michael sam wild Posted December 17, 2010 Share Posted December 17, 2010 (edited) 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 Link to comment Share on other sites More sharing options...
Ron123 Posted December 17, 2010 Share Posted December 17, 2010 Hello Michael Sam Wild Thank you for the link, it looks very interesting. Regards Ron Link to comment Share on other sites More sharing options...
Ransom Posted December 17, 2010 Share Posted December 17, 2010 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. Link to comment Share on other sites More sharing options...
David Barnert Posted December 17, 2010 Share Posted December 17, 2010 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 Link to comment Share on other sites More sharing options...
SteveS Posted December 17, 2010 Share Posted December 17, 2010 (edited) 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 Link to comment Share on other sites More sharing options...
michael sam wild Posted December 17, 2010 Author Share Posted December 17, 2010 (edited) 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 Link to comment Share on other sites More sharing options...
Frederick Wahl Posted December 17, 2010 Share Posted December 17, 2010 (edited) 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 Link to comment Share on other sites More sharing options...
SteveS Posted December 17, 2010 Share Posted December 17, 2010 (edited) 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 Link to comment Share on other sites More sharing options...
Frederick Wahl Posted December 17, 2010 Share Posted December 17, 2010 [ Thanks for posting Steve, check the revised table - I corrected a couple of mistakes. FW Link to comment Share on other sites More sharing options...
Michael Eskin Posted December 18, 2010 Share Posted December 18, 2010 It appears that this book is for sale on Amazon. Is posting an ebook OK with the author? Link to comment Share on other sites More sharing options...
JimLucas Posted December 19, 2010 Share Posted December 19, 2010 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. Link to comment Share on other sites More sharing options...
Michael Eskin Posted December 19, 2010 Share Posted December 19, 2010 (edited) I'm referring to the original poster's link to a 200 page PDF file. Edited December 19, 2010 by eskin Link to comment Share on other sites More sharing options...
JimLucas Posted December 19, 2010 Share Posted December 19, 2010 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. Link to comment Share on other sites More sharing options...
David Barnert Posted December 24, 2010 Share Posted December 24, 2010 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. Link to comment Share on other sites More sharing options...
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