**Date:** Fri, 8 Apr 2011 12:06:56 -

**Author:** Richard Berg

**Subject:** Re: Tuning forks

**Post:**

The flip side is trying to play any musics written after about 1750

(Bach) using anything but equal temperament.

I guess I must admit that some more recent atonal music is so complecated

harmonically that you can't even tell.

Dick

On Fri, 8 Apr 2011, Cliff Bettis wrote:

>

> For those of you who are interested, there is a book by Ross Duffin,

> ?How Equal Temperament Ruined Harmony (and why you should care)? that I

> enjoyed a lot.

>

>

>

> Cliff

>

>

>

> From: tap-l-owner@lists.ncsu.edu [mailto:tap-l-owner@lists.ncsu.edu] On

> Behalf Of Paul Nord

> Sent: Thursday, April 07, 2011 3:42 PM

> To: tap-l@lists.ncsu.edu

> Cc: Paul Nord

> Subject: Re: [tap-l] Tuning forks

>

>

>

> Tom,

>

>

>

> There are two mistakes in that scale. At the upper end it skips two

> half steps. In the highest octave, the difference between C# and D is a

> full step. Similarly, the difference between D# and E is a full step.

>

>

>

> If you fix that, then the A's are 109.9, 219.9, 440, 880.4, and 1762 Hz.

> Table below. This is what I've been told. The higher notes are

> pitched a little on the high side, and the lower notes are pitched a

> little low. This is because the harmonic overtones of the lower notes

> ring sharp.

>

>

>

> Modern electric pianos often have settings which allow you to change the

> temperament. The scale below is probably the most common temperament...

> not that I'd recognize one temperament from another.

>

>

>

> Paul

>

>

>

>

>

> C

>

> 65.3

>

> C#

>

> 69.2

>

> D

>

> 73.3

>

> D#

>

> 77.7

>

> E

>

> 82.3

>

> F

>

> 87.9

>

> F#

>

> 92.4

>

> G

>

> 97.9

>

> G#

>

> 103.7

>

> A

>

> 109.9

>

> A#

>

> 116.4

>

> B

>

> 123.4

>

> C

>

> 130.7

>

> C#

>

> 138.5

>

> D

>

> 146.7

>

> D#

>

> 155.5

>

> E

>

> 164.7

>

> F

>

> 174.5

>

> F#

>

> 184.9

>

> G

>

> 195.9

>

> G#

>

> 207.6

>

> A

>

> 219.9

>

> A#

>

> 233

>

> B

>

> 246.9

>

> C

>

> 261.5

>

> C#

>

> 277.1

>

> D

>

> 293.6

>

> D#

>

> 311.1

>

> E

>

> 329.6

>

> F

>

> 349.2

>

> F#

>

> 370

>

> G

>

> 392

>

> G#

>

> 415.3

>

> A

>

> 440

>

> A#

>

> 466.2

>

> B

>

> 493.6

>

> C

>

> 523.3

>

> C#

>

> 554.4

>

> D

>

> 587.4

>

> D#

>

> 622.4

>

> E

>

> 659.4

>

> F

>

> 698.7

>

> F#

>

> 740.2

>

> G

>

> 784.3

>

> G#

>

> 830.9

>

> A

>

> 880.4

>

> A#

>

> 932.7

>

> B

>

> 988.2

>

> C

>

> 1047

>

> C#

>

> 1109

>

> D

>

> D#

>

> 1245

>

> E

>

> 1319

>

> F

>

> F#

>

> 1481

>

> G

>

> 1569

>

> G#

>

> 1662

>

> A

>

> 1762

>

> A#

>

> 1866

>

> B

>

> 1977

>

> C

>

> 2095

>

> C#

>

> 2220

>

> D

>

> 2352

>

>

>

>

>

> On Apr 7, 2011, at 2:39 PM, Thomas J. Bauer wrote:

>

>

>

> Attached is a frequency scale given to me by our Physics of Music

> emeritus expert Dr. Judy Brown.

>

> Tom Bauer

>

> Physics Dept.

>

> Welelesley College

>

>

>

> tap-l@lists.ncsu.edu writes:

>

> Machele -

>

>

>

> I passed your question along to Dr. Bryan Suits - our resident physics

> of music expert - here's his response:

>

>

>

> "Using middle C = C4 = 256 Hz is known as the "Scientific Scale." It

> makes

>

> all of the C's be exactly 2^N Hz, N an integer, and happens to be close

> to

>

> the A4 = 440 Hz scale, for which C4 is 261.3 Hz for the equal tempered

> scale.

>

> Back when scientists used tuning forks to make measurements, this might

> have made some sense, though the origins are unclear to me (there are

> several different stories, I don't know which is correct) it seemed to

> arise in

>

> the early 20th century.

>

>

>

> Note also that this scale (usually) does not use equal tempering

>

> (i.e. intervals determined by powers of the 12th root of two), but

>

> uses the rational numbers of just tuning for a key of C. Hence, for

>

> example, the G above middle C, G4, is 3/2 * 256 = 384 Hz and

>

> A4 would be 5/3 * 256 = 426.667 Hz. It is much easier to tune

>

> notes to each other by ear with the Just scale since the frequencies

>

> are related by the ratio of (usually small) integers. I have seen

>

> tuning forks use C4 = 256 Hz and then other notes determined using

>

> equal tempering on top of that. That is some sort of mixed system.

>

>

>

> You can find a table for the Scientific Just Scale in the Handbook

>

> of Chemistry and Physics. The rational numbers for the Just intervals

>

> are at http://www.phy.mtu.edu/~suits/scales.html , among other places.

>

>

>

> I have never known any scientists who used this scale for music

>

> (or anything else, for that matter). I do not know why people still

>

> make tuning forks with this tuning, but they do. I guess because

>

> people buy them.

>

>

>

> - BHS"

>

>

>

> --

>

> Michael R. Meyer

>

> Lecturer/Lab Coordinator

>

> Mich Tech Physics Dept.

>

> mrmeyer@mtu.edu

>

> 906-487-2273

>

>

>

> ----- Original Message -----

>

> From: "Machele Kindle"

>

> To: "TAp-L"

>

> Sent: Thursday, April 7, 2011 12:52:13 PM GMT -05:00 US/Canada Eastern

>

> Subject: [tap-l] Tuning forks

>

>

>

> This is something I've never figured out. As a musician, A4 is 440Hz.

> But, it is common to get sets of tuning forks where A4 is declared to be

> 426.6Hz (making C4 256Hz and C5 512Hz = entire series is flat). This

> annoys me to no end. I'm sure there's some logical explanation... anyone

> know?

>

>

>

>

>

>

>

>

>

>

>

>

>

>

>

>

>

***********************************************************************

Dr. Richard E. Berg, Professor of the Practice, Retired

Physics Lecture-Demonstration Facility

U.S. mail address:

Department of Physics

University of Maryland

College Park, MD 20742-4111

Phone: (301) 405-5994

FAX: (301) 314-9525

e-mail reberg@umd.edu

www.physics.umd.edu/lecdem

***********************************************************************

From tap-l-owner@lists.ncsu.edu Fri Apr 8 12:31:03 2011