# Help! I'm giving a lecture on the development of music from Pythagoras to 12 tone.



## Don Fatale

I'm a member of a 'quasi-intellectual' dining club (their description!) and once a year I have to deliver a 1-2 hour lecture which should stimulate, educate and entertain fellow members. My previous talks have been on Wagner (in the words of others) and more recently logical fallacies. Both were considered successes and expectations are high that I'll deliver again. (I don't think they grasp how much effort I put into these talks, and that I do these as much for my own learning.)

This time around it's back to music, and given that the club includes Ancient Greek and Latin scholars (that reads both ways!), philosophy lovers, and musicians (I'm none of those!), I think the above subject would be of interest. Can you help me make it work?

First off, I'd like to talk about Pythagoras and the mathematics of music.
I'd also like to look at:
Pentatonic scale
The devil's note
19 & 31 TET
then move on to equal temperament, probably to finish with the Well Tempered Clavier.

I'm particularly interested in fascinating and entertaining facts and examples I can use to illustrate to the talk. I can use audio samples and visual aids although I prefer to avoid OHP slide shows! 

Ideas, anecdotes, any forms of encouragement welcome. I have until March.


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## Mahlerian

I recommend reading a bit about the concept of the hexachord as it relates to Medieval/Renaissance music theory, and then the system of eight modes (which became 12 with the addition of finals on A and C). Their concept of mode back then was not at all the same thing as our idea of a scale. Composers thought in terms of intervals above the bass and independent lines rather than chordal harmonic progressions.


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## Bridge

Don Fatale said:


> then move on to equal temperament, probably to finish with the Well Tempered Clavier.


The Well-Tempered Clavier is not even the beginning of equal temperament. Bach's instruments are generally thought to have been tuned in the Werckmeister III well temperament or at least something similar to it. It was definitely not written for a equal tempered keyboard, which is a late 19th century phenomenon.


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## Combinebobnt

Interval differences (especially for just intonation compared to something else) are extremely easy to illustrate with basic waves like Saw, square, and sine waves. This can illustrate the differences of changing tunings and harmony over this large time period, and how n-TET's lack the mathematical purity of just intervals.


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## EdwardBast

One fun historical accident is that medieval theorists thought they were rediscovering the Ancient Greek system of modes when they read the ancient treatises and borrowed names like Dorian, Phrygian and Lydian for the Church Modes. But they got them completely wrong because the Greeks counted the intervals from top to bottom rather than bottom to top.


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## Kieran

Is there any Ancient Greek music in existence that you can use, or refer to?


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## millionrainbows

Don Fatale said:


> First off, I'd like to talk about Pythagoras and the mathematics of music.


Talk about Pythagoras and the projection of the fifth, and how this relates to the present-day circle of fifths.


> I'd also like to look at:
> Pentatonic scale


Talk about how the projection or "stacking" of fifths gives the pent scale in the first five cycles: C-G-D-A-E (C-D-E-G-A).


> The devil's note


The 7-note diatonic is obtained by continuing the projection of the fifth to 7 notes, and how this introduces the interval of the tritone (not present in the pentatonic).Talk about how the two tetrachords Mahlerian mentioned earlier, C-D-E-F and G-A B-C both contain leading tones which reinforce moves to another key center, C-F and G-C respectively, and how this built-in dissonance (F-B) of the tritone creates an inherent restlessness or need to move to another key, creating the familiar I-IV-V triumvirate.


> 19 & 31 TET


 Why? Only used to approximate just intervals.


> then move on to equal temperament, probably to finish with the Well Tempered Clavier.


Explain how further stacking of fifths eventually yields all 12 notes. (F)-C-G-D-A-E-B-F#-C#-G#-D#-A#-E#(F).



> I'm particularly interested in fascinating and entertaining facts and examples I can use to illustrate to the talk. I can use audio samples and visual aids although I prefer to avoid OHP slide shows!


Dr. Bradley Lehman's site shows him tuning a harpsichord to Bach's "well" tempered tuning, an approximation of ET. larips.com


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## Don Fatale

Thanks for the replies so far. This is great food for thought. I think the framework is coming together.

I'm finding good material in Robert Greenberg's How to Listen to and Understand Great Music audiobook, and this has a very nice excerpt of ancient Greek music which I might use. I'd like to track down the original recording. He does a pretty good job of explain just versus equal temperament with some good examples. Some youtubers also have some interesting content too.

I think the mathematical aspect of musical harmony is generally interesting and I'll definitely lead with that. A key point is that everything in the universe is vibrating right down to atomic level. Does anyone know if the five note theme to Close Encounters of the Third Kind film has a worthwhile music theory behind it. The concept that even an alien would appreciate these particular intervals is interesting isn't it?

I'm still trying to track down some good 'human interest' stories to liven up the talk, and at some point will have to choose the best excerpts.


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## iskender

All that I learned about music theory I learned from Thomas Mann's Dr. Faustus. I'm sure you can entertain and intrigue your audience by just any discussion of that complex masterpiece (sorry, if I am repeating a well known fact- but Mann was almost sued for plagiarism by Schoenberg after he published this work).


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## Mahlerian

iskender said:


> All that I learned about music theory I learned from Thomas Mann's Dr. Faustus. I'm sure you can entertain and intrigue your audience by just any discussion of that complex masterpiece (sorry, if I am repeating a well known fact- but Mann was almost sued for plagiarism by Schoenberg after he published this work).


Well, the war broke out in part because he had put such a negative spin on Schoenberg's method, which perspective has continued to skew the way most people view it.


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## EdwardBast

iskender said:


> All that I learned about music theory I learned from Thomas Mann's Dr. Faustus. I'm sure you can entertain and intrigue your audience by just any discussion of that complex masterpiece (sorry, if I am repeating a well known fact- but Mann was almost sued for plagiarism by Schoenberg after he published this work).


Dostoyevsky, were he not dead, could have sued Mann for ripping off his seedy devil from _The Brothers Karamazov_.

Hey OP, I thought of something else: You really should take some time to talk about the Ars Subtilior and the music at the papal court at Avignon: Most complex rhythmic notation until well into the 20thc, some of the most beautiful graphic scores, and a cadre of musicians and composers called "The Smokers" - and they weren't talking about tobacco.


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## EdwardBast

Mahlerian said:


> Well, the war broke out in part because he had put such a negative spin on Schoenberg's method, which perspective has continued to skew the way most people view it.


It didn't bother Schoenberg that Adrian Leverkuhn had had sex only once in his life and it was with a syphilitic Spanish prostitute?


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