Dollars

We have various logarithmic measures for relative frequency, but the
Midi Tuning Standard in effect uses a logarithmic measure of absolute
frequency, where differences of an integer correspond to a semitone of
100 cents. As 100 cents make up a dollar, I propose the name "dollar"
for the following measure, bearing in mind it measures frequencies and
not ratios.

The MTS value for 55 Hz is 33, so we can get dollars in terms of
frequency f measured in Hertz by

d = 12 log2(f/55) + 33

To convert dollars to Hertz, we use

f = 55 2^((d-33)/12)

There are 100 cents in an Euro as well, so why not call them Euros
instead of Dollars? Or would that be eurocentric?

Laughing all the way to the bank,

Gabor

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> We have various logarithmic measures for relative frequency, but the
> Midi Tuning Standard in effect uses a logarithmic measure of
absolute
> frequency, where differences of an integer correspond to a semitone
of
> 100 cents. As 100 cents make up a dollar, I propose the
name "dollar"
> for the following measure, bearing in mind it measures frequencies
and
> not ratios.
>
> The MTS value for 55 Hz is 33, so we can get dollars in terms of
> frequency f measured in Hertz by
>
> d = 12 log2(f/55) + 33
>
> To convert dollars to Hertz, we use
>
> f = 55 2^((d-33)/12)

Unfortunately,

we in the eurozone also have cents, and 100 cents makes a Euro : viz: €

I hope that this symbol reproduces on your machine

Mark

On Friday, December 26, 2003, at 10:24 pm, tuning@yahoogroups.com
wrote:

>
> We have various logarithmic measures for relative frequency, but the
> Midi Tuning Standard in effect uses a logarithmic measure of absolute
> frequency, where differences of an integer correspond to a semitone of
> 100 cents. As 100 cents make up a dollar, I propose the name "dollar"
> for the following measure, bearing in mind it measures frequencies and
> not ratios.

Maybe we could come up with a term which is based on what fraction of an
octave it is. 100 cents is also 1/12 octave, and perhaps there is some nice
latin or other suffix that means "reciprocal" or something that could be
used to build a word meaning for example reciprocal-12-octave? That way
we'd have a whole family of terms rather than a single one which is in
effect 12edo-centric.

This is probably a bad idea, but I decided not to censor it.

But for example it could be something really simple and easy to pronounce,
like a "12-er".

I'd certainly like to keep dollars out of it! ;)

-Kurt

on 12/26/03 3:53 PM, Mark Gould <mark.gould@argonet.co.uk> wrote:

> Unfortunately,
>
> we in the eurozone also have cents, and 100 cents makes a Euro : viz: €
>
> I hope that this symbol reproduces on your machine
>
> Mark
>
>
> On Friday, December 26, 2003, at 10:24 pm, tuning@yahoogroups.com
> wrote:
>
>>
>> We have various logarithmic measures for relative frequency, but the
>> Midi Tuning Standard in effect uses a logarithmic measure of absolute
>> frequency, where differences of an integer correspond to a semitone of
>> 100 cents. As 100 cents make up a dollar, I propose the name "dollar"
>> for the following measure, bearing in mind it measures frequencies and
>> not ratios.
>

>Maybe we could come up with a term which is based on what fraction of
>an octave it is.

I was trying to resist the 'we should definitely pick something
that'll be around in a few years' comment.

>This is probably a bad idea, but I decided not to censor it.

I think terminology threads should usually be censored, but it isn't
stopping me either...

>But for example it could be something really simple and easy to
>pronounce, like a "12-er".
>
>I'd certainly like to keep dollars out of it! ;)

Why don't we call it the Octave-Based Fraction Unlikely to Send
Caustic Antipathy To Europe?

-Carl

on 12/26/03 10:51 PM, Carl Lumma <ekin@lumma.org> wrote:

>> Maybe we could come up with a term which is based on what fraction of
>> an octave it is.
>
> I was trying to resist the 'we should definitely pick something
> that'll be around in a few years' comment.
>
>> This is probably a bad idea, but I decided not to censor it.
>
> I think terminology threads should usually be censored, but it isn't
> stopping me either...
>
>> But for example it could be something really simple and easy to
>> pronounce, like a "12-er".
>>
>> I'd certainly like to keep dollars out of it! ;)
>
> Why don't we call it the Octave-Based Fraction Unlikely to Send
> Caustic Antipathy To Europe?

Brilliant! ;)

>
> -Carl

--- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:

> Maybe we could come up with a term which is based on what fraction
of an
> octave it is.

How many log scales for frequency do you think we need?

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:

> Why don't we call it the Octave-Based Fraction Unlikely to Send
> Caustic Antipathy To Europe?

Last time I checked there were various kinds of dollars all over the
world. My impression is that the Europeans figured if dollars were
good enough for Singapore, Hong Kong or the Cayman Islands, they
would do for Europe--so long as no one called them that.

>> Why don't we call it the Octave-Based Fraction Unlikely to Send
>> Caustic Antipathy To Europe?
>
>Last time I checked there were various kinds of dollars all over the
>world. My impression is that the Europeans figured if dollars were
>good enough for Singapore, Hong Kong or the Cayman Islands, they
>would do for Europe--so long as no one called them that.

And Australia and New Zealand and Canada, IIRC. Not to mention the
post-WWII eurodollars that eventually caught us with our pants down
in the 70's.

-Carl

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> Why don't we call it the Octave-Based Fraction Unlikely to Send
> Caustic Antipathy To Europe?

Hee hee. :-) Well acronymmed.

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> Why don't we call it the Octave-Based Fraction Unlikely to Send
> Caustic Antipathy To Europe?

Quite, quite good! I think single malts have taken enough toll on the brain cells that I couldn't hope to match that level of Alphabeticles, Collected in a Rational Order to "Name Your Meaning"...

Cheers,
Jon (about to be booted to meta...)

on 12/26/03 11:08 PM, Gene Ward Smith <gwsmith@svpal.org> wrote:

> --- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:
>
>> Maybe we could come up with a term which is based on what fraction
> of an
>> octave it is.
>
> How many log scales for frequency do you think we need?

This one was actually a log of reciprocal scale, usually "named" by an
integer, and so a family of names. I thought a 12-er would be just as good
as a dollar, and it allows someone else to use a 19-er and be free of cents
entirely.

The log scale I always wanted was simple log base 2 with no scaling. Much
easier on the calculator fingers than working with cents. Maybe I should
join the always-using-at-least-a-spreadsheet crowd, but it goes against the
grain.

-Kurt

>The log scale I always wanted was simple log base 2 with no scaling.

Erv Wilson uses this a lot.

>Much easier on the calculator fingers than working with cents.

Howso?

>Maybe I should
>join the always-using-at-least-a-spreadsheet crowd, but it goes
>against the grain.

It goes against the grain to join the crowd?

-Carl

--- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:

> The log scale I always wanted was simple log base 2 with no
scaling.

For frequency, with a base of one Hz? The point of dollars is that
this works with midi.

on 12/27/03 2:01 PM, Carl Lumma <ekin@lumma.org> wrote:

>> The log scale I always wanted was simple log base 2 with no scaling.
>
> Erv Wilson uses this a lot.
>
>> Much easier on the calculator fingers than working with cents.
>
> Howso?

When computing cents by hand from a ratio, the keystrokes on an hp (RPN)
calculator, having already entered the ratio, are:

log 2 log / 1 2 0 0 *

versus if you didn't need to scale the log result to cents it is only 4
keystrokes instead of 9:

log 2 log /

And of course if I knew how to write a little program I could shorten all of
it. But I so rarely need to program the thing that I have never learned
how, or rather I forget again each time a year or two passes.

But alas cents are everywhere - so I need to use them.

>> Maybe I should
>> join the always-using-at-least-a-spreadsheet crowd, but it goes
>> against the grain.
>
> It goes against the grain to join the crowd?

No. To use a spreadsheet, when in fact I might otherwise not even need to
turn the computer on. Little by little the computer has whittled away at
the parts of my life that do not require its participation. I can still do
things with paper and a calculator and this is refreshing, sort of like
going camping and being away from it all.

-Kurt

>
> -Carl

on 12/27/03 2:43 PM, Gene Ward Smith <gwsmith@svpal.org> wrote:

> --- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:
>
>> The log scale I always wanted was simple log base 2 with no
> scaling.
>
> For frequency, with a base of one Hz? The point of dollars is that
> this works with midi.

Ok, right.