Re: Lumma, Eskelin and barbershop sevenths

Carl, I like the way you organized those scalse in your diatonic
search. As someone who experiments by "jamming with tuning tables",
this presentation gets immediately sent home for weekend play.
Thanks.

Eskelin, Keenan, re Fokkers naming conventions. I see the point
that B up to F should be termed a diminished fifth and that F
up to B should be termed an augmented fourth if ones terms are
going to match the traditional diatonic scale. However, for
F over B to be a 7/5 and B over F a 10/7, implies the belief
that the fourth should always be flattened as part of a
cadence. Perhaps that is what singers do, although I'd like
to see some numerical data to back that. Without that assumption
I would suspect that the diminished fifth is 64/45 and the
augmented fourth 45/32, which are very close to the exact
opposite view!

F 21/16 4/3
----- = 1.4 ----- = 1.422 diminished fifth
B 15/8 15/8

B 15/8 15/8
----- = 1.43 ---- = 1.41 augmented fourth
F 21/16 4/3

On the other hand, I could see leaving the fourth at 4/3
and having the leading tone sharp! [Not to get the high
third back into discussion...]

Since I'm not a big believer in nomenclature like "augmented
fourth", I won't read too much into Fokkers use of the term.
It is probably as consistent in his system as the term is
in the traditional system.

However, if I WERE to give a name to an interval, I would
call the 7:6 an "augmented second", since in a seven-limit
temperment it is aliased on the 'true' 75/64 augmented second
(from harmonic minor) and it is also my favorite 7#9 (Jimi
Hendrix) chord 12:15:18:21:28.

We've had the discussion here a few times (a big thread with
John Link prior to Gerald coming to the list) regarding tuning
of 'dominant seventh' chords. I can agree that functionally,
the reltionships are tenuous enough and, stylistically, because
they like it, barbershoppers will treat them as non-functional
'dom seventh' chords and tune them 4:5:6:7, as would someone
using them as consonances.

Bob Valentine

I tried like hell to stay out of this one, but my addiction to the List won
out.

Bob Valentine said:

> Eskelin, Keenan, re Fokkers naming conventions. I see the point
> that B up to F should be termed a diminished fifth and that F
> up to B should be termed an augmented fourth if ones terms are
> going to match the traditional diatonic scale.

Thanks. (I guess.)

> However, for
> F over B to be a 7/5 and B over F a 10/7, implies the belief
> that the fourth should always be flattened as part of a
> cadence. Perhaps that is what singers do, although I'd like
> to see some numerical data to back that. Without that assumption
> I would suspect that the diminished fifth is 64/45 and the
> augmented fourth 45/32, which are very close to the exact
> opposite view!
>
> F 21/16 4/3
> ----- = 1.4 ----- = 1.422 diminished fifth
> B 15/8 15/8
>
> B 15/8 15/8
> ----- = 1.43 ---- = 1.41 augmented fourth
> F 21/16 4/3

Why would you opt for these high numbers when it is so clear that 5:7 and
7:10 are so "available" to the human ear?
>
> On the other hand, I could see leaving the fourth at 4/3
> and having the leading tone sharp! [Not to get the high
> third back into discussion...]

Whether or not there really is a "high third," there certainly is a "low
seventh." Why would you consider a 4/3 seventh in a dominant 7th chord. The
whole chord generates directly from the dominant pitch as 4:7, not directly
from the tonic pitch. The 4/3 fourth belongs to the subdominant chord and
presents a very different sounding scale step 4.
>
> Since I'm not a big believer in nomenclature like "augmented
> fourth", I won't read too much into Fokkers use of the term.
> It is probably as consistent in his system as the term is
> in the traditional system.

Very likely. So what's in a name? "Standard" language is only of value to
those who agree to use words to mean roughly the same things. I think Fokker
(based on his terms) had little interest in traditional functional harmony.
>
> However, if I WERE to give a name to an interval, I would
> call the 7:6 an "augmented second",

Since 7:6 is very near 8:7, there is some rationale for considering that.
However,...

> since in a seven-limit
> temperment it is aliased on the 'true' 75/64 augmented second
> (from harmonic minor)

the "augmented second" of so-called "harmonic minor" is likely a
non-interval. The flat 6 relates melodically to (and tunes to) 5 and the
"raised" 7 relates to (and tunes to) the tonic pitch. That is why composers
frequently repaired that "pot hole" in the melodic road by raising step 6
when the leading tone was needed (as in the V7 chord) and lowering the
leading tone when flat-6 was needed to preserve the minor flavor (as in the
iv and i chords. (By the way, ascending and descending passages had nothing
to do with it.)

It seems to me that music teachers invented the term "harmonic minor" to
represent that this so-called "scale" reflected _harmonic_ practice rather
than melodic practice. BTW, it was this "three minor scales" nonsense that
first inspired my book "Lies My Music Teacher Told Me."

> and it is also my favorite 7#9 (Jimi
> Hendrix) chord 12:15:18:21:28.

Is that similar to the "Blood, Sweet and Tears" chord in "Spinning Wheel"?
I've come to think that the traditional "guitar chord" representation of
that chord has little to do with a raised ninth--rather contains both a
major and minor third as well as a minor seventh (C-E-Bb-Eb). That view
would support the notion that the upper third (b3) is a "blue" third
(roughly a 6:7 interval to tonic) that tunes to the blue seventh (4:7 to
tonic) as a perfect 3:4 fourth.

Of course, in tempered performance it wouldn't make any difference, thus the
common representation of that "blue third" as "#9."
>
> We've had the discussion here a few times (a big thread with
> John Link prior to Gerald coming to the list)

Sorry I missed it. (I think. ;-)

> regarding tuning
> of 'dominant seventh' chords. I can agree that functionally,
> the reltionships are tenuous

(?)

> enough and, stylistically, because
> they like it, barbershoppers will treat them as non-functional
> 'dom seventh' chords and tune them 4:5:6:7, as would someone
> using them as consonances.

Still getting this backwards, I think. While barbershoppers occasionally
sing non-functional "dominant sevenths" (for example, an augmented sixth
chord on flat 6), the quartets I've sung with tended to sing a functional
dominant seventh in a way that caused it to "lock;" and to me, locking is
equivalent to seeking mother nature's "natural" (sorry, Paul) tuning.

Okay. Looks like I'm "in." Let me have it (your rebuttal, that is), Bob.

Jerry

> [Bob Valentine, TD 525.22]
> However, if I WERE to give a name to an interval, I would
> call the 7:6 an "augmented second", since in a seven-limit
> temperment it is aliased on the 'true' 75/64 augmented second
> (from harmonic minor) and it is also my favorite 7#9 (Jimi
> Hendrix) chord 12:15:18:21:28.

> [Jerry Eskelin, TD 526.17]
> Is that similar to the "Blood, Sweet and Tears" chord in
> "Spinning Wheel"? I've come to think that the traditional
> "guitar chord" representation of that chord has little to do
> with a raised ninth--rather contains both a major and minor
> third as well as a minor seventh (C-E-Bb-Eb). That view
> would support the notion that the upper third (b3) is a "blue"
> third (roughly a 6:7 interval to tonic) that tunes to the blue
> seventh (4:7 to tonic) as a perfect 3:4 fourth.
>
> Of course, in tempered performance it wouldn't make any
> difference, thus the common representation of that "blue third"
> as "#9."

Jerry, I think you missed a loooooooong discussion Paul Erlich
and I (and a few others here and there) had almost two years
ago about the 'Hendrix Chord'. You might be interested
enough to wade thru the whole thing; thankfully, Drew Skyfyre
has put it online at
http://members.xoom.com/drew_skyfyre/xe/Hendrix.html

I got so into it that I began writing a piece around it;
my webpage on that is at
http://www.ixpres.com/interval/monzo/hendrix/hendrix.htm

but the coolest part of my piece, so far, is the last
minute or so of the MIDI link on my 'List of Works' page
http://www.ixpres.com/interval/monzo/hendrix/hendrix.mid
- the piece is still 'under construction'.

Paul also feels that the 6:7 'sharp 9th' is the most appropriate
for the 'Hendrix chord'; much of his argument was based
on the mechanics of guitar-playing, and I had to agree with
him on that, but 16:19 is still my favorite 'sharp 9th' in
this chord, giving 16:20:24:28:38 for the whole pentad.

-monz

Joseph L. Monzo Philadelphia monz@juno.com
http://www.ixpres.com/interval/monzo/homepage.html
|"...I had broken thru the lattice barrier..."|
| - Erv Wilson |
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Robert Valentine wrote,

>> On the other hand, I could see leaving the fourth at 4/3
>> and having the leading tone sharp! [Not to get the high
>> third back into discussion...]

Gerald Eskelin wrote,

>Whether or not there really is a "high third," there certainly is a "low
>seventh." Why would you consider a 4/3 seventh in a dominant 7th chord. The
>whole chord generates directly from the dominant pitch as 4:7, not directly
>from the tonic pitch. The 4/3 fourth belongs to the subdominant chord and
>presents a very different sounding scale step 4.

First of all, check out Mark Nowitzky's web page,
http://nowitzky.hypermart.net/justint/dom7.htm. Secondly, Mathieu explains
this in terms of the dominant chord being a dissonant structure which
"collapses" to the tonic on the lattice. The V triad is on one side, the IV
note (the seventh) is on the other, and they meet in the middle, resolving
to the tonic. Another very powerful dominant-type chord, the Carole King
chord (IV triad over V bass) can be seen in this way too, and is also not
very amenable to interpreation as a single set of simple ratios.

My own feeling is that the tritone is so unique in the diatonic scale, and
resolves in such a convincing, poweful manner, that any diatonic-conditioned
ears will "get the idea" regardless of the diminished fifth being 5:7, 7:10,
or anywhere in-between (45:32 and 64:45 are fine too, though you could never
tune them exactly by ear without tuning a few intermediary notes). Clearly
in its first 300 years of use by Western composers, the diminished fifth and
augmented fourth were reversed with respect to what Jerry prefers. When I
tuned my piano (by ear) to meantone, the thing that sounded worst at first
were the dominant seventh chords, the minor triads (no longer approximating
16:19:24) also being quite bothersome. After a while, I got used to both,
and then hearing 12-tET music really bothered me. It's remarkable how
pliable to conditioning our ears are, and must be experienced to be
believed.

>Very likely. So what's in a name? "Standard" language is only of value to
>those who agree to use words to mean roughly the same things. I think
Fokker
>(based on his terms) had little interest in traditional functional harmony.

Again, quite the contrary. As far as a fixed, non-dynamic tuning is
concerned, Fokker's terms are about the best you can do.

>the "augmented second" of so-called "harmonic minor" is likely a
>non-interval. The flat 6 relates melodically to (and tunes to) 5 and the
>"raised" 7 relates to (and tunes to) the tonic pitch. That is why composers
>frequently repaired that "pot hole" in the melodic road by raising step 6
>when the leading tone was needed (as in the V7 chord) and lowering the
>leading tone when flat-6 was needed to preserve the minor flavor (as in the
>iv and i chords. (By the way, ascending and descending passages had nothing
>to do with it.)

>It seems to me that music teachers invented the term "harmonic minor" to
>represent that this so-called "scale" reflected _harmonic_ practice rather
>than melodic practice. BTW, it was this "three minor scales" nonsense that
>first inspired my book "Lies My Music Teacher Told Me."

You'll find that this augmented second is one of the most important melodic
intervals in Eastern European and much Middle Eastern music -- try Klezmer
for a start.

>> and it is also my favorite 7#9 (Jimi
>> Hendrix) chord 12:15:18:21:28.

>Is that similar to the "Blood, Sweet and Tears" chord in "Spinning Wheel"?

At which point in the song?

>I've come to think that the traditional "guitar chord" representation of
>that chord has little to do with a raised ninth--rather contains both a
>major and minor third as well as a minor seventh (C-E-Bb-Eb). That view
>would support the notion that the upper third (b3) is a "blue" third
>(roughly a 6:7 interval to tonic) that tunes to the blue seventh (4:7 to
>tonic) as a perfect 3:4 fourth.

That's how I prefer to tune that chord when it's the tonic, as I discussed
here before in response to Joe Monzo's 8:10:12:14:19 interpretation.

> Robert Valentine wrote,
>
>>> On the other hand, I could see leaving the fourth at 4/3
>>> and having the leading tone sharp! [Not to get the high
>>> third back into discussion...]
>
> Gerald Eskelin wrote,
>
>>Whether or not there really is a "high third," there certainly is a "low
>>seventh." Why would you consider a 4/3 seventh in a dominant 7th chord. The
>>whole chord generates directly from the dominant pitch as 4:7, not directly
>>from the tonic pitch. The 4/3 fourth belongs to the subdominant chord and
>>presents a very different sounding scale step 4.

Paul Erlich wrote:

> First of all, check out Mark Nowitzky's web page,
> http://nowitzky.hypermart.net/justint/dom7.htm.

Been there, Paul. Interesting. Mark's search for the perfect V7 is
reminiscent of my search for the mysterious third.

> Secondly, Mathieu explains
> this in terms of the dominant chord being a dissonant structure which
> "collapses" to the tonic on the lattice. The V triad is on one side, the IV
> note (the seventh) is on the other, and they meet in the middle, resolving
> to the tonic.

This ivory tower talk makes no acoustic sense to me. Tell me something I can
touch, smell, see or hear. To me, a well-tuned dominant seventh chord
doesn't "collapse." It just tugs like hell toward its resolution. The more
the chord locks, the more it tugs toward its specific target chord.

> Another very powerful dominant-type chord, the Carole King
> chord (IV triad over V bass) can be seen in this way too, and is also not
> very amenable to interpreation as a single set of simple ratios.

I agree. This so-called dominant 11th chord appears to be a polychord,
mixing the important elements of both dominant and subdominant harmonies.
The difference, of course, is the absence of the powerful tritone--the
feature that makes this cadence sound so "cool."
>
> My own feeling is that the tritone is so unique in the diatonic scale, and
> resolves in such a convincing, poweful manner, that any diatonic-conditioned
> ears will "get the idea" regardless of the diminished fifth being 5:7, 7:10,
> or anywhere in-between (45:32 and 64:45 are fine too, though you could never
> tune them exactly by ear without tuning a few intermediary notes).

I won't argue with that. However, it is not very difficult to lock in the
5:7 and 7:10 "tritones" so that their acoustic context is clear. Granted, it
is easier when other pitches are included, but then one is likely tuning
each tritone member to those other, more consonant, pitches.

Also, note that the keyboard's tritone is ambiguous until a context is
provided. The well tuned "tritone" is not.

> Clearly
> in its first 300 years of use by Western composers, the diminished fifth and
> augmented fourth were reversed with respect to what Jerry prefers. When I
> tuned my piano (by ear) to meantone, the thing that sounded worst at first
> were the dominant seventh chords, the minor triads (no longer approximating
> 16:19:24) also being quite bothersome. After a while, I got used to both,
> and then hearing 12-tET music really bothered me. It's remarkable how
> pliable to conditioning our ears are, and must be experienced to be
> believed.

I have no difficulty believing that. The countless numbers of choirs singing
12-tET tuning is testimony enough. My own missionary zeal is to awaken the
choral community to the thrills of singing acoustically tuned music. I
really found a time-removed soul mate in Herr Helmholtz when I read his
similar feelings on the matter. In turn, it is gratifying to get feedback
from my own readers who relate their similar kinship to this experience.

>>Very likely. So what's in a name? "Standard" language is only of value to
>>those who agree to use words to mean roughly the same things. I think
>>Fokker (based on his terms) had little interest in traditional functional
>>harmony.
>
> Again, quite the contrary. As far as a fixed, non-dynamic tuning is
> concerned, Fokker's terms are about the best you can do.

Probably so. The key word here is "non-dynamic," however. It just seems a
shame to introduce terminology that inhibits practical musical insight in
musicians who are encumbered with an inflexible instrument.
>
>>the "augmented second" of so-called "harmonic minor" is likely a
>>non-interval. The flat 6 relates melodically to (and tunes to) 5 and the
>>"raised" 7 relates to (and tunes to) the tonic pitch. That is why composers
>>frequently repaired that "pot hole" in the melodic road by raising step 6
>>when the leading tone was needed (as in the V7 chord) and lowering the
>>leading tone when flat-6 was needed to preserve the minor flavor (as in the
>>iv and i chords. (By the way, ascending and descending passages had nothing
>>to do with it.)
>
>>It seems to me that music teachers invented the term "harmonic minor" to
>>represent that this so-called "scale" reflected _harmonic_ practice rather
>>than melodic practice. BTW, it was this "three minor scales" nonsense that
>>first inspired my book "Lies My Music Teacher Told Me."
>
> You'll find that this augmented second is one of the most important melodic
> intervals in Eastern European and much Middle Eastern music -- try Klezmer
> for a start.

Of course it is. That feature is one of the most distinctive in the music of
those regions. My discussion, however, had to do with Western common
practice music and was simply offered to demonstrate why composers often
camouflaged this "problem" by raising and/or lowering these pitches
appropriately in different harmonic contexts. The keyboard has, of course,
neutralized the acoustic "non relation" of the flat 6 and leading tone and
it now sounds like any other "augmented second."
>
>>> and it is also my favorite 7#9 (Jimi
>>> Hendrix) chord 12:15:18:21:28.
>
>>Is that similar to the "Blood, Sweet and Tears" chord in "Spinning Wheel"?
>
> At which point in the song?

In the intro and instrumental breaks (I believe). The brass repeats the
chord thusly: da-da-da-da-dut, da-da-da-dut, dut! (how's that for rhythmic
neumes? :-)

When I testified in the John Fogerty v. Fantasy Records case about twenty
years ago, John told me about his "secret chord" that he uses in his
mono-chord swamp blues songs. It contains both a major third and a higher
minor third (and occasionally a "blue" flat 7). I think that's the one we're
talking about. Right? He didn't say so, but I would imagine he would tune
his strings to accommodate that configuration, since the chord doesn't
change throughout the song.
>
>>I've come to think that the traditional "guitar chord" representation of
>>that chord has little to do with a raised ninth--rather contains both a
>>major and minor third as well as a minor seventh (C-E-Bb-Eb). That view
>>would support the notion that the upper third (b3) is a "blue" third
>>(roughly a 6:7 interval to tonic) that tunes to the blue seventh (4:7 to
>>tonic) as a perfect 3:4 fourth.
>
> That's how I prefer to tune that chord when it's the tonic, as I discussed
> here before in response to Joe Monzo's 8:10:12:14:19 interpretation.

Yes! Very tasty stuff!

Jerry