Yahoo Tuning Groups Ultimate Backup tuning am I talking about a scale built from the harmonic series?

Has anyone tried a scale that did not try to temper into an interval?

It seems the basic problem is that the ear defines sound by log and
the harmonic series is linear and all the various scales are trying to
fit one into the other.

I am curious as to what happens if you let the octaves not be exact -
but let the other intervals be exact.

It sounds like, on the surface, one gives up modulation - but I don't
think that has to be so.

You'd give up the circle of fifths returning to the same frequencies.

There was a link to a youtube video with a guitar that was fretted to
the harmonic series.

(can't find it now) Was that an example of what I'm talking about?

Thanks,

Chris

🔗Mike Battaglia <battaglia01@...>

There's been a lot of research into non-octave tunings. I think
nonoctave.org is the place to be for that stuff, if memory serves
right.

-Mike

On Thu, Oct 9, 2008 at 10:08 PM, Chris Vaisvil <chrisvaisvil@...> wrote:
> Has anyone tried a scale that did not try to temper into an interval?
>
> It seems the basic problem is that the ear defines sound by log and
> the harmonic series is linear and all the various scales are trying to
> fit one into the other.
>
> I am curious as to what happens if you let the octaves not be exact -
> but let the other intervals be exact.
>
> It sounds like, on the surface, one gives up modulation - but I don't
> think that has to be so.
>
> You'd give up the circle of fifths returning to the same frequencies.
>
> There was a link to a youtube video with a guitar that was fretted to
> the harmonic series.
>
> (can't find it now) Was that an example of what I'm talking about?
>
> Thanks,
>
> Chris
>
>

🔗Chris Vaisvil <chrisvaisvil@...>

I'm afraid it 404'd

I'll try google

On Thu, Oct 9, 2008 at 10:55 PM, Mike Battaglia <battaglia01@...> wrote:
> There's been a lot of research into non-octave tunings. I think
> nonoctave.org is the place to be for that stuff, if memory serves
> right.
>
> -Mike
>
> On Thu, Oct 9, 2008 at 10:08 PM, Chris Vaisvil <chrisvaisvil@...>
> wrote:
>> Has anyone tried a scale that did not try to temper into an interval?
>>
>> It seems the basic problem is that the ear defines sound by log and
>> the harmonic series is linear and all the various scales are trying to
>> fit one into the other.
>>
>> I am curious as to what happens if you let the octaves not be exact -
>> but let the other intervals be exact.
>>
>> It sounds like, on the surface, one gives up modulation - but I don't
>> think that has to be so.
>>
>> You'd give up the circle of fifths returning to the same frequencies.
>>
>> There was a link to a youtube video with a guitar that was fretted to
>> the harmonic series.
>>
>> (can't find it now) Was that an example of what I'm talking about?
>>
>> Thanks,
>>
>> Chris
>>
>>
>

🔗Graham Breed <gbreed@...>

On Thu, 2008-10-09 at 22:08 -0400, Chris Vaisvil wrote:
> Has anyone tried a scale that did not try to temper into an interval?

What would that entail? People have tried not tempering any intervals
(just intonation), tempering such that two intervals remain just (e.g.
quarter comma meantone), tempering such that only octaves are just (e.g.
equal temperaments), tempering such that no intervals are just (e.g.
TOP-RMS) and not trying to temper at all (e.g. equal divisions of phi).
There isn't much room left for innovation at this level.

> It seems the basic problem is that the ear defines sound by log and
> the harmonic series is linear and all the various scales are trying to
> fit one into the other.

Er, maybe. The basic problem is the fundamental theorem of arithmetic:
start with n primes and you need n distinct intervals.

> I am curious as to what happens if you let the octaves not be exact -
> but let the other intervals be exact.

As in TOP-max? It means the scale is slightly stretched or squashed
relative to an equivalently optimal tuning with pure octaves. It
doesn't make much difference in practice. Pianos are already tuned with
stretched octaves.

> It sounds like, on the surface, one gives up modulation - but I don't
> think that has to be so.

You can have an equal temperament with some interval other than the
octave just. It has nothing to do with modulation.

You can have a lumpy, just intonation scale and still modulate. All you
give up is the mathematically exact repetition of intervals.

> You'd give up the circle of fifths returning to the same frequencies.

If you gave up on 12 note well temperaments, yes. We do plenty of that.

> There was a link to a youtube video with a guitar that was fretted to
> the harmonic series.
>
> (can't find it now) Was that an example of what I'm talking about?

I don't know what you're talking about. Fretting a guitar to a
subharmonic series might make more sense because the frets would be
equally spaced. But if you want to fret to the harmonic series you can
surely do it. Either way you'll have octaves just.

Graham

🔗Carlo Serafini <carlo@...>

🔗Petr Parízek <p.parizek@...>

Carlo Serafini wrote:

> a fascinating example (for me) is the so called superpythagorean scale:
> 701,955 x 12 = 8.423,46
> 8.423,46 ÷ 7 = 1.203,35142857

This is 7 equal divisions of a perfect fifth, which is, however, not superpythagorean. Superpyth is a kind of regular temperament whose octaves are essentially pure and fifths are so sharp that an augmented fifth of C-G# sounds like a major sixth rather than minor.

Petr

🔗Carlo Serafini <carlo@...>

I guess this term has been used by different people with different meanings but never mind.
:-)

--- In tuning@yahoogroups.com, Petr Parízek <p.parizek@...> wrote:
>
> Carlo Serafini wrote:
>
> > a fascinating example (for me) is the so called superpythagorean scale:
> > 701,955 x 12 = 8.423,46
> > 8.423,46 ÷ 7 = 1.203,35142857
>
> This is 7 equal divisions of a perfect fifth, which is, however, not superpythagorean.
Superpyth is a kind of regular temperament whose octaves are essentially pure and fifths are
so sharp that an augmented fifth of C-G# sounds like a major sixth rather than minor.
>
> Petr
>

🔗Petr Parízek <p.parizek@...>

Carlo Serafini wrote:

> I guess this term has been used by different people with different meanings
> but never mind. :-)

As far as I've read, Graham Breed, Herman Miller, Paul Erlich, Gene Ward Smith (and perhaps even Joe Monzo), all of them used "superpyth" to describe a regular systém which tempers out the grave minor second of 20480/19683 -- i.e. the temperament in which C-D# (or 9 fifths minus 5 octaves) approximates 5/4.

Petr

🔗Mark Rankin <markrankin95511@...>

Excuse my ignorance - can anyone tell me what 404'd means?
Thanks,

Mark

--- On Fri, 10/10/08, Petr Parízek <p.parizek@...> wrote:

From: Petr Parízek <p.parizek@...>
Subject: Re: [tuning] Re: am I talking about a scale built from the harmonic series?
To: tuning@yahoogroups.com
Date: Friday, October 10, 2008, 7:25 AM

Carlo Serafini wrote:
> I guess this term has been used by different people with different meanings
> but never mind. :-)
As far as I’ve read, Graham Breed, Herman Miller, Paul Erlich, Gene Ward Smith (and perhaps even Joe Monzo), all of them used „superpyth“ to describe a regular systém which tempers out the grave minor second of 20480/19683 -- i.e. the temperament in which C-D# (or 9 fifths minus 5 octaves) approximates 5/4.
Petr

🔗chrisvaisvil@...

It means the page was not found
Sent via BlackBerry from T-Mobile

-----Original Message-----
From: Mark Rankin <markrankin95511@yahoo.com>

Date: Fri, 10 Oct 2008 07:42:02
To: <tuning@yahoogroups.com>
Subject: [tuning] Something tells me that a 404'd isn't referring to a '40 Ford

Excuse my ignorance - can anyone tell me what 404'd means?
Thanks,
�
Mark

--- On Fri, 10/10/08, Petr Par�zek <p.parizek@chello.cz> wrote:

From: Petr Par�zek <p.parizek@chello.cz>
Subject: Re: [tuning] Re: am I talking about a scale built from the harmonic series?
To: tuning@yahoogroups.com
Date: Friday, October 10, 2008, 7:25 AM

Carlo Serafini wrote:
> I guess this term has been used by different people with different meanings
> but never mind. :-)
As far as I�ve read, Graham Breed, Herman Miller, Paul Erlich, Gene Ward Smith (and perhaps even Joe Monzo), all of them used �superpyth� to describe a regular syst�m which tempers out the grave minor second of 20480/19683 -- i.e. the temperament in which C-D# (or 9 fifths minus 5 octaves) approximates 5/4.
Petr
�
�

🔗Carlo Serafini <carlo@...>

🔗Kraig Grady <kraiggrady@...>

A question about non octave scales,
What does one do when one wants to dbl a voice with a different timbre higher up without influencing the harmony?
I guess one could just beat all one wants, but do we really always want to do that?
why give that up? agreed not all languages need it.
Like non-tonal or non-beats or non anything else, it would seem more might be gain by doing 'something' than taking a puritanical approach to "thou shall not".
or if one wants to explore non octave- why not take it to its philosophical end. Don't bother with any intonation at all.
One can possibly go deeper 'into' nature or 'outside' of it.
--

/^_,',',',_ //^ /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/>

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

🔗Kraig Grady <kraiggrady@...>

Erv Wilson had a harmonically tuned guitar starting on 28?
Rod Poole had done some work on it.
--

/^_,',',',_ //^ /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/>

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

🔗Carl Lumma <carl@...>

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
>
> A question about non octave scales,
> What does one do when one wants to dbl a voice with a different
> timbre higher up without influencing the harmony?
> I guess one could just beat all one wants, but do we really
> always want to do that?
> why give that up? agreed not all languages need it.
> Like non-tonal or non-beats or non anything else, it would
> seem more might be gain by doing 'something' than taking a
> puritanical approach to "thou shall not".

The octave is an interval which can be tempered like any
other. It can be tempered more, to favor other intervals,
or less or not at all, to disfavor other intervals. Really
it is just a choice. TOP says you're better off tempering
octaves most of the time, but that you should temper them
less than the other intervals. But TOP is just one approach.

> or if one wants to explore non octave- why not take it to its
> philosophical end. Don't bother with any intonation at all.
> One can possibly go deeper 'into' nature or 'outside' of it.

Random scales do have a certain appeal, in that they free
us from theory, and put us back completely on our own
devices.

-Carl

🔗Mark Rankin <markrankin95511@...>

Thanks Chris

--- On Fri, 10/10/08, chrisvaisvil@... <chrisvaisvil@gmail.com> wrote:

From: chrisvaisvil@... <chrisvaisvil@...>
Subject: Re: [tuning] Something tells me that a 404'd isn't referring to a '40 Ford
To: tuning@yahoogroups.com
Date: Friday, October 10, 2008, 7:47 AM

It means the page was not found
Sent via BlackBerry from T-Mobile

From: Mark Rankin <markrankin95511@ yahoo.com>
Date: Fri, 10 Oct 2008 07:42:02 -0700 (PDT)
To: <tuning@yahoogroups. com>
Subject: [tuning] Something tells me that a 404'd isn't referring to a '40 Ford

Excuse my ignorance - can anyone tell me what 404'd means?
Thanks,

Mark

--- On Fri, 10/10/08, Petr Parízek <p.parizek@chello. cz> wrote:

From: Petr Parízek <p.parizek@chello. cz>
Subject: Re: [tuning] Re: am I talking about a scale built from the harmonic series?
To: tuning@yahoogroups. com
Date: Friday, October 10, 2008, 7:25 AM

🔗Mark Rankin <markrankin95511@...>

Grazie Carlo,

Marco

--- On Fri, 10/10/08, Carlo Serafini <carlo@seraph.it> wrote:

From: Carlo Serafini <carlo@...>
Subject:
To: tuning@yahoogroups.com
Date: Friday, October 10, 2008, 11:31 AM

http://en.wikipedia .org/wiki/ 404_error

--- In tuning@yahoogroups. com, Mark Rankin <markrankin95511@ ...> wrote:
>
> Excuse my ignorance - can anyone tell me what 404'd means?
> Thanks,
>
> Mark
>

🔗Chris Vaisvil <chrisvaisvil@...>

I think..... I think I'm talking about "freestyle JI"

http://xenharmonic.wikispaces.com/FreeStyleJI

It does sound complex - but I see how this could be done - like
building a lattice work.

I'm still tossing this around.

On Thu, Oct 9, 2008 at 11:01 PM, Graham Breed <gbreed@...> wrote:
> On Thu, 2008-10-09 at 22:08 -0400, Chris Vaisvil wrote:
>> Has anyone tried a scale that did not try to temper into an interval?
>
> What would that entail? People have tried not tempering any intervals
> (just intonation), tempering such that two intervals remain just (e.g.
>
>> It seems the basic problem is that the ear defines sound by log and
>> the harmonic series is linear and all the various scales are trying to
>> fit one into the other.
>
> Er, maybe. The basic problem is the fundamental theorem of arithmetic:
> start with n primes and you need n distinct intervals.
>

I'm not sure I understand you - I see two competing definitions of "correctness"

By default we define 2:1 as the supreme consonant interval (beyond
unison) and point to the harmonic series for justification
But.. when we apply the intervals generated in the harmonic series
they do not add up correctly and result in errors.

JI is living without notes to avoid the wolf
temperaments try to hide the error by dilution

- the octave defines intervals that do not fit into an octave.

At least that is as far as I've gotten at this point.

🔗Chris Vaisvil <chrisvaisvil@...>

These are values in cents?

How would you generate other note values from this?

Would you use perfect or stretched octaves?

On Fri, Oct 10, 2008 at 2:30 AM, Carlo Serafini <carlo@...> wrote:
> Hi Chris
> a fascinating example (for me) is the so called superpythagorean scale:
> 701,955 x 12 = 8.423,46
> 8.423,46 ÷ 7 = 1.203,35142857
> having 12 perfect fifths that DO NOT repeat at the octave!
>

🔗Chris Vaisvil <chrisvaisvil@...>

http://eceserv0.ece.wisc.edu/~sethares/consemi.html

with sinewaves it looks like you could do that with impunity by and large.

what would be the cusp of blending additive synthesis with traditional
musical intervals?

>
>> or if one wants to explore non octave- why not take it to its
>> philosophical end. Don't bother with any intonation at all.
>> One can possibly go deeper 'into' nature or 'outside' of it.
>
> Random scales do have a certain appeal, in that they free
> us from theory, and put us back completely on our own
> devices.
>
> -Carl

🔗Carl Lumma <carl@...>

Hi Chris,

> http://eceserv0.ece.wisc.edu/~sethares/consemi.html
>
> with sinewaves it looks like you could do that with impunity
> by and large.

Adaptive timbres let you get away with tempering any interval
with impunity, not just octaves. So the technique is
value-neutral there.

And it doesn't really give you impunity. It can always
reduce or remove beating, but it can only restore the quality
of 'justness' when the mistuning is below a certain amount.

> what would be the cusp of blending additive synthesis with
> traditional musical intervals?

Not sure what you mean...

-Carl

🔗Chris Vaisvil <chrisvaisvil@...>

Hi Carl,

If you look at the first graph of Sethares' page - dissonance with
sinewaves - you see there is no distinction beyond about a major 3rd.
Of course music with just sinewaves could be boring.

>> what would be the cusp of blending additive synthesis with
>> traditional musical intervals?
>
> Not sure what you mean...

what I mean is that the timbre of an instrument is the result of the
summation of sines and cosines at appropriate volumes.
but you can of course write music with just sinewaves as your instruments.

My question is - at what point do the two concepts blurr?

When does music = timbre ?

On Sat, Oct 11, 2008 at 12:54 AM, Carl Lumma <carl@...> wrote:
> Hi Chris,
>
>> http://eceserv0.ece.wisc.edu/~sethares/consemi.html
>>
>> with sinewaves it looks like you could do that with impunity
>> by and large.
>
> Adaptive timbres let you get away with tempering any interval
> with impunity, not just octaves. So the technique is
> value-neutral there.
>
> And it doesn't really give you impunity. It can always
> reduce or remove beating, but it can only restore the quality
> of 'justness' when the mistuning is below a certain amount.
>
>> what would be the cusp of blending additive synthesis with
>> traditional musical intervals?
>
> Not sure what you mean...
>
> -Carl
>
>

🔗Kraig Grady <kraiggrady@...>

I will just repeat the question. What do you do if you want to dbl. a voice above or below without increasing the harmony.

/^_,',',',_ //^ /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/>

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

🔗Chris Vaisvil <chrisvaisvil@...>

Pretty much all the tempered scales I've seen give up something.

Giving up pure octaves would be just another compromise I guess.

But in free style JI I would think the octave is available = but I
know little about it now.

On Sat, Oct 11, 2008 at 7:33 AM, Kraig Grady <kraiggrady@...> wrote:
> I will just repeat the question. What do you do if you want to dbl. a
> voice above or below without increasing the harmony.
>

🔗Carl Lumma <carl@...>

--- In tuning@yahoogroups.com, "Chris Vaisvil" <chrisvaisvil@...> wrote:
>
> Hi Carl,
>
> If you look at the first graph of Sethares' page - dissonance
> with sinewaves - you see there is no distinction beyond about
> a major 3rd. Of course music with just sinewaves could be
> boring.

That's apparently not what an experiment by a guy named
Vos found, but even if it is correct, you're right, pure sine
waves are hard to generate in typical musical settings.

> >> what would be the cusp of blending additive synthesis with
> >> traditional musical intervals?
> >
> > Not sure what you mean...
>
> what I mean is that the timbre of an instrument is the result
> of the summation of sines and cosines at appropriate volumes.
> but you can of course write music with just sinewaves as your
> instruments.
>
> My question is - at what point do the two concepts blurr?
>
> When does music = timbre ?

I often think of harmony in terms of "metatimbre", if you like.

-Carl

🔗Carl Lumma <carl@...>

🔗Kraig Grady <kraiggrady@...>

without doing what? makes absolutely no sense at all.
What do you do if you have a non octave scale and you want to have dbl a different timbre like at an octave . With stretched/shrunk octaves you can't do it easily without adding all types of beats or altering the harmonic feel. my point is that non octave scales limits this almost most basic timbre doubling. If one doesn't care, fine.

But don't worry i am not going to ask any more questions.

/^_,',',',_ //^ /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/>

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

🔗Carl Lumma <carl@...>

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
>
> without doing what? makes absolutely no sense at all.

You trimmed the original text:

>> What do you do if you want to dbl. a voice above or below
>> without increasing the harmony.
>
> Without doing *what*?

It's "increasing the harmony" that made no sense at all to me.
Now I think I see what you meant...

> What do you do if you have a non octave scale and you want
> to have dbl a different timbre like at an octave. With
> stretched/shrunk octaves you can't do it easily without
> adding all types of beats or altering the harmonic feel.

I guess it depends on the setting and how much the octaves
are stretched. TOP meantone has 1201-cent octaves. I do
not think you will notice. The 7th root of 1.5 tuning
being discussed in this thread has 1203-cent octaves. You
wouldn't notice in an orchestral setting but you might
notice in an electronic one depending on how much subtly
you're into. In the Bohlen-Pierce scale, you're supposed
to dbl. at the tritave. If you don't like any of that,
use pure octaves.

> my point is that non octave scales limits this almost
> most basic timbre doubling.

Sure. It does.

-Carl

🔗Chris Vaisvil <chrisvaisvil@...>

🔗Carl Lumma <carl@...>

Hi Chris,

> sure harmony can be thought of as meta-timbre
>
> However - at some point - pitches and volume of just sines - an
> aural summation of sines would cross that line into being
> perceived as traditional timbre.
>
> another way to say it - it is a continuum - I don't know if it
> is generally thought of that way.

The brain uses spectral (relative amplitudes in the stack
of sines), spatiotemporal, and musical context (melody) cues
to pick apart the metatimbre in typical settings.
If you're listening to a morphing electronic composition,
sure, it's a continuum. If you've retuned the partials to
something like 10-ET, the virtual pitch of the complex
gets pretty weak and you can lose the timbre aspect
altogether -- you wind up with something that sounds like
a bell.

> Is there a page associated with Vos?

Unfortunately a digital copy of the critical paper doesn't
seem to exist. I'm going to remedy that one of these days,
and when I do, I'll post about it here.

-Carl