Yahoo Tuning Groups Ultimate Backup tuning Higher primes, not Greek

Just some thoughts to stimulate more thoughts! I have for some time
been interested in and taken special notice of the "blues note"
corresponding to the F# in the following scale on C:

C Eb- F F# G Bb- C (where the minus sign indicates for the Eb the 7th
harmonic over an F and for the Bb the 7th over a C)

I have a somewhat more than sneaking suspicion that this F# is
actually the 11th harmonic of a C three octaves below the tonic. In
Afro-American PRACTICE (and not the "whitewashed" blues we often
hear their pale would-be imitators play), and also in Black
Gospel and other "bluesy" Afro-American musical traditions, I have
observed that the blues note just above the F is much closer to the F
than even the just 25:24 ratio chromatic semitone. The 11th harmonic
would be in a skinnier 33:32 ratio to the F, and has a bluesy bite to
it that sounds just right to my ear for what is actually going on in
good, well-tuned blues.

The 13th harmonic seems to appear in some Arabic and Persian
traditional scales and falls roughly in the middle of an Ab and an A
from a C-based perspective. It also has a certain melodic flavor and
characteristic bite that can become rather addictive once the ear
learns to accept it.

The 17th harmonic feels like it wants to be the true minor 9th of an
extended 7th chord using the 7th harmonic for the 7th. This would
produce an 8:10:12:14:17 sequence. I suspect that JI in fact
naturally seeks the simplest overall fit within a PATTERN of pitches,
rather than seeking simplicity by staying at lower primes all the
time. This would yield a diminished 7th chord by simply omitting the
root of the m9-extended seventh, yielding ratios of 10:12:14:17.

An acquaintance of mine who used to manufacture JI guitars with
interchangeable fretboards believes that the sudden popularity of the
minor mode during the romantic era after 12t-EQ became virtually
universal is owing to the minor 3rd of EQ being an extremely close
approximation of the 19th harmonic. It yields a stable minor triad
because the subtones it generates are in octave consonance with the
tonic as, of course, the fifth does.

All this implies to me that perhaps we should consider that human
beings with very musical, pitch-sensitive ears tend to construct
musical patterns for practical performance that are based on subtle,
intuitive perceptions of ideal relationships even when they fail to
reflect those relationships with total accuracy as they manifest in
practice.

If we accept this hypothesis, then we might consider that an
idealized, comprehensive lexicon of human musical expression mandates
an expansion of our thinking to 19-limit JI. Any feedback on this?

Many thanks in advance,

- Bob

🔗monz <joemonz@yahoo.com>

> From: <BobWendell@technet-inc.com>
> To: <tuning@yahoogroups.com>
> Sent: Wednesday, August 08, 2001 3:50 PM
> Subject: [tuning] Higher primes, not Greek
>
>
> Just some thoughts to stimulate more thoughts! I have for some time
> been interested in and taken special notice of the "blues note"
> corresponding to the F# in the following scale on C:
>
> C Eb- F F# G Bb- C (where the minus sign indicates for the Eb the 7th
> harmonic over an F and for the Bb the 7th over a C)
>
> I have a somewhat more than sneaking suspicion that this F# is
> actually the 11th harmonic of a C three octaves below the tonic. In
> Afro-American PRACTICE (and not the "whitewashed" blues we often
> hear their pale would-be imitators play), and also in Black
> Gospel and other "bluesy" Afro-American musical traditions, I have
> observed that the blues note just above the F is much closer to the F
> than even the just 25:24 ratio chromatic semitone. The 11th harmonic
> would be in a skinnier 33:32 ratio to the F, and has a bluesy bite to
> it that sounds just right to my ear for what is actually going on in
> good, well-tuned blues.

Hi Bob,

You'd be interested in reading my rational analysis of the vocals
in Robert Johnson's _Drunken Hearted Man_:
http://www.ixpres.com/interval/monzo/rjohnson/drunken.htm

In my analysis, the end of each of the first two lines of
the verse has these pitches (represented in my 72-EDO notation)

note Ab> G^ F#- D
Semitones 6.28 5.51 3.86 0.00
ratios 23/16 11/8 5/4 1/1

> If we accept this hypothesis, then we might consider that an
> idealized, comprehensive lexicon of human musical expression mandates
> an expansion of our thinking to 19-limit JI. Any feedback on this?

At the time I put together my book _JustMusic: A New Harmony_
http://www.ixpres.com/interval/monzo/book/book.htm

(1990-98) I was interested in a 19-limit JI system. I postulate
at one point in the book how the Euro-Western habit of building
chords in "3rds" might lead to a 13- or 19-limit conception of
JI harmony.

Since joining this list in early '98, my mind has been opened
to many other aspects of tuning which lie a bit outside of JI/RI,
and my interests have expanded accordingly.

love / peace / harmony ...

-monz
http://www.monz.org
"All roads lead to n^0"

_________________________________________________________
Do You Yahoo!?
Get your free @yahoo.com address at http://mail.yahoo.com

🔗jpehrson@rcn.com

--- In tuning@y..., BobWendell@t... wrote:

/tuning/topicId_26802.html#26802

Hello Bob!

Thank you so much for your interesting post. Do you know the music
of Ben Johnston?? He works a *lot* with higher-limit just intonation
in his music... It's quite exceptional, if it can really be
performed that way...

>
> The 17th harmonic feels like it wants to be the true minor 9th of
an extended 7th chord using the 7th harmonic for the 7th. This would
> produce an 8:10:12:14:17 sequence. I suspect that JI in fact
> naturally seeks the simplest overall fit within a PATTERN of
pitches, rather than seeking simplicity by staying at lower primes
all the time. This would yield a diminished 7th chord by simply
omitting the root of the m9-extended seventh, yielding ratios of
10:12:14:17.
>

This is a question for Paul Erlich.... Paul, does this derivation of
the diminished 7th chord make any sense??

> An acquaintance of mine who used to manufacture JI guitars with
> interchangeable fretboards believes that the sudden popularity of
the minor mode during the romantic era after 12t-EQ became virtually
> universal is owing to the minor 3rd of EQ being an extremely close
> approximation of the 19th harmonic. It yields a stable minor triad
> because the subtones it generates are in octave consonance with the
> tonic as, of course, the fifth does.
>

Isn't that rather a high partial for deriving a simple minor third??
Paul??

Not doubting, really... just confused...

____________ ____________ _________
Joseph Pehrson

🔗BobWendell@technet-inc.com

Jacky replied:
I make no claims about the audibility of higher primes, preferring to
just tune them up and make music and let my ear be my guide. I think
it is very important to not bog down in this issue of audibility, and
find out what it all means through active music making.

Bob answers:
I LOVE this, Jacky. Thank you! Practice must ALWAYS supercede theory.
Notice I did not say PRECEDE, but SUPERCEDE. Theory can lead to new
discoveries and so precede the practices that sprout forth from them,
but practice and the COMPOSER'S EAR are the final arbiters for me as
well.

Bob had also said:
If we accept this hypothesis, then we might consider that an
idealized, comprehensive lexicon of human musical expression
mandates an expansion of our thinking to 19-limit JI.

Jacky replied:
I like where you are going with this, and I would like to encourage
you to explore it further. Yes - 19 Limit JI can be very beautiful,
but so can many of the higher primes. I have found exploring in this
way to be very fruitful, and can tell you that there are many
treasures and wonders to be found.

Bob answers:
Sorry! Didn't mean to imply that we should never venture beyond 19-
limit JI. Rather, I was referring to a lexicon of harmonic resources
that would comprehend musical traditions of long standing, traditions
that did not require or at least involve electronic or other super-
precise technologies as an impetus for their development. I am
postulating that even with that restriction it might be necessary to
invoke 19-limit JI to explain the associated harmonic realities.

🔗BobWendell@technet-inc.com

Hi, Joe! Thanks once more for your input. I hope to follow up on your
suggestions soon. Time is a problem. I'm happily finding this group
so addictive, though, that it's already eating up more time than I
really have just to participate. I am unfortunately not in a position
to let go of a full-time job that has nothing to do with music, so
that restricts me enormously.

Gratefully,

Bob

----------------
> Joe Monz had replied:

> Hi Bob,
>
>
> You'd be interested in reading my rational analysis of the vocals
> in Robert Johnson's _Drunken Hearted Man_:
> http://www.ixpres.com/interval/monzo/rjohnson/drunken.htm
>
>
> In my analysis, the end of each of the first two lines of
> the verse has these pitches (represented in my 72-EDO notation)
>
> note Ab> G^ F#- D
> Semitones 6.28 5.51 3.86 0.00
> ratios 23/16 11/8 5/4 1/1
>
>
>
> > If we accept this hypothesis, then we might consider that an
> > idealized, comprehensive lexicon of human musical expression
mandates
> > an expansion of our thinking to 19-limit JI. Any feedback on this?
>
>
> At the time I put together my book _JustMusic: A New Harmony_
> http://www.ixpres.com/interval/monzo/book/book.htm
>
> (1990-98) I was interested in a 19-limit JI system. I postulate
> at one point in the book how the Euro-Western habit of building
> chords in "3rds" might lead to a 13- or 19-limit conception of
> JI harmony.
>
> Since joining this list in early '98, my mind has been opened
> to many other aspects of tuning which lie a bit outside of JI/RI,
> and my interests have expanded accordingly.
>
>
>
> love / peace / harmony ...
>
> -monz
> http://www.monz.org
> "All roads lead to n^0"
>
>
>
>
>
> _________________________________________________________
> Do You Yahoo!?
> Get your free @yahoo.com address at http://mail.yahoo.com

🔗BobWendell@technet-inc.com

Hi, Joseph. I'll try to address your question below -

Bob had said:
An acquaintance of mine who used to manufacture JI guitars with
interchangeable fretboards believes that the sudden popularity of
the minor mode during the romantic era after 12t-EQ became virtually
universal is owing to the minor 3rd of EQ being an extremely close
approximation of the 19th harmonic. It yields a stable minor triad
because the subtones it generates are in octave consonance with the
tonic as, of course, is true for the fifth also.

Joseph replied:
Isn't that rather a high partial for deriving a simple minor third??
Paul??
Not doubting, really... just confused...____________ ____________
_________
Joseph Pehrson

Bob answers (as best he can):
The point is that this 19:16 minor 3rd NATURALLY came up with the
advent of virtually universal acceptance of 12t-ET. It is already the
19th harmonic to such a close approximation that the difference is
totally negligible (1 or 2 cents? I forget and don't have the means
on hand to calculate it). Historically, at the same time composers
began to employ the minor mode MUCH more fequently than before. The
acquaintance I mentioned believes this is no mere coincidence.

I have also noticed many times that minor triads sound smooth on a
standard synth keyboard in ET using timbres that make the Major 3rds
sound totally gritty! Since the Perfect 5th is only 2 cents flat and
the minor 3rds are virtually a perfect 19:16 ratio, the difference
tones are in a consonant tonic and Perfect fifth relationship. The
6:5 minor third on C, by contrast, generates a difference tone on Ab
as it should, since it's the top a Major triad on Ab. This 16:20:24
triad is not as stable to my ear as the ET virtually perfect 16:19:24
triad for this very reason, I would conjecture.

🔗Paul Erlich <paul@stretch-music.com>

--- In tuning@y..., BobWendell@t... wrote:
>
> An acquaintance of mine who used to manufacture JI guitars with
> interchangeable fretboards

Name?

> believes that the sudden popularity of the
> minor mode during the romantic era after 12t-EQ became virtually
> universal is owing to the minor 3rd of EQ being an extremely close
> approximation of the 19th harmonic.

I believe this too, though I'd put the time much earlier, and perhaps
attribute the disappearance of the Picardy third to this.

> If we accept this hypothesis, then we might consider that an
> idealized, comprehensive lexicon of human musical expression
mandates
> an expansion of our thinking to 19-limit JI. Any feedback on this?

I wouldn't limit myself to 19-limit JI relationships. For example,
the chord C E G A D _requires_ temperament to maximize
consonance . . .

🔗Paul Erlich <paul@stretch-music.com>

--- In tuning@y..., jpehrson@r... wrote:
> --- In tuning@y..., BobWendell@t... wrote:
>
> /tuning/topicId_26802.html#26802
>
> Hello Bob!
>
> Thank you so much for your interesting post. Do you know the music
> of Ben Johnston?? He works a *lot* with higher-limit just
intonation
> in his music... It's quite exceptional, if it can really be
> performed that way...
>
> >
> > The 17th harmonic feels like it wants to be the true minor 9th of
> an extended 7th chord using the 7th harmonic for the 7th. This
would
> > produce an 8:10:12:14:17 sequence. I suspect that JI in fact
> > naturally seeks the simplest overall fit within a PATTERN of
> pitches, rather than seeking simplicity by staying at lower primes
> all the time. This would yield a diminished 7th chord by simply
> omitting the root of the m9-extended seventh, yielding ratios of
> 10:12:14:17.
> >
>
>
> This is a question for Paul Erlich.... Paul, does this derivation
of
> the diminished 7th chord make any sense??

I agree that 10:12:14:17 is sometimes the smoothest tuning for a
diminished seventh chord . . . on a harmonium yes; on an acoustic
guitar not always. As for _derivation_, I think the diminished chord
comes from diatonic tonal language, for the attempt to use tritones
to set up powerful resolutions, and not directly from an attempt to
use the 17th harmonic.
>
> > An acquaintance of mine who used to manufacture JI guitars with
> > interchangeable fretboards believes that the sudden popularity of
> the minor mode during the romantic era after 12t-EQ became
virtually
> > universal is owing to the minor 3rd of EQ being an extremely
close
> > approximation of the 19th harmonic. It yields a stable minor
triad
> > because the subtones it generates are in octave consonance with
the
> > tonic as, of course, the fifth does.
> >
>
> Isn't that rather a high partial for deriving a simple minor
third??
> Paul??

Joseph -- we had a rather extensive discussion about minor triads,
maybe a year ago . . . or maybe it was two . . . I put up some
listening examples and, one of the things we found was that Gerald
Eskelin, of _Lies My Music Teacher Told Me_, picked a minor triad
tuned very close to 16:19:24, as the one he thought was the regular
JI minor triad (1/6:1/5:1/4). I think we in the 12-tET ear are very
used to hearing a minor triad very near 16:19:24, and dislike
deviations from that because the implied root is octave-equivalent to
the fundamental (since 16 is a power of 2), hence giving it a sense
of stability and rootedness. By contrast, the JI minor triad is
10:12:15, and makes a lot of modern people uncomfortable at first,
since the impied root is the physically absent "minor sixth" of the
chord. Do you remember any of this discussion?

🔗Paul Erlich <paul@stretch-music.com>

🔗BobWendell@technet-inc.com

Paul Erlich replied:
Gerald Eskelin, of _Lies My Music Teacher Told Me_, picked a minor
triad tuned very close to 16:19:24, as the one he thought was the
regular JI minor triad (1/6:1/5:1/4). I think we in the 12-tET ear
are very used to hearing a minor triad very near 16:19:24, and
dislike deviations from that because the implied root is octave-
equivalent to the fundamental (since 16 is a power of 2), hence
giving it a sense of stability and rootedness. By contrast, the JI
minor triad is 10:12:15, and makes a lot of modern people
uncomfortable at first, since the impied root is the physically
absent "minor sixth" of the chord.

Bob's response:
Yes, Paul! Thanks again! Exactly my point, except that I would like
to stay open to the possibility that preference for 16:19:24 minor
triads and their virtually perfect approximations in some scales is
not merely a 12 EDO-conditioned prediliction of modern ears, but
quite possibly an INTRINSICALLY preferable and stable harmonic
structure since, as you point out, the root of the usual JI 10:12:15
chord is fighting a conflict from a different implicit root in the
subtonal structure, whereas the 16:19:24 structure has a subtonal
structure that reinforces the root of the chord rather than
conflicting with it.

🔗jpehrson@rcn.com

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:

/tuning/topicId_26802.html#26835

>
> Joseph -- we had a rather extensive discussion about minor triads,
> maybe a year ago . . . or maybe it was two . . . I put up some
> listening examples and, one of the things we found was that Gerald
> Eskelin, of _Lies My Music Teacher Told Me_, picked a minor triad
> tuned very close to 16:19:24, as the one he thought was the regular
> JI minor triad (1/6:1/5:1/4). I think we in the 12-tET ear are very
> used to hearing a minor triad very near 16:19:24, and dislike
> deviations from that because the implied root is octave-equivalent
to
> the fundamental (since 16 is a power of 2), hence giving it a sense
> of stability and rootedness. By contrast, the JI minor triad is
> 10:12:15, and makes a lot of modern people uncomfortable at first,
> since the impied root is the physically absent "minor sixth" of the
> chord. Do you remember any of this discussion?

Well... I do remember a huge discussion between you and Jerry about
the "high third..." That went on for *months!* But, I thought that
was concerned with a *major* third... not a *minor* one... (???)

___________ _________ ________
Joseph Pehrson

🔗BobWendell@technet-inc.com

Hi, Paul. Response to "Name?" question below: Tom Stone
He ended up manufacturing a fretless interchangeable fingerboard for
electric bass that was retrofitted on the musician's instrument using
a magnetc bed. A tough sell for obvious reasons, since it takes a lot
of trust to let someone make an aleration that radical to your
beloved axe. However, it is what was looking most commercially viable
(compared to meantone and other alternately-tuned fretboards for
regular Gibsons, classical guitars, etc.). The business ultimately
folded after a promising start. His fretless bass fingerboard had
some strong advocates in the jazz and pop world, some of whom
endorsed the product with enthusiasm, but still...... Oh, well. He
tried hard!

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> --- In tuning@y..., BobWendell@t... wrote:
> >
> > An acquaintance of mine who used to manufacture JI guitars with
> > interchangeable fretboards
>
> Name?
>
> > believes that the sudden popularity of the
> > minor mode during the romantic era after 12t-EQ became virtually
> > universal is owing to the minor 3rd of EQ being an extremely
close
> > approximation of the 19th harmonic.
>
> I believe this too, though I'd put the time much earlier, and
perhaps
> attribute the disappearance of the Picardy third to this.
>
> > If we accept this hypothesis, then we might consider that an
> > idealized, comprehensive lexicon of human musical expression
> mandates
> > an expansion of our thinking to 19-limit JI. Any feedback on this?
>
> I wouldn't limit myself to 19-limit JI relationships. For example,
> the chord C E G A D _requires_ temperament to maximize
> consonance . . .

🔗Paul Erlich <paul@stretch-music.com>

--- In tuning@y..., BobWendell@t... wrote:
> Paul Erlich replied:
> Gerald Eskelin, of _Lies My Music Teacher Told Me_, picked a minor
> triad tuned very close to 16:19:24, as the one he thought was the
> regular JI minor triad (1/6:1/5:1/4). I think we in the 12-tET ear
> are very used to hearing a minor triad very near 16:19:24, and
> dislike deviations from that because the implied root is octave-
> equivalent to the fundamental (since 16 is a power of 2), hence
> giving it a sense of stability and rootedness. By contrast, the JI
> minor triad is 10:12:15, and makes a lot of modern people
> uncomfortable at first, since the impied root is the physically
> absent "minor sixth" of the chord.
>
> Bob's response:
> Yes, Paul! Thanks again! Exactly my point, except that I would like
> to stay open to the possibility that preference for 16:19:24 minor
> triads and their virtually perfect approximations in some scales is
> not merely a 12 EDO-conditioned prediliction of modern ears, but
> quite possibly an INTRINSICALLY preferable and stable harmonic
> structure since, as you point out, the root of the usual JI
10:12:15
> chord is fighting a conflict from a different implicit root in the
> subtonal structure, whereas the 16:19:24 structure has a subtonal
> structure that reinforces the root of the chord rather than
> conflicting with it.

Agreed completely, but . . . for Renaissance and early Baroque music,
where tonality had not been invented yet, and cadences typically end
on a major triad, I would say that 1/6:1/5:1/4 (aka 10:12:15) _is_
the appropriate tuning for a minor triad. It has that extra modicum
of smoothness, allows dyads to be held constant from preceding and
succeeding major triads, is consistent with a melodic practice when
near-meantone intervals are the norm, and the root of the chord
doesn't really carry much structural relevance in the style (the
minor triads are probably in first inversion (1/5:1/4:1/3) more often
than root position anyway).

🔗Paul Erlich <paul@stretch-music.com>

🔗jpehrson@rcn.com

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:

/tuning/topicId_26802.html#26843

> --- In tuning@y..., jpehrson@r... wrote:
>
> >
> > Well... I do remember a huge discussion between you and Jerry
about
> > the "high third..." That went on for *months!* But, I thought
> that
> > was concerned with a *major* third... not a *minor* one... (???)
>
> A major _triad_, yes. But I turned the discussion toward minor
triads
> at one point because I thought it could help point out that Gerald
> may have convinced himself of various things that weren't really
> true. Basically, I feel that we demonstrated rather well,
especially
> through this experiment, that Gerald was a victim of "Lies I Told
> Myself".
>
> This should all be in the archives should anyone care to revisit
> it . . .

Hi Paul!

This is coming back to me now... and, yes, I *do* think it was about
a year and a half ago, for anybody doing the search. (I will have
been on the list two years this coming November...)

I remember ruminating on the idea of a 12-tET minor triad
resembling "higher-limit" harmonics...

It was rather a "sideline" to the big "high third" discussion....

_______ _______ _________
Joseph Pehrson

🔗jpehrson@rcn.com

--- In tuning@y..., BobWendell@t... wrote:

/tuning/topicId_26802.html#26819

> Hi, Joseph. I'll try to address your question below -
>
> Bob had said:
> An acquaintance of mine who used to manufacture JI guitars with
> interchangeable fretboards believes that the sudden popularity of
> the minor mode during the romantic era after 12t-EQ became
virtually
> universal is owing to the minor 3rd of EQ being an extremely close
> approximation of the 19th harmonic. It yields a stable minor triad
> because the subtones it generates are in octave consonance with the
> tonic as, of course, is true for the fifth also.
>
> Joseph replied:
> Isn't that rather a high partial for deriving a simple minor
third??
> Paul??
> Not doubting, really... just confused...____________ ____________
> _________
> Joseph Pehrson
>
> Bob answers (as best he can):
> The point is that this 19:16 minor 3rd NATURALLY came up with the
> advent of virtually universal acceptance of 12t-ET. It is already
the
> 19th harmonic to such a close approximation that the difference is
> totally negligible (1 or 2 cents? I forget and don't have the means
> on hand to calculate it). Historically, at the same time composers
> began to employ the minor mode MUCH more fequently than before. The
> acquaintance I mentioned believes this is no mere coincidence.
>
> I have also noticed many times that minor triads sound smooth on a
> standard synth keyboard in ET using timbres that make the Major
3rds
> sound totally gritty! Since the Perfect 5th is only 2 cents flat
and
> the minor 3rds are virtually a perfect 19:16 ratio, the difference
> tones are in a consonant tonic and Perfect fifth relationship. The
> 6:5 minor third on C, by contrast, generates a difference tone on
Ab
> as it should, since it's the top a Major triad on Ab. This 16:20:24
> triad is not as stable to my ear as the ET virtually perfect
16:19:24
> triad for this very reason, I would conjecture.

Thanks so much, Bob, for your elaboration of this.... Yes, now I
remember Paul Erlich discussing it some time ago... This is really
fascinating to see the relationship between the higher harmonics and
12-tET! Frankly, I forgot all about it... *somebody's* got to have
amnesia on this list, and I guess I'm the current candidate...

best,

_________ __________ _______
Joseph Pehrson

🔗jpehrson@rcn.com

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:

/tuning/topicId_26802.html#26833

> --- In tuning@y..., BobWendell@t... wrote:
> >
> > An acquaintance of mine who used to manufacture JI guitars with
> > interchangeable fretboards
>
> Name?
>
> > believes that the sudden popularity of the
> > minor mode during the romantic era after 12t-EQ became virtually
> > universal is owing to the minor 3rd of EQ being an extremely
close
> > approximation of the 19th harmonic.
>
> I believe this too, though I'd put the time much earlier, and
perhaps attribute the disappearance of the Picardy third to this.
>

What I'm not "getting" in this is... how are people actually
*hearing* the 19th partial... through timbral resonances??

____________ ________ _____
Joseph Pehrson

🔗jpehrson@rcn.com

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:

/tuning/topicId_26802.html#26842

> >
> Agreed completely, but . . . for Renaissance and early Baroque
music,
> where tonality had not been invented yet, and cadences typically
end
> on a major triad, I would say that 1/6:1/5:1/4 (aka 10:12:15) _is_
> the appropriate tuning for a minor triad. It has that extra modicum
> of smoothness, allows dyads to be held constant from preceding and
> succeeding major triads, is consistent with a melodic practice when
> near-meantone intervals are the norm, and the root of the chord
> doesn't really carry much structural relevance in the style (the
> minor triads are probably in first inversion (1/5:1/4:1/3) more
often than root position anyway).

Paul... is this the tuning of the minor triad in meantone??

_________ __________ _______
Joseph Pehrson

🔗BobWendell@technet-inc.com

What I'm not "getting" in this is... how are people actually
*hearing* the 19th partial... through timbral resonances??
____________ ________ _____Joseph Pehrson

Bob's answer:
I have never run across this association of using higher prime limits
in JI with hearing the corresponding overtone in the harmonic series.
I don't believe it is important that anyone hear the corresponding
harmonic in order to use a given prime in JI tunings. Dont' even
think it's necessary that the harmonic be physically present in the
overtone series of the timbre used.

The key point in the discussion of the 16:19:24 minor triad is the
subtones, the difference tones generated by each possible pair of
tones in the structure and the implicit fundamental or fundamentals
and their compatibility with each other and the chordal root.
16:19:24 has a single implicit fundamental (1)that is in octave
identity with the root. The 10:12:15 triad has an implicit
fundamental (1) that is in octave identity with a Major 3rd below the
root.

--- In tuning@y..., jpehrson@r... wrote:
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
>
> /tuning/topicId_26802.html#26833
>
>
> > --- In tuning@y..., BobWendell@t... wrote:
> > >
> > > An acquaintance of mine who used to manufacture JI guitars with
> > > interchangeable fretboards
> >
> > Name?
> >
> > > believes that the sudden popularity of the
> > > minor mode during the romantic era after 12t-EQ became
virtually
> > > universal is owing to the minor 3rd of EQ being an extremely
> close
> > > approximation of the 19th harmonic.
> >
> > I believe this too, though I'd put the time much earlier, and
> perhaps attribute the disappearance of the Picardy third to this.
> >
>
> What I'm not "getting" in this is... how are people actually
> *hearing* the 19th partial... through timbral resonances??
>
> ____________ ________ _____
> Joseph Pehrson

🔗BobWendell@technet-inc.com

Hi, Joe! LOVED your Robert Johnson page! Thanks tons! I'm a bit naive
concerning some of your analytical notation. However, I can grock the
gist of a lot of it and the midi file transcription you did was
SUPER!

It confirmed for me beyond what I would have imagined that the
delicious melodic/harmonic "bite" of authentic blues comes from the
use of higher primes, especially 11. I don't believe that just being
"out of tune" with more standard tunings would EVER generate the same
sense of pure "delectability" and harmonic deliciousness that these
pitches do.

I also liked that your minor 3rd analysis tends to favor a 7:6 ratio
as I postulated in my initial message at the beginning of this
thread. I might add that another possible source of the idea of the
"high" minor 3rd between major and minor might be the tendency in
blues to sing a minor 3rd over major chord stuctures at times,
especially when the melody anticipates a change from a chord on I to
a chord on IV. The famous "minor 7th/flat 3rd" chord in jazz (e.g., C
E G Bb- Eb-) ubiquitous in many jazz arrangements probably evolved
from this, although it's usually executed in 12 EDO and in more
"citified" bluesy contexts.

I know that some musicians, myself included at one ancient point,
believed this was an attempt to harmonically reproduce an alleged
melodic 3rd between major and minor in the blues. As you can see from
the previous paragraph's example, I have since come to believe that a
just tuning of this chord would use the low "subminor" third of a 7:6
ratio. I do not, however, completely eliminate the possiblity that
some singers might actually use a high minor 3rd or low Major 3rd as
they shift back and fourth between harmonic structures on I and IV.

- Bob

--- In tuning@y..., "monz" <joemonz@y...> wrote:
>
> > From: <BobWendell@t...>
> > To: <tuning@y...>
> > Sent: Wednesday, August 08, 2001 3:50 PM
> > Subject: [tuning] Higher primes, not Greek
> >
> >
> > Just some thoughts to stimulate more thoughts! I have for some
time
> > been interested in and taken special notice of the "blues note"
> > corresponding to the F# in the following scale on C:
> >
> > C Eb- F F# G Bb- C (where the minus sign indicates for the Eb the
7th
> > harmonic over an F and for the Bb the 7th over a C)
> >
> > I have a somewhat more than sneaking suspicion that this F# is
> > actually the 11th harmonic of a C three octaves below the tonic.
In
> > Afro-American PRACTICE (and not the "whitewashed" blues we often
> > hear their pale would-be imitators play), and also in Black
> > Gospel and other "bluesy" Afro-American musical traditions, I
have
> > observed that the blues note just above the F is much closer to
the F
> > than even the just 25:24 ratio chromatic semitone. The 11th
harmonic
> > would be in a skinnier 33:32 ratio to the F, and has a bluesy
bite to
> > it that sounds just right to my ear for what is actually going on
in
> > good, well-tuned blues.
>
>
>
> Hi Bob,
>
>
> You'd be interested in reading my rational analysis of the vocals
> in Robert Johnson's _Drunken Hearted Man_:
> http://www.ixpres.com/interval/monzo/rjohnson/drunken.htm
>
>
> In my analysis, the end of each of the first two lines of
> the verse has these pitches (represented in my 72-EDO notation)
>
> note Ab> G^ F#- D
> Semitones 6.28 5.51 3.86 0.00
> ratios 23/16 11/8 5/4 1/1
>
>
>
> > If we accept this hypothesis, then we might consider that an
> > idealized, comprehensive lexicon of human musical expression
mandates
> > an expansion of our thinking to 19-limit JI. Any feedback on this?
>
>
> At the time I put together my book _JustMusic: A New Harmony_
> http://www.ixpres.com/interval/monzo/book/book.htm
>
> (1990-98) I was interested in a 19-limit JI system. I postulate
> at one point in the book how the Euro-Western habit of building
> chords in "3rds" might lead to a 13- or 19-limit conception of
> JI harmony.
>
> Since joining this list in early '98, my mind has been opened
> to many other aspects of tuning which lie a bit outside of JI/RI,
> and my interests have expanded accordingly.
>
>
>
> love / peace / harmony ...
>
> -monz
> http://www.monz.org
> "All roads lead to n^0"
>
>
>
>
>
> _________________________________________________________
> Do You Yahoo!?
> Get your free @yahoo.com address at http://mail.yahoo.com

🔗Paul Erlich <paul@stretch-music.com>

--- In tuning@y..., jpehrson@r... wrote:
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
>
> /tuning/topicId_26802.html#26842
>
> > >
> > Agreed completely, but . . . for Renaissance and early Baroque
> music,
> > where tonality had not been invented yet, and cadences typically
> end
> > on a major triad, I would say that 1/6:1/5:1/4 (aka 10:12:15)
_is_
> > the appropriate tuning for a minor triad. It has that extra
modicum
> > of smoothness, allows dyads to be held constant from preceding
and
> > succeeding major triads, is consistent with a melodic practice
when
> > near-meantone intervals are the norm, and the root of the chord
> > doesn't really carry much structural relevance in the style (the
> > minor triads are probably in first inversion (1/5:1/4:1/3) more
> often than root position anyway).
>
> Paul... is this the tuning of the minor triad in meantone??

Very close . . . as you know, meantone deviates a little from 5-limit
JI, but not too much (not more than 6 cents, typically). On the other
hand, 16:19:24 is much closer to 12-tET than to meantone.

🔗jpehrson@rcn.com

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
/tuning/topicId_26802.html#26890

> --- In tuning@y..., jpehrson@r... wrote:
> >
> > What I'm not "getting" in this is... how are people actually
> > *hearing* the 19th partial... through timbral resonances??
>
> You don't hear the 19th partial of anything . . . but if you play a
> minor chord nice and high and loud, and it's tuned right, it'll
> correspond to the 16th, 19th, and 24th harmonics of a missing
> fundamental. You'll actually hear this missing fundamental, due to
> combinational tones, virtual pitch effects, and various
combinations
> of the two. And this fundamental will be exactly four octaves below
> the "root" of the minor chord. Mmmm . . . very stable. Try moving
the minor third around and you'll notice the decrease in stability,
even when you hit the usual 10:12:15 JI minor triad.

Got it, finally! Wow... that was a clear explanation...

_______ ________ ________
Joseph Pehrson

🔗BobWendell@technet-inc.com

Thank you, Paul! Your answer is clearer than mine was, even though
we're saying the same thing.

Sincerely,

Bob

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> --- In tuning@y..., jpehrson@r... wrote:
> >
> > What I'm not "getting" in this is... how are people actually
> > *hearing* the 19th partial... through timbral resonances??
>
> You don't hear the 19th partial of anything . . . but if you play a
> minor chord nice and high and loud, and it's tuned right, it'll
> correspond to the 16th, 19th, and 24th harmonics of a missing
> fundamental. You'll actually hear this missing fundamental, due to
> combinational tones, virtual pitch effects, and various
combinations
> of the two. And this fundamental will be exactly four octaves below
> the "root" of the minor chord. Mmmm . . . very stable. Try moving
the
> minor third around and you'll notice the decrease in stability,
even
> when you hit the usual 10:12:15 JI minor triad.

🔗Paul Erlich <paul@stretch-music.com>

🔗monz <joemonz@yahoo.com>

> From: <BobWendell@technet-inc.com>
> To: <tuning@yahoogroups.com>
> Sent: Friday, August 10, 2001 9:41 AM
> Subject: [tuning] Re: Higher primes, not Greek
>
>
> Hi, Joe! LOVED your Robert Johnson page! Thanks tons! I'm a bit naive
> concerning some of your analytical notation. However, I can grock the
> gist of a lot of it and the midi file transcription you did was
> SUPER!

Thanks, Bob. And as I wrote in the last post, I'll be going into
more detail about it at the El Paso conference, November 1-4.

> It confirmed for me beyond what I would have imagined that the
> delicious melodic/harmonic "bite" of authentic blues comes from the
> use of higher primes, especially 11. I don't believe that just being
> "out of tune" with more standard tunings would EVER generate the same
> sense of pure "delectability" and harmonic deliciousness that these
> pitches do.

My ears tell me that Johnson very deliberately sang these microtonal
pitches... in _Drunken Hearted Man_ they occur over and over again
in all the verses.

> I also liked that your minor 3rd analysis tends to favor a 7:6 ratio
> as I postulated in my initial message at the beginning of this
> thread. I might add that another possible source of the idea of the
> "high" minor 3rd between major and minor might be the tendency in
> blues to sing a minor 3rd over major chord stuctures at times,
> especially when the melody anticipates a change from a chord on I to
> a chord on IV. The famous "minor 7th/flat 3rd" chord in jazz (e.g., C
> E G Bb- Eb-) ubiquitous in many jazz arrangements probably evolved
> from this, although it's usually executed in 12 EDO and in more
> "citified" bluesy contexts.

Paul Erlich and I had a big debate about the rational implications
of precisely that type of chord, Paul saying that the "minor 3rd"
on top was implying 7:6, and me saying that it implied 19:16.
It resulted in my writing a piece (never really finished) based
on Jimi Hendrix's _Foxey Lady_:
http://www.ixpres.com/interval/monzo/hendrix/hendrix.htm

Drew Skyfyre has put the whole discussion up on his website
if you're interested:
http://members.nbci.com/drew_skyfyre/xe/Hendrix.html

>
> I know that some musicians, myself included at one ancient point,
> believed this was an attempt to harmonically reproduce an alleged
> melodic 3rd between major and minor in the blues. As you can see from
> the previous paragraph's example, I have since come to believe that a
> just tuning of this chord would use the low "subminor" third of a 7:6
> ratio. I do not, however, completely eliminate the possiblity that
> some singers might actually use a high minor 3rd or low Major 3rd as
> they shift back and fourth between harmonic structures on I and IV.

My conclusion in the debate with Paul was that he was right, that
on a 12-EDO guitar with a skilled performer bending the lower pitches
of the "sharp 9" chord, the top two pitches would make the "minor 3rd"
imply a 7:6 more strongly than any other ratio. However, my personal
preference for tuning this chord remains a 19:16 on top. You can hear
both in the last part of the excerpt of my piece. The 19:16 has a
bluesy, funky sound that I simply love.

love / peace / harmony ...

-monz
http://www.monz.org
"All roads lead to n^0"

_________________________________________________________
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