whole number in hertz

the property of whole numbers doesn't exist in lower octaves, and that the beats are consistent with the second does not make it easier to tune by ear, since the second is not any type of 'internal' measurement

Message: 11 Date: Mon, 23 May 2005 23:18:00 -0000
From: "Tom Dent" <tdent@auth.gr>
Subject: Whole numbers of Hertz

I present a tempered scale where every note is a whole number of Hertz, in the pitch range just above middle C. The resulting circulating temperament has a range of different cent values for the fifth, major third, etc. The scale is particularly well adapted to being tuned by ear as all the beat rates are whole numbers per second (or half integers when tuned in a lower octave). I chose A=421 since it is a common Baroque pitch standard. Other A pitches would lead to different whole number temperaments...

E 315
F 335
F# 354
G 376
G# 398
A 421 Bb 447
B 472
C 502
C# 531
D 563
Eb 597

A rough description of the temperament would be: C-G, G-D, D-A, A-E, Eb-Bb noticeably flat; E-B, C#-G#, Bb-F, F-C barely flat; B-F#, F#-
C#, G#-Eb pure.

~~~Thomas~~~

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--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@a...> wrote:
> the property of whole numbers doesn't exist in lower octaves,

well, duh! I didn't claim any specially wonderful property arises
from the fact that notes are whole numbers of Hz. It was just for the
hell of it, if I can use that expression.

>and that the beats are consistent with the second does not make it
easier to tune by ear, since the second is not any type of 'internal'
measurement

The second corresponds quite closely to the average healthy heartbeat
at rest. The tempo of music was, before metronomes, often described
with reference to the human pulse, and many Renaissance pieces work
best when their basic tempo ('tactus') is around that speed.

Also, I assume that people are able to use their ears and their
watches or clocks at the same time. Otherwise how could organ tuners
work by beat rates (which they certainly did before electronic
tuners)?

~~~T~~~

> I present a tempered scale where every note is a whole number of
> Hertz, in the pitch range just above middle C. The resulting
> circulating temperament has a range of different cent values for
the
> fifth, major third, etc. The scale is particularly well adapted to
> being tuned by ear as all the beat rates are whole numbers per
second
> (or half integers when tuned in a lower octave). I chose A=421
since
> it is a common Baroque pitch standard. Other A pitches would lead
to
> different whole number temperaments...
>
> E 315
> F 335
> F# 354
> G 376
> G# 398
> A 421
> Bb 447
> B 472
> C 502
> C# 531
> D 563
> Eb 597
>
> A rough description of the temperament would be: C-G, G-D, D-A, A-
E,
> Eb-Bb noticeably flat; E-B, C#-G#, Bb-F, F-C barely flat; B-F#, F#-
> C#, G#-Eb pure.
>
> ~~~Thomas~~~

Message: 18 Date: Tue, 24 May 2005 20:23:59 -0000
From: "Tom Dent" <tdent@auth.gr>
Subject: Re: whole number in hertz

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@a...> wrote:

>> the property of whole numbers doesn't exist in lower octaves,
> >

well, duh! I didn't claim any specially wonderful property arises from the fact that notes are whole numbers of Hz. It was just for the hell of it, if I can use that expression.

fine then, if seemed to mean something >>and that the beats are consistent with the second does not make it > >
easier to tune by ear, since the second is not any type of 'internal' measurement

The second corresponds quite closely to the average healthy heartbeat at rest. The tempo of music was, before metronomes, often described with reference to the human pulse, and many Renaissance pieces work best when their basic tempo ('tactus') is around that speed.

that is interesting to learn Also, I assume that people are able to use their ears and their watches or clocks at the same time. Otherwise how could organ tuners work by beat rates (which they certainly did before electronic tuners)?

i thought this was done relatively. As someone who has done quite a bit of tuning, i have never used a clock or metronome
and would be pretty scared if i had to. especially some many high numbers if you can count that high in a second. Besides all this i am sure it is a great scale -- Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles