Michael Sheiman's Harmonic Series based scale

Ok,

Michael sent me a microtonal scale he was working on and I improvised
using it. I midi recorded the improvisation, cleaned it up, sped it
up, and added z3ta+ synth 4 times to it.

The scale contains parts of the harmonic series a fifth apart. He
would be able to talk about it much more intelligently then I. This
will be cross-posted to MMM.

!e:\Music\harmonicious scale.scl
!
Harmonicious 12-tone scale
12
!
203.91000173
291.51301613
386.31371386
470.78090733
551.3179423647566
628.2743472684155
701.9550008653874
772.6274277296696
905.8650025961624
1049.3629100223864
1145.0355724642502
2/1

http://clones.soonlabel.com/mp3/harmonioussynth.mp3

and as piano for completeness - the microtonal scale is much more
apparent.

http://clones.soonlabel.com/mp3/harmoniouspiano.mp3

> http://clones.soonlabel.com/mp3/harmonioussynth.mp3
>
>and as piano for completeness - the microtonal scale is much more
>apparent.
>
> http://clones.soonlabel.com/mp3/harmoniouspiano.mp3

Me like!

-Carl

Thanks for the listen and liking the piece Carl!
Sent via BlackBerry from T-Mobile

-----Original Message-----
From: Carl Lumma <carl@...>

Date: Thu, 29 Jan 2009 00:08:46
To: <MakeMicroMusic@yahoogroups.com>
Subject: Re: [MMM] Michael Sheiman's Harmonic Series based scale

> http://clones.soonlabel.com/mp3/harmonioussynth.mp3
>
>and as piano for completeness - the microtonal scale is much more
>apparent.
>
> http://clones.soonlabel.com/mp3/harmoniouspiano.mp3

Me like!

-Carl

[Non-text portions of this message have been removed]

For those who might find this more useful or understandable in terms of rational numbers:

!
Harmonicious 12-tone scale (rational version)
12
!
9/8
58/49
5/4
21/16
11/8
23/16
3/2
25/16
27/16
11/6
31/16
2/1

I did this using two online tools:
http://www.sengpielaudio.com/calculator-centsratio.htm
and
http://superspace.epfl.ch/approximator/

- Dave

vaisvil wrote:
> Ok,
> > Michael sent me a microtonal scale he was working on and I improvised
> using it. I midi recorded the improvisation, cleaned it up, sped it
> up, and added z3ta+ synth 4 times to it.
> > The scale contains parts of the harmonic series a fifth apart. He
> would be able to talk about it much more intelligently then I. This
> will be cross-posted to MMM.
> > !e:\Music\harmonicious scale.scl
> !
> Harmonicious 12-tone scale
> 12
> !
> 203.91000173
> 291.51301613
> 386.31371386
> 470.78090733
> 551.3179423647566
> 628.2743472684155
> 701.9550008653874
> 772.6274277296696
> 905.8650025961624
> 1049.3629100223864
> 1145.0355724642502
> 2/1
> > http://clones.soonlabel.com/mp3/harmonioussynth.mp3
> > and as piano for completeness - the microtonal scale is much more
> apparent.
> > http://clones.soonlabel.com/mp3/harmoniouspiano.mp3
> -- ~DaveSeidel = [
http://mysterybear.net,
http://daveseidel.tumblr.com,
http://twitter.com/DaveSeidel
];

At 06:32 AM 1/31/2009, you wrote:
>For those who might find this more useful or understandable in terms of
>rational numbers:
>
>!
>Harmonicious 12-tone scale (rational version)
>12
>!
>9/8
>58/49
>5/4
>21/16
>11/8
>23/16
>3/2
>25/16
>27/16
>11/6
>31/16
>2/1
>
>I did this using two online tools:
> http://www.sengpielaudio.com/calculator-centsratio.htm
>and
> http://superspace.epfl.ch/approximator/
>
>- Dave

Doesn't look right though (at least, it's not a combination of
two harmonic series segments a 3:2 apart as Michael seemed to
claim).

-Carl

That's what I got from the tools I mentioned, which may or may not be accurate. I can't speak to whether Michael's statement is an accurate description of the original scale. Maybe someone who actually understands the math (i.e., someone other than me) can take a stab at making the conversions.

Wouldn't it be cool if Scala could do rational approximation from decimal numbers?

- Dave

Carl Lumma wrote:
> At 06:32 AM 1/31/2009, you wrote:
>> For those who might find this more useful or understandable in terms of >> rational numbers:
>>
>> !
>> Harmonicious 12-tone scale (rational version)
>> 12
>> !
>> 9/8
>> 58/49
>> 5/4
>> 21/16
>> 11/8
>> 23/16
>> 3/2
>> 25/16
>> 27/16
>> 11/6
>> 31/16
>> 2/1
>>
>> I did this using two online tools:
>> http://www.sengpielaudio.com/calculator-centsratio.htm
>> and
>> http://superspace.epfl.ch/approximator/
>>
>> - Dave
> > Doesn't look right though (at least, it's not a combination of
> two harmonic series segments a 3:2 apart as Michael seemed to
> claim).
> > -Carl

--
~DaveSeidel = [
http://mysterybear.net,
http://daveseidel.tumblr.com,
http://twitter.com/DaveSeidel
];

Dave wrote:
>That's what I got from the tools I mentioned, which may or may not be
>accurate. I can't speak to whether Michael's statement is an accurate
>description of the original scale. Maybe someone who actually
>understands the math (i.e., someone other than me) can take a stab at
>making the conversions.

Sorry, I wasn't criticizing you. Rather, it's an example of why
the author of the scale should preserve the information.

>Wouldn't it be cool if Scala could do rational approximation from
>decimal numbers?

It can. It can even do this under the constraint of a prime limit.

-Carl

No problem, I didn't take it personally, but I guess I can get a little defensive due to my lack of adequate math knowledge.

Can you point me in the direction of the Scala command(s) that can do rational approximation? I'd appreciate it.

- Dave

Carl Lumma wrote:
> Dave wrote:
>> That's what I got from the tools I mentioned, which may or may not be >> accurate. I can't speak to whether Michael's statement is an accurate >> description of the original scale. Maybe someone who actually >> understands the math (i.e., someone other than me) can take a stab at >> making the conversions.
> > Sorry, I wasn't criticizing you. Rather, it's an example of why
> the author of the scale should preserve the information.
> >> Wouldn't it be cool if Scala could do rational approximation from >> decimal numbers?
> > It can. It can even do this under the constraint of a prime limit.
> > -Carl
> -- ~DaveSeidel = [
http://mysterybear.net,
http://daveseidel.tumblr.com,
http://twitter.com/DaveSeidel
];

Dave wrote:
>Can you point me in the direction of the Scala command(s) that can do
>rational approximation? I'd appreciate it.

I never learned the commands back when Scala was command-line only.
However, there's an Approximate menu in the GUI version.
The top two options in the menu transform a scale in memory from
irrational to rational, which is what we want. The Rational
Approximation choice is what I was thinking of, but it's taking
an awful long time on my machine. I think I ran into this problem
before. The Farey version is quicker, but I don't know exactly
what it's doing (should be explained in the help).

-Carl

Thanks! I'll try it out.

Carl Lumma wrote:
> Dave wrote:
>> Can you point me in the direction of the Scala command(s) that can do >> rational approximation? I'd appreciate it.
> > I never learned the commands back when Scala was command-line only.
> However, there's an Approximate menu in the GUI version.
> The top two options in the menu transform a scale in memory from
> irrational to rational, which is what we want. The Rational
> Approximation choice is what I was thinking of, but it's taking
> an awful long time on my machine. I think I ran into this problem
> before. The Farey version is quicker, but I don't know exactly
> what it's doing (should be explained in the help).
> > -Carl
> -- ~DaveSeidel = [
http://mysterybear.net,
http://daveseidel.tumblr.com,
http://twitter.com/DaveSeidel
];

Ok, I guess I have to clear some things up.

The basic scale (this is about the 5th time I have said this), is based on the intervals

     (first harmonic series)
1 9/8 5/4 11/8 3/2
 (*9/8 * 10/9 * 11/10 * 12/11)

AND then (the second series using 3/2 as the split point)            
3/2 * 10/9  (* 11/10 )  (* 12/11 octave)

    That's 7 notes based on essentially
A) the harmonic series ratios 9/8 * 10/9 * 11/10 * 12/11 to get to the 5th
B) that result times 10/9 * 11/10 * 12/11 to get to the octave
 
   Note I do cheat a tad by starting at 10/9 instead of 9/8 for the second series, but the results are very very close.

   Let me put it this way, judging the difference between this and two exactly stacked harmonic series...is like comparing ET to Just Intonation diatonic...they are different, but, on the average, not by much.
*********************************************************************
   BTW, I wonder why people are SO interested in this "nearly perfect stacked harmonic series" tuning when my latest "imitation-ET" tuning uses a PERFECT split to make the harmonic series instead of a "half split" (note, it's the exact same ratios IE
1/1 (first note to generate harmonic series from)
18/17
19/17
20/17
21/17
22/17
23/17
24/17 (second note to generate harmonic series from)
--------------
18/17 * 24/17
19/17 * 24/17
20/17 * 24/17
21/17 * 24/17
22/17 * 24/17
23/17 * 24/17
24/17 * 24/17

-Michael

--- On Sat, 1/31/09, Dave Seidel <dave@...> wrote:

From: Dave Seidel <dave@...>
Subject: Re: [MMM] Michael Sheiman's Harmonic Series based scale
To: MakeMicroMusic@yahoogroups.com
Date: Saturday, January 31, 2009, 2:35 PM

That's what I got from the tools I mentioned, which may or may not be

accurate. I can't speak to whether Michael's statement is an accurate

description of the original scale. Maybe someone who actually

understands the math (i.e., someone other than me) can take a stab at

making the conversions.

Wouldn't it be cool if Scala could do rational approximation from

decimal numbers?

- Dave

Carl Lumma wrote:

> At 06:32 AM 1/31/2009, you wrote:

>> For those who might find this more useful or understandable in terms of

>> rational numbers:

>>

>> !

>> Harmonicious 12-tone scale (rational version)

>> 12

>> !

>> 9/8

>> 58/49

>> 5/4

>> 21/16

>> 11/8

>> 23/16

>> 3/2

>> 25/16

>> 27/16

>> 11/6

>> 31/16

>> 2/1

>>

>> I did this using two online tools:

>> http://www.sengpiel audio.com/ calculator- centsratio. htm

>> and

>> http://superspace. epfl.ch/approxim ator/

>>

>> - Dave

>

> Doesn't look right though (at least, it's not a combination of

> two harmonic series segments a 3:2 apart as Michael seemed to

> claim).

>

> -Carl

--

~DaveSeidel = [

http://mysterybear. net,

http://daveseidel. tumblr.com,

http://twitter. com/DaveSeidel

];

[Non-text portions of this message have been removed]

There is something wrong here Michael . a 24/17 above a 24/17 does not equal an octave.
the other 11 limit harmonic series a 3/2 apart has been used countlessly by others. the concept can be seen here.
http://anaphoria.com/hel.PDF

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Michael Sheiman wrote:
>
>
> *********************************************************************
> BTW, I wonder why people are SO interested in this "nearly perfect > stacked harmonic series" tuning when my latest "imitation-ET" tuning > uses a PERFECT split to make the harmonic series instead of a "half > split" (note, it's the exact same ratios IE
> 1/1 (first note to generate harmonic series from)
> 18/17
> 19/17
> 20/17
> 21/17
> 22/17
> 23/17
> 24/17 (second note to generate harmonic series from)
> --------------
> 18/17 * 24/17
> 19/17 * 24/17
> 20/17 * 24/17
> 21/17 * 24/17
> 22/17 * 24/17
> 23/17 * 24/17
> 24/17 * 24/17
>
> -Michael
>
> --- On Sat, 1/31/09, Dave Seidel <dave@... > <mailto:dave%40superluminal.com>> wrote:
>
> From: Dave Seidel <dave@... <mailto:dave%40superluminal.com>>
> Subject: Re: [MMM] Michael Sheiman's Harmonic Series based scale
> To: MakeMicroMusic@yahoogroups.com > <mailto:MakeMicroMusic%40yahoogroups.com>
> Date: Saturday, January 31, 2009, 2:35 PM
>
> That's what I got from the tools I mentioned, which may or may not be
>
> accurate. I can't speak to whether Michael's statement is an accurate
>
> description of the original scale. Maybe someone who actually
>
> understands the math (i.e., someone other than me) can take a stab at
>
> making the conversions.
>
> Wouldn't it be cool if Scala could do rational approximation from
>
> decimal numbers?
>
> - Dave
>
> Carl Lumma wrote:
>
> > At 06:32 AM 1/31/2009, you wrote:
>
> >> For those who might find this more useful or understandable in > terms of
>
> >> rational numbers:
>
> >>
>
> >> !
>
> >> Harmonicious 12-tone scale (rational version)
>
> >> 12
>
> >> !
>
> >> 9/8
>
> >> 58/49
>
> >> 5/4
>
> >> 21/16
>
> >> 11/8
>
> >> 23/16
>
> >> 3/2
>
> >> 25/16
>
> >> 27/16
>
> >> 11/6
>
> >> 31/16
>
> >> 2/1
>
> >>
>
> >> I did this using two online tools:
>
> >> http://www.sengpiel audio.com/ calculator- centsratio. htm
>
> >> and
>
> >> http://superspace. epfl.ch/approxim ator/
>
> >>
>
> >> - Dave
>
> >
>
> > Doesn't look right though (at least, it's not a combination of
>
> > two harmonic series segments a 3:2 apart as Michael seemed to
>
> > claim).
>
> >
>
> > -Carl
>
> -- >
> ~DaveSeidel = [
>
> http://mysterybear. net,
>
> http://daveseidel. tumblr.com,
>
> http://twitter. com/DaveSeidel
>
> ];
>
>
>
>
>
>
>
>
>
>
>
> [Non-text portions of this message have been removed]
>
>

At 07:10 PM 1/31/2009, you wrote:
>Ok, I guess I have to clear some things up.
>
>The basic scale (this is about the 5th time I have said this),

Have you considered the possibility that the way in which
you are saying it may be flawed?

> (first harmonic series)
>1 9/8 5/4 11/8 3/2
> (*9/8 * 10/9 * 11/10 * 12/11)
>
>AND then (the second series using 3/2 as the split point)
>3/2 * 10/9 (* 11/10 ) (* 12/11 octave)

Nobody wants to read this, including me. Give the scale in
a standard, easy to read form, not some multicolumnar
convolution of decimal factors, asterisks and parentheses.

-Carl