Yahoo Tuning Groups Ultimate Backup tuning The mighty strange Bohlen-Pierce scale...

Well, maybe it isn't so strange to some of *YOU,* if you've had
experience with it... but to *ME* the Bohlen-Pierce scale seems
mighty "weird."

I think it's the lack of octave equivalence anyplace that contributes
to this effect. Am I correct in assuming that the scale does not
repeat itself at all in an octave equivalent respect??

Maybe also, the fact that the scale steps are *somewhat* in the
vicinity of "traditional" 12-tET... well, they're more like a step
and a half... and also that there are 13 notes.

But, I'm confused here. What happens when you reach the 14th pitch??
It doesn't seem to repeat anything lower...

Anyway, I've seen this website before, but it didn't mean so much to
me until I got a chance to actually AUDITION the scale:

http://members.aol.com/bpsite/index.html

I think Graham Breed has unleased a "monster" with his MIDI RELAY...
since now I get to hear so many thing so quickly. I would sing
Graham Breed's praises again... but I am well aware that he is
adequately capable in that department... :)

But, of all the cursory "messing around.." this Bohlen-Pierce really
stands out. One of the most "out there" from the point of view of
12-tET perception... at least that's MY perception.

Any comments or suggestions about this scale would be welcome for
me... I'm only just discovering it... so any assistance would be
appreciated!

Thanks!
___________ ____ __ _
Joseph Pehrson

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

Joseph wrote,

>Well, maybe it isn't so strange to some of *YOU,* if you've had
>experience with it... but to *ME* the Bohlen-Pierce scale seems
>mighty "weird."

>I think it's the lack of octave equivalence anyplace that contributes
>to this effect. Am I correct in assuming that the scale does not
>repeat itself at all in an octave equivalent respect??

Yup!

>Maybe also, the fact that the scale steps are *somewhat* in the
>vicinity of "traditional" 12-tET... well, they're more like a step
>and a half... and also that there are 13 notes.

>But, I'm confused here. What happens when you reach the 14th pitch??
>It doesn't seem to repeat anything lower...

It's a 3:1 ratio above the 1st pitch.

>Any comments or suggestions about this scale would be welcome for
>me... I'm only just discovering it... so any assistance would be
>appreciated!

Randy Winchester and Charles Carpentier have made some cool music in this
scale . . . I know many others have worked with it as well, due to Pierce's
advocacy . . .

🔗Rick McGowan <rmcgowan@apple.com>

Since Joseph brought it up...

It's been my impression that the Bohlen-Pierce scale's gimmick (the so-called "tritave" or base of nth-root of 3) is just a cute (and somewhat hyped) gimmick, and doesn't mean anything particular in acoustical terms. Acoustically speaking, isn't it merely one of a class of non-octave-repeating tunings of some equal step size?

In my opinion, a better and more useful member of that class is the Wendy Carlos "alpha scale" which is fairly close to 15 tET, but has better triads. If you're interested in the strangeness of lacking octaves, I highly recommend messing around with the alpha scale. Local harmony is "excellent" (in terms of traditional 1-3-5 triads), but non-local (> 1 octave) harmony is "bizarre" due to lack of octave repeats.

I'd be curious to know if other people have worked with these non-octave tunings. I've done some extended work in the alpha scale and like it quite a bit.

Rick

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

Rick wrote,

>It's been my impression that the Bohlen-Pierce scale's gimmick (the
so-called "tritave" or base of >nth-root of 3) is just a cute (and somewhat
hyped) gimmick, and doesn't mean anything particular >in acoustical terms.

If you said psychoacoustical terms, I agree, the octave really seems to be
the only interval of equivalence, though scales to tend to have similar
tetrachords at fourths and fifths . . .

>Acoustically speaking, isn't it merely one of a class of
non-octave-repeating tunings of some >equal step size?

Well, it's quite special, as it approximates all ratios of _odd numbers_
through 9 extremely well, and the triple-BP scale (39 steps per tritave)
approximates all ratios of odd numbers through 15 extremely well.

>In my opinion, a better and more useful member of that class is the Wendy
Carlos "alpha scale" >which is fairly close to 15 tET, but has better
triads.

But the triads only work in one inversion -- if you look at first or second
inversion triads, or any open voicings, 15-tET looks better.

🔗Kees van Prooijen <kees@dnai.com>

I recently started a page with some of the investigations I've done on this
subject. It's a work in progress:

http://www.kees.cc/music/scale13/scale13.html

Kees

> -----Original Message-----
> From: Joseph Pehrson [mailto:pehrson@pubmedia.com]
> Sent: Tuesday, September 26, 2000 1:18 PM
> To: tuning@egroups.com
> Subject: [tuning] The mighty strange Bohlen-Pierce scale...
>
>
> Well, maybe it isn't so strange to some of *YOU,* if you've had
> experience with it... but to *ME* the Bohlen-Pierce scale seems
> mighty "weird."
>
> I think it's the lack of octave equivalence anyplace that contributes
> to this effect. Am I correct in assuming that the scale does not
> repeat itself at all in an octave equivalent respect??
>
> Maybe also, the fact that the scale steps are *somewhat* in the
> vicinity of "traditional" 12-tET... well, they're more like a step
> and a half... and also that there are 13 notes.
>
> But, I'm confused here. What happens when you reach the 14th pitch??
> It doesn't seem to repeat anything lower...
>
> Anyway, I've seen this website before, but it didn't mean so much to
> me until I got a chance to actually AUDITION the scale:
>
> http://members.aol.com/bpsite/index.html
>
> I think Graham Breed has unleased a "monster" with his MIDI RELAY...
> since now I get to hear so many thing so quickly. I would sing
> Graham Breed's praises again... but I am well aware that he is
> adequately capable in that department... :)
>
> But, of all the cursory "messing around.." this Bohlen-Pierce really
> stands out. One of the most "out there" from the point of view of
> 12-tET perception... at least that's MY perception.
>
> Any comments or suggestions about this scale would be welcome for
> me... I'm only just discovering it... so any assistance would be
> appreciated!
>
> Thanks!
> ___________ ____ __ _
> Joseph Pehrson
>
>
>
>
>
>
>
> You do not need web access to participate. You may subscribe through
> email. Send an empty email to one of these addresses:
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>
>
>

🔗Rosati <dante@pop.interport.net>

🔗Mats �ljare <oljare@hotmail.com>

>It's been my impression that the Bohlen-Pierce scale's gimmick (the
>so-called "tritave" or base of nth-root of 3) is just a cute (and
>somewhat hyped) gimmick, and doesn't mean anything particular in

It doesn�t if you have not heard it played the proper way-with odd-harmonic timbres.Clarinets,electronic triangle and square(not asymmetrical pulse)waves are examples of that.They are identifiable by that the second half of the waveform is identical to the first part turned upside down.

Any instrumental or vocal sounds can be transformed to this kind of sound by mixing them with an inverted signal,delayed by exactly half the time of one cycle,or ring modulation with a sine wave one octave lower than the pitch(3/2 also works).The later cause the result to be one octave(not tritave)in pitch.

>acoustical terms. Acoustically speaking, isn't it merely one of a >class >of non-octave-repeating tunings of some equal step size?

No,because most other non-octave tunings(like Alpha,Beta,Gamma)is meant to recreate octave-reduced just intervals as well as possible(such as 5/4,3/2,7/4 etc.).Tritave scales are based on the concept of _tritave reduced_ intervals like 5/3,7/3,11/9 etc.See my later post about this...

��
Mats �ljare
Eskilstuna,Sweden
http://www.angelfire.com/mo/oljare

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🔗Mats �ljare <oljare@hotmail.com>

>Well, maybe it isn't so strange to some of *YOU,* if you've had experience >with it... but to *ME* the Bohlen-Pierce scale seems
>mighty "weird."

It is,because it has a harmonic and melodic structure that is not just different,but totally incompatible with ideas from diatonic and other octave-based tunings.

>I think it's the lack of octave equivalence anyplace that contributes to >this effect. Am I correct in assuming that the scale does not
>repeat itself at all in an octave equivalent respect??

The tritave concept of reduction works in the exact same way as octave reduction does.Apparently some people do not percieve it...i heard it the first time i tried the scale,but i might also be adapting to new things exceptionally fast.

>I think Graham Breed has unleased a "monster" with his MIDI RELAY... since >now I get to hear so many thing so quickly. I would sing
>Graham Breed's praises again... but I am well aware that he is adequately >capable in that department... :)

Very good program.Am i right in that the"old Windows"version is more stable than the W95/98 one?

>Any comments or suggestions about this scale would be welcome for me... I'm >only just discovering it... so any assistance would be appreciated!

I am personally not fond of the 13 note equal scale,cause of its lack of 11 and 13-limit approximations.See my later post for details.

��
Mats �ljare
Eskilstuna,Sweden
http://www.angelfire.com/mo/oljare

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🔗Monz <MONZ@JUNO.COM>

--- In tuning@egroups.com, "Rosati" <dante@p...> wrote:
> http://www.egroups.com/message/tuning/13573
>
> It seems to me that 2/1, 3/1, 4/1, 5/1 etc should exhibit a
> continuous, perhaps exponential, decrease of equivalence,
> rather than 2/1 being 100% equivalent, and all others 0%
> equivilent.

Dante, this is one of the things my lattice formula attempts
to portray. The length of the 2-step is the shortest, with
each subsequent prime having a length equal to the prime itself,
so 2 is 2 units, 3 is 3 units, 5 is 5 units, etc.

Take another look at my lattices and see if this agrees with
your intuition. I've just been discussing with Paul Erlich
how to change this, and have discussed it in the past, but
ever since I stumbled onto this particular formula 2 years ago,
I've stubbornly clung to it because it seems to make more
sense to me than the other alternatives.

-monz
http://www.ixpres.com/interval/monzo/homepage.html

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

Dante Rosati wrote,

>I've often wondered if there isn't a shade of "fifth equivalence", or even
>moreso "twelfth equivalence". Isn't the classical reason for the
prohibition
>of parallel fifths because they destroy part independence? Parallel octaves
>and fifths are prohibited due to this, while parallel thirds have been
>deemed "o.k." since Dunstable et al.

Right -- parallel 1:2s and parallel 2:3s are a lot closer to a "timbre" than
4:5s alternating with 5:6s. It's not about equivalence.

>It seems to me that 2/1, 3/1, 4/1, 5/1 etc should exhibit a continuous,
>perhaps exponential, decrease of equivalence, rather than 2/1 being 100%
>equivalent, and all others 0% equivilent.

Psychologically, only octaves give the impression of a single pitch; and
with sine waves, this octave is about 1209 cents. With more complex timbres,
understandably there can sometimes be confusion between tones a fourth or
fifth apart; but even when there are no harmonics, the brain seems to spiral
the pitch range into a helix that coils once per octave.

🔗Joseph Pehrson <josephpehrson@compuserve.com>

--- In tuning@egroups.com, "Rosati" <dante@p...> wrote:

http://www.egroups.com/message/tuning/13573

>
> It seems to me that 2/1, 3/1, 4/1, 5/1 etc should exhibit a
continuous, perhaps exponential, decrease of equivalence, rather than
2/1 being 100% equivalent, and all others 0% equivilent.
>
> Dante

Gee... that's interesting Dante... but, the 12th serving as the
"octave" doesn't seem to be doing the same thing as the "walloping"
2/1. I don't think it's "accustomization" either. It doesn't seem
like these other "boundary" ratios are further gradations from the
octave. The octave seems like a "whole different animal." In fact,
that's why the scale seems so odd... and I don't believe it is just
"accustomization..." Paul??

__________ ____ __ _ _
Joseph Pehrson

🔗Joseph Pehrson <josephpehrson@compuserve.com>

--- In tuning@egroups.com, "Mats Öljare" <oljare@h...> wrote:

http://www.egroups.com/message/tuning/13577

> >I think it's the lack of octave equivalence anyplace that
contributes to this effect. Am I correct in assuming that the scale
does not repeat itself at all in an octave equivalent respect??
>
> The tritave concept of reduction works in the exact same way as
octave reduction does.Apparently some people do not percieve it...i
heard it the first time i tried the scale,but i might also be
adapting to new things exceptionally fast.
>

Thanks, Mats for your informative commentary. I'm not really hearing
the "tritave" as an "axis" yet... but I'll work on it. So far it
just seems like "another interval" not a SPECIAL class of sonority
likethe octave is... but I'll keep working on it. Perhaps my
perception will change. What do *YOU* think, Paul?? Can we
accustomize ourselves to something like this or is the octave
something absolutely special??

My guess would be the latter... but, as I say, my mind is totally
open...

_________ ____ __ __ _
Joseph Pehrson

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

Dante wrote,

>> It seems to me that 2/1, 3/1, 4/1, 5/1 etc should exhibit a
>> continuous, perhaps exponential, decrease of equivalence,
>> rather than 2/1 being 100% equivalent, and all others 0%
>> equivilent.

Monz wrote,

>Dante, this is one of the things my lattice formula attempts
>to portray. The length of the 2-step is the shortest, with
>each subsequent prime having a length equal to the prime itself,
>so 2 is 2 units, 3 is 3 units, 5 is 5 units, etc.

Are you sure about that, Monz? All of your work that I've seen assumes
octave-equivalence but no other equivalence relations.

>Take another look at my lattices and see if this agrees with
>your intuition. I've just been discussing with Paul Erlich
>how to change this, and have discussed it in the past, but
>ever since I stumbled onto this particular formula 2 years ago,
>I've stubbornly clung to it because it seems to make more
>sense to me than the other alternatives.

This is a different issue -- how to make lattices reflect concordance. So,
on that subject, Monz, are you willing to consider the possibility that
Tenney's idea (using log(p) as the length of a step along prime axis p)
actually makes nore sense than your original idea?

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

Joseph wrote,

>What do *YOU* think, Paul?? Can we
>accustomize ourselves to something like this or is the octave
>something absolutely special??

You must have missed the post I just made . . . the octave (and multiple
octaves) seems to be the only interval that evokes a repetition of pitch
class, even when pure sine waves are used . . . the effect has been observed
in animals, so acculturization doesn't seem to be the answer . . .
evolutionarily, a two-dimensional representation of the pitch continuum as a
helix which winds around once per octave may have been a survival advantage
as the even partials give so much redundant information on the content of
many natural sounds . . .

🔗Joseph Pehrson <josephpehrson@compuserve.com>

🔗Rosati <dante@pop.interport.net>

----- Original Message -----
From: Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>
.> the octave (and multiple
> octaves) seems to be the only interval that evokes a repetition of pitch
> class, even when pure sine waves are used . . . the effect has been
observed
> in animals, so acculturization doesn't seem to be the answer . . .
> evolutionarily, a two-dimensional representation of the pitch continuum as
a
> helix which winds around once per octave may have been a survival
advantage
> as the even partials give so much redundant information on the content of
> many natural sounds . . .

Then this would be some fundamental difference between even and odd. Even is
always perceived as duplication, with powers of 2 duplicating the
fundamental or tonic. Odds would introduce something "new". This would
explain why octave equivalence is as Joe put it "a whole different animal",
as opposed to 3/1 just being a "lesser shade" of animal from 2/1. This is
also related to the prime/odd question. Is 9/1, for example, completely new,
or is it in some way an "equivalence" of 3, resulting from 3X3? Also, do
Pythagorean tunings have a pervasive quality resulting from the
"equivalence" of the generating interval 3/2, so that even the high-odd
ratios share a "family resemblance"?

There is no question that octave equivalence is universal. The only question
is if there is >any< perception of equivalence in 3/1 at all. Is there some
way that even and odd >numbers< are fundamentally different so that this
difference is reflected in the psychoacoustic phenomena of octave
equivalence, or is the difference merely an accident of physiology, which is
what I believe Paul is saying above in his evolutionary reference? If even
partials were totally redundant, would we perceive them at all? Register is
a conveyer of musical meaning, so it cant be completely redundant.

Dante

🔗Joseph Pehrson <josephpehrson@compuserve.com>

--- In tuning@egroups.com, "Rosati" <dante@p...> wrote:

http://www.egroups.com/message/tuning/13598

or is the difference merely an accident of physiology,
which is what I believe Paul is saying above in his evolutionary
reference? If even partials were totally redundant, would we perceive
them at all? Register is
> a conveyer of musical meaning, so it cant be completely redundant.
>
> Dante

Hi Dante...

Isn't using the term an "accident" of physiology perhaps giving
physiology a bit less importance than it deserves?? One doesn't need
to be a philosopher (they're ALWAYS talking about "perception") to
know that we have nothing else.... No other "Doors of Perception..."
__________ ___ __ _ _ _
Joseph Pehrson

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

🔗M. Edward Borasky <znmeb@teleport.com>

Well, I'll certainly check out the web page. Sethares has a page or two on
Bohlen-Pierce; it looks like he acknowledges their influence on his
theories.

Speaking of Sethares, I have his CD "Xentonality", which is just his
compositions, not exercises/demonstrations. It's ... well ... interesting.
He mixes a soft-rock style with his tunings, so you almost think you're
listening to conventional music, except you aren't ... the scales, timbres
and tunings are all foreign. I'm not sure whether I'll grow to love it, but
at least it is something I will listen to again. I suspect I would have
liked it better if he hadn't tried so hard to use conventional rhythms from
the pop arena and had instead gone for sweeping "soundscapes" or done some
spatial stuff. Still, xentonality is another tool in a composer's workshop
and Sethares seems to be the best source on the mathematics.

I finally managed to get my Derive calculation of the dissonance curves
working. The difficulty is that the equations in Appendix E, the BASIC
program in Appendix E and the Matlab program in Appendix E are all
different! What is interesting is that in both programs, he uses different
amplitudes for the partials. In the Matlab program all the amplitudes are 1
but in the BASIC program they start at 10 and descend to about 5 or 6. What
troubled me is that when I tried descending amplitudes (1, 1/2, 1/3, 1/4,
1/5, 1/6) I got a dissonance curve with essentially only one minimum at the
fifth. If I can hard-code all the amplitudes to 1 it will make my code a
*lot* simpler.

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

🔗M. Edward Borasky <znmeb@teleport.com>

Is the code on the web page different from the code in the book? The Matlab
code in the book has the amplitudes set to 1. BTW, quite a few of his
synthesized spectra have on the order of six partials with roughly equal
amplitudes, but non-harmonic frequencies. It's beginning to look like he's
trying to simplify the process.

> -----Original Message-----
> From: Paul H. Erlich [mailto:PERLICH@ACADIAN-ASSET.COM]
> Sent: Tuesday, September 26, 2000 8:19 PM
> To: 'tuning@egroups.com'
> Subject: RE: [tuning] The mighty strange Bohlen-Pierce scale...
>
>
> Ed Borasky wrote,
>
> >What
> >troubled me is that when I tried descending amplitudes (1, 1/2, 1/3, 1/4,
> >1/5, 1/6) I got a dissonance curve with essentially only one
> minimum at the
> >fifth. If I can hard-code all the amplitudes to 1 it will make my code a
> >*lot* simpler.
>
> Unfortunately that doesn't sound like it would model reality very
> well. I'll
> try the Matlab program on his website, which requires you to
> input _all_ the
> amplitudes . . .
>
>
> You do not need web access to participate. You may subscribe through
> email. Send an empty email to one of these addresses:
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> individual emails.
>
>
>

🔗Rosati <dante@pop.interport.net>

----- Original Message -----
From: Joseph Pehrson <josephpehrson@compuserve.com>
> Isn't using the term an "accident" of physiology perhaps giving
> physiology a bit less importance than it deserves?? One doesn't need
> to be a philosopher (they're ALWAYS talking about "perception") to
> know that we have nothing else.... No other "Doors of Perception..."

One possibility is that certain properties of numbers are audibly manifest
in musical sound. Another is that our response to musical sound is a
function of the physiology of our ears and brains. Of course, if "all is
number" than they are the same thing. But if "number mysticism" is a red
herring, then we are left with musical culture as a byproduct of evolution:
"accidental" because while certain aural capabilities are useful to
survival, I doubt it can be argued that a complex musical language is
reducable to a darwinian survival mechanism.

BTW, physiology is not the only "door of perception" available to us, as
dreams, OBEs, intuitions, meditational and drug experiences shows. (No use
arguing that all these phenomena are physiologically based - when it comes
right down to it only pure perceptual information is directly experienced -
"the body" is a concept imputed onto percepts just like any other.)

Dante

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

🔗Joseph Pehrson <josephpehrson@compuserve.com>

--- In tuning@egroups.com, "Paul H. Erlich" <PERLICH@A...> wrote:

http://www.egroups.com/message/tuning/13602

>
> Have you ever seen the representation of pitch as a helix in a
psychology of music book?

Never have... I must be missing something important...

But I think I'm kind of getting the idea, perhaps, of "sensory
overload" so maybe some of the pitches could be "weeded out" from
natural sounds with such a helix so that more immediate things...
like the bear eating your arm... would be more immediately
noticable...

_______ ___ __ _ _
Joseph Pehrson

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

🔗Joseph Pehrson <josephpehrson@compuserve.com>

🔗Monz <MONZ@JUNO.COM>

--- In tuning@egroups.com, "Paul H. Erlich" <PERLICH@A...> wrote:
> http://www.egroups.com/message/tuning/13591
>
> --- In tuning@egroups.com, "Paul H. Erlich" <PERLICH@A...> wrote:
>
> ... All of your work that I've seen assumes
> octave-equivalence but no other equivalence relations.

Well, most of my work, but not all. Last year I did start
making '8ve'-specific lattices which included a 2-axis.

I needed these for my book, where I discuss ancient Greek
tuning systems, because the Greeks thought of all pitches
as being higher and lower than the central _mese_. They
did not use a concept of '8ve'-equivalence in their music;
if anything, their theory used '4th'-equivalence (tetrachords).

For those who want more info on ancient Greek theory:
http://www.ixpres.com/interval/monzo/aristoxenus/tutorial.htm

You are correct that I've never assumed any 'other equivalence
relations', unless you count among that my ideas on 'cross-
exponent direct lattice connections', which I posted at

http://www.egroups.com/message/tuning/2179

- but what I was really exploring there was categorical perception:
higher-integer ratios 'substituting for' or functioning as
lower-integer ones.

>
> > Take another look at my lattices and see if this agrees with
> > your intuition. I've just been discussing with Paul Erlich
> > how to change this, and have discussed it in the past, but
> > ever since I stumbled onto this particular formula 2 years ago,
> > I've stubbornly clung to it because it seems to make more
> > sense to me than the other alternatives.
>
> This is a different issue -- how to make lattices reflect
> concordance.

Well, concordance is only one thing I try to portray on
my lattices, and possibly not even the most important thing.

What I'm really most interested in is simply a unique way
to represent each ratio, so that I can do without the
cumbersome numbers but still have a clear view of harmonic
relationships.

This has been the whole impetus of my work from the beginning,
ever since I digested Partch's theories and began expanding
them into much larger JI systems (with huge numbers).

> So, on that subject, Monz, are you willing to consider the
> possibility that Tenney's idea (using log(p) as the length
> of a step along prime axis p) actually makes nore sense than
> your original idea?

For the purpose of portraying concordance, yes.

If portraying concordance is not the issue, I still like my old
formula. I am also interested, however, in modifying it by using
180 degrees instead of 360 to represent the '8ve'.

-monz
http://www.ixpres.com/interval/monzo/homepage.html

🔗Monz <MONZ@JUNO.COM>

--- In tuning@egroups.com, "Rosati" <dante@p...> wrote:
> http://www.egroups.com/message/tuning/13598
>
>
> Then this would be some fundamental difference between even
> and odd. Even is always perceived as duplication, with powers
> of 2 duplicating the fundamental or tonic. Odds would introduce
> something "new".

Dante, in my research I've found that the ancient Greeks invented
the concept of 'even and odd', precisely as a result of their
musical explorations.

(Of course, the Greeks probably borrowed the idea from the
Babylonians, who got it from the Sumerians... but I haven't
found any evidence to prove that yet.)

> This would explain why octave equivalence is as Joe put it
> "a whole different animal", as opposed to 3/1 just being a
> "lesser shade" of animal from 2/1.

One thing I've read about and noticed many times myself that's
being overlooked here: very often, people without any
musical training, when singing in what they think is unison,
are actually singing a 'perfect 4th' or '5th' above or below
the 'lead' singer.

Listen carefully the next time a group of non-musicians sings
'Happy Birthday' at a party - I guarantee you'll hear it!

So '4th'- and '5th'-equivalence most definitely do exist, but
probably more among non-musicians than among musicians. Musical
training seems strip away that kind of perception.

The other questions you raise about 'families' of prime multiples
have been asked here before - check the archives, probably
somewhere around February-May 1999.

-monz
http://www.ixpres.com/interval/monzo/homepage.html

🔗Carl Lumma <CLUMMA@NNI.COM>

>>What do *YOU* think, Paul?? Can we accustomize ourselves to something
>>like this or is the octave something absolutely special??
>
>You must have missed the post I just made . . . the octave (and multiple
>octaves) seems to be the only interval that evokes a repetition of pitch
>class, even when pure sine waves are used . . . the effect has been
>observed in animals, so acculturization doesn't seem to be the answer . . .
>evolutionarily, a two-dimensional representation of the pitch continuum
>as a helix which winds around once per octave may have been a survival
>advantage as the even partials give so much redundant information on the
>content of many natural sounds . . .

Well... where do we draw the line? I'm not convinced that equivalence
completely disappears as soon as we leave the base 2's. Charles Carpenter's
BP stuff is definitely working a sound... And who knows -- maybe the use of
sine tones increases the difference between base-2's and everything else.
If tetrachordality has any meaning -- and I think it does -- then there must
be something left of equivalence for factor(s) of 3. In an old post on
tetrachordality, Paul commented on how singers are often off by a fifth in
novice sing-alongs. True fact. Also, according to David L. Burge, musicians
new to ear training often confuse the octave and perfect fifth in relative-
pitch drills.

-Carl

🔗Monz <MONZ@JUNO.COM>

--- In tuning@egroups.com, "Rosati" <dante@p...> wrote:
> http://www.egroups.com/message/tuning/13610
>
> ... if "all is number" than they are the same thing. But if
> "number mysticism" is a red herring, then we are left with
> musical culture as a byproduct of evolution: "accidental"
> because while certain aural capabilities are useful to
> survival, I doubt it can be argued that a complex musical
> language is reducable to a darwinian survival mechanism.

I wouldn't be too quick to agree with that, Dante. I just posted
something a few weeks ago about the possibility that, since
humans were able to talk for 40,000 years before they ever
figured out how to write anything down, music may indeed have
evolved as a *very* important component of human life.

Without being able to record information in writing, the only
way to pass it on was by oral means, and poetry and song have
proven themselves to be (together) by far the most effective
way to do this.

It reminds me of something Jim Morrison (of the Doors, speaking
of the 'Doors of Perception - that book inspired their name)
said once: if there were some terrible planet-wide disaster
and all the books and art-works were destroyed, the only art
that would still be left (presuming there were still people
left) would be songs, embedded into people's memories.

And, for the record, I agree with you about alternate 'Doors'.
As I also posted a little while back (regarding 'light cones'),
there's a *whole* lot happening out there in that big universe
that we can't, and may never, perceive. Just because we can't
see doesn't mean it doesn't exist, and it also doesn't mean
that it can't affect us in some way.

-monz
http://www.ixpres.com/interval/monzo/homepage.html

🔗Graham Breed <graham@microtonal.co.uk>

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

Monz wrote,

>Well, concordance is only one thing I try to portray on
>my lattices, and possibly not even the most important thing.

>What I'm really most interested in is simply a unique way
>to represent each ratio, so that I can do without the
>cumbersome numbers but still have a clear view of harmonic
>relationships.

>This has been the whole impetus of my work from the beginning,
>ever since I digested Partch's theories and began expanding
>them into much larger JI systems (with huge numbers).

Great. It's wonderful, then, that with a simple modification, your lattices
will allow for an excellent measure of concordance.

>For the purpose of portraying concordance, yes.

>If portraying concordance is not the issue, I still like my old
>formula.

For any reason other than that you're accustomed to it? I fail to see how
using the log would obscure the view of harmonic/prime relationships.

🔗Herman Miller <hmiller@IO.COM>

On Wed, 27 Sep 2000 00:31:58 -0000, "Joseph Pehrson"
<josephpehrson@compuserve.com> wrote:

>Thanks, Mats for your informative commentary. I'm not really hearing
>the "tritave" as an "axis" yet... but I'll work on it. So far it
>just seems like "another interval" not a SPECIAL class of sonority
>likethe octave is... but I'll keep working on it. Perhaps my
>perception will change. What do *YOU* think, Paul?? Can we
>accustomize ourselves to something like this or is the octave
>something absolutely special??
>
>My guess would be the latter... but, as I say, my mind is totally
>open...

The interesting thing about the octave is that throughout the range of
pitches commonly used in music, pitches an octave apart sound like
different shades of the same pitch, but (at least in my experience) this
perception is distorted at the extreme high and low ends. At the low end
it's hard to perceive any sense of pitch at all without the help of
overtones. But somewhere in the octave above the highest octave on the
piano, pitches start sounding FLATTER than they really are! I first noticed
this effect when listening to slowed-down recordings of bird songs.

Also relevant is the perception that octave-equivalence of sounds with
stretched partials starts to break down beyond a certain maximum (but
small) amount of stretching. The first several times I listened to William
Sethares' "October 21st" (with "octaves" stretched to a proportion of 2.1
to 1), it sounded utterly atonal and cacophonous to me. Then one day
something "clicked" and I was able to perceive the individual voices. But I
still don't perceive anything like octave-equivalence, and I feel no sense
of harmonic progression even though I can mentally reconstruct it by
following the separate voices. I'm skeptical that the perception of
equivalence would suddenly reappear with octaves stretched to a ratio of
3/1, but I haven't done as much experimentation with the Bohlen-Pierce
scale as I'd like to.

--
see my music page ---> ---<http://www.io.com/~hmiller/music/music.html>--
hmiller (Herman Miller) "If all Printers were determin'd not to print any
@io.com email password: thing till they were sure it would offend no body,
\ "Subject: teamouse" / there would be very little printed." -Ben Franklin

🔗Joseph Pehrson <josephpehrson@compuserve.com>

--- In tuning@egroups.com, Herman Miller <hmiller@I...> wrote:

http://www.egroups.com/message/tuning/13697

But somewhere in the octave above the highest octave on
the piano, pitches start sounding FLATTER than they really are! I
first noticed this effect when listening to slowed-down recordings of
bird songs.

Paul has also mentioned it, and I find it exceedingly interesting! I
wonder why that is?? Is it the structure of the ear mechanism?? I'll
have to do some more careful listening of octaves... (and *NOT* on
the
piano :) ))

________ ___ __ _ _
Joseph Pehrson

🔗Mats �ljare <oljare@hotmail.com>

>One thing I've read about and noticed many times myself that's
>being overlooked here: very often, people without any
>musical training, when singing in what they think is unison,
>are actually singing a 'perfect 4th' or '5th' above or below
>the 'lead' singer.

But there is a major difference between 3/2 or whatever-SIMILARITY and EQUALITY,right?

��
Mats �ljare
Eskilstuna,Sweden
http://www.angelfire.com/mo/oljare
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🔗Monz <MONZ@JUNO.COM>

--- In tuning@egroups.com, "Mats Öljare" <oljare@h...> wrote:
> http://www.egroups.com/message/tuning/13723
>
> >[me, monz]
> >One thing I've read about and noticed many times myself that's
> >being overlooked here: very often, people without any
> >musical training, when singing in what they think is unison,
> >are actually singing a 'perfect 4th' or '5th' above or below
> >the 'lead' singer.
>
> But there is a major difference between 3/2 or whatever-
> SIMILARITY and EQUALITY,right?

Right. That's precisely why Margo Schulter recently sent some
posts discussing the use of 'affinity' instead of 'equivalence'.

In early medieval theory, such as the treatises by Guido d'Arezzo
and (I think) Hermannus Contractus and Johannes Afflighemensis,
there was a distinct category of interval called 'equison', which
contained only the unison (and the '8ves'?).

It's been quite a while since I've read this stuff, so it's
possible that I'm about to butcher what these theorists really
said (Margo, please help!). But my recollection is that the
unison, '8ve', and 'double 8ve' were considered 'equisonant',
while the '4ths' and '5ths' and their '8ve'-doublings were
'consonant', and all other intervals were 'dissonant'.

In any case, whatever the actual members of each category,
there were three distinct categories: equisonant, consonant,
and dissonant. Somewhere down the line (c. 1200 or so?)
the concept of 'equisonance' was pretty much dispensed with
in theory, leaving on 'consonance' and 'dissonance'.

Then shortly after, the idea of 'imperfect' and 'perfect'
consonances and dissonances crept in, to distinguish further
shades of degree of sonance.

(Actually, Margo, if you have the time, I for one would welcome
a typically long and detailed article from you on this...and
by all means, please name names of the theorists so that I can
get my history straight. Or if it's been posted before, some
links to the archive...)

-monz
http://www.ixpres.com/interval/monzo/homepage.html

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

🔗Kees van Prooijen <kees@dnai.com>

----- Original Message -----
From: "Paul H. Erlich" <PERLICH@ACADIAN-ASSET.COM>
To: <tuning@egroups.com>
Cc: "'Kees van Prooijen'" <kees@dnai.com>
Sent: Thursday, October 05, 2000 5:41 PM
Subject: RE: [tuning] The mighty strange Bohlen-Pierce scale...

> As for the BP scale, I wonder if
> you're familiar with the literature, such as on Bohlen's site,
particularly
>
> http://hometown.aol.com/bpsite/tonality.html
>

Yes I am, that's mainly why I link to Heinz's site from mine. Saves me a lot
of explaining.

> I happen to disagree with your view of the usual diatonic scale, but
that's
> another matter . . .
>

Actually, I always thought diatonic was low calorie Schweppes.

The mighty strange Bohlen-Pierce scale...

🔗Joseph Pehrson <pehrson@pubmedia.com>

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

🔗Rick McGowan <rmcgowan@apple.com>

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

🔗Kees van Prooijen <kees@dnai.com>

🔗Rosati <dante@pop.interport.net>

🔗Mats �ljare <oljare@hotmail.com>

🔗Mats �ljare <oljare@hotmail.com>

🔗Monz <MONZ@JUNO.COM>

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

🔗Joseph Pehrson <josephpehrson@compuserve.com>

🔗Joseph Pehrson <josephpehrson@compuserve.com>

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

🔗Joseph Pehrson <josephpehrson@compuserve.com>

🔗Joseph Pehrson <josephpehrson@compuserve.com>

🔗Rosati <dante@pop.interport.net>

🔗Joseph Pehrson <josephpehrson@compuserve.com>

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

🔗M. Edward Borasky <znmeb@teleport.com>

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

🔗M. Edward Borasky <znmeb@teleport.com>

🔗Rosati <dante@pop.interport.net>

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

🔗Joseph Pehrson <josephpehrson@compuserve.com>

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

🔗Joseph Pehrson <josephpehrson@compuserve.com>

🔗Monz <MONZ@JUNO.COM>

🔗Monz <MONZ@JUNO.COM>

🔗Carl Lumma <CLUMMA@NNI.COM>

🔗Monz <MONZ@JUNO.COM>

🔗Graham Breed <graham@microtonal.co.uk>

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

🔗Herman Miller <hmiller@IO.COM>

🔗Joseph Pehrson <josephpehrson@compuserve.com>

🔗Mats �ljare <oljare@hotmail.com>

🔗Monz <MONZ@JUNO.COM>

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

🔗Kees van Prooijen <kees@dnai.com>