifths - what is an interval of a fifth and how would this help Pythagoras to calculate the intervals required to produce every note on the scale 10:50 - Calculations of the ratios required to produce every interval required to produce each note on the scale - this is done in incredible detail so hopefully it's easier to understand 21:03 - The Pythagorean comma - what it is and why it occurs 23:48 - The Wolf Interval - what it is and why we need it (includes a small bit on Pythagorean tuning to modern day tuning (equal temperament) - This is just touched on here but there is a larger section on this later in the video) 30:11 - Changing the position of the Wolf Interval between E flat and G sharp and calculating the new Pythagorean comma - is it the same? 36:35 - How Pythagoras used his interval ratios to produce every note on the scale 37:40 - The failings of Pythagorean tuning and if we think Pythagoras knew about them 38:50 - Evidence that Pythagoras knew about the comma 41:48 - Conclusion - The need to have whole number ratios and equal temperament ➡️ VISIT MY WEBSITE - https://serenitymusictuition.co.uk/ ➡️ FREE PRINTABLE RESOURCES - https://serenitymusictuition.co.uk/fr... ➡️FREE MUSIC NOTES AND SYMBOLS PNG IMAGES https://serenitymusictuition.co.uk/mu... ➡️MUSIC THEORY VIDEOS - https://serenitymusictuition.co.uk/mu... ➡️FOLLOW US ON FACEBOOK -   / serenitymusictuition   I have other videos in my YouTube channel which focus on key concepts you need to know for ABRSM grades 1 - 5 theory exams. I have arranged them into topics on my website. You will find videos on: Rhythm - Note names Pitch including staff notation Sharps, Flats and Naturals Ledger Lines - Quizzes which test note names Time Signatures Note and rest groupings in simple time Note and rest groupings in compound time Intervals within an octave - Intervals outside of an octave (compound intervals) Dynamics Music Terms and Signs GCSE Music Key Terms Key Signatures - Circle of Fifths Major and Minor Scales and Keys Tonic Triads ***If you have any questions about any aspects of music theory or piano performance, drop them in the comments - I'd be happy to answer them for you!*** #pythagoras #tuning #intervals