Yahoo Tuning Groups Ultimate Backup makemicromusic Re: [MMM] Digest Number 3749

Wow! Thank you for your feedback! Now I have to re-consider some things before I could give a meaningful answer...

________________________________
From: "MakeMicroMusic@yahoogroups.com" <MakeMicroMusic@yahoogroups.com>
To: MakeMicroMusic@yahoogroups.com
Sent: Saturday, November 19, 2011 12:25 AM
Subject: [MMM] Digest Number 3749

Making Microtonal Music
Making Microtonal Music
Messages In This Digest (25 Messages)

1a.
Re: Is there a way to calculate a sum of harmonics in a chord? From: kraiggrady
1b.
Re: Is there a way to calculate a sum of harmonics in a chord? From: Freeman Gilmore
1c.
Re: Is there a way to calculate a sum of harmonics in a chord? From: kraiggrady
1d.
Re: Is there a way to calculate a sum of harmonics in a chord? From: Mike Battaglia
1e.
Re: Is there a way to calculate a sum of harmonics in a chord? From: kraiggrady
1f.
Re: Is there a way to calculate a sum of harmonics in a chord? From: Freeman Gilmore
1g.
Re: Is there a way to calculate a sum of harmonics in a chord? From: kraiggrady
1h.
Re: Is there a way to calculate a sum of harmonics in a chord? From: kraiggrady
1i.
Re: Is there a way to calculate a sum of harmonics in a chord? From: Freeman Gilmore
1j.
Re: Is there a way to calculate a sum of harmonics in a chord? From: Mike Battaglia
1k.
Re: Is there a way to calculate a sum of harmonics in a chord? From: Freeman Gilmore
1l.
Re: Is there a way to calculate a sum of harmonics in a chord? From: kraiggrady
1m.
Re: Is there a way to calculate a sum of harmonics in a chord? From: Freeman Gilmore
1n.
Re: Is there a way to calculate a sum of harmonics in a chord? From: kraiggrady
1o.
Re: Is there a way to calculate a sum of harmonics in a chord? From: Freeman Gilmore
1p.
Re: Is there a way to calculate a sum of harmonics in a chord? From: Mike Battaglia
1q.
Re: Is there a way to calculate a sum of harmonics in a chord? From: Mike Battaglia
1r.
Re: Is there a way to calculate a sum of harmonics in a chord? From: Mike Battaglia
1s.
Re: Is there a way to calculate a sum of harmonics in a chord? From: Freeman Gilmore
1t.
Re: Is there a way to calculate a sum of harmonics in a chord? From: Freeman Gilmore
1u.
Re: Is there a way to calculate a sum of harmonics in a chord? From: kraiggrady
2a.
Three Imperfections From: Chris Vaisvil
2b.
Re: Three Imperfections From: Jake Freivald
3a.
Lament for classical guitar and flute From: Jake Freivald
3b.
Re: Lament for classical guitar and flute From: Chris Vaisvil View All Topics | Create New Topic Messages
1a.
Re: Is there a way to calculate a sum of harmonics in a chord?
Posted by: "kraiggrady" kraiggrady@... banaphshu
Fri Nov 18, 2011 3:46 am (PST)

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:MakeMicroMu sic%40yahoogroup s.com>
> > <mailto:MakeMicroMu sic%40yahoogroup s.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://anaphoriasou th.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://anaphoriasou th.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://anaphoriasou th.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]

Back to top Reply to sender | Reply to group | Reply via web post
Messages in this topic (26)
1b.
Re: Is there a way to calculate a sum of harmonics in a chord?
Posted by: "Freeman Gilmore" freeman.gilmore@... freeman.gilmore
Fri Nov 18, 2011 5:25 am (PST)

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@anaphori a.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:MakeMicroMu sic%40yahoogroup s.com>
> > > <mailto:MakeMicroMu sic%40yahoogroup s.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://anaphoriasou th.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://anaphoriasou th.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://anaphoriasou th.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]

Back to top Reply to sender | Reply to group | Reply via web post
Messages in this topic (26)
1c.
Re: Is there a way to calculate a sum of harmonics in a chord?
Posted by: "kraiggrady" kraiggrady@... banaphshu
Fri Nov 18, 2011 5:42 am (PST)

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@anaphori a.com
> <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@yahoo. com
> <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:MakeMicroMu sic%40yahoogroup s.com>
> > > <mailto:MakeMicroMu sic%40yahoogroup s.com>
> > > > <mailto:MakeMicroMu sic%40yahoogroup s.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://anaphoriasou th.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://anaphoriasou th.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://anaphoriasou th.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://anaphoriasou th.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]

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Messages in this topic (26)
1d.
Re: Is there a way to calculate a sum of harmonics in a chord?
Posted by: "Mike Battaglia" battaglia01@... battaglia01
Fri Nov 18, 2011 5:45 am (PST)

On Fri, Nov 18, 2011 at 8:25 AM, Freeman Gilmore
<freeman.gilmore@ gmail.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

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Messages in this topic (26)
1e.
Re: Is there a way to calculate a sum of harmonics in a chord?
Posted by: "kraiggrady" kraiggrady@... banaphshu
Fri Nov 18, 2011 5:49 am (PST)

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://anaphoriasou th.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]

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Messages in this topic (26)
1f.
Re: Is there a way to calculate a sum of harmonics in a chord?
Posted by: "Freeman Gilmore" freeman.gilmore@... freeman.gilmore
Fri Nov 18, 2011 5:50 am (PST)

3 is a mistake sorry.
ƒg

On Fri, Nov 18, 2011 at 8:42 AM, kraiggrady <kraiggrady@anaphori a.com>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@anaphori a.com
> > <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@yahoo. com
> > <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:MakeMicroMu sic%40yahoogroup s.com>
> > > > <mailto:MakeMicroMu sic%40yahoogroup s.com>
> > > > > <mailto:MakeMicroMu sic%40yahoogroup s.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://anaphoriasou th.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://anaphoriasou th.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://anaphoriasou th.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://anaphoriasou th.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]

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Messages in this topic (26)
1g.
Re: Is there a way to calculate a sum of harmonics in a chord?
Posted by: "kraiggrady" kraiggrady@... banaphshu
Fri Nov 18, 2011 5:54 am (PST)

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>> 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://anaphoriasou th.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]

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Messages in this topic (26)
1h.
Re: Is there a way to calculate a sum of harmonics in a chord?
Posted by: "kraiggrady" kraiggrady@... banaphshu
Fri Nov 18, 2011 6:02 am (PST)

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>> 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://anaphoriasou th.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://anaphoriasou th.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]

Back to top Reply to sender | Reply to group | Reply via web post
Messages in this topic (26)
1i.
Re: Is there a way to calculate a sum of harmonics in a chord?
Posted by: "Freeman Gilmore" freeman.gilmore@... freeman.gilmore
Fri Nov 18, 2011 6:24 am (PST)

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@anaphori a.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>> 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 Anaph
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