Messiaen's Resonant Chord

[@jazzstandards2]

Andrew, regarding the overtone series that you diagram around 5:10, if the fundamental is C, the 11th overtone is in between F and F#, but it is slightly closer to F# than it is to F natural. Here are the details, assuming an even-tempered chromatic scale. F will have a frequency of 2^(5/12) times whatever frequency C is. The decimal approximation is 1.334839854
. F# will have a frequency of 2^(6/12)..., which has a decimal approximation of 1.414213562
. The 11th harmonic will have a frequency of 11/8 which is 1.375 exactly. If you take the ratio of F and the 11th harmonic, you get a ratio of 0.970792621
. However, if you take the ratio of the 11th harmonic and F#, you get a ratio of 0.972271824
, which is closer to 1. This means that 11th harmonic is closer to F# than F, which means that Messiaen didn't arbitrarily sharpen the F. He chose the note in the even-tempered chromatic scale that is closest to the 11th harmonic.

[@brandendowning1714]

thanks for that!

[@ziqianliu1997]

Thank you!!!!❤

[@paulgarthwaite9734]

Thank you so much you work is incredible!!!

[@leopilsudski8168]

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[@sylwestersosniak220]

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[@ScottLHines]

I could use some clarification on “bump it down.” And skip reading the French text. We have an English translation

[@andrewkaiser]

let me go back through that video and take some notes...I'll put out an update in the next week or so. thanks for the comment.

[@andrewkaiser]

@ScottLHines let me know fi this helps, thanks again for your original comment. ruclips.net/video/mIyhdNxBbhM/видео.html