Topic by nightwatch

  • Avatar
  • nightwatch
  • Member
  • Offline
  • Registered: 13-01-2010
  • Posts: 44

Topic: Question about the Advanced Tuning panel - Newton Scale

I'm trying to recreate Newton's simple palindromic scale which is:

D      E        F       G      A        B        C      D
   9:8   16:15  10:9   9:8   10:9  16:15   9:8

He starts his scale on D. I converted ratios to cents and ended up with this. I just entered the values in the Keyboard Mapping area after moving D to the first position. Does this look correct? First time to use this.

D = 1/1
E = 203.91
F = 315.64
G = 498.04
A = 701.95
B = 884.35
C = 996.08
D =1,199.99 or 2/1

Black keys stayed on multiples of 100. Not using them anyway.

Thanks,
Steve

Regards,
Steve Steele
stevesteele.com
Music theorist, composer, Vienna Ensemble Pro templates, YouTube channel (Mains: 2 Mac Pros, Digital Performer, Vienna Ensemble Pro, and an iPad Pro.)

nightwatch's Website

Reply by dazric

  • Avatar
  • dazric
  • Member
  • Offline
  • Registered: 16-09-2016
  • Posts: 1,015

Re: Question about the Advanced Tuning panel - Newton Scale

That looks correct as far as I can tell (I used http://www.sengpielaudio.com/calculator-centsratio.htm to check). If you switch to display 'Diff. from ET' values in the Advanced Tuning window (button just beneath Temperament), you can see the palindromic structure.

I was surprised not to find this tuning in the vast Scala archive ( http://www.huygens-fokker.org/scala/scl_format.html ). Maybe it is in there somewhere, but I couldn't find it under 'Newton' or 'Palindromic'.

Last edited by dazric (22-10-2019 11:29)

Reply by nightwatch

  • Avatar
  • nightwatch
  • Member
  • Offline
  • Registered: 13-01-2010
  • Posts: 44

Re: Question about the Advanced Tuning panel - Newton Scale

Thanks dazric,

Are you good with calculations and formulas related to acoustics?

I was a music theory and composition major, and and took an intensive acoustics course, but it wasn't my speciality. However, about a year ago I went into full self study mode and have become utterly obsessed with it. It's opened my eyes in regards to orchestration, theory and composition. I recently bought Audulus 3 (the modular synth for iOS and macOS), and I couldn't put it down. I taught myself how to build several useful synths in a few hours, and within minutes I kinda knew what I was doing. I've built a harmonic series synthesizer with it (for demonstrating the harmonic series in lectures and classes). I'm currently working my way through a graphing calculator, and memorizing trigonometric functions, but my main interest is Fourier Transforms, and from a math perspective, tuning and temperament. What about you?

I upgraded to PianoTEQ 6 exclusively for the Keyboard Mapping feature. Love it.

Regards,
Steve Steele
stevesteele.com
Music theorist, composer, Vienna Ensemble Pro templates, YouTube channel (Mains: 2 Mac Pros, Digital Performer, Vienna Ensemble Pro, and an iPad Pro.)

nightwatch's Website

Reply by dazric

  • Avatar
  • dazric
  • Member
  • Offline
  • Registered: 16-09-2016
  • Posts: 1,015

Re: Question about the Advanced Tuning panel - Newton Scale

Haha, I wouldn't say that I was particularly good with calculations (although I can follow a formula if it's not too complicated), but I've always been fascinated by the science behind the music. When I was a music student, I learned about the harmonic series, the Pythagorean comma, and Well Temperament, but it was all just theory. Discovering Pianoteq, with Advanced Tuning, was like a dream come true - I could finally hear these things, and experiment with many other temperaments and ethnic tunings.

The Newton scale got me wondering: did he have some practical purpose in mind, or was it an academic exercise?

Reply by nightwatch

  • Avatar
  • nightwatch
  • Member
  • Offline
  • Registered: 13-01-2010
  • Posts: 44

Re: Question about the Advanced Tuning panel - Newton Scale

dazric wrote:

The Newton scale got me wondering: did he have some practical purpose in mind, or was it an academic exercise?

It’s been written that Newton didn’t like music as an art but was interested in harmonics like many mathematicians /scientists of his time. He attended only one opera and reportedly, “heard the first act with pleasure, the 2nd stretched his patience, and the 3rd he ran away.”

Supposedly the palindrome scale was an attempt to search for numerical patterns in the ratios of scales. I just read Music by the Numbers by Eli Maor. A near perfect overview of the history of math and music. I think you’d like it. It’s where I read about  the Newton scale. You can find it on Amazon or iBooks.

Thanks for the tip to switch to ‘Different to ET values’ That was it! Although probably due to a math error, there’s a 15.6 and a 15.7 difference in one spot. Everything else is equal.

Anytime you want to talk acoustics, hit me up.

Last edited by nightwatch (25-10-2019 03:51)
Regards,
Steve Steele
stevesteele.com
Music theorist, composer, Vienna Ensemble Pro templates, YouTube channel (Mains: 2 Mac Pros, Digital Performer, Vienna Ensemble Pro, and an iPad Pro.)

nightwatch's Website