The "out of tune" harmonics in the Harmonic Series

Hello ALL, Can you please show me the aesthetics (or, logic) behind the 7th partial ( b-sesquiflat) having been most unceremoniously shoved off into oblivion in connection with JI ? In fact,the 7th, 11th, 13th and the 14th harmonics occur naturally as a part of the Harmonic series, but are considered out of tune in the ordinary twelve-tone scales. Do we take this to mean that the notes falling in line with the JI concept are more important than these naturally occurring notes?

Thanking you for your time, and regards,
Haresh.

--- In tuning@yahoogroups.com, "Haresh BAKSHI" <hareshbakshi@h...>
wrote:
> Hello ALL, Can you please show me the aesthetics (or, logic) behind
the 7th partial ( b-sesquiflat) having been most unceremoniously
shoved off into oblivion in connection with JI ? In fact,the 7th,
11th, 13th and the 14th harmonics occur naturally as a part of the
Harmonic series, but are considered out of tune in the ordinary
twelve-tone scales. Do we take this to mean that the notes falling in
line with the JI concept are more important than these naturally
occurring notes?

Hello Haresh,

I'm interested to hear how others here may reply to your questions
and I wonder if these notes are in line with the JI concept - seems
like they're pretty important ones since they occur naturally and are
fairly low in the harmonic overtone series (we hear them on some
level frequently).

LaMonte Young has been incorporating the 7th into his work throughout
his career and has extensive interest in JI, I believe (his Dream
House installations use intervals of harmonic overtones way up in the
series).

I sing harmonic overtones, and contrary to most traditional throat
singing, I use harmonics 7, 11, 13, 14 in my music.

Not sure how this bears on the 'JI concept' but I've often heard
folks refer to our music as a form of JI.

~Jim

http://www.spectralvoices.com

--- In tuning@yahoogroups.com, "Jim Cole" <thejimcole@y...> wrote:
> --- In tuning@yahoogroups.com, "Haresh BAKSHI" <hareshbakshi@h...>
> wrote:
> > Hello ALL, Can you please show me the aesthetics (or, logic)
behind
> the 7th partial ( b-sesquiflat) having been most unceremoniously
> shoved off into oblivion in connection with JI ? In fact,the 7th,
> 11th, 13th and the 14th harmonics occur naturally as a part of the
> Harmonic series, but are considered out of tune in the ordinary
> twelve-tone scales. Do we take this to mean that the notes falling
in
> line with the JI concept are more important than these naturally
> occurring notes?
>
> Hello Haresh,
>
> I'm interested to hear how others here may reply to your questions
> and I wonder if these notes are in line with the JI concept -
seems
> like they're pretty important ones since they occur naturally and
are
> fairly low in the harmonic overtone series (we hear them on some
> level frequently).
>
> LaMonte Young has been incorporating the 7th into his work
throughout
> his career and has extensive interest in JI, I believe (his Dream
> House installations use intervals of harmonic overtones way up in
the
> series).
>
> I sing harmonic overtones, and contrary to most traditional throat
> singing, I use harmonics 7, 11, 13, 14 in my music.
>
> Not sure how this bears on the 'JI concept' but I've often heard
> folks refer to our music as a form of JI.
>
> ~Jim

Hi Haresh and Jim-

It seems you are both confused about the difference between 'JI' and
'5 limit JI'. Haresh, many musicians incorporate all sorts of
harmonics, including the 7th harmonic, in their work. It all depends
on how far up the harmonic series one wants to incorporate its
factors into a tuning--hence the term 'limit'. '5 limit JI' stops at
the fifth harmonic, the one we recognize as a major third, etc.

BTW, using the term '14th harmonic' is redundant when talking about
octave reducing tunings--it's the same as the 7th harmonic, but one
octave higher. Only the prime factors give us new subjective
affects, but for example the 9th harmonic, being the P5th of a P5th,
is often latticed as being a colorful factor in its own right.

Also Haresh, JI genrally only considers notes that are part of the
overtonal or undertonal series, i.e. naturally occurring pitches of
a harmonic timbre, plus their mirror fractional inversions.

As for the word 'natural', be careful--there are plenty of
'naturally occuring sounds' whose spectra are *far* from being
harmonic. In fact more sounds than not are inharmonic.

Best,
Aaron.

--- In tuning@yahoogroups.com, "Haresh BAKSHI" <hareshbakshi@h...> wrote:

> Hello ALL, Can you please show me the aesthetics (or, logic) behind
the 7th partial ( b-sesquiflat) having been most unceremoniously
shoved off into oblivion in connection with JI ?

I don't see that this is true, but in any case sometimes they only
appear to be gone. If you take the 22 srutis of the scale Scala calls
"indian.scl", you see listed a 5-limit scale. However, ask Scala to
list all utonal tetrads--chords of the form 1-5/4-3/2-7/4--and it
lists seven of them. It also gives errors of 32805/32768, 225/224, or
the ratio of these, 5120/5103. The error could be distributed by
tempering out 32805/32768 and 225/224, the "garibaldi" temperament.
You could do this by for instance tuning everything to 94-equal, which
has what I call a "copoptimal fifth" (optimum in a certain sense in
both the 7 and 9 odd limits.)

It would not be surprising if, when you took your favorite 5-limit
scale from Indian music theory and analyzed it in Scala, you found
7-limit implications.

hi Haresh, Jim, and Aaron,

Haresh:

--- In tuning@yahoogroups.com, "akjmicro" <akjmicro@c...> wrote:

> --- In tuning@yahoogroups.com, "Jim Cole" <thejimcole@y...> wrote:
> > --- In tuning@yahoogroups.com, "Haresh BAKSHI" <hareshbakshi@h...>
> > wrote:
> >
> > > Hello ALL, Can you please show me the aesthetics
> > > (or, logic) behind the 7th partial (b-sesquiflat)
> > > having been most unceremoniously shoved off into
> > > oblivion in connection with JI ? In fact,the 7th,
> > > 11th, 13th and the 14th harmonics occur naturally as
> > > a part of the Harmonic series, but are considered
> > > out of tune in the ordinary twelve-tone scales.
> > > Do we take this to mean that the notes falling in
> > > line with the JI concept are more important than these
> > > naturally occurring notes?

a big part of the reason why ratios of 7 were not
canonically admitted into Western harmony in modern
times, is that not long after 5 was finally accepted
(c.1480), the lute and then a few centuries later
the keyboard became the preeminent instruments, and
the physical structure of both, encouraged musicians
to want to limit their scales to only 12 notes.
(of course, there were experiments with larger
tuning systems, but this was the norm.)

at first, these 12 notes were generally tuned in
meantone, then around 1700 well-temperaments became
popular, which brought the scale overall closer
to 12edo, then finally from 1800-1900 12edo itself
solidified into the standard tuning ... and 12edo
is not so great at emulating ratios of 7, with
error from JI for those ratios typically around
30 cents or ~1/7-tone.

it is true that many meantones (including 1/4-comma)
give an excellent representation of the 7th partial
but spelled as an "augmented-6th" (i.e., A# sounds
like "B sesquiflat"). the similarity of this chord to
a 4:5:7 triad ("Italian 6th") or 4:5:6:7 tetrad
("German 6th") probably caused composers to enjoy
employing it ... i've just made a nice applet which
shows how various meantones approximate 4:5:6:7 :

http://tonalsoft.com/enc/index2.htm?augmented-6th.htm

but until some serious is research is done, examining
together the the occurence of possible 7-limit harmonies
in a piece of music, along with the tuning most likely
intended by the composer, there is little hard evidence
that can be presented.

the only thing which i *can* document is that the
"standard" tunings in Europe historically followed
a rough trend from more to->less temperament of the
"5th", i.e., from 19edo to 12edo, as if going from
the bottom of the list in my applet, to the top.

as meantone tuning moved further and further away from
1/4-comma and 31edo (which gives a very good 4:5:6:7)
and simultaneously closer and closer to 12edo (with
its mediocre 5:4 and lousy 7:4), ratios of 7 seem
to have generally fallen more and more out of favor.

there were always advocates of 7, but mainstream
music-theory of the 1700s-1900s didn't admit it as
an implied prime-factor in the harmony.

during the later 1800s there was quite a flurry of
activity in microtonal experimentation, particularly
in England and Germany, and particularly concerned
with encompassing the ratios of 7 in harmony. but
it was Partch who really opened the door to the
higher-prime factors of 7 and 11.

now of course, i've presented the Euro-centric view
here. in folk music from all over the world, in particular
the Turkish/Persian/Arab music, i hear lots of intervals
resembling 7- and 11-limit ratios.

Jim:

> > Hello Haresh,
> >
> > I'm interested to hear how others here may reply to your
> > questions and I wonder if these notes are in line with
> > the JI concept - seems like they're pretty important
> > ones since they occur naturally and are fairly low in
> > the harmonic overtone series (we hear them on some
> > level frequently).
> >
> > LaMonte Young has been incorporating the 7th into his work
> > throughout his career and has extensive interest in JI,
> > I believe (his Dream House installations use intervals
> > of harmonic overtones way up in the series).

Young's current Dream House installation uses primes all
the way up to 283.

but this is nothing new ... Boethius in his renowned treatise
of c.505 AD used 499 as a factor in the ratios of his
enharmonic genus.

> > I sing harmonic overtones, and contrary to most
> > traditional throat singing, I use harmonics
> > 7, 11, 13, 14 in my music.
> >
> > Not sure how this bears on the 'JI concept' but
> > I've often heard folks refer to our music as a form of JI.
> >
> > ~Jim

certainly "extended-JI", if one wants to use the qualifier.
it would usually be called 13-limit JI.

Aaron:

> Hi Haresh and Jim-
>
> It seems you are both confused about the difference between 'JI' and
> '5 limit JI'. Haresh, many musicians incorporate all sorts of
> harmonics, including the 7th harmonic, in their work. It all depends
> on how far up the harmonic series one wants to incorporate its
> factors into a tuning--hence the term 'limit'. '5 limit JI' stops at
> the fifth harmonic, the one we recognize as a major third, etc.

it became fairly common for awhile to call JI tunings
with odd- or prime-limit higher than 5, "extended-JI",
with the implication that 5-limit was just plain "JI".

exactly what should and should not be referred to as "JI"
is a very hot topic of debate around here, and in fact
each time it flares up it causes some list-members to leave.

-monz

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:

> It would not be surprising if, when you took your favorite 5-limit
> scale from Indian music theory and analyzed it in Scala, you found
> 7-limit implications.

To test this theory out, I took the scale which comes alphabetically
immediately after "indian.scl" in the archives, which is
"indian_12.scl", and fed it to Scala. It turns out to be loaded with
chords which get to within 225/224 of being just 7-limit otonal and
utonal quintads, tetrads, supermajor and subminor triads, etc. It
would hardly be surprising if these made their appearance in actual
music using this scale.

The scale looks like what I could call a 5-limit reduction or
projection of a marvel-tempered scale. In fact, the 5-limit projection
of Kraig Grady's 7-limit JI scale Centaur is a mode of this scale;
that means both Centaur and Indian_12 could be tempered via marvel
(225/224-planar tempering), and if they were, would end up being the
same thing.

Below I list what Scala has as Indian_12 and Centaur; one is 5-limit
and one is 7-limit, but look under the hood and there are very strong
similarities.

! INDIAN_12.scl
!
North Indian Gamut, modern Hindustani gamut out of 22 or more shrutis

12
!
16/15
9/8
6/5
5/4
4/3
45/32
3/2
8/5
27/16
9/5
15/8
2/1

! grady7.scl
!
Kraig Grady's 7-limit "Centaur" scale, 1987. See Xenharmonikon 16

12
!
21/20
9/8
7/6
5/4
4/3
7/5
3/2
14/9
5/3
7/4
15/8
2/1