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

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