Music and Mathematics

Hipparion

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In Newton's scale the 9/8's and 10/9's are two different sizes of whole tone and the 16/15 is his semitone.
That's what I was missing, thanks !

To correct (whoopsie !) my example of palindromic scale, and in order to make clearer the way it was built:
C-Db-D-Eb-E-F-Gb-G-Ab-A-Bb-B-C
C-Db-D-Eb-E-F-Gb-G-Ab-A-Bb-B-C
C-Db-D-Eb-E-F-Gb-G-Ab-A-Bb-B-C
C-Db-D-Eb-E-F-Gb-G-Ab-A-Bb-B-C
C-Db-D-Eb-E-F-Gb-G-Ab-A-Bb-B-C
which only makes for 5 palindromic scales...
 
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jbtsax

jbtsax

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Here's my attempt to compare Newton's palindromic scale with Pythagorean and equal temperament.
If we start on an A, then the notes in Newton's scale are approximately: A, B, C, D, E, F#, G
I have constructed a chart showing the frequencies of the notes in the three scales:
Brilliant! Thank you. I'm impressed that you could work it out this quickly and put it into such a clear presentation. Who would have thought it would be as simple as a Dorian Mode?
 

nigeld

I don't need another mouthpiece; but . . .
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Who would have thought it would be as simple as a Dorian Mode?
The Newton scale is like a Pythagorean Dorian with a sharpened 3rd and a flattened 6th.
The second, fourth, fifth and seventh are the same in both scales.

As with Pythagorean, there is an attempt to express all the intervals in terms of whole-number ratios. But whereas the Pythagorean scale has justification in terms of harmonic overtones, the Newtonian one appears to me to be based on numerical tidiness rather than acoustics.
 

Hipparion

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There's no shortage of group theory in modern academic music theory.

Try neo-riemannian theory. For a gentle(ish) introduction Audacious Euphony: Chromatic Harmony and the Triad's Second Nature (Oxford Studies in Music Theory):Amazon.co.uk:Books

This is a little more challenging but very interesting and covers a lot more ground: https:://www.amazon.co.uk/Geometry-Music-Counterpoint-Extended-Practice/dp/0195336674/ref=pd_bxgy_14_img_2/262-4310014-5542751?_encoding=UTF8&pd_rd_i=0195336674&pd_rd_r=b72aa5b8-42c8-461d-a9bb-bebd905bec0a&pd_rd_w=BjuXq&pd_rd_wg=n5Nfx&pf_rd_p=7a9d3b22-47b7-4932-be38-57f4219c3325&pf_rd_r=85EAAQWX52ZC1QQ21BAN&psc=1&refRID=85EAAQWX52ZC1QQ21BAN
I guess I'll have to try and find that.

Here's an academic paper by the same guy that's more "mathsy" than his book. I struggle at this level. You might enjoy it.. http://dmitri.mycpanel.princeton.edu/voiceleading.pdf
This is exactly the kind of work I wanted to read !

OK, this guy certainly knows what he is talking about, but I didn't like this video one bit since I find it more confusing than helping, and that is despite the fact I perfectly know where he is going at. If you (anyone) have a hard time to understand that video, don't blame yourself !
 
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jbtsax

jbtsax

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I learned all I needed to know about music and maths in th 60s.

New math (sic)
Curse you Targa. You reminded me of Tom Lehr and his irreverent comedy that was such a big part of my college/drinking days in the '60's. After I went to your link, I wasted the next hour watching a number of his videos and got nothing else done. :p
 
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