New Pages: Systematic Music Theory

A new area has been added to the H-Pi website about Western music theory. I originally created these pages in 2003 and 2004 to aid first year students in the understanding of basic concepts in Western music theory, and have now revived them with some small changes in organization and a few improvements for the H-Pi site. There are 34 pages organized into 6 chapters, starting here:

www.h-pi.com/theory/foreword.html

Enjoy,
Aaron Hunt
H-Pi Instruments

Thanks Aaron, that is a nice read. / Magnus

On Fri, 9 Nov 2007, Aaron Andrew Hunt wrote:

> A new area has been added to the H-Pi website about Western music
> theory. I originally created these pages in 2003 and 2004 to aid
> first year students in the understanding of basic concepts in Western
> music theory, and have now revived them with some small changes in
> organization and a few improvements for the H-Pi site. There are 34
> pages organized into 6 chapters, starting here:
>
> www.h-pi.com/theory/foreword.html
>
> Enjoy,
> Aaron Hunt
> H-Pi Instruments
>

--- In MakeMicroMusic@yahoogroups.com, Aaron Andrew Hunt <aahunt@...>
wrote:
>
> A new area has been added to the H-Pi website about Western music
> theory. I originally created these pages in 2003 and 2004 to aid
> first year students in the understanding of basic concepts in Western
> music theory, and have now revived them with some small changes in
> organization and a few improvements for the H-Pi site. There are 34
> pages organized into 6 chapters, starting here:
>
> www.h-pi.com/theory/foreword.html

Hey, other Aaron!

This is a great resource...I like the way you start explaining music
theory by referencing the logical natural source---the harmonic
series, and go from there. This is not done enough by people
explaining music theory.

I like, too, how you introduce that the ear hears logarithmically, and
we have to introduce the 'congruence' or 'identity' of the
octave....so we have to translate 1,2,4,8,16 into a linear function by
using logarithmic measure (octaves, cents, millioctaves, or whatever
measure you want that uses base 2)

Well done!

-A.

Aaron wrote:

"This is a great resource...I like the way you start explaining music
theory by referencing the logical natural source---the harmonic
series, and go from there. This is not done enough by people
explaining music theory."

I'm a bit troubled by this, but the trouble is subtle, and if readers are not in a mood to follow a subtle point, please let's not get into a spam war. My trouble is this: the harmonic series does indeed serve as a useful -- and I believe perhaps the most useful -- tool, if only as a point of departure, in describing and investigating intonational resources and tonal practice in general, and it does, indeed, have great explanatory power for phenomena in music history. However, for most of music history and in most music cultures, the abstract idea of a harmonic series was not available to either practicing musicians nor to theorists. It is a relatively late discovery, and musically useful facility with its properties is an even later development. Nevertheless, productive music theories were produced within the limitations imposed by an absence of harmonic theory, and to an extent -- presumably large -- the direction of creative work was shaped by this absence. Thus, at least three great lines of exploration were established in classical Greek and Hellenistic music theory that have persisted despite this deficit: the so-called pythagorean line, in which one attempted to describe or invent scales through the reiteration of the simplest ratio beyond the non-productive ratios of the two-limit; a more complex practice, with which the names Archytas, Eratosthenes, and Ptolemy are associated, in which one sought out the simplest, or most elegant, representations of real genera by ratios without the restrictions of the three-limit; and the tradition associated with Aristoxenus, which attempted to describe details of scales without the use of ratios, but rather as perceptual units without precise measure (a similar tradition may very well underly the srutis of Indian theory). (This tradition would eventual develop a number of more precisely quantified theories, ascribing to these units precise, and eventually logarithmic, values).

In modern theory and practice, working without the resources of this particular tool is confining, if not foolish. A harmonic series has great explanatory power for phenomena of consonance and dissonance, and can be very useful in creating harmonic and contrapuntal textures, and in orchestration. It is even useful in cases in which the instruments used do not have simple harmonic spectra or in tuning enviroments which correspond only weakly to the intervals of a harmonic series, if only as a point of departure. However, the retroactive use of this tool can be misleading: choices made in real, historical, musical practice, and often choices of great musical ingenuity, were made without these resources.

It might be argued that the harmonic series, being ever present in pipes and strings, and present in the harmonic division of a string length, was known but simply not articulated in ancient harmonic theory or even that an ancient intuition of a relationship between sensory consonance and rational intervals implied the harmonic series and did not need to be articulated. In the Washington Monthly blog today, Kevin Drum has a provocative small item (here: http://www.washingtonmonthly.com/archives/individual/2007_11/012487.php ) about a similar "obvious" phenomena in the history of physical science -- the fact that no one seems to have figured out that gravity accelerates all objects at the same speed until that business in Pisa -- and perhaps the absence of a modern harmonic theory is an even more concrete example of missing the obvious, simply because the existing theory was sophisticated enough to produce all the music that one needed or even imagined needing. In any case, an account of the historical development of musical practice should at least take this into consideration.

Daniel Wolf
Frankfurt

Magnus and AaronKJ, thanks for the kind words.
There are still many pages lacking, but I'm
relatively happy with what is there.

Daniel, I think AKJ wrote "logical natural source",
not be taken to mean "historical natural source".
The word "natural" might make one cringe having
the knowledge that a pure harmonic series is
encountered in nature about as often as is a
frictionless surface; yet physicists often talk about
a frictionless surface just as a theorist talks about
a perfect harmonic series, that is, as an abstract
ideal state or structure.

You wrote:

> In any case, an account of the historical
> development of musical practice should at least take
> this into consideration.

I agree. I hope you see that my pages make no claim to
be "an account of the historical development
of musical practice". As a theorist, I see a great difficulty
of reconciling history with logic. In the foreword for the
theory pages I state plainly that I include history when it is
both logical and relevant, and even then I may choose
to simplify some things. I certainly make no claims as to
the historicity of the harmonic series as the basis
for Western harmony.

When teaching this way using logic I also make it a
point to stop along the way as the structure is built
to state at least a few times that history is much more
complicated and is being sidestepped at one or another
juncture, because I want students to be made aware
that there is a much more complicated
world than the simple one being built, but I feel it is
important not to inundate students with history
when teaching theory, unless specifically teaching
about the history of theory, simply because the world
is filled with too many contradictions. Delving into
history is rich and instructive, but in terms of theory
I feel it is an activity better saved for a much later
stage of exploration, and in general I feel instruction
in history should be left to an expert in that area,
(that is, to a musicologist) which I am not.

It may be noted that many logical structures worked
out by theorists throughout history can be seen to
have resulted from the taking of a similar
approach - that is, of the theorist choosing to eschew
many aspects of his own history, and in many cases
this is precisely what makes his ideas so compelling.

As a theorist and composer, I personally feel that
music theory exists to inform practice, not to explain it.
This is its great beauty and power. Knowledge of
abstract structure is there to be to be applied at
creative whim.

Yours,
Aaron Hunt
H-Pi Instruments

--- In MakeMicroMusic@yahoogroups.com, Daniel Wolf <djwolf@...> wrote:
>
> Aaron wrote:
>
> "This is a great resource...I like the way you start explaining music
> theory by referencing the logical natural source---the harmonic
> series, and go from there. This is not done enough by people
> explaining music theory."
>
> I'm a bit troubled by this, but the trouble is subtle, and if readers
> are not in a mood to follow a subtle point, please let's not get into a
> spam war.
>
> My trouble is this: the harmonic series does indeed serve as a useful --
> and I believe perhaps the most useful -- tool, if only as a point of
> departure, in describing and investigating intonational resources and
> tonal practice in general, and it does, indeed, have great explanatory
> power for phenomena in music history. However, for most of music history
> and in most music cultures, the abstract idea of a harmonic series was
> not available to either practicing musicians nor to theorists. It is a
> relatively late discovery, and musically useful facility with its
> properties is an even later development. Nevertheless, productive music
> theories were produced within the limitations imposed by an absence of
> harmonic theory, and to an extent -- presumably large -- the direction
> of creative work was shaped by this absence. Thus, at least three great
> lines of exploration were established in classical Greek and Hellenistic
> music theory that have persisted despite this deficit: the so-called
> pythagorean line, in which one attempted to describe or invent scales
> through the reiteration of the simplest ratio beyond the non-productive
> ratios of the two-limit; a more complex practice, with which the names
> Archytas, Eratosthenes, and Ptolemy are associated, in which one sought
> out the simplest, or most elegant, representations of real genera by
> ratios without the restrictions of the three-limit; and the tradition
> associated with Aristoxenus, which attempted to describe details of
> scales without the use of ratios, but rather as perceptual units without
> precise measure (a similar tradition may very well underly the srutis of
> Indian theory). (This tradition would eventual develop a number of more
> precisely quantified theories, ascribing to these units precise, and
> eventually logarithmic, values).
>
> In modern theory and practice, working without the resources of this
> particular tool is confining, if not foolish. A harmonic series has
> great explanatory power for phenomena of consonance and dissonance, and
> can be very useful in creating harmonic and contrapuntal textures, and
> in orchestration. It is even useful in cases in which the instruments
> used do not have simple harmonic spectra or in tuning enviroments which
> correspond only weakly to the intervals of a harmonic series, if only as
> a point of departure. However, the retroactive use of this tool can be
> misleading: choices made in real, historical, musical practice, and
> often choices of great musical ingenuity, were made without these resources.
>
> It might be argued that the harmonic series, being ever present in pipes
> and strings, and present in the harmonic division of a string length,
> was known but simply not articulated in ancient harmonic theory or even
> that an ancient intuition of a relationship between sensory consonance
> and rational intervals implied the harmonic series and did not need to
> be articulated. In the Washington Monthly blog today, Kevin Drum has a
> provocative small item (here:
> http://www.washingtonmonthly.com/archives/individual/2007_11/012487.php
> ) about a similar "obvious" phenomena in the history of physical science
> -- the fact that no one seems to have figured out that gravity
> accelerates all objects at the same speed until that business in Pisa --
> and perhaps the absence of a modern harmonic theory is an even more
> concrete example of missing the obvious, simply because the existing
> theory was sophisticated enough to produce all the music that one needed
> or even imagined needing. In any case, an account of the historical
> development of musical practice should at least take this into
> consideration.
>
> Daniel Wolf
> Frankfurt
>

This is a common argrument that the harmonic series is not heardin its pure form. the same can also be said of a steady beat or tempowhich measurements would show , absent a machine, do not exist. stillit seems to be what we hear. I have yet to hear any arguments againtsthe interger divisions/additions of duration. perhaps we are missingsomething by tempering them:)
-----Original Message-----
From: Aaron Andrew Hunt [mailto:aahunt@...]
Sent: Tuesday, November 13, 2007 12:14 AM
To: MakeMicroMusic@yahoogroups.com
Subject: [MMM] Re: New Pages: Systematic Music Theory

Magnus and AaronKJ, thanks for the kind words.
There are still many pages lacking, but I'm
relatively happy with what is there.

Daniel, I think AKJ wrote "logical natural source",
not be taken to mean "historical natural source".
The word "natural" might make one cringe having
the knowledge that a pure harmonic series is
encountered in nature about as often as is a
frictionless surface; yet physicists often talk about
a frictionless surface just as a theorist talks about
a perfect harmonic series, that is, as an abstract
ideal state or structure.

You wrote:

> In any case, an account of the historical
> development of musical practice should at least take
> this into consideration.

I agree. I hope you see that my pages make no claim to
be "an account of the historical development
of musical practice". As a theorist, I see a great difficulty
of reconciling history with logic. In the foreword for the
theory pages I state plainly that I include history when it is
both logical and relevant, and even then I may choose
to simplify some things. I certainly make no claims as to
the historicity of the harmonic series as the basis
for Western harmony.

When teaching this way using logic I also make it a
point to stop along the way as the structure is built
to state at least a few times that history is much more
complicated and is being sidestepped at one or another
juncture, because I want students to be made aware
that there is a much more complicated
world than the simple one being built, but I feel it is
important not to inundate students with history
when teaching theory, unless specifically teaching
about the history of theory, simply because the world
is filled with too many contradictions. Delving into
history is rich and instructive, but in terms of theory
I feel it is an activity better saved for a much later
stage of exploration, and in general I feel instruction
in history should be left to an expert in that area,
(that is, to a musicologist) which I am not.

It may be noted that many logical structures worked
out by theorists throughout history can be seen to
have resulted from the taking of a similar
approach - that is, of the theorist choosing to eschew
many aspects of his own history, and in many cases
this is precisely what makes his ideas so compelling.

As a theorist and composer, I personally feel that
music theory exists to inform practice, not to explain it.
This is its great beauty and power. Knowledge of
abstract structure is there to be to be applied at
creative whim.

Yours,
Aaron Hunt
H-Pi Instruments

--- In MakeMicroMusic@yahoogroups.com, Daniel Wolf <djwolf@...> wrote:
>
> Aaron wrote:
>
> "This is a great resource...I like the way you start explaining music
> theory by referencing the logical natural source---the harmonic
> series, and go from there. This is not done enough by people
> explaining music theory."
>
> I'm a bit troubled by this, but the trouble is subtle, and if readers
> are not in a mood to follow a subtle point, please let's not get into a
> spam war.
>
> My trouble is this: the harmonic series does indeed serve as a useful --
> and I believe perhaps the most useful -- tool, if only as a point of
> departure, in describing and investigating intonational resources and
> tonal practice in general, and it does, indeed, have great explanatory
> power for phenomena in music history. However, for most of music history
> and in most music cultures, the abstract idea of a harmonic series was
> not available to either practicing musicians nor to theorists. It is a
> relatively late discovery, and musically useful facility with its
> properties is an even later development. Nevertheless, productive music
> theories were produced within the limitations imposed by an absence of
> harmonic theory, and to an extent -- presumably large -- the direction
> of creative work was shaped by this absence. Thus, at least three great
> lines of exploration were established in classical Greek and Hellenistic
> music theory that have persisted despite this deficit: the so-called
> pythagorean line, in which one attempted to describe or invent scales
> through the reiteration of the simplest ratio beyond the non-productive
> ratios of the two-limit; a more complex practice, with which the names
> Archytas, Eratosthenes, and Ptolemy are associated, in which one sought
> out the simplest, or most elegant, representations of real genera by
> ratios without the restrictions of the three-limit; and the tradition
> associated with Aristoxenus, which attempted to describe details of
> scales without the use of ratios, but rather as perceptual units without
> precise measure (a similar tradition may very well underly the srutis of
> Indian theory). (This tradition would eventual develop a number of more
> precisely quantified theories, ascribing to these units precise, and
> eventually logarithmic, values).
>
> In modern theory and practice, working without the resources of this
> particular tool is confining, if not foolish. A harmonic series has
> great explanatory power for phenomena of consonance and dissonance, and
> can be very useful in creating harmonic and contrapuntal textures, and
> in orchestration. It is even useful in cases in which the instruments
> used do not have simple harmonic spectra or in tuning enviroments which
> correspond only weakly to the intervals of a harmonic series, if only as
> a point of departure. However, the retroactive use of this tool can be
> misleading: choices made in real, historical, musical practice, and
> often choices of great musical ingenuity, were made without these resources.
>
> It might be argued that the harmonic series, being ever present in pipes
> and strings, and present in the harmonic division of a string length,
> was known but simply not articulated in ancient harmonic theory or even
> that an ancient intuition of a relationship between sensory consonance
> and rational intervals implied the harmonic series and did not need to
> be articulated. In the Washington Monthly blog today, Kevin Drum has a
> provocative small item (here:
> http://www.washingtonmonthly.com/archives/individual/2007_11/012487.php
> ) about a similar "obvious" phenomena in the history of physical science
> -- the fact that no one seems to have figured out that gravity
> accelerates all objects at the same speed until that business in Pisa --
> and perhaps the absence of a modern harmonic theory is an even more
> concrete example of missing the obvious, simply because the existing
> theory was sophisticated enough to produce all the music that one needed
> or even imagined needing. In any case, an account of the historical
> development of musical practice should at least take this into
> consideration.
>
> Daniel Wolf
> Frankfurt
>

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

--- In MakeMicroMusic@yahoogroups.com, kraiggrady@... wrote:
>
> This is a common argrument that the harmonic series is not heardin
its pure form. the same can also be said of a steady beat or
tempowhich measurements would show , absent a machine, do not exist.
stillit seems to be what we hear. I have yet to hear any arguments
againtsthe interger divisions/additions of duration. perhaps we are
missingsomething by tempering them:)

AARON:
Well, there is often a reaction against purely metronomic playing
without rubato! (in certain scenarios). In other contexts, rubato is
really wrong (electronic dance music for example). Most music explores
to some degree an internal tension between both poles.

Kraig, I think the exploration of tempered rhythm is a great idea...it
might lead to some interesting textures!

That said, I still the the harmonic series, pure or impure, is an
extremely logical gestalt for explaining consonance and dissonance.
And whether or not it was understood to exist, its force was felt.
Gravity existed before Newton gave his equations in 'Principia'.

I think there is some beauty in the impurity of things--we long for
slight imperfection--most people don't like the absolute pure tones of
JI possible in electronic music, a lot of ethnic musics don't
use/don't like pure octaves, considering them 'dead'---and the
messiness and complexity of acoustic instruments lends an instability
that is considered by most to be a positive thing....it's an
interesting dichotomy to be a JI purist, but an acoustic musician (and
Kriag, I think the tension between those ideas is very good and
fruitful--I'm not criticising)

I for one celebrate the multiple and various theoretical and practical
approaches to tuning...and even the tensions and flame wars...dialog
and cretive struggle and wrestling is a good thing to me. These
various arguments actually take place *within* me as a single artist,
and I think it's been great to go back and forth exploring different
avenues.

Best,
Aaron.

Oh a couple of things here!
my example was just to put forwardthat we hear the harmonic series as interger ratios even when it isnot. which is kinda the basis of temperment in the first place. similarto the phenomenon of most people seeing right angle with a 89 degreeangle. we do get quite close with vowel sounds though.
Ithink DJ Wolf has a point here and personally i might cast the wholewithin that scales and such are based on acoustical phenomenon ingeneral of which the harmonic series is on of the most basic.in seemsthe examples put forth do involve lower ratios. the exception of onebeing based on what one might call just noticable difference. I imaginethis coming about out of the lack of the JI theory to capture many ofthe indigenous tunings going on in the greek and nearby musics,probably including african at the time.
I am really not a JI purist as i don't work with limitbased systems anymore for quite some time. I will confess to being antiET for the most part.
Whilemost cultures like interval that might function with simularity, most cultures prefer tunings and scales that are unequal insize. This is expedient in having the most variety with the fewernumber of tones. So a just (as an example) pentatonic will havemore different size intervals than 12 ET. for certain music it seemsthat et might be preferred, but even in the case of bach we can seesome tuning that varies brings much of life that 12 et seems tohomogenize.

that most people don't like JI on simpletones is a bit problematic cause most people don't like simpleelectronic sounds in the first place as them being bland from thestart.
that octaves are not liked by some cultures mighthave more to do with wanting all their notes to beat cause they soundlouder. in much the same way the type of operatic timbre developed tocut over the volume of orchestras.
notto down play near octave intervals, but like everything else in musicthere are so many factors that go into any tuning that it iswhy it ishard to reproduce something that can withstand any duration.

Likeatonality though i don't think much is gained by avoiding certainthings and i have yet to see the advantage in non octave arrays outsideof slight mistunings that bring difference tones in line possibly.having a scale that has both i have found useful in having a choice ofsomething more forceful or not and just adding color to a line orpart.

-----Original Message-----
From: Aaron Krister Johnson [mailto:aaron@...]
Sent: Tuesday, November 13, 2007 11:05 AM
To: MakeMicroMusic@yahoogroups.com,
Subject: [MMM] Re: New Pages: Systematic Music Theory

--- In MakeMicroMusic@yahoogroups.com, kraiggrady@... wrote:
>
> This is a common argrument that the harmonic series is not heardin
its pure form. the same can also be said of a steady beat or
tempowhich measurements would show , absent a machine, do not exist.
stillit seems to be what we hear. I have yet to hear any arguments
againtsthe interger divisions/additions of duration. perhaps we are
missingsomething by tempering them:)

AARON:
Well, there is often a reaction against purely metronomic playing
without rubato! (in certain scenarios). In other contexts, rubato is
really wrong (electronic dance music for example). Most music explores
to some degree an internal tension between both poles.

Kraig, I think the exploration of tempered rhythm is a great idea...it
might lead to some interesting textures!

That said, I still the the harmonic series, pure or impure, is an
extremely logical gestalt for explaining consonance and dissonance.
And whether or not it was understood to exist, its force was felt.
Gravity existed before Newton gave his equations in 'Principia'.

I think there is some beauty in the impurity of things--we long for
slight imperfection--most people don't like the absolute pure tones of
JI possible in electronic music, a lot of ethnic musics don't
use/don't like pure octaves, considering them 'dead'---and the
messiness and complexity of acoustic instruments lends an instability
that is considered by most to be a positive thing....it's an
interesting dichotomy to be a JI purist, but an acoustic musician (and
Kriag, I think the tension between those ideas is very good and
fruitful--I'm not criticising)

I for one celebrate the multiple and various theoretical and practical
approaches to tuning...and even the tensions and flame wars...dialog
and cretive struggle and wrestling is a good thing to me. These
various arguments actually take place *within* me as a single artist,
and I think it's been great to go back and forth exploring different
avenues.

Best,
Aaron.

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

Good reply, Kraig...a couple of thoughts below...

--- In MakeMicroMusic@yahoogroups.com, kraiggrady@... wrote:
>
> Oh a couple of things here!
> my example was just to put forwardthat we hear the harmonic series
as interger ratios even when it isnot. which is kinda the basis of
temperment in the first place. similarto the phenomenon of most people
seeing right angle with a 89 degreeangle. we do get quite close with
vowel sounds though.
> Ithink DJ Wolf has a point here and personally i might cast the
wholewithin that scales and such are based on acoustical phenomenon
ingeneral of which the harmonic series is one of the most basic.in
seemsthe examples put forth do involve lower ratios. the exception of
onebeing based on what one might call just noticable difference. I
imaginethis coming about out of the lack of the JI theory to capture
many ofthe indigenous tunings going on in the greek and nearby
musics,probably including african at the time.
> I am really not a JI purist as i don't work with limitbased systems
anymore for quite some time. I will confess to being antiET for the
most part.
> Whilemost cultures like interval that might function with
simularity, most cultures prefer tunings and scales that are unequal
insize.

What most cultures do is useful to know, butI hardly see it as an
argument for what anyone should do. The 'argument from popularity' is
a fallacy. During the post-9/11 period, Bush became a popular
president...was he a good president?

> This is expedient in having the most variety with the fewernumber of
tones.

Although this is true, I never felt bored hearing all those recordings
of 12-equal piano music my whole life growing up...I suppose partly
because ture 12-equal is so hard to get exactly anyway, but also
because I think it's not a foreground consideration for me, at least
not as much as whether I'm hearing a master musician play or not.

> So a just (as an example) pentatonic will havemore different size
intervals than 12 ET. for certain music it seemsthat et might be
preferred, but even in the case of bach we can seesome tuning that
varies brings much of life that 12 et seems tohomogenize.

I agree. Then again, some might argue that a pure interval is lifeless
(I wouldn't, but I've heard the charge made)

> that most people don't like JI on simpletones is a bit problematic
cause most people don't like simpleelectronic sounds in the first
place as them being bland from thestart.

Yes, but my point was merely to say that there is an interesting
tension between getting pure JI (as pure as possible) and the inherent
dynamic instability of most acoustic instruments.

> that octaves are not liked by some cultures mighthave more to do
with wanting all their notes to beat cause they soundlouder. in much
the same way the type of operatic timbre developed tocut over the
volume of orchestras.

Yes, and I've also heard a direct quote by Bill Alves I think that one
native musician he knew said that a true octave was 'dead sounding',
which I took to mean that he liked beating because it was lively.

> notto down play near octave intervals, but like everything else in
musicthere are so many factors that go into any tuning that it iswhy
it ishard to reproduce something that can withstand any duration.
>
> Likeatonality though i don't think much is gained by avoiding
certainthings and i have yet to see the advantage in non octave arrays
outsideof slight mistunings that bring difference tones in line
possibly.having a scale that has both i have found useful in having a
choice ofsomething more forceful or not and just adding color to a
line orpart.

Hey, you never said whether you liked the idea of tempered rhythm!

> -----Original Message-----
> From: Aaron Krister Johnson [mailto:aaron@...]
> Sent: Tuesday, November 13, 2007 11:05 AM
> To: MakeMicroMusic@yahoogroups.com,
> Subject: [MMM] Re: New Pages: Systematic Music Theory
>
> --- In MakeMicroMusic@yahoogroups.com, kraiggrady@ wrote:
> >
> > This is a common argrument that the harmonic series is not heardin
> its pure form. the same can also be said of a steady beat or
> tempowhich measurements would show , absent a machine, do not exist.
> stillit seems to be what we hear. I have yet to hear any arguments
> againtsthe interger divisions/additions of duration. perhaps we are
> missingsomething by tempering them:)
>
> AARON:
> Well, there is often a reaction against purely metronomic playing
> without rubato! (in certain scenarios). In other contexts, rubato is
> really wrong (electronic dance music for example). Most music explores
> to some degree an internal tension between both poles.
>
> Kraig, I think the exploration of tempered rhythm is a great idea...it
> might lead to some interesting textures!
>
> That said, I still the the harmonic series, pure or impure, is an
> extremely logical gestalt for explaining consonance and dissonance.
> And whether or not it was understood to exist, its force was felt.
> Gravity existed before Newton gave his equations in 'Principia'.
>
> I think there is some beauty in the impurity of things--we long for
> slight imperfection--most people don't like the absolute pure tones of
> JI possible in electronic music, a lot of ethnic musics don't
> use/don't like pure octaves, considering them 'dead'---and the
> messiness and complexity of acoustic instruments lends an instability
> that is considered by most to be a positive thing....it's an
> interesting dichotomy to be a JI purist, but an acoustic musician (and
> Kriag, I think the tension between those ideas is very good and
> fruitful--I'm not criticising)
>
> I for one celebrate the multiple and various theoretical and practical
> approaches to tuning...and even the tensions and flame wars...dialog
> and cretive struggle and wrestling is a good thing to me. These
> various arguments actually take place *within* me as a single artist,
> and I think it's been great to go back and forth exploring different
> avenues.
>
> Best,
> Aaron.
>
>
>
>
>
>
> [Non-text portions of this message have been removed]
>

oh! i am not sure exactly how one would temper a rythumn cause assoon as you shaved something off then that would just become the newtempo.
but possibly the idea hit you in a different waywhich might be interesting to pursue. how would you temperduration?

-----Original Message-----
From: Aaron Krister Johnson [mailto:aaron@...]
Sent: Wednesday, November 14, 2007 12:03 AM
To: MakeMicroMusic@yahoogroups.com
Subject: [MMM] Re: New Pages: Systematic Music Theory

Good reply, Kraig...a couple of thoughts below...

--- In MakeMicroMusic@yahoogroups.com, kraiggrady@... wrote:
>
> Oh a couple of things here!
> my example was just to put forwardthat we hear the harmonic series
as interger ratios even when it isnot. which is kinda the basis of
temperment in the first place. similarto the phenomenon of most people
seeing right angle with a 89 degreeangle. we do get quite close with
vowel sounds though.
> Ithink DJ Wolf has a point here and personally i might cast the
wholewithin that scales and such are based on acoustical phenomenon
ingeneral of which the harmonic series is one of the most basic.in
seemsthe examples put forth do involve lower ratios. the exception of
onebeing based on what one might call just noticable difference. I
imaginethis coming about out of the lack of the JI theory to capture
many ofthe indigenous tunings going on in the greek and nearby
musics,probably including african at the time.
> I am really not a JI purist as i don't work with limitbased systems
anymore for quite some time. I will confess to being antiET for the
most part.
> Whilemost cultures like interval that might function with
simularity, most cultures prefer tunings and scales that are unequal
insize.

What most cultures do is useful to know, butI hardly see it as an
argument for what anyone should do. The 'argument from popularity' is
a fallacy. During the post-9/11 period, Bush became a popular
president...was he a good president?

> This is expedient in having the most variety with the fewernumber of
tones.

Although this is true, I never felt bored hearing all those recordings
of 12-equal piano music my whole life growing up...I suppose partly
because ture 12-equal is so hard to get exactly anyway, but also
because I think it's not a foreground consideration for me, at least
not as much as whether I'm hearing a master musician play or not.

> So a just (as an example) pentatonic will havemore different size
intervals than 12 ET. for certain music it seemsthat et might be
preferred, but even in the case of bach we can seesome tuning that
varies brings much of life that 12 et seems tohomogenize.

I agree. Then again, some might argue that a pure interval is lifeless
(I wouldn't, but I've heard the charge made)

> that most people don't like JI on simpletones is a bit problematic
cause most people don't like simpleelectronic sounds in the first
place as them being bland from thestart.

Yes, but my point was merely to say that there is an interesting
tension between getting pure JI (as pure as possible) and the inherent
dynamic instability of most acoustic instruments.

> that octaves are not liked by some cultures mighthave more to do
with wanting all their notes to beat cause they soundlouder. in much
the same way the type of operatic timbre developed tocut over the
volume of orchestras.

Yes, and I've also heard a direct quote by Bill Alves I think that one
native musician he knew said that a true octave was 'dead sounding',
which I took to mean that he liked beating because it was lively.

> notto down play near octave intervals, but like everything else in
musicthere are so many factors that go into any tuning that it iswhy
it ishard to reproduce something that can withstand any duration.
>
> Likeatonality though i don't think much is gained by avoiding
certainthings and i have yet to see the advantage in non octave arrays
outsideof slight mistunings that bring difference tones in line
possibly.having a scale that has both i have found useful in having a
choice ofsomething more forceful or not and just adding color to a
line orpart.

Hey, you never said whether you liked the idea of tempered rhythm!

> -----Original Message-----
> From: Aaron Krister Johnson [mailto:aaron@...]
> Sent: Tuesday, November 13, 2007 11:05 AM
> To: MakeMicroMusic@yahoogroups.com,
> Subject: [MMM] Re: New Pages: Systematic Music Theory
>
> --- In MakeMicroMusic@yahoogroups.com, kraiggrady@ wrote:
> >
> > This is a common argrument that the harmonic series is not heardin
> its pure form. the same can also be said of a steady beat or
> tempowhich measurements would show , absent a machine, do not exist.
> stillit seems to be what we hear. I have yet to hear any arguments
> againtsthe interger divisions/additions of duration. perhaps we are
> missingsomething by tempering them:)
>
> AARON:
> Well, there is often a reaction against purely metronomic playing
> without rubato! (in certain scenarios). In other contexts, rubato is
> really wrong (electronic dance music for example). Most music explores
> to some degree an internal tension between both poles.
>
> Kraig, I think the exploration of tempered rhythm is a great idea...it
> might lead to some interesting textures!
>
> That said, I still the the harmonic series, pure or impure, is an
> extremely logical gestalt for explaining consonance and dissonance.
> And whether or not it was understood to exist, its force was felt.
> Gravity existed before Newton gave his equations in 'Principia'.
>
> I think there is some beauty in the impurity of things--we long for
> slight imperfection--most people don't like the absolute pure tones of
> JI possible in electronic music, a lot of ethnic musics don't
> use/don't like pure octaves, considering them 'dead'---and the
> messiness and complexity of acoustic instruments lends an instability
> that is considered by most to be a positive thing....it's an
> interesting dichotomy to be a JI purist, but an acoustic musician (and
> Kriag, I think the tension between those ideas is very good and
> fruitful--I'm not criticising)
>
> I for one celebrate the multiple and various theoretical and practical
> approaches to tuning...and even the tensions and flame wars...dialog
> and cretive struggle and wrestling is a good thing to me. These
> various arguments actually take place *within* me as a single artist,
> and I think it's been great to go back and forth exploring different
> avenues.
>
> Best,
> Aaron.
>
>
>
>
>
>
> [Non-text portions of this message have been removed]
>

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

--- In MakeMicroMusic@yahoogroups.com, kraiggrady@... wrote:
>
> oh! i am not sure exactly how one would temper a rhythm cause assoon
as you shaved something off then that would just become the newtempo.
> but possibly the idea hit you in a different waywhich might be
interesting to pursue. how would you temperduration?

Kraig-

My first thought would be to have polyphony analogous to tempered
intervals, e.g. instead of 2-against-3 (1-against-1.5), we might have
1-against-1.4953, which would give us a rhythmic, macro-version of the
meantone fifth.....I dunno, maybe it works, maybe it doesn't.

I know Nancarrow did some interesting things with irrational rhythm.
The mileage probably varies.

Best,
Aaron.