Modal Scales good information

[michael sam wild]

I just found this via a roundabout route from melodeon. net. I found it very comprehensible. Scroll down to find the beginning on the blank page.

 

 

http://gfax.ch/liter...provisation.pdf

 

 

By the way , if you divide the octave scale into 12 equal steps are the number of cycles per second equal fractions. In the absence of an oscilltor I don't know. Any link to a site that shows it on the screen?

Edited December 17, 2010 by michael sam wild

[Ron123]

Hello Michael Sam Wild

 

Thank you for the link, it looks very interesting.

 

Regards

Ron

[Ransom]

By the way , if you divide the octave scale into 12 equal steps are the number of cycles per second equal fractions. In the absence of an oscilltor I don't know. Any link to a site that shows it on the screen?

 

The number of cycles difference between C and C# will not be equal to the number of cycles difference between C# and D. But the relative proportions C/C# and C#/D would be equal.

[David Barnert]

By the way , if you divide the octave scale into 12 equal steps are the number of cycles per second equal fractions. In the absence of an oscilltor I don't know.

Cycles per second varies with pitch not linearly but exponentially. Follow along, it's really not that hard to grasp:

 

For every octave (12 semitones) the frequency is multiplied by 2.

 

Therefore, for every semitone, the frequency is multiplied by the 12th root of 2, or approx 1.06.

 

If A = 440, then the rest of the octave is:

 

Bb = 466.16376152

B_ = 493.88330126

C_ = 523.2511306

C# = 554.36526195

D_ = 587.32953583

Eb = 622.25396744

E_ = 659.25511383

F_ = 698.45646287

F# = 739.98884542

G_ = 783.99087196

G# = 830.60939516

A_ = 880

[SteveS]

By the way , if you divide the octave scale into 12 equal steps are the number of cycles per second equal fractions. In the absence of an oscilltor I don't know.

Cycles per second varies with pitch not linearly but exponentially. Follow along, it's really not that hard to grasp:

 

For every octave (12 semitones) the frequency is multiplied by 2.

 

Therefore, for every semitone, the frequency is multiplied by the 12th root of 2, or approx 1.06.

 

If A = 440, then the rest of the octave is:

 

Bb = 466.16376152

B_ = 493.88330126

C_ = 523.2511306

C# = 554.36526195

D_ = 587.32953583

Eb = 622.25396744

E_ = 659.25511383

F_ = 698.45646287

F# = 739.98884542

G_ = 783.99087196

G# = 830.60939516

A_ = 880

This is good - thanks for posting - I'll print this out and keep in with my tuning/repair kit to remind myself.

 

Do you know what the frequencies would be for meantone tuning?

Edited December 17, 2010 by SteveS

[michael sam wild]

By the way , if you divide the octave scale into 12 equal steps are the number of cycles per second equal fractions. In the absence of an oscilltor I don't know. Any link to a site that shows it on the screen?

 

The number of cycles difference between C and C# will not be equal to the number of cycles difference between C# and D. But the relative proportions C/C# and C#/D would be equal.

 

 

Thanks david and Ransom that makes sense to my limited brain cells! And that meantone question is still a teaser

Edited December 17, 2010 by michael sam wild

[Frederick Wahl]

Do you know what the frequencies would be for meantone tuning?

 

 

If A = 440, then the rest of the octave is:

 

Bb = 466.16376152 x 1.7889 = 936.0439 / 2 = 468.0220

B_ = 493.88330126 x 1.8692 = 978.0610 / 2 = 489.0305

C_ = 523.25113060 x 1.0000 = 523.2511

C# = 554.36526195 x 1.0449 = 546.7451

D_ = 587.32953583 x 1.1180 = 584.9948

Eb = 622.25396744 x 1.1963 = 625.9653

E_ = 659.25511383 x 1.2500 = 654.0639

F_ = 698.45646287 x 1.3375 = 699.8484

F# = 739.98884542 x 1.3975 = 731.2434

G_ = 783.99087196 x 1.4953 = 782.4174

G# = 830.60939516 x 1.6000 = 837.2018

A_ = 880.00000000 x 1.6719 = 874.8236

 

Divide or multiply by 2.0000 to get the appropriate octave.

Mean Tone ratios taken from "The Physics of Sound" by Richard E. Berg/David G. Stork.

 

Edit: because the original table starts with A_ and the ratios begin with C_, Bb and B_ are divided by two.

Correction: the ratios are in relation to C_ (523.25113060), not each particular note.

So, C# = 523.25113060 x 1.0449 not 554.36526195 x 1.0449

 

FW

Edited December 17, 2010 by Frederick Wahl

[SteveS]

Do you know what the frequencies would be for meantone tuning?

 

 

If A = 440, then the rest of the octave is:

 

Equal Tempered---------------Mean tone

 

Bb = 466.16376152 x 1.7889 = 833.9203

B_ = 493.88330126 x 1.8692 = 923.1667

C_ = 523.25113060 x 1.0000 = 523.2511

C# = 554.36526195 x 1.0449 = 579.2563

D_ = 587.32953583 x 1.1180 = 656.6344

Eb = 622.25396744 x 1.1963 = 744.4092

E_ = 659.25511383 x 1.2500 = 824.0687

F_ = 698.45646287 x 1.3375 = 934.1855

F# = 739.98884542 x 1.3975 = 1034.1344

G_ = 783.99087196 x 1.4953 = 1172.3015

G# = 830.60939516 x 1.6000 = 1328.9750

A_ = 880.00000000 x 1.6719 = 1471.2720

 

Divide or multiply by 2.0000 to get the appropriate octave.

Mean Tone ratios taken from "The Physics of Sound" by Richard E. Berg/David G. Stork.

Thanks for posting

Edited December 17, 2010 by SteveS

[Frederick Wahl]

[

Thanks for posting

 

Steve, check the revised table - I corrected a couple of mistakes.

 

FW

[Michael Eskin]

It appears that this book is for sale on Amazon. Is posting an ebook OK with the author?

[JimLucas]

It appears that this book is for sale on Amazon. Is posting an ebook OK with the author?

Was that table of ratios the entire book?

In fact, I suspect that the table is information which Berg and Stork themselves copied from elsewhere, since I believe meantone tuning would have been in use before either was born.

[Michael Eskin]

I'm referring to the original poster's link to a 200 page PDF file.

Edited December 19, 2010 by eskin

[JimLucas]

I'm referring to the original poster's link to a 200 page PDF file.

Sorry for the misunderstanding.

You do have a point, but with 8 other posts between your comment and the post you were commenting on, I missed the connection.

 

That's why I try to always quote or otherwise identify whatever I refer to in my posts.

[David Barnert]

Now that I've got the thread sorted out with the help of the last couple of posts...

 

It appears that this book is for sale on Amazon. Is posting an ebook OK with the author?

Of course not. The pdf even contains the words:

 

No part of this book may be reproduced or transmitted in any form or by any means, graphic, electronic, or mechanical, including photocopying, recording, taping, or by any information storage or retrieval system, without the permission in writing from the publisher.