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  #21  
Old 02-04-2007, 07:42 PM
drurb's Avatar
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Really interesting history Don. Thanks.

How do you calculate the difference between D# and Eb as a 1/4 tone? I assume you are saying that the deviation introduced by the well-tempered scale, which makes D# and Eb equal, is equal to a quarter tone. Given that the just-ratio of a minor second is 1.064 and that of the equal-tempered scale is 1.059, I don't understand how the error could be a full quarter-tone. A quarter-tone on the just-scale has a ratio of 1.032 (square-root of 1.064). The deviation between the just-and equal-tempered half-step is (1.064/1.059)= 1.005, just shy of 1/16 of a tone.

Where did I go wrong?

See this.
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Last edited by drurb : 02-04-2007 at 07:50 PM.
  #22  
Old 02-04-2007, 08:18 PM
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Originally Posted by drurb View Post
Really interesting history Don. Thanks.

How do you calculate the difference between D# and Eb as a 1/4 tone? I assume you are saying that the deviation introduced by the well-tempered scale, which makes D# and Eb equal, is equal to a quarter tone. Given that the just-ratio of a minor second is 1.064 and that of the equal-tempered scale is 1.059, I don't understand how the error could be a full quarter-tone. A quarter-tone on the just-scale has a ratio of 1.032 (square-root of 1.064). The deviation between the just-and equal-tempered half-step is (1.064/1.059)= 1.005, just shy of 1/16 of a tone.

Where did I go wrong?

See this.
ART vs. SCIENCE
Shakespeare tells us "science is measurement". So it follows that what CAN'T BE MEASURED is art. You are trying to nail down divine dimensions. Scientists shall NEVER understand that art is beyond understanding. So, in the same way the bastards reinvented standard pitch to A=440 FOR THEIR ON GOD DAMN CONVIENCE, so too, they imagine they can "measure" the devine. Concert pitch used to be as low as A=418, so the vocal tenor could easily reach high C. But nooooo, the damn scientists thought it would be much nicer if everone could work with simple mathematics. The good news is the bastards shall never understand and are consigned to their own hand made hell of sounds. May they rot in hell. They also screwed up microphones so they mostly record only down to low E "because that's the lowest note on the bass". ********. For hundreds of years basses have reached low C below E, but scientists don't want to do the work and spend the money to produce very large magnetic speakers, etc. Phoney bastards. Oh boy, that felt good!!! Don Carrigan
Photo: My 1820 Prescott restrung with gut strings for "period" pictch (A=418) by the Boston Handel & Haydn Society at Boston Symphony Hall. Click below:
http://home.earthlink.net/~prescottv...apRestring.jpg
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  #23  
Old 02-05-2007, 07:35 AM
drurb's Avatar
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Originally Posted by Don Carrigan View Post
ART vs. SCIENCE
Shakespeare tells us "science is measurement". So it follows that what CAN'T BE MEASURED is art. You are trying to nail down divine dimensions. Scientists shall NEVER understand that art is beyond understanding. So, in the same way the bastards reinvented standard pitch to A=440 FOR THEIR ON GOD DAMN CONVIENCE, so too, they imagine they can "measure" the devine. Concert pitch used to be as low as A=418, so the vocal tenor could easily reach high C. But nooooo, the damn scientists thought it would be much nicer if everone could work with simple mathematics. The good news is the bastards shall never understand and are consigned to their own hand made hell of sounds. May they rot in hell. They also screwed up microphones so they mostly record only down to low E "because that's the lowest note on the bass". ********. For hundreds of years basses have reached low C below E, but scientists don't want to do the work and spend the money to produce very large magnetic speakers, etc. Phoney bastards. Oh boy, that felt good!!! Don Carrigan
Photo: My 1820 Prescott restrung with gut strings for "period" pictch (A=418) by the Boston Handel & Haydn Society at Boston Symphony Hall. Click below:
http://home.earthlink.net/~prescottv...apRestring.jpg
"Shakespeare tells us "science is measurement". So it follows that what CAN'T BE MEASURED is art."

No, it does not follow logically at all-- although I agree that art cannot be satisfactorily quantified.


"So, in the same way the bastards reinvented standard pitch to A=440 FOR THEIR ON GOD DAMN CONVIENCE"

This was certainly not done for the convenience of scientists! You really should read the history of changing concert pitch. Try this. The substantial rise in concert pitch in the 19th century was not precipitated by scientists! The reference I gave suggests it was at the behest of vocalists. Alexander Woods, in his classic text, The Physics of Music, argues that it was the result of the development of brass instruments.

Well, you've basically told me to rot in hell. After all, I am one of those scientists. It is folly to think that the intervals used in music cannot be measured although I agree that art cannot. I'd like to think Pythagoras is not rotting in hell either.

You made a statement about the difference between just intonation and equal temperament regarding a quarter-tone. That is a mathematical statement subject to quantitative verification! For all I can tell, the statement is incorrect and I politely asked you what was wrong with my calculations. Your response amounts to dismissing the mathematics entirely. So, you say the difference is a quarter-tone, I ask you to show me the basis for that claim and you respond that I shouldn't be appealing to mathematics. Hmm.

You are completely off the mark regarding the constraints of microphones, loudspeakers, and the physics of music. The low-frequency response of professional microphones is certainly not low-pass above or around the fundamental of the E string (~43 Hz). With regard to loudspeakers-- wrong again. Gee, the pair I have at home has usable output down to 12 Hz! Ever see or hear a Klipschorn, Don (I had those too)? The problem is it takes a large cabinet and substantial $$$ to be able to reproduce those frequencies. That's physics and economics, not art.

I can regularly enjoy the pedal tones of the organ in the Saint Saens' "Organ" Symphony No. 3. Interestingly, some 40+ years ago, Angel released this
recording of that symphony. I remember the pedal tones shaking our home as they were reproduced with a Bell2200C amplifier and 15-inch Tannoy. That was in the 1960s, Don, and those pedal tones were recorded to the delight of many by those "evil" microphones invented by some "misguided" scientists. By the way, the two pieces of equipment just mentioned are over 50 years old and are alive and well and in my office.

drurb
Fellow, Acoustical Society of America

Edit: Check this out as well. I trust you will appreciate the relevance.

Last edited by drurb : 02-05-2007 at 08:25 AM.
  #24  
Old 02-05-2007, 08:57 AM
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Science is Art (or at least it used to be)

OK. The DB was invented in Europe and perfected by an American named Abraham Prescott. (Please don't quote me or try to argue this point). And I have it on good aurthority that Pepitone was banished to the minors for using Ernie Ball roundworms.

Two great links on history of the DB:
http://www.mdw.ac.at/I105/orpheon/Se...bra/Portal.htm

http://violadagamba.org/

If you must have a precise name of maker as inventor, I think Gasparo Da Salo might be a popular choice. That's quite a jump really. Sort of like saying Amati invented the violin.
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  #25  
Old 02-05-2007, 09:18 AM
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Originally Posted by Marcus Johnson View Post
Hah! We're a lot of help! This poor guy's never gonna get his term paper done at this rate.
Quote:
Originally Posted by drurb View Post
Sometimes the internet is not the best place to use as a source for a school report.

Yes - I dont think we should be bypassing the learning process - it's not really helping anybody in the long run...
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Last edited by Bruce Lindfield : 02-05-2007 at 09:22 AM.
  #26  
Old 02-05-2007, 10:21 AM
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Harmonic Divergence: OT

I'm building a new studio workshop. The ratio of the area of the second floor to the first is 1:2. the ratio of the width of the building to the legnth is 2:3. The ratio of the width of the 2nd floor to the length of the second floor is 3:4. The ratio of the height of the (north wall) first floor to the second is 4:5. The ratio of the height of the (south wall) second floor to first is 7 to 8. I think I left something out.

Anyway, the church wanted me to build it with a steeple of their design which would have messed up the proportions. I told them the gods ruled harmony and the steeple was not possible. One of the contractors I condidered at first said he wanted to make it easier to switch between metric units and English units and suggested I measure it all out in twelfth roots of two. That didn't make cents so I immediatedly fired him.

Anyway you can get a graphical explanation of all of this from this handy chart prepared by the inventor of the BAZANTAR.
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