Yahoo Tuning Groups Ultimate Backup makemicromusic Is there a way to calculate a sum of harmonics in a chord?

Yuriy:

For a good book that talk about combination tones: ON THE SENSATIONS OF
TONE, by Hermann Helmholtz, translated to English, by Alexander Ellis [he
added much to the book]; also a Dover reprint. Can be found on the
internet, but it is over 500 pages.

Combination tones are caused by intermediation distortion in the ear and in
electronic equipment [usually not desired]. At normal sound pressure
levels in air there is no distortion but at high sound pressure levels like
found in the throat of a horn type speaker there may be some distortion.

Start with two notes, each has over tones. [I use the word overtones
because not all notes have overtones that are exactly in the harmonic
series.] Take each tone of the first note [including the fundamental],
one at a time, sum it with each tone of the second, note one at a time. This
will give a series of sum tones. Now do this, in like manner, for the
difference of the tones. This will give the series of difference tones.
Now continue with this process by taking the sum and difference of all
the new tone and the original tone. And keep doing this for ever, [if
you do not have anything to do]. Do this for 3 and 4 note chord the same
way. [Even the overtones of a single note will produce sun and difference
tones.]

Fortunately the intensity of the combination tones falls off quickly, so
using the stronger over tone [the first few of the note] and just taking
the sum and difference of these will work well and most of these the ear
will not hear anyway.

If the chord is built with notes that have overtone that are in the
harmonic series, some of the sum and difference tones may be the same as
some of the harmonics and sum and difference tones. If the chords are
built with notes that have overtones that are not in the harmonic series,
the sum and difference tone will be in clusters. These clusters may
produce beats, along with the beats of the mismatched overtones.

If the notes of the chord are built with tempered notes, there will also be
clusters of tones that may produce beats, along with the beats of the
mismatched overtones of the tempered notes.

Take the major chord, it has the ratio 4:5:6; do the math will gives the
following series or ratio 1:2:3:4:5:6:7: 8:9: …. The root of the chord
is 4, two octaves down is 1 [the same note!!]. The minor chord has the
ratio 5:6::4:5, the 5th still has the ratio 4:6 which will also prepuce the
same lower root 1 but there will be more than one series of tones which
over lap. This works with other chords but series may be complicated and
have overlapping series. The German 6th also works nice and simple; it
has the ratio 4:5:6:7, [found in the ¼ c meantone]; but the dominant 7th
chord with ratio 4:5:6::5:6 is a little ruff. The diminished chord
5:6::5:6 is ruff; but 5:6:7 sounds good, with a simple series, using the
septimal third [also found in the ¼ c meantone]. The ratio 5:6:7 will
also produce the 1, two and one half ½ octaves down; but the root 5 from
the ratio of the chord is a 5th to the 1, two and one half down, could say
that the 1 is the the real root of the chord not the 5.

The 1 of the chord is like the fundamental of a note. the real root. This
could explain why the viiº chord has the dominant function the real root
being the 5th of the scale.

The sub tones are clusters of tones when the notes of the chords are
tempered.

ƒg

On Thu, Nov 17, 2011 at 7:08 AM, ruxxes <ruxxes@...> wrote:

> **
>
>
> Hello Mike,
>
> Ah-ha, so it's the combination note what I was looking for! Now being
> digging more on the Web.
>
> I am curious how would this apply to irrational ratios of equal tunings?
> Is there any concept similar to comb.tone that "extracts" more subtlety out
> of a sound mass (http://en.wikipedia.org/wiki/Sound_mass)?
>
> Thank you very much!
> Yuriy.
>
> --- In MakeMicroMusic@yahoogroups.com, kraiggrady <kraiggrady@...> wrote:
> >
> > Hello Ruxxes~
> > You can do this at least in Just intonation by treating your chord
> > as how it appears in a harmonic series. the resultant number would be
> > what is called a combination tone. I experimented quite a bit with this
> > and difference tones adding these both trying omitting dulicates and
> > other patterns. like most things, the human mind can follow patterns and
> > so it is hard to say what method here might be best. i would experiment
> > and see what you come up with.
> >
> > On 11/11/11 1:03 AM, ruxxes wrote:
> > >
> > > Hey people,
> > >
> > > This one is for nerds I guess:
> > >
> > > Can I get a resultant ratio of a chord by calculating a sum of all
> > > intervals present in a chord?
> > >
> > > How can I do this for a 4-note chord?
> > >
> > > Does this make sense at all?
> > >
> > > Thank you!
> > >
> > >
> > >
> > > /^_,',',',_ //^/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/
> >
> > >
> > > ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
> > >
> > > a momentary antenna as i turn to water
> > > this evaporates - an island once again
> >
> >
> > [Non-text portions of this message have been removed]
> >
>
>
>

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

🔗kraiggrady <kraiggrady@...>

Hi Freeman and Yuriy~
Helmholtz was my own source is figuring these out~one can start on page
214 and the next 11 pages most of what he has to say on the subject.
It is quite easy to add. take 4:5:6 this equals 15 if you want to add
first order difference tones that would be 1+1+2 to what is above which
will give you another 4. I figured this out for all 4 chords involving
the 11in all inversions where no tone is further than an octave apart
from the next. It was the basis of quite a few pieces. some being
merely a single chord and its inversions.

On 18/11/11 5:58 PM, Freeman Gilmore wrote:
>
> Yuriy:
>
> For a good book that talk about combination tones: ON THE SENSATIONS OF
> TONE, by Hermann Helmholtz, translated to English, by Alexander Ellis [he
> added much to the book]; also a Dover reprint. Can be found on the
> internet, but it is over 500 pages.
>
> Combination tones are caused by intermediation distortion in the ear
> and in
> electronic equipment [usually not desired]. At normal sound pressure
> levels in air there is no distortion but at high sound pressure levels
> like
> found in the throat of a horn type speaker there may be some distortion.
>
> Start with two notes, each has over tones. [I use the word overtones
> because not all notes have overtones that are exactly in the harmonic
> series.] Take each tone of the first note [including the fundamental],
> one at a time, sum it with each tone of the second, note one at a
> time. This
> will give a series of sum tones. Now do this, in like manner, for the
> difference of the tones. This will give the series of difference tones.
> Now continue with this process by taking the sum and difference of all
> the new tone and the original tone. And keep doing this for ever, [if
> you do not have anything to do]. Do this for 3 and 4 note chord the same
> way. [Even the overtones of a single note will produce sun and difference
> tones.]
>
> Fortunately the intensity of the combination tones falls off quickly, so
> using the stronger over tone [the first few of the note] and just taking
> the sum and difference of these will work well and most of these the ear
> will not hear anyway.
>
> If the chord is built with notes that have overtone that are in the
> harmonic series, some of the sum and difference tones may be the same as
> some of the harmonics and sum and difference tones. If the chords are
> built with notes that have overtones that are not in the harmonic series,
> the sum and difference tone will be in clusters. These clusters may
> produce beats, along with the beats of the mismatched overtones.
>
> If the notes of the chord are built with tempered notes, there will
> also be
> clusters of tones that may produce beats, along with the beats of the
> mismatched overtones of the tempered notes.
>
> Take the major chord, it has the ratio 4:5:6; do the math will gives the
> following series or ratio 1:2:3:4:5:6:7: 8:9: …. The root of the chord
> is 4, two octaves down is 1 [the same note!!]. The minor chord has the
> ratio 5:6::4:5, the 5th still has the ratio 4:6 which will also
> prepuce the
> same lower root 1 but there will be more than one series of tones which
> over lap. This works with other chords but series may be complicated and
> have overlapping series. The German 6th also works nice and simple; it
> has the ratio 4:5:6:7, [found in the ¼ c meantone]; but the dominant 7th
> chord with ratio 4:5:6::5:6 is a little ruff. The diminished chord
> 5:6::5:6 is ruff; but 5:6:7 sounds good, with a simple series, using the
> septimal third [also found in the ¼ c meantone]. The ratio 5:6:7 will
> also produce the 1, two and one half ½ octaves down; but the root 5 from
> the ratio of the chord is a 5th to the 1, two and one half down, could say
> that the 1 is the the real root of the chord not the 5.
>
> The 1 of the chord is like the fundamental of a note. the real root. This
> could explain why the viiº chord has the dominant function the real root
> being the 5th of the scale.
>
> The sub tones are clusters of tones when the notes of the chords are
> tempered.
>
> ƒg
>
> On Thu, Nov 17, 2011 at 7:08 AM, ruxxes <ruxxes@...
> <mailto:ruxxes%40yahoo.com>> wrote:
>
> > **
> >
> >
> > Hello Mike,
> >
> > Ah-ha, so it's the combination note what I was looking for! Now being
> > digging more on the Web.
> >
> > I am curious how would this apply to irrational ratios of equal tunings?
> > Is there any concept similar to comb.tone that "extracts" more
> subtlety out
> > of a sound mass (http://en.wikipedia.org/wiki/Sound_mass)?
> >
> > Thank you very much!
> > Yuriy.
> >
> > --- In MakeMicroMusic@yahoogroups.com
> <mailto:MakeMicroMusic%40yahoogroups.com>, kraiggrady <kraiggrady@...>
> wrote:
> > >
> > > Hello Ruxxes~
> > > You can do this at least in Just intonation by treating your chord
> > > as how it appears in a harmonic series. the resultant number would be
> > > what is called a combination tone. I experimented quite a bit with
> this
> > > and difference tones adding these both trying omitting dulicates and
> > > other patterns. like most things, the human mind can follow
> patterns and
> > > so it is hard to say what method here might be best. i would
> experiment
> > > and see what you come up with.
> > >
> > > On 11/11/11 1:03 AM, ruxxes wrote:
> > > >
> > > > Hey people,
> > > >
> > > > This one is for nerds I guess:
> > > >
> > > > Can I get a resultant ratio of a chord by calculating a sum of all
> > > > intervals present in a chord?
> > > >
> > > > How can I do this for a 4-note chord?
> > > >
> > > > Does this make sense at all?
> > > >
> > > > Thank you!
> > > >
> > > >
> > > >
> > > > /^_,',',',_ //^/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/
> > >
> > > >
> > > > ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
> > > >
> > > > a momentary antenna as i turn to water
> > > > this evaporates - an island once again
> > >
> > >
> > > [Non-text portions of this message have been removed]
> > >
> >
> >
> >
>
> [Non-text portions of this message have been removed]
>
>

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

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

a momentary antenna as i turn to water
this evaporates - an island once again

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

🔗kraiggrady <kraiggrady@...>

actually the method i liked most was omitting the duplicates so you
would only omit 1 from this chord. let me know if something other hits
you right!

On 18/11/11 7:02 PM, kraiggrady wrote:
>
> Hi Freeman and Yuriy~
> Helmholtz was my own source is figuring these out~one can start on page
> 214 and the next 11 pages most of what he has to say on the subject.
> It is quite easy to add. take 4:5:6 this equals 15 if you want to add
> first order difference tones that would be 1+1+2 to what is above which
> will give you another 4. I figured this out for all 4 chords involving
> the 11in all inversions where no tone is further than an octave apart
> from the next. It was the basis of quite a few pieces. some being
> merely a single chord and its inversions.
>
> On 18/11/11 5:58 PM, Freeman Gilmore wrote:
> >
> > Yuriy:
> >
> > For a good book that talk about combination tones: ON THE SENSATIONS OF
> > TONE, by Hermann Helmholtz, translated to English, by Alexander
> Ellis [he
> > added much to the book]; also a Dover reprint. Can be found on the
> > internet, but it is over 500 pages.
> >
> > Combination tones are caused by intermediation distortion in the ear
> > and in
> > electronic equipment [usually not desired]. At normal sound pressure
> > levels in air there is no distortion but at high sound pressure levels
> > like
> > found in the throat of a horn type speaker there may be some distortion.
> >
> > Start with two notes, each has over tones. [I use the word overtones
> > because not all notes have overtones that are exactly in the harmonic
> > series.] Take each tone of the first note [including the fundamental],
> > one at a time, sum it with each tone of the second, note one at a
> > time. This
> > will give a series of sum tones. Now do this, in like manner, for the
> > difference of the tones. This will give the series of difference tones.
> > Now continue with this process by taking the sum and difference of all
> > the new tone and the original tone. And keep doing this for ever, [if
> > you do not have anything to do]. Do this for 3 and 4 note chord the same
> > way. [Even the overtones of a single note will produce sun and
> difference
> > tones.]
> >
> > Fortunately the intensity of the combination tones falls off quickly, so
> > using the stronger over tone [the first few of the note] and just taking
> > the sum and difference of these will work well and most of these the ear
> > will not hear anyway.
> >
> > If the chord is built with notes that have overtone that are in the
> > harmonic series, some of the sum and difference tones may be the same as
> > some of the harmonics and sum and difference tones. If the chords are
> > built with notes that have overtones that are not in the harmonic
> series,
> > the sum and difference tone will be in clusters. These clusters may
> > produce beats, along with the beats of the mismatched overtones.
> >
> > If the notes of the chord are built with tempered notes, there will
> > also be
> > clusters of tones that may produce beats, along with the beats of the
> > mismatched overtones of the tempered notes.
> >
> > Take the major chord, it has the ratio 4:5:6; do the math will gives the
> > following series or ratio 1:2:3:4:5:6:7: 8:9: …. The root of the chord
> > is 4, two octaves down is 1 [the same note!!]. The minor chord has the
> > ratio 5:6::4:5, the 5th still has the ratio 4:6 which will also
> > prepuce the
> > same lower root 1 but there will be more than one series of tones which
> > over lap. This works with other chords but series may be complicated and
> > have overlapping series. The German 6th also works nice and simple; it
> > has the ratio 4:5:6:7, [found in the ¼ c meantone]; but the dominant 7th
> > chord with ratio 4:5:6::5:6 is a little ruff. The diminished chord
> > 5:6::5:6 is ruff; but 5:6:7 sounds good, with a simple series, using the
> > septimal third [also found in the ¼ c meantone]. The ratio 5:6:7 will
> > also produce the 1, two and one half ½ octaves down; but the root 5 from
> > the ratio of the chord is a 5th to the 1, two and one half down,
> could say
> > that the 1 is the the real root of the chord not the 5.
> >
> > The 1 of the chord is like the fundamental of a note. the real root.
> This
> > could explain why the viiº chord has the dominant function the real root
> > being the 5th of the scale.
> >
> > The sub tones are clusters of tones when the notes of the chords are
> > tempered.
> >
> > ƒg
> >
> > On Thu, Nov 17, 2011 at 7:08 AM, ruxxes <ruxxes@yahoo.com
> <mailto:ruxxes%40yahoo.com>
> > <mailto:ruxxes%40yahoo.com>> wrote:
> >
> > > **
> > >
> > >
> > > Hello Mike,
> > >
> > > Ah-ha, so it's the combination note what I was looking for! Now being
> > > digging more on the Web.
> > >
> > > I am curious how would this apply to irrational ratios of equal
> tunings?
> > > Is there any concept similar to comb.tone that "extracts" more
> > subtlety out
> > > of a sound mass (http://en.wikipedia.org/wiki/Sound_mass)?
> > >
> > > Thank you very much!
> > > Yuriy.
> > >
> > > --- In MakeMicroMusic@yahoogroups.com
> <mailto:MakeMicroMusic%40yahoogroups.com>
> > <mailto:MakeMicroMusic%40yahoogroups.com>, kraiggrady <kraiggrady@...>
> > wrote:
> > > >
> > > > Hello Ruxxes~
> > > > You can do this at least in Just intonation by treating your chord
> > > > as how it appears in a harmonic series. the resultant number
> would be
> > > > what is called a combination tone. I experimented quite a bit with
> > this
> > > > and difference tones adding these both trying omitting dulicates and
> > > > other patterns. like most things, the human mind can follow
> > patterns and
> > > > so it is hard to say what method here might be best. i would
> > experiment
> > > > and see what you come up with.
> > > >
> > > > On 11/11/11 1:03 AM, ruxxes wrote:
> > > > >
> > > > > Hey people,
> > > > >
> > > > > This one is for nerds I guess:
> > > > >
> > > > > Can I get a resultant ratio of a chord by calculating a sum of all
> > > > > intervals present in a chord?
> > > > >
> > > > > How can I do this for a 4-note chord?
> > > > >
> > > > > Does this make sense at all?
> > > > >
> > > > > Thank you!
> > > > >
> > > > >
> > > > >
> > > > > /^_,',',',_ //^/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/
> > > >
> > > > >
> > > > > ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
> > > > >
> > > > > a momentary antenna as i turn to water
> > > > > this evaporates - an island once again
> > > >
> > > >
> > > > [Non-text portions of this message have been removed]
> > > >
> > >
> > >
> > >
> >
> > [Non-text portions of this message have been removed]
> >
> >
>
> --
>
> /^_,',',',_ //^/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/>
>
> ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
>
> a momentary antenna as i turn to water
> this evaporates - an island once again
>
> [Non-text portions of this message have been removed]
>
>

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

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

a momentary antenna as i turn to water
this evaporates - an island once again

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

🔗Freeman Gilmore <freeman.gilmore@...>

For the major chord, it has the ratio 4:5:6 just for the fundamentals [to
overtones], first order.

4:5 gives 1 and 9

4:6 gives 2 and 10

5:6 gives 1 and 11
So you have the tone 1,2,3,4,5,6,9,10,11 with just the fundamentals.
ƒg

On Fri, Nov 18, 2011 at 6:46 AM, kraiggrady <kraiggrady@anaphoria.com>wrote:

> **
>
>
> actually the method i liked most was omitting the duplicates so you
> would only omit 1 from this chord. let me know if something other hits
> you right!
>
> On 18/11/11 7:02 PM, kraiggrady wrote:
> >
> > Hi Freeman and Yuriy~
> > Helmholtz was my own source is figuring these out~one can start on page
> > 214 and the next 11 pages most of what he has to say on the subject.
> > It is quite easy to add. take 4:5:6 this equals 15 if you want to add
> > first order difference tones that would be 1+1+2 to what is above which
> > will give you another 4. I figured this out for all 4 chords involving
> > the 11in all inversions where no tone is further than an octave apart
> > from the next. It was the basis of quite a few pieces. some being
> > merely a single chord and its inversions.
> >
> > On 18/11/11 5:58 PM, Freeman Gilmore wrote:
> > >
> > > Yuriy:
> > >
> > > For a good book that talk about combination tones: ON THE SENSATIONS OF
> > > TONE, by Hermann Helmholtz, translated to English, by Alexander
> > Ellis [he
> > > added much to the book]; also a Dover reprint. Can be found on the
> > > internet, but it is over 500 pages.
> > >
> > > Combination tones are caused by intermediation distortion in the ear
> > > and in
> > > electronic equipment [usually not desired]. At normal sound pressure
> > > levels in air there is no distortion but at high sound pressure levels
> > > like
> > > found in the throat of a horn type speaker there may be some
> distortion.
> > >
> > > Start with two notes, each has over tones. [I use the word overtones
> > > because not all notes have overtones that are exactly in the harmonic
> > > series.] Take each tone of the first note [including the fundamental],
> > > one at a time, sum it with each tone of the second, note one at a
> > > time. This
> > > will give a series of sum tones. Now do this, in like manner, for the
> > > difference of the tones. This will give the series of difference tones.
> > > Now continue with this process by taking the sum and difference of all
> > > the new tone and the original tone. And keep doing this for ever, [if
> > > you do not have anything to do]. Do this for 3 and 4 note chord the
> same
> > > way. [Even the overtones of a single note will produce sun and
> > difference
> > > tones.]
> > >
> > > Fortunately the intensity of the combination tones falls off quickly,
> so
> > > using the stronger over tone [the first few of the note] and just
> taking
> > > the sum and difference of these will work well and most of these the
> ear
> > > will not hear anyway.
> > >
> > > If the chord is built with notes that have overtone that are in the
> > > harmonic series, some of the sum and difference tones may be the same
> as
> > > some of the harmonics and sum and difference tones. If the chords are
> > > built with notes that have overtones that are not in the harmonic
> > series,
> > > the sum and difference tone will be in clusters. These clusters may
> > > produce beats, along with the beats of the mismatched overtones.
> > >
> > > If the notes of the chord are built with tempered notes, there will
> > > also be
> > > clusters of tones that may produce beats, along with the beats of the
> > > mismatched overtones of the tempered notes.
> > >
> > > Take the major chord, it has the ratio 4:5:6; do the math will gives
> the
> > > following series or ratio 1:2:3:4:5:6:7: 8:9: …. The root of the chord
> > > is 4, two octaves down is 1 [the same note!!]. The minor chord has the
> > > ratio 5:6::4:5, the 5th still has the ratio 4:6 which will also
> > > prepuce the
> > > same lower root 1 but there will be more than one series of tones which
> > > over lap. This works with other chords but series may be complicated
> and
> > > have overlapping series. The German 6th also works nice and simple; it
> > > has the ratio 4:5:6:7, [found in the ¼ c meantone]; but the dominant
> 7th
> > > chord with ratio 4:5:6::5:6 is a little ruff. The diminished chord
> > > 5:6::5:6 is ruff; but 5:6:7 sounds good, with a simple series, using
> the
> > > septimal third [also found in the ¼ c meantone]. The ratio 5:6:7 will
> > > also produce the 1, two and one half ½ octaves down; but the root 5
> from
> > > the ratio of the chord is a 5th to the 1, two and one half down,
> > could say
> > > that the 1 is the the real root of the chord not the 5.
> > >
> > > The 1 of the chord is like the fundamental of a note. the real root.
> > This
> > > could explain why the viiº chord has the dominant function the real
> root
> > > being the 5th of the scale.
> > >
> > > The sub tones are clusters of tones when the notes of the chords are
> > > tempered.
> > >
> > > ƒg
> > >
> > > On Thu, Nov 17, 2011 at 7:08 AM, ruxxes <ruxxes@yahoo.com
> > <mailto:ruxxes%40yahoo.com>
> > > <mailto:ruxxes%40yahoo.com>> wrote:
> > >
> > > > **
> > > >
> > > >
> > > > Hello Mike,
> > > >
> > > > Ah-ha, so it's the combination note what I was looking for! Now being
> > > > digging more on the Web.
> > > >
> > > > I am curious how would this apply to irrational ratios of equal
> > tunings?
> > > > Is there any concept similar to comb.tone that "extracts" more
> > > subtlety out
> > > > of a sound mass (http://en.wikipedia.org/wiki/Sound_mass)?
> > > >
> > > > Thank you very much!
> > > > Yuriy.
> > > >
> > > > --- In MakeMicroMusic@yahoogroups.com
> > <mailto:MakeMicroMusic%40yahoogroups.com>
> > > <mailto:MakeMicroMusic%40yahoogroups.com>, kraiggrady <kraiggrady@...>
> > > wrote:
> > > > >
> > > > > Hello Ruxxes~
> > > > > You can do this at least in Just intonation by treating your chord
> > > > > as how it appears in a harmonic series. the resultant number
> > would be
> > > > > what is called a combination tone. I experimented quite a bit with
> > > this
> > > > > and difference tones adding these both trying omitting dulicates
> and
> > > > > other patterns. like most things, the human mind can follow
> > > patterns and
> > > > > so it is hard to say what method here might be best. i would
> > > experiment
> > > > > and see what you come up with.
> > > > >
> > > > > On 11/11/11 1:03 AM, ruxxes wrote:
> > > > > >
> > > > > > Hey people,
> > > > > >
> > > > > > This one is for nerds I guess:
> > > > > >
> > > > > > Can I get a resultant ratio of a chord by calculating a sum of
> all
> > > > > > intervals present in a chord?
> > > > > >
> > > > > > How can I do this for a 4-note chord?
> > > > > >
> > > > > > Does this make sense at all?
> > > > > >
> > > > > > Thank you!
> > > > > >
> > > > > >
> > > > > >
> > > > > > /^_,',',',_ //^/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/
> > > > >
> > > > > >
> > > > > > ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
> > > > > >
> > > > > > a momentary antenna as i turn to water
> > > > > > this evaporates - an island once again
> > > > >
> > > > >
> > > > > [Non-text portions of this message have been removed]
> > > > >
> > > >
> > > >
> > > >
> > >
> > > [Non-text portions of this message have been removed]
> > >
> > >
> >
> > --
> >
> > /^_,',',',_ //^/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/>
> >
> > ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
> >
> > a momentary antenna as i turn to water
> > this evaporates - an island once again
> >
> > [Non-text portions of this message have been removed]
> >
> >
>
> --
>
> /^_,',',',_ //^/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/>
>
> ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
>
> a momentary antenna as i turn to water
> this evaporates - an island once again
>
> [Non-text portions of this message have been removed]
>
>
>

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

🔗kraiggrady <kraiggrady@...>

where are you getting 3?

outside of that what is the difference?

On 19/11/11 12:25 AM, Freeman Gilmore wrote:
>
> For the major chord, it has the ratio 4:5:6 just for the fundamentals [to
> overtones], first order.
>
> 4:5 gives 1 and 9
>
> 4:6 gives 2 and 10
>
> 5:6 gives 1 and 11
> So you have the tone 1,2,3,4,5,6,9,10,11 with just the fundamentals.
> ƒg
>
> On Fri, Nov 18, 2011 at 6:46 AM, kraiggrady <kraiggrady@...
> <mailto:kraiggrady%40anaphoria.com>>wrote:
>
> > **
> >
> >
> > actually the method i liked most was omitting the duplicates so you
> > would only omit 1 from this chord. let me know if something other hits
> > you right!
> >
> > On 18/11/11 7:02 PM, kraiggrady wrote:
> > >
> > > Hi Freeman and Yuriy~
> > > Helmholtz was my own source is figuring these out~one can start on
> page
> > > 214 and the next 11 pages most of what he has to say on the subject.
> > > It is quite easy to add. take 4:5:6 this equals 15 if you want to add
> > > first order difference tones that would be 1+1+2 to what is above
> which
> > > will give you another 4. I figured this out for all 4 chords involving
> > > the 11in all inversions where no tone is further than an octave apart
> > > from the next. It was the basis of quite a few pieces. some being
> > > merely a single chord and its inversions.
> > >
> > > On 18/11/11 5:58 PM, Freeman Gilmore wrote:
> > > >
> > > > Yuriy:
> > > >
> > > > For a good book that talk about combination tones: ON THE
> SENSATIONS OF
> > > > TONE, by Hermann Helmholtz, translated to English, by Alexander
> > > Ellis [he
> > > > added much to the book]; also a Dover reprint. Can be found on the
> > > > internet, but it is over 500 pages.
> > > >
> > > > Combination tones are caused by intermediation distortion in the ear
> > > > and in
> > > > electronic equipment [usually not desired]. At normal sound pressure
> > > > levels in air there is no distortion but at high sound pressure
> levels
> > > > like
> > > > found in the throat of a horn type speaker there may be some
> > distortion.
> > > >
> > > > Start with two notes, each has over tones. [I use the word overtones
> > > > because not all notes have overtones that are exactly in the
> harmonic
> > > > series.] Take each tone of the first note [including the
> fundamental],
> > > > one at a time, sum it with each tone of the second, note one at a
> > > > time. This
> > > > will give a series of sum tones. Now do this, in like manner,
> for the
> > > > difference of the tones. This will give the series of difference
> tones.
> > > > Now continue with this process by taking the sum and difference
> of all
> > > > the new tone and the original tone. And keep doing this for
> ever, [if
> > > > you do not have anything to do]. Do this for 3 and 4 note chord the
> > same
> > > > way. [Even the overtones of a single note will produce sun and
> > > difference
> > > > tones.]
> > > >
> > > > Fortunately the intensity of the combination tones falls off
> quickly,
> > so
> > > > using the stronger over tone [the first few of the note] and just
> > taking
> > > > the sum and difference of these will work well and most of these the
> > ear
> > > > will not hear anyway.
> > > >
> > > > If the chord is built with notes that have overtone that are in the
> > > > harmonic series, some of the sum and difference tones may be the
> same
> > as
> > > > some of the harmonics and sum and difference tones. If the
> chords are
> > > > built with notes that have overtones that are not in the harmonic
> > > series,
> > > > the sum and difference tone will be in clusters. These clusters may
> > > > produce beats, along with the beats of the mismatched overtones.
> > > >
> > > > If the notes of the chord are built with tempered notes, there will
> > > > also be
> > > > clusters of tones that may produce beats, along with the beats
> of the
> > > > mismatched overtones of the tempered notes.
> > > >
> > > > Take the major chord, it has the ratio 4:5:6; do the math will gives
> > the
> > > > following series or ratio 1:2:3:4:5:6:7: 8:9: …. The root of the
> chord
> > > > is 4, two octaves down is 1 [the same note!!]. The minor chord
> has the
> > > > ratio 5:6::4:5, the 5th still has the ratio 4:6 which will also
> > > > prepuce the
> > > > same lower root 1 but there will be more than one series of
> tones which
> > > > over lap. This works with other chords but series may be complicated
> > and
> > > > have overlapping series. The German 6th also works nice and
> simple; it
> > > > has the ratio 4:5:6:7, [found in the ¼ c meantone]; but the dominant
> > 7th
> > > > chord with ratio 4:5:6::5:6 is a little ruff. The diminished chord
> > > > 5:6::5:6 is ruff; but 5:6:7 sounds good, with a simple series, using
> > the
> > > > septimal third [also found in the ¼ c meantone]. The ratio 5:6:7
> will
> > > > also produce the 1, two and one half ½ octaves down; but the root 5
> > from
> > > > the ratio of the chord is a 5th to the 1, two and one half down,
> > > could say
> > > > that the 1 is the the real root of the chord not the 5.
> > > >
> > > > The 1 of the chord is like the fundamental of a note. the real root.
> > > This
> > > > could explain why the viiº chord has the dominant function the real
> > root
> > > > being the 5th of the scale.
> > > >
> > > > The sub tones are clusters of tones when the notes of the chords are
> > > > tempered.
> > > >
> > > > ƒg
> > > >
> > > > On Thu, Nov 17, 2011 at 7:08 AM, ruxxes <ruxxes@...
> <mailto:ruxxes%40yahoo.com>
> > > <mailto:ruxxes%40yahoo.com>
> > > > <mailto:ruxxes%40yahoo.com>> wrote:
> > > >
> > > > > **
> > > > >
> > > > >
> > > > > Hello Mike,
> > > > >
> > > > > Ah-ha, so it's the combination note what I was looking for!
> Now being
> > > > > digging more on the Web.
> > > > >
> > > > > I am curious how would this apply to irrational ratios of equal
> > > tunings?
> > > > > Is there any concept similar to comb.tone that "extracts" more
> > > > subtlety out
> > > > > of a sound mass (http://en.wikipedia.org/wiki/Sound_mass)?
> > > > >
> > > > > Thank you very much!
> > > > > Yuriy.
> > > > >
> > > > > --- In MakeMicroMusic@yahoogroups.com
> <mailto:MakeMicroMusic%40yahoogroups.com>
> > > <mailto:MakeMicroMusic%40yahoogroups.com>
> > > > <mailto:MakeMicroMusic%40yahoogroups.com>, kraiggrady
> <kraiggrady@...>
> > > > wrote:
> > > > > >
> > > > > > Hello Ruxxes~
> > > > > > You can do this at least in Just intonation by treating your
> chord
> > > > > > as how it appears in a harmonic series. the resultant number
> > > would be
> > > > > > what is called a combination tone. I experimented quite a
> bit with
> > > > this
> > > > > > and difference tones adding these both trying omitting dulicates
> > and
> > > > > > other patterns. like most things, the human mind can follow
> > > > patterns and
> > > > > > so it is hard to say what method here might be best. i would
> > > > experiment
> > > > > > and see what you come up with.
> > > > > >
> > > > > > On 11/11/11 1:03 AM, ruxxes wrote:
> > > > > > >
> > > > > > > Hey people,
> > > > > > >
> > > > > > > This one is for nerds I guess:
> > > > > > >
> > > > > > > Can I get a resultant ratio of a chord by calculating a sum of
> > all
> > > > > > > intervals present in a chord?
> > > > > > >
> > > > > > > How can I do this for a 4-note chord?
> > > > > > >
> > > > > > > Does this make sense at all?
> > > > > > >
> > > > > > > Thank you!
> > > > > > >
> > > > > > >
> > > > > > >
> > > > > > > /^_,',',',_ //^/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/
> > > > > >
> > > > > > >
> > > > > > > ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
> > > > > > >
> > > > > > > a momentary antenna as i turn to water
> > > > > > > this evaporates - an island once again
> > > > > >
> > > > > >
> > > > > > [Non-text portions of this message have been removed]
> > > > > >
> > > > >
> > > > >
> > > > >
> > > >
> > > > [Non-text portions of this message have been removed]
> > > >
> > > >
> > >
> > > --
> > >
> > > /^_,',',',_ //^/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/>
> > >
> > > ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
> > >
> > > a momentary antenna as i turn to water
> > > this evaporates - an island once again
> > >
> > > [Non-text portions of this message have been removed]
> > >
> > >
> >
> > --
> >
> > /^_,',',',_ //^/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/>
> >
> > ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
> >
> > a momentary antenna as i turn to water
> > this evaporates - an island once again
> >
> > [Non-text portions of this message have been removed]
> >
> >
> >
>
> [Non-text portions of this message have been removed]
>
>

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

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

a momentary antenna as i turn to water
this evaporates - an island once again

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

🔗Mike Battaglia <battaglia01@...>

🔗kraiggrady <kraiggrady@...>

basically there are many ways to play with it, the point is which do you
find musically significant and useful?
have you tried a series of these and placing them in order to see if the
numbers satisfy a consonant/dissonant curve?
this chord is 41 according to your system.

no one has ever heard combination tones yet a sequence of which we can
surely feel, {at least i have in the past] so i have limited my own to
the pitches and the difference tones. i have my list if you wish to
figure out yours and we can compare.

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

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

a momentary antenna as i turn to water
this evaporates - an island once again

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

🔗Freeman Gilmore <freeman.gilmore@...>

3 is a mistake sorry.
ƒg

On Fri, Nov 18, 2011 at 8:42 AM, kraiggrady <kraiggrady@...>wrote:

> **
>
>
> where are you getting 3?
>
> outside of that what is the difference?
>
> On 19/11/11 12:25 AM, Freeman Gilmore wrote:
> >
> > For the major chord, it has the ratio 4:5:6 just for the fundamentals [to
> > overtones], first order.
> >
> > 4:5 gives 1 and 9
> >
> > 4:6 gives 2 and 10
> >
> > 5:6 gives 1 and 11
> > So you have the tone 1,2,3,4,5,6,9,10,11 with just the fundamentals.
> > ƒg
> >
> > On Fri, Nov 18, 2011 at 6:46 AM, kraiggrady <kraiggrady@...
> > <mailto:kraiggrady%40anaphoria.com>>wrote:
> >
> > > **
> > >
> > >
> > > actually the method i liked most was omitting the duplicates so you
> > > would only omit 1 from this chord. let me know if something other hits
> > > you right!
> > >
> > > On 18/11/11 7:02 PM, kraiggrady wrote:
> > > >
> > > > Hi Freeman and Yuriy~
> > > > Helmholtz was my own source is figuring these out~one can start on
> > page
> > > > 214 and the next 11 pages most of what he has to say on the subject.
> > > > It is quite easy to add. take 4:5:6 this equals 15 if you want to add
> > > > first order difference tones that would be 1+1+2 to what is above
> > which
> > > > will give you another 4. I figured this out for all 4 chords
> involving
> > > > the 11in all inversions where no tone is further than an octave apart
> > > > from the next. It was the basis of quite a few pieces. some being
> > > > merely a single chord and its inversions.
> > > >
> > > > On 18/11/11 5:58 PM, Freeman Gilmore wrote:
> > > > >
> > > > > Yuriy:
> > > > >
> > > > > For a good book that talk about combination tones: ON THE
> > SENSATIONS OF
> > > > > TONE, by Hermann Helmholtz, translated to English, by Alexander
> > > > Ellis [he
> > > > > added much to the book]; also a Dover reprint. Can be found on the
> > > > > internet, but it is over 500 pages.
> > > > >
> > > > > Combination tones are caused by intermediation distortion in the
> ear
> > > > > and in
> > > > > electronic equipment [usually not desired]. At normal sound
> pressure
> > > > > levels in air there is no distortion but at high sound pressure
> > levels
> > > > > like
> > > > > found in the throat of a horn type speaker there may be some
> > > distortion.
> > > > >
> > > > > Start with two notes, each has over tones. [I use the word
> overtones
> > > > > because not all notes have overtones that are exactly in the
> > harmonic
> > > > > series.] Take each tone of the first note [including the
> > fundamental],
> > > > > one at a time, sum it with each tone of the second, note one at a
> > > > > time. This
> > > > > will give a series of sum tones. Now do this, in like manner,
> > for the
> > > > > difference of the tones. This will give the series of difference
> > tones.
> > > > > Now continue with this process by taking the sum and difference
> > of all
> > > > > the new tone and the original tone. And keep doing this for
> > ever, [if
> > > > > you do not have anything to do]. Do this for 3 and 4 note chord the
> > > same
> > > > > way. [Even the overtones of a single note will produce sun and
> > > > difference
> > > > > tones.]
> > > > >
> > > > > Fortunately the intensity of the combination tones falls off
> > quickly,
> > > so
> > > > > using the stronger over tone [the first few of the note] and just
> > > taking
> > > > > the sum and difference of these will work well and most of these
> the
> > > ear
> > > > > will not hear anyway.
> > > > >
> > > > > If the chord is built with notes that have overtone that are in the
> > > > > harmonic series, some of the sum and difference tones may be the
> > same
> > > as
> > > > > some of the harmonics and sum and difference tones. If the
> > chords are
> > > > > built with notes that have overtones that are not in the harmonic
> > > > series,
> > > > > the sum and difference tone will be in clusters. These clusters may
> > > > > produce beats, along with the beats of the mismatched overtones.
> > > > >
> > > > > If the notes of the chord are built with tempered notes, there will
> > > > > also be
> > > > > clusters of tones that may produce beats, along with the beats
> > of the
> > > > > mismatched overtones of the tempered notes.
> > > > >
> > > > > Take the major chord, it has the ratio 4:5:6; do the math will
> gives
> > > the
> > > > > following series or ratio 1:2:3:4:5:6:7: 8:9: …. The root of the
> > chord
> > > > > is 4, two octaves down is 1 [the same note!!]. The minor chord
> > has the
> > > > > ratio 5:6::4:5, the 5th still has the ratio 4:6 which will also
> > > > > prepuce the
> > > > > same lower root 1 but there will be more than one series of
> > tones which
> > > > > over lap. This works with other chords but series may be
> complicated
> > > and
> > > > > have overlapping series. The German 6th also works nice and
> > simple; it
> > > > > has the ratio 4:5:6:7, [found in the ¼ c meantone]; but the
> dominant
> > > 7th
> > > > > chord with ratio 4:5:6::5:6 is a little ruff. The diminished chord
> > > > > 5:6::5:6 is ruff; but 5:6:7 sounds good, with a simple series,
> using
> > > the
> > > > > septimal third [also found in the ¼ c meantone]. The ratio 5:6:7
> > will
> > > > > also produce the 1, two and one half ½ octaves down; but the root 5
> > > from
> > > > > the ratio of the chord is a 5th to the 1, two and one half down,
> > > > could say
> > > > > that the 1 is the the real root of the chord not the 5.
> > > > >
> > > > > The 1 of the chord is like the fundamental of a note. the real
> root.
> > > > This
> > > > > could explain why the viiº chord has the dominant function the real
> > > root
> > > > > being the 5th of the scale.
> > > > >
> > > > > The sub tones are clusters of tones when the notes of the chords
> are
> > > > > tempered.
> > > > >
> > > > > ƒg
> > > > >
> > > > > On Thu, Nov 17, 2011 at 7:08 AM, ruxxes <ruxxes@...
> > <mailto:ruxxes%40yahoo.com>
> > > > <mailto:ruxxes%40yahoo.com>
> > > > > <mailto:ruxxes%40yahoo.com>> wrote:
> > > > >
> > > > > > **
> > > > > >
> > > > > >
> > > > > > Hello Mike,
> > > > > >
> > > > > > Ah-ha, so it's the combination note what I was looking for!
> > Now being
> > > > > > digging more on the Web.
> > > > > >
> > > > > > I am curious how would this apply to irrational ratios of equal
> > > > tunings?
> > > > > > Is there any concept similar to comb.tone that "extracts" more
> > > > > subtlety out
> > > > > > of a sound mass (http://en.wikipedia.org/wiki/Sound_mass)?
> > > > > >
> > > > > > Thank you very much!
> > > > > > Yuriy.
> > > > > >
> > > > > > --- In MakeMicroMusic@yahoogroups.com
> > <mailto:MakeMicroMusic%40yahoogroups.com>
> > > > <mailto:MakeMicroMusic%40yahoogroups.com>
> > > > > <mailto:MakeMicroMusic%40yahoogroups.com>, kraiggrady
> > <kraiggrady@...>
> > > > > wrote:
> > > > > > >
> > > > > > > Hello Ruxxes~
> > > > > > > You can do this at least in Just intonation by treating your
> > chord
> > > > > > > as how it appears in a harmonic series. the resultant number
> > > > would be
> > > > > > > what is called a combination tone. I experimented quite a
> > bit with
> > > > > this
> > > > > > > and difference tones adding these both trying omitting
> dulicates
> > > and
> > > > > > > other patterns. like most things, the human mind can follow
> > > > > patterns and
> > > > > > > so it is hard to say what method here might be best. i would
> > > > > experiment
> > > > > > > and see what you come up with.
> > > > > > >
> > > > > > > On 11/11/11 1:03 AM, ruxxes wrote:
> > > > > > > >
> > > > > > > > Hey people,
> > > > > > > >
> > > > > > > > This one is for nerds I guess:
> > > > > > > >
> > > > > > > > Can I get a resultant ratio of a chord by calculating a sum
> of
> > > all
> > > > > > > > intervals present in a chord?
> > > > > > > >
> > > > > > > > How can I do this for a 4-note chord?
> > > > > > > >
> > > > > > > > Does this make sense at all?
> > > > > > > >
> > > > > > > > Thank you!
> > > > > > > >
> > > > > > > >
> > > > > > > >
> > > > > > > > /^_,',',',_ //^/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/
> > > > > > >
> > > > > > > >
> > > > > > > > ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
> > > > > > > >
> > > > > > > > a momentary antenna as i turn to water
> > > > > > > > this evaporates - an island once again
> > > > > > >
> > > > > > >
> > > > > > > [Non-text portions of this message have been removed]
> > > > > > >
> > > > > >
> > > > > >
> > > > > >
> > > > >
> > > > > [Non-text portions of this message have been removed]
> > > > >
> > > > >
> > > >
> > > > --
> > > >
> > > > /^_,',',',_ //^/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/>
> > > >
> > > > ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
> > > >
> > > > a momentary antenna as i turn to water
> > > > this evaporates - an island once again
> > > >
> > > > [Non-text portions of this message have been removed]
> > > >
> > > >
> > >
> > > --
> > >
> > > /^_,',',',_ //^/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/
> >
> > >
> > > ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
> > >
> > > a momentary antenna as i turn to water
> > > this evaporates - an island once again
> > >
> > > [Non-text portions of this message have been removed]
> > >
> > >
> > >
> >
> > [Non-text portions of this message have been removed]
> >
> >
>
> --
>
> /^_,',',',_ //^/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/>
>
> ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
>
> a momentary antenna as i turn to water
> this evaporates - an island once again
>
> [Non-text portions of this message have been removed]
>
>
>

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

🔗kraiggrady <kraiggrady@...>

I do think that helmholtz's idea is worth investigating with as many
different ways of adding the data as possible, then we can compare, but
this requires people doing the work and willing to let go of what they
assume. I have tried numerous ways until i abandoned the idea as not
fruitful. Even if a consonant/dissonant formula could be conceived, it
would be such a burden to composing that i think i would rather do
something else that be it slave. I mean wouldn't you rather hear duke
ellington do everything wrong according to what rules would come out of
it? [money jungle for example]

On 19/11/11 12:54 AM, kraiggrady wrote:
>
>
> the primaries are found in even when the fundamental are put in separate
> ears, there is no evidence of secondary ones that i have seen. you might
> as well in clude the third and fourth or go on until you fill the whole
> series anfd then where are you?
>
> On 19/11/11 12:45 AM, Mike Battaglia wrote:
> >
> > On Fri, Nov 18, 2011 at 8:25 AM, Freeman Gilmore
> > <freeman.gilmore@... <mailto:freeman.gilmore%40gmail.com>
> <mailto:freeman.gilmore%40gmail.com>> wrote:
> > >
> > > For the major chord, it has the ratio 4:5:6 just for the
> > fundamentals [to
> > > overtones], first order.
> > >
> > > 4:5 gives 1 and 9
> > >
> > > 4:6 gives 2 and 10
> > >
> > > 5:6 gives 1 and 11
> > > So you have the tone 1,2,3,4,5,6,9,10,11 with just the fundamentals.
> > > ƒg
> >
> > If you really care about difference tones and such, then the even
> > second-order ones are probably more what you're after. So for 7:9:11
> > you end up getting ...:3:5:7:9:11:13:15:17:19:..., etc.
> >
> > -Mike
> >
> >
>
> --
>
> /^_,',',',_ //^/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/>
>
> ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
>
> a momentary antenna as i turn to water
> this evaporates - an island once again
>
> [Non-text portions of this message have been removed]
>
>

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

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

a momentary antenna as i turn to water
this evaporates - an island once again

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

🔗Freeman Gilmore <freeman.gilmore@...>

Keep it simple, Helmholtz carried this beyond what could be heard. Just
realize that the sub tones are there and can be head or the brain will fill
them is or both. And that the higher tones may be loud enough to add to
the hash in a tempered system. As for chord progression or tuning use the
simple ratios, if that is what you are doing, and not get carried away with
tone that you can not hear.
ƒg
On Fri, Nov 18, 2011 at 9:02 AM, kraiggrady <kraiggrady@...>wrote:

> **
>
>
> I do think that helmholtz's idea is worth investigating with as many
> different ways of adding the data as possible, then we can compare, but
> this requires people doing the work and willing to let go of what they
> assume. I have tried numerous ways until i abandoned the idea as not
> fruitful. Even if a consonant/dissonant formula could be conceived, it
> would be such a burden to composing that i think i would rather do
> something else that be it slave. I mean wouldn't you rather hear duke
> ellington do everything wrong according to what rules would come out of
> it? [money jungle for example]
>
> On 19/11/11 12:54 AM, kraiggrady wrote:
> >
> >
> > the primaries are found in even when the fundamental are put in separate
> > ears, there is no evidence of secondary ones that i have seen. you might
> > as well in clude the third and fourth or go on until you fill the whole
> > series anfd then where are you?
> >
> > On 19/11/11 12:45 AM, Mike Battaglia wrote:
> > >
> > > On Fri, Nov 18, 2011 at 8:25 AM, Freeman Gilmore
> > > <freeman.gilmore@... <mailto:freeman.gilmore%40gmail.com>
> > <mailto:freeman.gilmore%40gmail.com>> wrote:
> > > >
> > > > For the major chord, it has the ratio 4:5:6 just for the
> > > fundamentals [to
> > > > overtones], first order.
> > > >
> > > > 4:5 gives 1 and 9
> > > >
> > > > 4:6 gives 2 and 10
> > > >
> > > > 5:6 gives 1 and 11
> > > > So you have the tone 1,2,3,4,5,6,9,10,11 with just the fundamentals.
> > > > ƒg
> > >
> > > If you really care about difference tones and such, then the even
> > > second-order ones are probably more what you're after. So for 7:9:11
> > > you end up getting ...:3:5:7:9:11:13:15:17:19:..., etc.
> > >
> > > -Mike
> > >
> > >
> >
> > --
> >
> > /^_,',',',_ //^/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/>
> >
> > ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
> >
> > a momentary antenna as i turn to water
> > this evaporates - an island once again
> >
> > [Non-text portions of this message have been removed]
> >
> >
>
> --
>
> /^_,',',',_ //^/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/>
>
> ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
>
> a momentary antenna as i turn to water
> this evaporates - an island once again
>
> [Non-text portions of this message have been removed]
>
>
>

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

🔗Mike Battaglia <battaglia01@...>

🔗Freeman Gilmore <freeman.gilmore@...>

Would be nice if the electronic distortion was less then the ear.

I would like to add that amplifiers are designed using two tubes or
transistors in push pull [one working against the other] to help suppress
the even ordered harmonics generated by the amp which also helps reduce the
intermediation distortion.

ƒg

On Fri, Nov 18, 2011 at 9:33 AM, Mike Battaglia <battaglia01@...>wrote:

> **
>
>
> On Fri, Nov 18, 2011 at 8:54 AM, kraiggrady <kraiggrady@...>
> wrote:
> >
> > the primaries are found in even when the fundamental are put in separate
> > ears, there is no evidence of secondary ones that i have seen. you might
> > as well in clude the third and fourth or go on until you fill the whole
> > series anfd then where are you?
>
> For one example of evidence for their existence, see
> http://en.wikipedia.org/wiki/Tube_sound#Harmonic_content_and_distortion
>
> Freeman mentioned that the intermodulation distortion (not quite the
> full picture) generated by electronic equipment is louder than that
> generated by the ears. He's correct, so I addressed that. The sort of
> distortion that might be generated by a speaker, or even a distortion
> pedal, often tends to be symmetric, which means you DO get third,
> fifth, etc order difference tones, which roll off and become lower and
> lower in amplitude. An extreme example of this is a hard clipper,
> which you can then send a sine wave through; this will turn the sine
> wave into a square wave, which turns 1 into 1, 3, 5, 7, 9, 11, 13,
> etc. There are an infinite amount of combination tones generated in
> this way - second, fourth, sixth, eighth, and in general all
> "even-order" sum tones will appear in the output. But as you can see,
> there's no 2.
>
> Also, when you talk about the "primaries" that are found when the
> fundamental are put in separate ears, you're probably talking about
> virtual pitches generated by the brain's complex pitch detection
> mechanism, not combination tones - if you put 7/4 in separate ears,
> the VF you hear (if any) will be octave-equivalent to (1):4:7, not
> (3):4:7.
>
> -Mike
>
>

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

🔗kraiggrady <kraiggrady@...>

but we can hear patterns as i have had people play me progression based
on combination tones and after a few it was quite predictable. So I at
least can hear it on some level and i don't think i am that exceptional
that it not to be so with others. And i don't care if someone proves it
for the masses or not, i am not going to wait. I want to know exactly
what experience you have had with this material . i have had at least a
few years looking at it as a constant. not that this means much but at
least requires some to validate or dismiss it, not conjecture.
.
On 19/11/11 1:24 AM, Freeman Gilmore wrote:
>
> Keep it simple, Helmholtz carried this beyond what could be heard. Just
> realize that the sub tones are there and can be head or the brain will
> fill
> them is or both. And that the higher tones may be loud enough to add to
> the hash in a tempered system. As for chord progression or tuning use the
> simple ratios, if that is what you are doing, and not get carried away
> with
> tone that you can not hear.
> ƒg
> On Fri, Nov 18, 2011 at 9:02 AM, kraiggrady <kraiggrady@...
> <mailto:kraiggrady%40anaphoria.com>>wrote:
>
> > **
> >
> >
> > I do think that helmholtz's idea is worth investigating with as many
> > different ways of adding the data as possible, then we can compare, but
> > this requires people doing the work and willing to let go of what they
> > assume. I have tried numerous ways until i abandoned the idea as not
> > fruitful. Even if a consonant/dissonant formula could be conceived, it
> > would be such a burden to composing that i think i would rather do
> > something else that be it slave. I mean wouldn't you rather hear duke
> > ellington do everything wrong according to what rules would come out of
> > it? [money jungle for example]
> >
> > On 19/11/11 12:54 AM, kraiggrady wrote:
> > >
> > >
> > > the primaries are found in even when the fundamental are put in
> separate
> > > ears, there is no evidence of secondary ones that i have seen. you
> might
> > > as well in clude the third and fourth or go on until you fill the
> whole
> > > series anfd then where are you?
> > >
> > > On 19/11/11 12:45 AM, Mike Battaglia wrote:
> > > >
> > > > On Fri, Nov 18, 2011 at 8:25 AM, Freeman Gilmore
> > > > <freeman.gilmore@... <mailto:freeman.gilmore%40gmail.com>
> <mailto:freeman.gilmore%40gmail.com>
> > > <mailto:freeman.gilmore%40gmail.com>> wrote:
> > > > >
> > > > > For the major chord, it has the ratio 4:5:6 just for the
> > > > fundamentals [to
> > > > > overtones], first order.
> > > > >
> > > > > 4:5 gives 1 and 9
> > > > >
> > > > > 4:6 gives 2 and 10
> > > > >
> > > > > 5:6 gives 1 and 11
> > > > > So you have the tone 1,2,3,4,5,6,9,10,11 with just the
> fundamentals.
> > > > > ƒg
> > > >
> > > > If you really care about difference tones and such, then the even
> > > > second-order ones are probably more what you're after. So for 7:9:11
> > > > you end up getting ...:3:5:7:9:11:13:15:17:19:..., etc.
> > > >
> > > > -Mike
> > > >
> > > >
> > >
> > > --
> > >
> > > /^_,',',',_ //^/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/>
> > >
> > > ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
> > >
> > > a momentary antenna as i turn to water
> > > this evaporates - an island once again
> > >
> > > [Non-text portions of this message have been removed]
> > >
> > >
> >
> > --
> >
> > /^_,',',',_ //^/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/>
> >
> > ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
> >
> > a momentary antenna as i turn to water
> > this evaporates - an island once again
> >
> > [Non-text portions of this message have been removed]
> >
> >
> >
>
> [Non-text portions of this message have been removed]
>
>

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

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

a momentary antenna as i turn to water
this evaporates - an island once again

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

🔗Freeman Gilmore <freeman.gilmore@...>

First off I am not a composer. I am interested in mathematics music
theory and tuning and temperaments. What you have done makes sense to me
in a different way. I am not sure what all you have done. Chords
progress many ways, some by common tone some not, some like 13th century
triad, the harsh intervals move to more pleasing intervals of the triad for
the cadence, modern cadence end on the tonic chord. Just different
patterns.

I would like to know just how you do this and what chords you use? Are
you basing you tuning on these combination tones? E.g. the modern the
scale [maj or min] the notes of the scale are based on the tonic, dominant
and the subdominant chords.

ƒg

On Fri, Nov 18, 2011 at 9:59 AM, kraiggrady <kraiggrady@...>wrote:

> **
>
>
> but we can hear patterns as i have had people play me progression based
> on combination tones and after a few it was quite predictable. So I at
> least can hear it on some level and i don't think i am that exceptional
> that it not to be so with others. And i don't care if someone proves it
> for the masses or not, i am not going to wait. I want to know exactly
> what experience you have had with this material . i have had at least a
> few years looking at it as a constant. not that this means much but at
> least requires some to validate or dismiss it, not conjecture.
> .
> On 19/11/11 1:24 AM, Freeman Gilmore wrote:
> >
> > Keep it simple, Helmholtz carried this beyond what could be heard. Just
> > realize that the sub tones are there and can be head or the brain will
> > fill
> > them is or both. And that the higher tones may be loud enough to add to
> > the hash in a tempered system. As for chord progression or tuning use the
> > simple ratios, if that is what you are doing, and not get carried away
> > with
> > tone that you can not hear.
> > ƒg
> > On Fri, Nov 18, 2011 at 9:02 AM, kraiggrady <kraiggrady@...
> > <mailto:kraiggrady%40anaphoria.com>>wrote:
> >
> > > **
> > >
> > >
> > > I do think that helmholtz's idea is worth investigating with as many
> > > different ways of adding the data as possible, then we can compare, but
> > > this requires people doing the work and willing to let go of what they
> > > assume. I have tried numerous ways until i abandoned the idea as not
> > > fruitful. Even if a consonant/dissonant formula could be conceived, it
> > > would be such a burden to composing that i think i would rather do
> > > something else that be it slave. I mean wouldn't you rather hear duke
> > > ellington do everything wrong according to what rules would come out of
> > > it? [money jungle for example]
> > >
> > > On 19/11/11 12:54 AM, kraiggrady wrote:
> > > >
> > > >
> > > > the primaries are found in even when the fundamental are put in
> > separate
> > > > ears, there is no evidence of secondary ones that i have seen. you
> > might
> > > > as well in clude the third and fourth or go on until you fill the
> > whole
> > > > series anfd then where are you?
> > > >
> > > > On 19/11/11 12:45 AM, Mike Battaglia wrote:
> > > > >
> > > > > On Fri, Nov 18, 2011 at 8:25 AM, Freeman Gilmore
> > > > > <freeman.gilmore@... <mailto:freeman.gilmore%40gmail.com>
> > <mailto:freeman.gilmore%40gmail.com>
> > > > <mailto:freeman.gilmore%40gmail.com>> wrote:
> > > > > >
> > > > > > For the major chord, it has the ratio 4:5:6 just for the
> > > > > fundamentals [to
> > > > > > overtones], first order.
> > > > > >
> > > > > > 4:5 gives 1 and 9
> > > > > >
> > > > > > 4:6 gives 2 and 10
> > > > > >
> > > > > > 5:6 gives 1 and 11
> > > > > > So you have the tone 1,2,3,4,5,6,9,10,11 with just the
> > fundamentals.
> > > > > > ƒg
> > > > >
> > > > > If you really care about difference tones and such, then the even
> > > > > second-order ones are probably more what you're after. So for
> 7:9:11
> > > > > you end up getting ...:3:5:7:9:11:13:15:17:19:..., etc.
> > > > >
> > > > > -Mike
> > > > >
> > > > >
> > > >
> > > > --
> > > >
> > > > /^_,',',',_ //^/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/>
> > > >
> > > > ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
> > > >
> > > > a momentary antenna as i turn to water
> > > > this evaporates - an island once again
> > > >
> > > > [Non-text portions of this message have been removed]
> > > >
> > > >
> > >
> > > --
> > >
> > > /^_,',',',_ //^/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/
> >
> > >
> > > ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
> > >
> > > a momentary antenna as i turn to water
> > > this evaporates - an island once again
> > >
> > > [Non-text portions of this message have been removed]
> > >
> > >
> > >
> >
> > [Non-text portions of this message have been removed]
> >
> >
>
> --
>
> /^_,',',',_ //^/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/>
>
> ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
>
> a momentary antenna as i turn to water
> this evaporates - an island once again
>
> [Non-text portions of this message have been removed]
>
>
>

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

🔗kraiggrady <kraiggrady@...>

well yes electronic distortion can bring these out. i don't know what
the point of that is.
roederer seemed to imply that it was the 3 in a 4:7 chord that came out
. otherwise what happens when one has a high entropy dyad? some random
fundemental and if so doesn't this make entropy impossible?

On 19/11/11 1:33 AM, Mike Battaglia wrote:
>
> On Fri, Nov 18, 2011 at 8:54 AM, kraiggrady <kraiggrady@...
> <mailto:kraiggrady%40anaphoria.com>> wrote:
> >
> > the primaries are found in even when the fundamental are put in separate
> > ears, there is no evidence of secondary ones that i have seen. you might
> > as well in clude the third and fourth or go on until you fill the whole
> > series anfd then where are you?
>
> For one example of evidence for their existence, see
> http://en.wikipedia.org/wiki/Tube_sound#Harmonic_content_and_distortion
>
> Freeman mentioned that the intermodulation distortion (not quite the
> full picture) generated by electronic equipment is louder than that
> generated by the ears. He's correct, so I addressed that. The sort of
> distortion that might be generated by a speaker, or even a distortion
> pedal, often tends to be symmetric, which means you DO get third,
> fifth, etc order difference tones, which roll off and become lower and
> lower in amplitude. An extreme example of this is a hard clipper,
> which you can then send a sine wave through; this will turn the sine
> wave into a square wave, which turns 1 into 1, 3, 5, 7, 9, 11, 13,
> etc. There are an infinite amount of combination tones generated in
> this way - second, fourth, sixth, eighth, and in general all
> "even-order" sum tones will appear in the output. But as you can see,
> there's no 2.
>
> Also, when you talk about the "primaries" that are found when the
> fundamental are put in separate ears, you're probably talking about
> virtual pitches generated by the brain's complex pitch detection
> mechanism, not combination tones - if you put 7/4 in separate ears,
> the VF you hear (if any) will be octave-equivalent to (1):4:7, not
> (3):4:7.
>
> -Mike
>
>

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

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

a momentary antenna as i turn to water
this evaporates - an island once again

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

🔗Freeman Gilmore <freeman.gilmore@...>

I am new to this list. What is a "high entropy dyad"?
ƒg

On Fri, Nov 18, 2011 at 10:42 AM, kraiggrady <kraiggrady@...>wrote:

> **
>
>
> well yes electronic distortion can bring these out. i don't know what
> the point of that is.
> roederer seemed to imply that it was the 3 in a 4:7 chord that came out
> . otherwise what happens when one has a high entropy dyad? some random
> fundemental and if so doesn't this make entropy impossible?
>
> On 19/11/11 1:33 AM, Mike Battaglia wrote:
> >
> > On Fri, Nov 18, 2011 at 8:54 AM, kraiggrady <kraiggrady@...
> > <mailto:kraiggrady%40anaphoria.com>> wrote:
> > >
> > > the primaries are found in even when the fundamental are put in
> separate
> > > ears, there is no evidence of secondary ones that i have seen. you
> might
> > > as well in clude the third and fourth or go on until you fill the whole
> > > series anfd then where are you?
> >
> > For one example of evidence for their existence, see
> > http://en.wikipedia.org/wiki/Tube_sound#Harmonic_content_and_distortion
> >
> > Freeman mentioned that the intermodulation distortion (not quite the
> > full picture) generated by electronic equipment is louder than that
> > generated by the ears. He's correct, so I addressed that. The sort of
> > distortion that might be generated by a speaker, or even a distortion
> > pedal, often tends to be symmetric, which means you DO get third,
> > fifth, etc order difference tones, which roll off and become lower and
> > lower in amplitude. An extreme example of this is a hard clipper,
> > which you can then send a sine wave through; this will turn the sine
> > wave into a square wave, which turns 1 into 1, 3, 5, 7, 9, 11, 13,
> > etc. There are an infinite amount of combination tones generated in
> > this way - second, fourth, sixth, eighth, and in general all
> > "even-order" sum tones will appear in the output. But as you can see,
> > there's no 2.
> >
> > Also, when you talk about the "primaries" that are found when the
> > fundamental are put in separate ears, you're probably talking about
> > virtual pitches generated by the brain's complex pitch detection
> > mechanism, not combination tones - if you put 7/4 in separate ears,
> > the VF you hear (if any) will be octave-equivalent to (1):4:7, not
> > (3):4:7.
> >
> > -Mike
> >
> >
>
> --
>
> /^_,',',',_ //^/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/>
>
> ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
>
> a momentary antenna as i turn to water
> this evaporates - an island once again
>
> [Non-text portions of this message have been removed]
>
>
>

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

🔗Mike Battaglia <battaglia01@...>

🔗Freeman Gilmore <freeman.gilmore@...>

🔗kraiggrady <kraiggrady@...>

It is something Mike uses more than myself, but an interval that is hard
to define in terms of simple ratios uless he wishes to correct that.

On 19/11/11 2:54 AM, Freeman Gilmore wrote:
>
> I am new to this list. What is a "high entropy dyad"?
> ƒg
>
> On Fri, Nov 18, 2011 at 10:42 AM, kraiggrady <kraiggrady@...
> <mailto:kraiggrady%40anaphoria.com>>wrote:
>
> > **
> >
> >
> > well yes electronic distortion can bring these out. i don't know what
> > the point of that is.
> > roederer seemed to imply that it was the 3 in a 4:7 chord that came out
> > . otherwise what happens when one has a high entropy dyad? some random
> > fundemental and if so doesn't this make entropy impossible?
> >
> > On 19/11/11 1:33 AM, Mike Battaglia wrote:
> > >
> > > On Fri, Nov 18, 2011 at 8:54 AM, kraiggrady
> <kraiggrady@... <mailto:kraiggrady%40anaphoria.com>
> > > <mailto:kraiggrady%40anaphoria.com>> wrote:
> > > >
> > > > the primaries are found in even when the fundamental are put in
> > separate
> > > > ears, there is no evidence of secondary ones that i have seen. you
> > might
> > > > as well in clude the third and fourth or go on until you fill
> the whole
> > > > series anfd then where are you?
> > >
> > > For one example of evidence for their existence, see
> > >
> http://en.wikipedia.org/wiki/Tube_sound#Harmonic_content_and_distortion
> > >
> > > Freeman mentioned that the intermodulation distortion (not quite the
> > > full picture) generated by electronic equipment is louder than that
> > > generated by the ears. He's correct, so I addressed that. The sort of
> > > distortion that might be generated by a speaker, or even a distortion
> > > pedal, often tends to be symmetric, which means you DO get third,
> > > fifth, etc order difference tones, which roll off and become lower and
> > > lower in amplitude. An extreme example of this is a hard clipper,
> > > which you can then send a sine wave through; this will turn the sine
> > > wave into a square wave, which turns 1 into 1, 3, 5, 7, 9, 11, 13,
> > > etc. There are an infinite amount of combination tones generated in
> > > this way - second, fourth, sixth, eighth, and in general all
> > > "even-order" sum tones will appear in the output. But as you can see,
> > > there's no 2.
> > >
> > > Also, when you talk about the "primaries" that are found when the
> > > fundamental are put in separate ears, you're probably talking about
> > > virtual pitches generated by the brain's complex pitch detection
> > > mechanism, not combination tones - if you put 7/4 in separate ears,
> > > the VF you hear (if any) will be octave-equivalent to (1):4:7, not
> > > (3):4:7.
> > >
> > > -Mike
> > >
> > >
> >
> > --
> >
> > /^_,',',',_ //^/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/>
> >
> > ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
> >
> > a momentary antenna as i turn to water
> > this evaporates - an island once again
> >
> > [Non-text portions of this message have been removed]
> >
> >
> >
>
> [Non-text portions of this message have been removed]
>
>

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

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

a momentary antenna as i turn to water
this evaporates - an island once again

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

🔗kraiggrady <kraiggrady@...>

I think Helmholtz's method is superior than my own which i will explain
below
In this case it was just some experiments and primarily worked out on a
single tonic. I added up the pitches and the first order difference
tones omitting dublicates as better than including them testing by ear
and place the sequence in order from lower to higher. i actually redid
this recently with adding the 13. the sound file though is an hour and
15 minutes and i plan on editing it down as at this point i don't feel
like i need to use every inversion. Possibly i will post if requested in
part.

It does not provide progressions but exposes one to say inversions one
might miss otherwise. I assumed that the posters original idea was to
use the the numbers as a guide to consonance/dissonance. I am sorry if i
am wrong in this assumption. I am not satisfied with this method but it
does illustrate how different inversion do indeed vary. Helmholtz was
right about this. One time a quantum physicist gave me a version of a
wave equation. this two produced some interested perceptible results

His method is superior in that it takes into consideration also range
as he defines i think it was 32 beats per sec as the most rough so the
same chord on a different tonic would vary as well as register. At the
time i had limited instruments, being before electronics and so opted to
approach it the way i did but it would be interesting to figure out a
way to quantify his method. Possibly someone might choose a different
rate at this point or not as i think he was not set in stone, thinking
it as the fastest rhythm not heard as a pitch [he knew sometimes even
slower ones are so one would have to read what he says here about it as
would not be fair for me to guess.

On 19/11/11 2:38 AM, Freeman Gilmore wrote:
>
> First off I am not a composer. I am interested in mathematics music
> theory and tuning and temperaments. What you have done makes sense to me
> in a different way. I am not sure what all you have done. Chords
> progress many ways, some by common tone some not, some like 13th century
> triad, the harsh intervals move to more pleasing intervals of the
> triad for
> the cadence, modern cadence end on the tonic chord. Just different
> patterns.
>
> I would like to know just how you do this and what chords you use? Are
> you basing you tuning on these combination tones? E.g. the modern the
> scale [maj or min] the notes of the scale are based on the tonic, dominant
> and the subdominant chords.
>
> ƒg
>
> On Fri, Nov 18, 2011 at 9:59 AM, kraiggrady <kraiggrady@...
> <mailto:kraiggrady%40anaphoria.com>>wrote:
>
> > **
> >
> >
> > but we can hear patterns as i have had people play me progression based
> > on combination tones and after a few it was quite predictable. So I at
> > least can hear it on some level and i don't think i am that exceptional
> > that it not to be so with others. And i don't care if someone proves it
> > for the masses or not, i am not going to wait. I want to know exactly
> > what experience you have had with this material . i have had at least a
> > few years looking at it as a constant. not that this means much but at
> > least requires some to validate or dismiss it, not conjecture.
> > .
> > On 19/11/11 1:24 AM, Freeman Gilmore wrote:
> > >
> > > Keep it simple, Helmholtz carried this beyond what could be heard.
> Just
> > > realize that the sub tones are there and can be head or the brain will
> > > fill
> > > them is or both. And that the higher tones may be loud enough to
> add to
> > > the hash in a tempered system. As for chord progression or tuning
> use the
> > > simple ratios, if that is what you are doing, and not get carried away
> > > with
> > > tone that you can not hear.
> > > ƒg
> > > On Fri, Nov 18, 2011 at 9:02 AM, kraiggrady
> <kraiggrady@... <mailto:kraiggrady%40anaphoria.com>
> > > <mailto:kraiggrady%40anaphoria.com>>wrote:
> > >
> > > > **
> > > >
> > > >
> > > > I do think that helmholtz's idea is worth investigating with as many
> > > > different ways of adding the data as possible, then we can
> compare, but
> > > > this requires people doing the work and willing to let go of
> what they
> > > > assume. I have tried numerous ways until i abandoned the idea as not
> > > > fruitful. Even if a consonant/dissonant formula could be
> conceived, it
> > > > would be such a burden to composing that i think i would rather do
> > > > something else that be it slave. I mean wouldn't you rather hear
> duke
> > > > ellington do everything wrong according to what rules would come
> out of
> > > > it? [money jungle for example]
> > > >
> > > > On 19/11/11 12:54 AM, kraiggrady wrote:
> > > > >
> > > > >
> > > > > the primaries are found in even when the fundamental are put in
> > > separate
> > > > > ears, there is no evidence of secondary ones that i have seen. you
> > > might
> > > > > as well in clude the third and fourth or go on until you fill the
> > > whole
> > > > > series anfd then where are you?
> > > > >
> > > > > On 19/11/11 12:45 AM, Mike Battaglia wrote:
> > > > > >
> > > > > > On Fri, Nov 18, 2011 at 8:25 AM, Freeman Gilmore
> > > > > > <freeman.gilmore@...
> <mailto:freeman.gilmore%40gmail.com> <mailto:freeman.gilmore%40gmail.com>
> > > <mailto:freeman.gilmore%40gmail.com>
> > > > > <mailto:freeman.gilmore%40gmail.com>> wrote:
> > > > > > >
> > > > > > > For the major chord, it has the ratio 4:5:6 just for the
> > > > > > fundamentals [to
> > > > > > > overtones], first order.
> > > > > > >
> > > > > > > 4:5 gives 1 and 9
> > > > > > >
> > > > > > > 4:6 gives 2 and 10
> > > > > > >
> > > > > > > 5:6 gives 1 and 11
> > > > > > > So you have the tone 1,2,3,4,5,6,9,10,11 with just the
> > > fundamentals.
> > > > > > > ƒg
> > > > > >
> > > > > > If you really care about difference tones and such, then the
> even
> > > > > > second-order ones are probably more what you're after. So for
> > 7:9:11
> > > > > > you end up getting ...:3:5:7:9:11:13:15:17:19:..., etc.
> > > > > >
> > > > > > -Mike
> > > > > >
> > > > > >
> > > > >
> > > > > --
> > > > >
> > > > > /^_,',',',_ //^/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/>
> > > > >
> > > > > ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
> > > > >
> > > > > a momentary antenna as i turn to water
> > > > > this evaporates - an island once again
> > > > >
> > > > > [Non-text portions of this message have been removed]
> > > > >
> > > > >
> > > >
> > > > --
> > > >
> > > > /^_,',',',_ //^/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/
> > >
> > > >
> > > > ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
> > > >
> > > > a momentary antenna as i turn to water
> > > > this evaporates - an island once again
> > > >
> > > > [Non-text portions of this message have been removed]
> > > >
> > > >
> > > >
> > >
> > > [Non-text portions of this message have been removed]
> > >
> > >
> >
> > --
> >
> > /^_,',',',_ //^/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/>
> >
> > ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
> >
> > a momentary antenna as i turn to water
> > this evaporates - an island once again
> >
> > [Non-text portions of this message have been removed]
> >
> >
> >
>
> [Non-text portions of this message have been removed]
>
>

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

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

a momentary antenna as i turn to water
this evaporates - an island once again

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

🔗Mike Battaglia <battaglia01@...>

On Fri, Nov 18, 2011 at 2:34 PM, kraiggrady <kraiggrady@...> wrote:
>
> It is something Mike uses more than myself, but an interval that is hard
> to define in terms of simple ratios uless he wishes to correct that.

I don't really care about harmonic entropy as much as I used to. The
way I used to look at it was too limiting.

HE doesn't stop you from cognitively distinguishing something like 6/5
and 19/16. It only tells you how likely it is that a single virtual
fundamental pitch will be produced for a certain dyad. That's about
it.

-Mike

> On 19/11/11 2:54 AM, Freeman Gilmore wrote:
> >
> > I am new to this list. What is a "high entropy dyad"?
> > ƒg
> >
> > On Fri, Nov 18, 2011 at 10:42 AM, kraiggrady <kraiggrady@anaphoria.com
> > <mailto:kraiggrady%40anaphoria.com>>wrote:
> >
> > > **
> > >
> > >
> > > well yes electronic distortion can bring these out. i don't know what
> > > the point of that is.
> > > roederer seemed to imply that it was the 3 in a 4:7 chord that came out
> > > . otherwise what happens when one has a high entropy dyad? some random
> > > fundemental and if so doesn't this make entropy impossible?
> > >
> > > On 19/11/11 1:33 AM, Mike Battaglia wrote:
> > > >
> > > > On Fri, Nov 18, 2011 at 8:54 AM, kraiggrady
> > <kraiggrady@... <mailto:kraiggrady%40anaphoria.com>
> > > > <mailto:kraiggrady%40anaphoria.com>> wrote:
> > > > >
> > > > > the primaries are found in even when the fundamental are put in
> > > separate
> > > > > ears, there is no evidence of secondary ones that i have seen. you
> > > might
> > > > > as well in clude the third and fourth or go on until you fill
> > the whole
> > > > > series anfd then where are you?
> > > >
> > > > For one example of evidence for their existence, see
> > > >
> > http://en.wikipedia.org/wiki/Tube_sound#Harmonic_content_and_distortion
> > > >
> > > > Freeman mentioned that the intermodulation distortion (not quite the
> > > > full picture) generated by electronic equipment is louder than that
> > > > generated by the ears. He's correct, so I addressed that. The sort of
> > > > distortion that might be generated by a speaker, or even a distortion
> > > > pedal, often tends to be symmetric, which means you DO get third,
> > > > fifth, etc order difference tones, which roll off and become lower and
> > > > lower in amplitude. An extreme example of this is a hard clipper,
> > > > which you can then send a sine wave through; this will turn the sine
> > > > wave into a square wave, which turns 1 into 1, 3, 5, 7, 9, 11, 13,
> > > > etc. There are an infinite amount of combination tones generated in
> > > > this way - second, fourth, sixth, eighth, and in general all
> > > > "even-order" sum tones will appear in the output. But as you can see,
> > > > there's no 2.
> > > >
> > > > Also, when you talk about the "primaries" that are found when the
> > > > fundamental are put in separate ears, you're probably talking about
> > > > virtual pitches generated by the brain's complex pitch detection
> > > > mechanism, not combination tones - if you put 7/4 in separate ears,
> > > > the VF you hear (if any) will be octave-equivalent to (1):4:7, not
> > > > (3):4:7.
> > > >
> > > > -Mike
> > > >
> > > >
> > >
> > > --
> > >
> > > /^_,',',',_ //^/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/>
> > >
> > > ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
> > >
> > > a momentary antenna as i turn to water
> > > this evaporates - an island once again
> > >
> > > [Non-text portions of this message have been removed]
> > >
> > >
> > >
> >
> > [Non-text portions of this message have been removed]
> >
> >
>
> --
>
> /^_,',',',_ //^/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/>
>
> ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
>
> a momentary antenna as i turn to water
> this evaporates - an island once again
>
> [Non-text portions of this message have been removed]
>
>

🔗Freeman Gilmore <freeman.gilmore@...>

Take the tonic chord

4:5:6 [:7, etc. ?]

invert

5:6:8

and

6:8:10

assume all to start on the same tonic note [?], LCD would be 120

120:150:180

120:140:192

and

120:126:200

so far

120,126,140,150,180,192,200 and 240 would be the octave.

Now take the difference tones and bring them up in to the octave.

Is this how you started? Are creating a scale? I do not need the
details just the general idea.

If you think this is of no interest to the group; take it off line.

thanks,

ƒg

On Fri, Nov 18, 2011 at 3:26 PM, kraiggrady <kraiggrady@...>wrote:

> **
>
>
> I think Helmholtz's method is superior than my own which i will explain
> below
> In this case it was just some experiments and primarily worked out on a
> single tonic. I added up the pitches and the first order difference
> tones omitting dublicates as better than including them testing by ear
> and place the sequence in order from lower to higher. i actually redid
> this recently with adding the 13. the sound file though is an hour and
> 15 minutes and i plan on editing it down as at this point i don't feel
> like i need to use every inversion. Possibly i will post if requested in
> part.
>
> It does not provide progressions but exposes one to say inversions one
> might miss otherwise. I assumed that the posters original idea was to
> use the the numbers as a guide to consonance/dissonance. I am sorry if i
> am wrong in this assumption. I am not satisfied with this method but it
> does illustrate how different inversion do indeed vary. Helmholtz was
> right about this. One time a quantum physicist gave me a version of a
> wave equation. this two produced some interested perceptible results
>
> His method is superior in that it takes into consideration also range
> as he defines i think it was 32 beats per sec as the most rough so the
> same chord on a different tonic would vary as well as register. At the
> time i had limited instruments, being before electronics and so opted to
> approach it the way i did but it would be interesting to figure out a
> way to quantify his method. Possibly someone might choose a different
> rate at this point or not as i think he was not set in stone, thinking
> it as the fastest rhythm not heard as a pitch [he knew sometimes even
> slower ones are so one would have to read what he says here about it as
> would not be fair for me to guess.
>
> On 19/11/11 2:38 AM, Freeman Gilmore wrote:
> >
> > First off I am not a composer. I am interested in mathematics music
> > theory and tuning and temperaments. What you have done makes sense to me
> > in a different way. I am not sure what all you have done. Chords
> > progress many ways, some by common tone some not, some like 13th century
> > triad, the harsh intervals move to more pleasing intervals of the
> > triad for
> > the cadence, modern cadence end on the tonic chord. Just different
> > patterns.
> >
> > I would like to know just how you do this and what chords you use? Are
> > you basing you tuning on these combination tones? E.g. the modern the
> > scale [maj or min] the notes of the scale are based on the tonic,
> dominant
> > and the subdominant chords.
> >
> > ƒg
> >
> > On Fri, Nov 18, 2011 at 9:59 AM, kraiggrady <kraiggrady@...
> > <mailto:kraiggrady%40anaphoria.com>>wrote:
> >
> > > **
> > >
> > >
> > > but we can hear patterns as i have had people play me progression based
> > > on combination tones and after a few it was quite predictable. So I at
> > > least can hear it on some level and i don't think i am that exceptional
> > > that it not to be so with others. And i don't care if someone proves it
> > > for the masses or not, i am not going to wait. I want to know exactly
> > > what experience you have had with this material . i have had at least a
> > > few years looking at it as a constant. not that this means much but at
> > > least requires some to validate or dismiss it, not conjecture.
> > > .
> > > On 19/11/11 1:24 AM, Freeman Gilmore wrote:
> > > >
> > > > Keep it simple, Helmholtz carried this beyond what could be heard.
> > Just
> > > > realize that the sub tones are there and can be head or the brain
> will
> > > > fill
> > > > them is or both. And that the higher tones may be loud enough to
> > add to
> > > > the hash in a tempered system. As for chord progression or tuning
> > use the
> > > > simple ratios, if that is what you are doing, and not get carried
> away
> > > > with
> > > > tone that you can not hear.
> > > > ƒg
> > > > On Fri, Nov 18, 2011 at 9:02 AM, kraiggrady
> > <kraiggrady@... <mailto:kraiggrady%40anaphoria.com>
> > > > <mailto:kraiggrady%40anaphoria.com>>wrote:
> > > >
> > > > > **
> > > > >
> > > > >
> > > > > I do think that helmholtz's idea is worth investigating with as
> many
> > > > > different ways of adding the data as possible, then we can
> > compare, but
> > > > > this requires people doing the work and willing to let go of
> > what they
> > > > > assume. I have tried numerous ways until i abandoned the idea as
> not
> > > > > fruitful. Even if a consonant/dissonant formula could be
> > conceived, it
> > > > > would be such a burden to composing that i think i would rather do
> > > > > something else that be it slave. I mean wouldn't you rather hear
> > duke
> > > > > ellington do everything wrong according to what rules would come
> > out of
> > > > > it? [money jungle for example]
> > > > >
> > > > > On 19/11/11 12:54 AM, kraiggrady wrote:
> > > > > >
> > > > > >
> > > > > > the primaries are found in even when the fundamental are put in
> > > > separate
> > > > > > ears, there is no evidence of secondary ones that i have seen.
> you
> > > > might
> > > > > > as well in clude the third and fourth or go on until you fill the
> > > > whole
> > > > > > series anfd then where are you?
> > > > > >
> > > > > > On 19/11/11 12:45 AM, Mike Battaglia wrote:
> > > > > > >
> > > > > > > On Fri, Nov 18, 2011 at 8:25 AM, Freeman Gilmore
> > > > > > > <freeman.gilmore@...
> > <mailto:freeman.gilmore%40gmail.com> <mailto:freeman.gilmore%40gmail.com
> >
> > > > <mailto:freeman.gilmore%40gmail.com>
> > > > > > <mailto:freeman.gilmore%40gmail.com>> wrote:
> > > > > > > >
> > > > > > > > For the major chord, it has the ratio 4:5:6 just for the
> > > > > > > fundamentals [to
> > > > > > > > overtones], first order.
> > > > > > > >
> > > > > > > > 4:5 gives 1 and 9
> > > > > > > >
> > > > > > > > 4:6 gives 2 and 10
> > > > > > > >
> > > > > > > > 5:6 gives 1 and 11
> > > > > > > > So you have the tone 1,2,3,4,5,6,9,10,11 with just the
> > > > fundamentals.
> > > > > > > > ƒg
> > > > > > >
> > > > > > > If you really care about difference tones and such, then the
> > even
> > > > > > > second-order ones are probably more what you're after. So for
> > > 7:9:11
> > > > > > > you end up getting ...:3:5:7:9:11:13:15:17:19:..., etc.
> > > > > > >
> > > > > > > -Mike
> > > > > > >
> > > > > > >
> > > > > >
> > > > > > --
> > > > > >
> > > > > > /^_,',',',_ //^/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/>
> > > > > >
> > > > > > ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
> > > > > >
> > > > > > a momentary antenna as i turn to water
> > > > > > this evaporates - an island once again
> > > > > >
> > > > > > [Non-text portions of this message have been removed]
> > > > > >
> > > > > >
> > > > >
> > > > > --
> > > > >
> > > > > /^_,',',',_ //^/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/
> > > >
> > > > >
> > > > > ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
> > > > >
> > > > > a momentary antenna as i turn to water
> > > > > this evaporates - an island once again
> > > > >
> > > > > [Non-text portions of this message have been removed]
> > > > >
> > > > >
> > > > >
> > > >
> > > > [Non-text portions of this message have been removed]
> > > >
> > > >
> > >
> > > --
> > >
> > > /^_,',',',_ //^/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/
> >
> > >
> > > ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
> > >
> > > a momentary antenna as i turn to water
> > > this evaporates - an island once again
> > >
> > > [Non-text portions of this message have been removed]
> > >
> > >
> > >
> >
> > [Non-text portions of this message have been removed]
> >
> >
>
> --
>
> /^_,',',',_ //^/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/>
>
> ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
>
> a momentary antenna as i turn to water
> this evaporates - an island once again
>
> [Non-text portions of this message have been removed]
>
>
>

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

🔗Freeman Gilmore <freeman.gilmore@...>

Thank,

Just never heard the term before.

ƒg

On Fri, Nov 18, 2011 at 4:00 PM, Mike Battaglia <battaglia01@...>wrote:

> **
>
>
> On Fri, Nov 18, 2011 at 2:34 PM, kraiggrady <kraiggrady@...>
> wrote:
> >
> > It is something Mike uses more than myself, but an interval that is hard
> > to define in terms of simple ratios uless he wishes to correct that.
>
> I don't really care about harmonic entropy as much as I used to. The
> way I used to look at it was too limiting.
>
> HE doesn't stop you from cognitively distinguishing something like 6/5
> and 19/16. It only tells you how likely it is that a single virtual
> fundamental pitch will be produced for a certain dyad. That's about
> it.
>
> -Mike
>
> > On 19/11/11 2:54 AM, Freeman Gilmore wrote:
> > >
> > > I am new to this list. What is a "high entropy dyad"?
> > > ƒg
> > >
> > > On Fri, Nov 18, 2011 at 10:42 AM, kraiggrady <kraiggrady@...
> > > <mailto:kraiggrady%40anaphoria.com>>wrote:
> > >
> > > > **
> > > >
> > > >
> > > > well yes electronic distortion can bring these out. i don't know what
> > > > the point of that is.
> > > > roederer seemed to imply that it was the 3 in a 4:7 chord that came
> out
> > > > . otherwise what happens when one has a high entropy dyad? some
> random
> > > > fundemental and if so doesn't this make entropy impossible?
> > > >
> > > > On 19/11/11 1:33 AM, Mike Battaglia wrote:
> > > > >
> > > > > On Fri, Nov 18, 2011 at 8:54 AM, kraiggrady
> > > <kraiggrady@... <mailto:kraiggrady%40anaphoria.com>
> > > > > <mailto:kraiggrady%40anaphoria.com>> wrote:
> > > > > >
> > > > > > the primaries are found in even when the fundamental are put in
> > > > separate
> > > > > > ears, there is no evidence of secondary ones that i have seen.
> you
> > > > might
> > > > > > as well in clude the third and fourth or go on until you fill
> > > the whole
> > > > > > series anfd then where are you?
> > > > >
> > > > > For one example of evidence for their existence, see
> > > > >
> > >
> http://en.wikipedia.org/wiki/Tube_sound#Harmonic_content_and_distortion
> > > > >
> > > > > Freeman mentioned that the intermodulation distortion (not quite
> the
> > > > > full picture) generated by electronic equipment is louder than that
> > > > > generated by the ears. He's correct, so I addressed that. The sort
> of
> > > > > distortion that might be generated by a speaker, or even a
> distortion
> > > > > pedal, often tends to be symmetric, which means you DO get third,
> > > > > fifth, etc order difference tones, which roll off and become lower
> and
> > > > > lower in amplitude. An extreme example of this is a hard clipper,
> > > > > which you can then send a sine wave through; this will turn the
> sine
> > > > > wave into a square wave, which turns 1 into 1, 3, 5, 7, 9, 11, 13,
> > > > > etc. There are an infinite amount of combination tones generated in
> > > > > this way - second, fourth, sixth, eighth, and in general all
> > > > > "even-order" sum tones will appear in the output. But as you can
> see,
> > > > > there's no 2.
> > > > >
> > > > > Also, when you talk about the "primaries" that are found when the
> > > > > fundamental are put in separate ears, you're probably talking about
> > > > > virtual pitches generated by the brain's complex pitch detection
> > > > > mechanism, not combination tones - if you put 7/4 in separate ears,
> > > > > the VF you hear (if any) will be octave-equivalent to (1):4:7, not
> > > > > (3):4:7.
> > > > >
> > > > > -Mike
> > > > >
> > > > >
> > > >
> > > > --
> > > >
> > > > /^_,',',',_ //^/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/>
> > > >
> > > > ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
> > > >
> > > > a momentary antenna as i turn to water
> > > > this evaporates - an island once again
> > > >
> > > > [Non-text portions of this message have been removed]
> > > >
> > > >
> > > >
> > >
> > > [Non-text portions of this message have been removed]
> > >
> > >
> >
> > --
> >
> > /^_,',',',_ //^/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/>
> >
> > ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
> >
> > a momentary antenna as i turn to water
> > this evaporates - an island once again
> >
> > [Non-text portions of this message have been removed]
> >
> >
>
>

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

🔗kraiggrady <kraiggrady@...>

On 19/11/11 8:18 AM, Freeman Gilmore wrote:
>
> Take the tonic chord
>
> 4:5:6 [:7, etc. ?]
>
(4+5+6) add the sounding tones
(1+1+1+2)add the difference tones =20

(1+2) or only add unique tones =18

using second method in the rest here
>
>
> invert
>
> 5:6:8
>
[5+6+8]+[1+2+3]=25
>
>
> and
>
> 6:8:10
>
this reduces to 3:4:5
[3+4+5]+[1+1+2]=15
>
>
> assume all to start on the same tonic note [?], LCD would be 120
>
I did not multiply
>
>
> 120:150:180
>
> 120:140:192
>
> and
>
> 120:126:200
>
> so far
>
> 120,126,140,150,180,192,200 and 240 would be the octave.
>
> Now take the difference tones and bring them up in to the octave.
>
> Is this how you started?
>
It is how i first listened to JI chords on a reed organ
>
> Are creating a scale?
>
the scale was made before this, it was to look at what i had available

> I do not need the
> details just the general idea.
>
> If you think this is of no interest to the group; take it off line.
>
> thanks,
>
> ƒg
>
> On Fri, Nov 18, 2011 at 3:26 PM, kraiggrady <kraiggrady@anaphoria.com
> <mailto:kraiggrady%40anaphoria.com>>wrote:
>
> > **
> >
> >
> > I think Helmholtz's method is superior than my own which i will explain
> > below
> > In this case it was just some experiments and primarily worked out on a
> > single tonic. I added up the pitches and the first order difference
> > tones omitting dublicates as better than including them testing by ear
> > and place the sequence in order from lower to higher. i actually redid
> > this recently with adding the 13. the sound file though is an hour and
> > 15 minutes and i plan on editing it down as at this point i don't feel
> > like i need to use every inversion. Possibly i will post if requested in
> > part.
> >
> > It does not provide progressions but exposes one to say inversions one
> > might miss otherwise. I assumed that the posters original idea was to
> > use the the numbers as a guide to consonance/dissonance. I am sorry if i
> > am wrong in this assumption. I am not satisfied with this method but it
> > does illustrate how different inversion do indeed vary. Helmholtz was
> > right about this. One time a quantum physicist gave me a version of a
> > wave equation. this two produced some interested perceptible results
> >
> > His method is superior in that it takes into consideration also range
> > as he defines i think it was 32 beats per sec as the most rough so the
> > same chord on a different tonic would vary as well as register. At the
> > time i had limited instruments, being before electronics and so opted to
> > approach it the way i did but it would be interesting to figure out a
> > way to quantify his method. Possibly someone might choose a different
> > rate at this point or not as i think he was not set in stone, thinking
> > it as the fastest rhythm not heard as a pitch [he knew sometimes even
> > slower ones are so one would have to read what he says here about it as
> > would not be fair for me to guess.
> >
> > On 19/11/11 2:38 AM, Freeman Gilmore wrote:
> > >
> > > First off I am not a composer. I am interested in mathematics music
> > > theory and tuning and temperaments. What you have done makes sense
> to me
> > > in a different way. I am not sure what all you have done. Chords
> > > progress many ways, some by common tone some not, some like 13th
> century
> > > triad, the harsh intervals move to more pleasing intervals of the
> > > triad for
> > > the cadence, modern cadence end on the tonic chord. Just different
> > > patterns.
> > >
> > > I would like to know just how you do this and what chords you use? Are
> > > you basing you tuning on these combination tones? E.g. the modern the
> > > scale [maj or min] the notes of the scale are based on the tonic,
> > dominant
> > > and the subdominant chords.
> > >
> > > ƒg
> > >
> > > On Fri, Nov 18, 2011 at 9:59 AM, kraiggrady
> <kraiggrady@anaphoria.com <mailto:kraiggrady%40anaphoria.com>
> > > <mailto:kraiggrady%40anaphoria.com>>wrote:
> > >
> > > > **
> > > >
> > > >
> > > > but we can hear patterns as i have had people play me
> progression based
> > > > on combination tones and after a few it was quite predictable.
> So I at
> > > > least can hear it on some level and i don't think i am that
> exceptional
> > > > that it not to be so with others. And i don't care if someone
> proves it
> > > > for the masses or not, i am not going to wait. I want to know
> exactly
> > > > what experience you have had with this material . i have had at
> least a
> > > > few years looking at it as a constant. not that this means much
> but at
> > > > least requires some to validate or dismiss it, not conjecture.
> > > > .
> > > > On 19/11/11 1:24 AM, Freeman Gilmore wrote:
> > > > >
> > > > > Keep it simple, Helmholtz carried this beyond what could be heard.
> > > Just
> > > > > realize that the sub tones are there and can be head or the brain
> > will
> > > > > fill
> > > > > them is or both. And that the higher tones may be loud enough to
> > > add to
> > > > > the hash in a tempered system. As for chord progression or tuning
> > > use the
> > > > > simple ratios, if that is what you are doing, and not get carried
> > away
> > > > > with
> > > > > tone that you can not hear.
> > > > > ƒg
> > > > > On Fri, Nov 18, 2011 at 9:02 AM, kraiggrady
> > > <kraiggrady@... <mailto:kraiggrady%40anaphoria.com>
> <mailto:kraiggrady%40anaphoria.com>
> > > > > <mailto:kraiggrady%40anaphoria.com>>wrote:
> > > > >
> > > > > > **
> > > > > >
> > > > > >
> > > > > > I do think that helmholtz's idea is worth investigating with as
> > many
> > > > > > different ways of adding the data as possible, then we can
> > > compare, but
> > > > > > this requires people doing the work and willing to let go of
> > > what they
> > > > > > assume. I have tried numerous ways until i abandoned the idea as
> > not
> > > > > > fruitful. Even if a consonant/dissonant formula could be
> > > conceived, it
> > > > > > would be such a burden to composing that i think i would
> rather do
> > > > > > something else that be it slave. I mean wouldn't you rather hear
> > > duke
> > > > > > ellington do everything wrong according to what rules would come
> > > out of
> > > > > > it? [money jungle for example]
> > > > > >
> > > > > > On 19/11/11 12:54 AM, kraiggrady wrote:
> > > > > > >
> > > > > > >
> > > > > > > the primaries are found in even when the fundamental are
> put in
> > > > > separate
> > > > > > > ears, there is no evidence of secondary ones that i have seen.
> > you
> > > > > might
> > > > > > > as well in clude the third and fourth or go on until you
> fill the
> > > > > whole
> > > > > > > series anfd then where are you?
> > > > > > >
> > > > > > > On 19/11/11 12:45 AM, Mike Battaglia wrote:
> > > > > > > >
> > > > > > > > On Fri, Nov 18, 2011 at 8:25 AM, Freeman Gilmore
> > > > > > > > <freeman.gilmore@gmail.com
> <mailto:freeman.gilmore%40gmail.com>
> > > <mailto:freeman.gilmore%40gmail.com>
> <mailto:freeman.gilmore%40gmail.com
> > >
> > > > > <mailto:freeman.gilmore%40gmail.com>
> > > > > > > <mailto:freeman.gilmore%40gmail.com>> wrote:
> > > > > > > > >
> > > > > > > > > For the major chord, it has the ratio 4:5:6 just for the
> > > > > > > > fundamentals [to
> > > > > > > > > overtones], first order.
> > > > > > > > >
> > > > > > > > > 4:5 gives 1 and 9
> > > > > > > > >
> > > > > > > > > 4:6 gives 2 and 10
> > > > > > > > >
> > > > > > > > > 5:6 gives 1 and 11
> > > > > > > > > So you have the tone 1,2,3,4,5,6,9,10,11 with just the
> > > > > fundamentals.
> > > > > > > > > ƒg
> > > > > > > >
> > > > > > > > If you really care about difference tones and such, then the
> > > even
> > > > > > > > second-order ones are probably more what you're after.
> So for
> > > > 7:9:11
> > > > > > > > you end up getting ...:3:5:7:9:11:13:15:17:19:..., etc.
> > > > > > > >
> > > > > > > > -Mike
> > > > > > > >
> > > > > > > >
> > > > > > >
> > > > > > > --
> > > > > > >
> > > > > > > /^_,',',',_ //^/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/>
> > > > > > >
> > > > > > > ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
> > > > > > >
> > > > > > > a momentary antenna as i turn to water
> > > > > > > this evaporates - an island once again
> > > > > > >
> > > > > > > [Non-text portions of this message have been removed]
> > > > > > >
> > > > > > >
> > > > > >
> > > > > > --
> > > > > >
> > > > > > /^_,',',',_ //^/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/
> > > > >
> > > > > >
> > > > > > ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
> > > > > >
> > > > > > a momentary antenna as i turn to water
> > > > > > this evaporates - an island once again
> > > > > >
> > > > > > [Non-text portions of this message have been removed]
> > > > > >
> > > > > >
> > > > > >
> > > > >
> > > > > [Non-text portions of this message have been removed]
> > > > >
> > > > >
> > > >
> > > > --
> > > >
> > > > /^_,',',',_ //^/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/
> > >
> > > >
> > > > ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
> > > >
> > > > a momentary antenna as i turn to water
> > > > this evaporates - an island once again
> > > >
> > > > [Non-text portions of this message have been removed]
> > > >
> > > >
> > > >
> > >
> > > [Non-text portions of this message have been removed]
> > >
> > >
> >
> > --
> >
> > /^_,',',',_ //^/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/>
> >
> > ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
> >
> > a momentary antenna as i turn to water
> > this evaporates - an island once again
> >
> > [Non-text portions of this message have been removed]
> >
> >
> >
>
> [Non-text portions of this message have been removed]
>
>

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

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

a momentary antenna as i turn to water
this evaporates - an island once again

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

🔗Freeman Gilmore <freeman.gilmore@...>

Simplified:

>> Take the tonic chord

>> 4:5:6 [:7, etc. ?]

>(4+5+6) add the sounding tones

>(1+1+1+2)add the difference tones =20

>(1+2) or only add unique tones =18

>using second method in the rest here

>>invert

>> 5:6:8

>[5+6+8]+[1+2+3]=25

>> and

>> 6:8:10

>this reduces to 3:4:5

>[3+4+5]+[1+1+2]=15

>>>

>t is how i first listened to JI chords on a reed organ

>>Are you creating a scale?

>the scale was made before this, it was to look at what i had available

So you have a scale with many notes and you are choosing a subset for your
compassion, based on the numbers 20 or 18, 25 and 15? Or are they the
notes that your chords can progress to [your patterns that you speak of].?

> It is how i first listened to JI chords on a reed organ

What are JI chords?

ƒg

> I do not need the

> details just the general idea.

> If you think this is of no interest to the group; take it off line.

> thanks,

> ƒg

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

🔗kraiggrady <kraiggrady@...>

🔗Freeman Gilmore <freeman.gilmore@...>

🔗kraiggrady <kraiggrady@...>

the numbers are a rating of the chords

I was able to find one 23 year old example this is based on a 6 note
chord of a structure called the hexany this being the 1-3-5-9 one. the
chords are also played melodically. I think it is as long as it is for
at the time i really wanted to be able to hear the chord long enough to
really take it in. http://anaphoria.com/wash2.mp3
i guess there is a version of another like piece on this track based on
a 7-9-11-15 which i put forward some time back in revised version

On 19/11/11 11:17 AM, Freeman Gilmore wrote:
>
> So you are playing four notes [15,18,20,25], [15,18,25, [30]], or
> [15,20,25,[30]]?
> ƒg
>
> On Fri, Nov 18, 2011 at 6:48 PM, kraiggrady <kraiggrady@...
> <mailto:kraiggrady%40anaphoria.com>>wrote:
>
> > **
> >
> >
> > On 19/11/11 10:23 AM, Freeman Gilmore wrote:
> > >
> > > Simplified:
> > >
> > >
> > > So you have a scale with many notes and you are choosing a subset for
> > your
> > > compassion, based on the numbers 20 or 18, 25 and 15? Or are they the
> > > notes that your chords can progress to [your patterns that you speak
> > of].?
> > >
> > going from lower number to higher usually as a way to build without
> > moving to another chord. this way i could get players to learn only 4
> > notes.
> > >
> > >
> > > > It is how i first listened to JI chords on a reed organ
> > >
> > > What are JI chords?
> > >
> > Just intonation sorry
> > >
> > >
> > > ƒg
> > >
> >
> > --
> >
> > /^_,',',',_ //^/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/>
> >
> > ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
> >
> > a momentary antenna as i turn to water
> > this evaporates - an island once again
> >
> > [Non-text portions of this message have been removed]
> >
> >
> >
>
> [Non-text portions of this message have been removed]
>
>

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

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

a momentary antenna as i turn to water
this evaporates - an island once again

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

Is there a way to calculate a sum of harmonics in a chord?

🔗ruxxes <ruxxes@...>

🔗kraiggrady <kraiggrady@...>

🔗ruxxes <ruxxes@...>

🔗Freeman Gilmore <freeman.gilmore@...>

🔗kraiggrady <kraiggrady@...>

🔗kraiggrady <kraiggrady@...>

🔗Freeman Gilmore <freeman.gilmore@...>

🔗kraiggrady <kraiggrady@...>

🔗Mike Battaglia <battaglia01@...>

🔗kraiggrady <kraiggrady@...>

🔗Freeman Gilmore <freeman.gilmore@...>

🔗kraiggrady <kraiggrady@...>

🔗kraiggrady <kraiggrady@...>

🔗Freeman Gilmore <freeman.gilmore@...>

🔗Mike Battaglia <battaglia01@...>

🔗Freeman Gilmore <freeman.gilmore@...>

🔗kraiggrady <kraiggrady@...>

🔗Freeman Gilmore <freeman.gilmore@...>

🔗kraiggrady <kraiggrady@...>

🔗Freeman Gilmore <freeman.gilmore@...>

🔗Mike Battaglia <battaglia01@...>

🔗Mike Battaglia <battaglia01@...>

🔗Mike Battaglia <battaglia01@...>

🔗Freeman Gilmore <freeman.gilmore@...>

🔗Freeman Gilmore <freeman.gilmore@...>

🔗kraiggrady <kraiggrady@...>

🔗kraiggrady <kraiggrady@...>

🔗Mike Battaglia <battaglia01@...>

🔗Freeman Gilmore <freeman.gilmore@...>

🔗Freeman Gilmore <freeman.gilmore@...>

🔗kraiggrady <kraiggrady@...>

🔗Freeman Gilmore <freeman.gilmore@...>

🔗kraiggrady <kraiggrady@...>

🔗Freeman Gilmore <freeman.gilmore@...>

🔗kraiggrady <kraiggrady@...>

🔗Acoustrokes <acoustroke@...>