Yahoo Tuning Groups Ultimate Backup tuning Article: Indie rocker mixes math with music

Thanks, Aaron. There's a YouTube video of Robert Schneider demonstrating his natural logarithm-based "non-Pythagorean" scale:

http://www.youtube.com/watch?v=9TzZPsVMtYM

And his Wiki article: http://en.wikipedia.org/wiki/Robert_Schneider

He doesn't discuss in depth exactly how he gets his scale, though, and I have no idea what formula, temperament or method he's using.

But I did discover - and mention here on the list a while back in fact - that if you use a generator of e (the natural logarithmic base, 2.718281828459...) and a period of pi, and produce a chain of 87 "fifths", you get something very close to 53-tone equal temperament, with 11 steps being the ratio pi/e. Maybe Mr. Schneider has discovered that phenomenon, or will soon.

~D.

----- Original Message ----- From: Aaron Andrew Hunt
To: tuning@yahoogroups.com ; MakeMicroMusic@yahoogroups.com
Sent: Monday, August 06, 2007 5:31 PM
Subject: [tuning] Article: Indie rocker mixes math with music

Indie rocker mixes math with music
WOWS PROS IN THE FIELD WITH NEW NOTES SCALE

http://www.mercurynews.com/ci_6554005?source=email&nclick_check=1

Cheers,
Aaron Hunt
H-Pi Instruments

🔗Aaron Andrew Hunt <aahunt@h-pi.com>

Hi Dan. I followed the wiki link you posted and found this
page where he outlines his scale:

http://www.applesinstereo.com/newmusicalscale.html

Yours,
Aaron Hunt
H-Pi Instruments

--- In tuning@yahoogroups.com, "Danny Wier" <dawiertx@...> wrote:
>
> Thanks, Aaron. There's a YouTube video of Robert Schneider demonstrating his
> natural logarithm-based "non-Pythagorean" scale:
>
> http://www.youtube.com/watch?v=9TzZPsVMtYM
>
> And his Wiki article: http://en.wikipedia.org/wiki/Robert_Schneider
>
> He doesn't discuss in depth exactly how he gets his scale, though, and I
> have no idea what formula, temperament or method he's using.
>
> But I did discover - and mention here on the list a while back in fact -
> that if you use a generator of e (the natural logarithmic base,
> 2.718281828459...) and a period of pi, and produce a chain of 87 "fifths",
> you get something very close to 53-tone equal temperament, with 11 steps
> being the ratio pi/e. Maybe Mr. Schneider has discovered that phenomenon, or
> will soon.
>
> ~D.
>
> ----- Original Message -----
> From: Aaron Andrew Hunt
> To: tuning@yahoogroups.com ; MakeMicroMusic@yahoogroups.com
> Sent: Monday, August 06, 2007 5:31 PM
> Subject: [tuning] Article: Indie rocker mixes math with music
>
>
> Indie rocker mixes math with music
> WOWS PROS IN THE FIELD WITH NEW NOTES SCALE
>
>
> http://www.mercurynews.com/ci_6554005?source=email&nclick_check=1
>
>
> Cheers,
> Aaron Hunt
> H-Pi Instruments
>

🔗Aaron Andrew Hunt <aahunt@h-pi.com>

OK, so he is multiplying a natural number series times a
base frequency. I don't know about you, but when I run
the numbers in a spreadsheet, I get slightly different results.
It looks like he was sometimes rounding to one decimal
place and sometimes not, but rounding errors do not
account for the discrepancies here:

His numbers:
K = 190.4357454
Tone 1 = K ln 4 = 264 Hz (middle C)
Tone 2 = K ln 5 = 306.24 Hz
Tone 3 = K ln 6 = 340.56 Hz
Tone 4 = K ln 7 = 369.6 Hz
Tone 5 = K ln 8 = 396 Hz
Tone 6 = K ln 9 = 417.12 Hz
Tone 7 = K ln 10 = 438.24 Hz
Tone 8 = K ln 11 = 456.72 Hz
Tone 9 = K ln 12 = 472.56 Hz
Tone 10= K ln 13 = 488.4 Hz
Tone 11= K ln 14 = 501.6 Hz
Tone 12= K ln 15 = 514.8 Hz
Tone 13= K ln 16 = 528 Hz

Spreadsheet numbers:
K = 190.4357454 Hz
K ln(4) = 264
K ln(5) = 306.49
K ln(6) = 341.22
K ln(7) = 370.57
K ln(8) = 396
K ln(9) = 418.43
K ln(10) = 438.49
K ln(11) = 456.64
K ln(12) = 473.22
K ln(13) = 488.46
K ln(14) = 502.57
K ln(15) = 515.71
K ln(16) = 528

In cents:

According to his frequencies:
0
256.95
440.85
582.51
701.96
791.91
877.42
948.93
1007.95
1065.03
1111.2
1156.17
1200

According to the spredsheet:
0
258.36
444.2
587.05
701.96
797.34
878.41
948.62
1010.37
1065.24
1114.54
1159.23
1200

Hmm...

Aaron Hunt
H-Pi Instruments

--- In tuning@yahoogroups.com, "Aaron Andrew Hunt" <aahunt@...> wrote:
>
> Hi Dan. I followed the wiki link you posted and found this
> page where he outlines his scale:
>
> http://www.applesinstereo.com/newmusicalscale.html
>
> Yours,
> Aaron Hunt
> H-Pi Instruments
>
>
>
> --- In tuning@yahoogroups.com, "Danny Wier" <dawiertx@> wrote:
> >
> > Thanks, Aaron. There's a YouTube video of Robert Schneider demonstrating his
> > natural logarithm-based "non-Pythagorean" scale:
> >
> > http://www.youtube.com/watch?v=9TzZPsVMtYM
> >
> > And his Wiki article: http://en.wikipedia.org/wiki/Robert_Schneider
> >
> > He doesn't discuss in depth exactly how he gets his scale, though, and I
> > have no idea what formula, temperament or method he's using.
> >
> > But I did discover - and mention here on the list a while back in fact -
> > that if you use a generator of e (the natural logarithmic base,
> > 2.718281828459...) and a period of pi, and produce a chain of 87 "fifths",
> > you get something very close to 53-tone equal temperament, with 11 steps
> > being the ratio pi/e. Maybe Mr. Schneider has discovered that phenomenon, or
> > will soon.
> >
> > ~D.
> >
> > ----- Original Message -----
> > From: Aaron Andrew Hunt
> > To: tuning@yahoogroups.com ; MakeMicroMusic@yahoogroups.com
> > Sent: Monday, August 06, 2007 5:31 PM
> > Subject: [tuning] Article: Indie rocker mixes math with music
> >
> >
> > Indie rocker mixes math with music
> > WOWS PROS IN THE FIELD WITH NEW NOTES SCALE
> >
> >
> > http://www.mercurynews.com/ci_6554005?source=email&nclick_check=1
> >
> >
> > Cheers,
> > Aaron Hunt
> > H-Pi Instruments
> >
>

🔗Joe <tamahome02000@yahoo.com>

🔗Mark Rankin <markrankin95511@yahoo.com>

Thanks, Danny, for the crucial information that a
while back you discovered that if you use a generator
of e, (the natural logarithmic base,
2.718281828459...) and a period of pi (3.14159...),
and produce a chain of 87 fifths, you get something
very close to 53-tone equal temperament, with 11 steps
being the ratio pi/e.

Newcomers should be aware that 53-tone equal
temperament, though impractical for use as a 53-tone
per octave fretted instrument, is a very close
approximation to 5-limit just intonation, and is quite
practical for subsets of 53-tone per octave scales and
for various keyboard instruments.

The 53-tone equal temperament happens to be one of the
terms in a Recurrent Integer Sequence discovered by
the author which goes: 1, 2, 3, 5, 7, 12, 19, 31, 34,
53, 118, 171, 289, 323, 441, 612, 1171, 1783, 2513,
3684, 4296, 12276,16572, 20868, 25164, 46032, 48545,
52841, 73709, 78005, 151714, 229719, 307724, 537443,
714321, 792326, 866035, 944040, 1022045, 1173759,
1251764, 2733247, 2811252, 3985011, 4063016, 5314780,
5544499, 6796263, 24451805....

The formula for this Recurrent Integer Sequence can be
rendered in everyday prose or in mathematical lingo,
to wit:

The next term equals the present term plus one or more
previous terms, and:

a(n+1) = a(n) + a(n-x)...+a(n-y)...+a(n-z)...etc.

This sequence and 11 others by the author may be
visited by going to The On-Line Encyclopedia of
Integer Sequences, changing the opening selection to
"word", deleting the example integer sequence, typing
in Mark William Rankin, and pressing Enter.

These Integer Sequences were calculated using brute
force, i.e., a computer program, which was conceived
by Mark Rankin and created by Stephen Malinowski, Earl
Crabb, and Eric Carr.

Dutch programmer Kees van Prooijen wrote a similar
computer program independently, but he applied
"weights" to his program which appear to have stifled
the numerical complexity known as recurrence.

Finally, it should be pointed out that when Fibonacci
discovered his Recurrent Series in Italy in 1202 AD,
he discovered one and only one Recurrent Sequence
which obeyed his formula that: F(n) = F(n-1) +
F(n-2), e.g. 13 = 5 + 8.

Your author's formula:

a(n+1) = a(n) + a(n-x)...+a(n-y)...+a(n-z)...etc,
e.g. 118 = 53 + 34 + 31
delivers both Non-recurrent and Recurrent Sequences,
moreover, this one formula delivers an *infinite
number* of Non-recurrent Integer Sequences, and an
*infinite number* of Recurrent Integer Sequences.

--- Danny Wier <dawiertx@sbcglobal.net> wrote:

> Thanks, Aaron. There's a YouTube video of Robert
> Schneider demonstrating his
> natural logarithm-based "non-Pythagorean" scale:
>
> http://www.youtube.com/watch?v=9TzZPsVMtYM
>
> And his Wiki article:
> http://en.wikipedia.org/wiki/Robert_Schneider
>
> He doesn't discuss in depth exactly how he gets his
> scale, though, and I
> have no idea what formula, temperament or method
> he's using.
>
> But I did discover - and mention here on the list a
> while back in fact -
> that if you use a generator of e (the natural
> logarithmic base,
> 2.718281828459...) and a period of pi, and produce a
> chain of 87 "fifths",
> you get something very close to 53-tone equal
> temperament, with 11 steps
> being the ratio pi/e. Maybe Mr. Schneider has
> discovered that phenomenon, or
> will soon.
>
> ~D.
>
> ----- Original Message -----
> From: Aaron Andrew Hunt
> To: tuning@yahoogroups.com ;
> MakeMicroMusic@yahoogroups.com
> Sent: Monday, August 06, 2007 5:31 PM
> Subject: [tuning] Article: Indie rocker mixes math
> with music
>
>
> Indie rocker mixes math with music
> WOWS PROS IN THE FIELD WITH NEW NOTES SCALE
>
>
>
http://www.mercurynews.com/ci_6554005?source=email&nclick_check=1
>
>
> Cheers,
> Aaron Hunt
> H-Pi Instruments
>
>
>

____________________________________________________________________________________
Sick sense of humor? Visit Yahoo! TV's
Comedy with an Edge to see what's on, when.
http://tv.yahoo.com/collections/222

🔗Mark Rankin <markrankin95511@yahoo.com>

To be hyper correct, the equation 13 = 5 + 8 should
read 13 = 8 + 5.

--- Mark Rankin <markrankin95511@yahoo.com> wrote:

> Thanks, Danny, for the crucial information that a
> while back you discovered that if you use a
> generator
> of e, (the natural logarithmic base,
> 2.718281828459...) and a period of pi (3.14159...),
> and produce a chain of 87 fifths, you get something
> very close to 53-tone equal temperament, with 11
> steps
> being the ratio pi/e.
>
> Newcomers should be aware that 53-tone equal
> temperament, though impractical for use as a 53-tone
> per octave fretted instrument, is a very close
> approximation to 5-limit just intonation, and is
> quite
> practical for subsets of 53-tone per octave scales
> and
> for various keyboard instruments.
>
> The 53-tone equal temperament happens to be one of
> the
> terms in a Recurrent Integer Sequence discovered by
> the author which goes: 1, 2, 3, 5, 7, 12, 19, 31,
> 34,
> 53, 118, 171, 289, 323, 441, 612, 1171, 1783, 2513,
> 3684, 4296, 12276,16572, 20868, 25164, 46032, 48545,
> 52841, 73709, 78005, 151714, 229719, 307724, 537443,
> 714321, 792326, 866035, 944040, 1022045, 1173759,
> 1251764, 2733247, 2811252, 3985011, 4063016,
> 5314780,
> 5544499, 6796263, 24451805....
>
> The formula for this Recurrent Integer Sequence can
> be
> rendered in everyday prose or in mathematical lingo,
> to wit:
>
> The next term equals the present term plus one or
> more
> previous terms, and:
>
> a(n+1) = a(n) + a(n-x)...+a(n-y)...+a(n-z)...etc.
>
> This sequence and 11 others by the author may be
> visited by going to The On-Line Encyclopedia of
> Integer Sequences, changing the opening selection to
> "word", deleting the example integer sequence,
> typing
> in Mark William Rankin, and pressing Enter.
>
> These Integer Sequences were calculated using brute
> force, i.e., a computer program, which was conceived
> by Mark Rankin and created by Stephen Malinowski,
> Earl
> Crabb, and Eric Carr.
>
> Dutch programmer Kees van Prooijen wrote a similar
> computer program independently, but he applied
> "weights" to his program which appear to have
> stifled
> the numerical complexity known as recurrence.
>
> Finally, it should be pointed out that when
> Fibonacci
> discovered his Recurrent Series in Italy in 1202 AD,
> he discovered one and only one Recurrent Sequence
> which obeyed his formula that: F(n) = F(n-1) +
> F(n-2), e.g. 13 = 5 + 8.
>
> Your author's formula:
>
> a(n+1) = a(n) + a(n-x)...+a(n-y)...+a(n-z)...etc,
> e.g. 118 = 53 + 34 + 31
> delivers both Non-recurrent and Recurrent Sequences,
> moreover, this one formula delivers an *infinite
> number* of Non-recurrent Integer Sequences, and an
> *infinite number* of Recurrent Integer Sequences.
>
>
>
>
>
>
>
> --- Danny Wier <dawiertx@sbcglobal.net> wrote:
>
> > Thanks, Aaron. There's a YouTube video of Robert
> > Schneider demonstrating his
> > natural logarithm-based "non-Pythagorean" scale:
> >
> > http://www.youtube.com/watch?v=9TzZPsVMtYM
> >
> > And his Wiki article:
> > http://en.wikipedia.org/wiki/Robert_Schneider
> >
> > He doesn't discuss in depth exactly how he gets
> his
> > scale, though, and I
> > have no idea what formula, temperament or method
> > he's using.
> >
> > But I did discover - and mention here on the list
> a
> > while back in fact -
> > that if you use a generator of e (the natural
> > logarithmic base,
> > 2.718281828459...) and a period of pi, and produce
> a
> > chain of 87 "fifths",
> > you get something very close to 53-tone equal
> > temperament, with 11 steps
> > being the ratio pi/e. Maybe Mr. Schneider has
> > discovered that phenomenon, or
> > will soon.
> >
> > ~D.
> >
> > ----- Original Message -----
> > From: Aaron Andrew Hunt
> > To: tuning@yahoogroups.com ;
> > MakeMicroMusic@yahoogroups.com
> > Sent: Monday, August 06, 2007 5:31 PM
> > Subject: [tuning] Article: Indie rocker mixes math
> > with music
> >
> >
> > Indie rocker mixes math with music
> > WOWS PROS IN THE FIELD WITH NEW NOTES SCALE
> >
> >
> >
>
http://www.mercurynews.com/ci_6554005?source=email&nclick_check=1
> >
> >
> > Cheers,
> > Aaron Hunt
> > H-Pi Instruments
> >
> >
> >
>
>
>
>
>
____________________________________________________________________________________
> Sick sense of humor? Visit Yahoo! TV's
> Comedy with an Edge to see what's on, when.
> http://tv.yahoo.com/collections/222
>

____________________________________________________________________________________
Need a vacation? Get great deals
to amazing places on Yahoo! Travel.
http://travel.yahoo.com/

🔗Graham Breed <gbreed@gmail.com>

Aaron Andrew Hunt wrote:
> OK, so he is multiplying a natural number series times a
> base frequency. I don't know about you, but when I run > the numbers in a spreadsheet, I get slightly different results. > It looks like he was sometimes rounding to one decimal > place and sometimes not, but rounding errors do not
> account for the discrepancies here:

Yes. I think maybe K got rounded off as well, but I can't think what to. 190.44, as on the web page, doesn't work and 190 is too drastic.

> According to the spredsheet:
> 0
> 258.36
> 444.2
> 587.05
> 701.96
> 797.34
> 878.41
> 948.62
> 1010.37
> 1065.24
> 1114.54
> 1159.23
> 1200
> > Hmm...

Note that it has a just perfect fifth, because ln(8)/ln(4) = (3*ln(2))/(2*ln2) = 3/2.

Graham

🔗Danny Wier <dawiertx@sbcglobal.net>

----- Original Message ----- From: "Aaron Andrew Hunt" <aahunt@h-pi.com>
To: <tuning@yahoogroups.com>
Sent: Monday, August 06, 2007 11:20 PM
Subject: [tuning] Re: Article: Indie rocker mixes math with music

> OK, so he is multiplying a natural number series times a
> base frequency. I don't know about you, but when I run
> the numbers in a spreadsheet, I get slightly different results.
> It looks like he was sometimes rounding to one decimal
> place and sometimes not, but rounding errors do not
> account for the discrepancies here:
>
> His numbers:
> K = 190.4357454
> Tone 1 = K ln 4 = 264 Hz (middle C)
> Tone 2 = K ln 5 = 306.24 Hz
> Tone 3 = K ln 6 = 340.56 Hz
[and so on]

I got the same results you got using an old-fashioned calculator, so he's got some math errors. The point of his scale, I guess, is to divide the octave into twelve unequal divisions using something uber-exotic.

(And I think I proposed using natural logarithms as a measurement of intervals as a joke years ago, to argue against "octave bias" or something.)

~D.

🔗Danny Wier <dawiertx@sbcglobal.net>

----- Original Message ----- From: "Joe" <tamahome02000@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: Tuesday, August 07, 2007 12:04 AM
Subject: [tuning] Re: Article: Indie rocker mixes math with music

> --- In tuning@yahoogroups.com, Aaron Andrew Hunt <aahunt@...> wrote:
>>
>> Indie rocker mixes math with music
>> WOWS PROS IN THE FIELD WITH NEW NOTES SCALE
>>
>> http://www.mercurynews.com/ci_6554005?source=email&nclick_check=1
>>
>> Cheers,
>> Aaron Hunt
>> H-Pi Instruments
>>
>
> Sine waves aren't very sexy. Kudos to him for experimenting though.
> Anyone find the rest of the podcast videos on Itunes?

I haven't checked iTunes yet - but they're available on YouTube:

1/5: http://www.youtube.com/watch?v=4HFBxn7KbsA
2/5: http://www.youtube.com/watch?v=I8j-E2VpEoU
3/5: http://www.youtube.com/watch?v=QyqOb5k0Ozk
4/5: http://www.youtube.com/watch?v=ZZ9Jy85rbZk
5/5: http://www.youtube.com/watch?v=9TzZPsVMtYM

I haven't seen the other videos yet, so I can't comment.

And sine waves may be as exciting as water-flavored Kool-Aid, but you definitely want them around for demonstrating acoustics.

~D.