10:12:14:17 and brass instruments

> From: "Paul Erlich" <paul@stretch-music.com>
>--- In tuning@y..., "monz" <joemonz@y...> wrote:
>>
>>The only musical genre where this 10:12:14:17 "harmonic diminished 7th" >>is common is barbershop.
>>
>Perhaps brass sections gravitate toward this tuning, in middle-to-
>high-register close voicings?

10, 12 and (approximation of) 17 will use the 5-limit fingerings.
14 will probably use the 5-limit fingering too. Brass players are told to avoid 7-limit fingerings. Except maybe for Louis Armstrong, who loved to have play high A's with two different fingerings (2 and 1-2), a sixth tone apart. Melodically. One right after the other.

Let's suppose open sounds are harmonics,
fingering 2 lowers pitch by 16/15,
fingering 1 lowers pitch by 9/8, and
fingering 1-2 lowers pich by 32/27.

9/8 * 16/15 = 6/5 != 32/27, but this is a tube, not a string.

10 E- fingering is open
12 G fingering is open
14 7Bb fingering is 1 (probably not opened)
17 C# fingering is probably 1-2 or 2 (pitch would be the same)

So, using 5-limit fingerings and without lip correction,
if the C# is fingering 1-2 the intonation would be
5/4
3/2
(2/1) / (9/8) = 16/9
(5/2) / (32/27) = 135/64

5/4 3/2 16/9 135/64
or
1/1 6/5 64/45 27/16
720:864:1024:1215 ----> horrible!

With the 7-limit fingering, it would be
5/4 3/2 7/4 135/64
or
1/1 6/5 7/5 27/16
80:96:112:135 -----> not really better :(

With a 3-limit fingering for the E (10 in 10:12:14:17)
81/64 3/2 16/9 135/64
1/1 32/27 1024/729 135/81
729:864:1024:1215 -----> worse :(

In this context, all regular approximations of 10:12:14:17 are dissonant.
Which explains why musicians play this jazz chord in quasi-12-tET.

-Kami
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--- In tuning@y..., "Kami ROUSSEAU" <kamikulture@h...> wrote:
> > From: "Paul Erlich" <paul@s...>
> >--- In tuning@y..., "monz" <joemonz@y...> wrote:
> >>
> >>The only musical genre where this 10:12:14:17 "harmonic
diminished 7th"
> >>is common is barbershop.
> >>
> >Perhaps brass sections gravitate toward this tuning, in middle-to-
> >high-register close voicings?
>
> 10, 12 and (approximation of) 17 will use the 5-limit fingerings.

Hi Kami . . . haven't heard from you in a long time! Anyhow, I don't
think the issue of fingerings is too relevant, because a valved-brass
ensemble will make fine-tuning adjustments using their _lips_ and not
their fingers, and any kind of JI in performance is a result of the
combination of ears and lips . . . never fingers.

Paul Erlich schrieb:
> , I don't
> think the issue of fingerings is too relevant, because a valved-brass
> ensemble will make fine-tuning adjustments using their _lips_ and not
> their fingers, and any kind of JI in performance is a result of the
> combination of ears and lips . . . never fingers.

No, Paul, the fingering does matter. There is no way (short of
unhinging all resonance by half-valving) to lip down more than half
(by whatever undetermined definition) the distance towards the next
harmonic. And with those chords typically being a bit higher up,
this would be half the distance towards on of those unknown,
*unusable* and *out of tune* higher prime harmonics. No way a
trumpet will even risk that!

To make things seem even worse: the trumpet fingering has a tendency
towards 3-limit. Typically the 2nd to 6th harmonics (plus octaves
thereof) are used, but #9 seems to be employed occasionally, whereas
#5 is another one of those *out of tune* notes. (Never have I heard
mention of specific keys where it should be avoided - but it is
avoided mostly over Bb.)

Klaus

> ----- Original Message -----
> From: Kami ROUSSEAU <kamikulture@hotmail.com>
> To: <tuning@yahoogroups.com>
> Sent: Thursday, June 07, 2001 2:10 PM
> Subject: [tuning] 10:12:14:17 and brass instruments
>

> 10, 12 and (approximation of) 17 will use the 5-limit fingerings.
> 14 will probably use the 5-limit fingering too. Brass players are told to
> avoid 7-limit fingerings. Except maybe for Louis Armstrong, who loved to
> have play high A's with two different fingerings (2 and 1-2), a sixth tone
> apart. Melodically. One right after the other.
>
> Let's suppose open sounds are harmonics,
> fingering 2 lowers pitch by 16/15,
> fingering 1 lowers pitch by 9/8, and
> fingering 1-2 lowers pich by 32/27.
>
> 9/8 * 16/15 = 6/5 != 32/27, but this is a tube, not a string.
>
> 10 E- fingering is open
> 12 G fingering is open
> 14 7Bb fingering is 1 (probably not opened)
> 17 C# fingering is probably 1-2 or 2 (pitch would be the same)

Kami, this is fascinating! Where did you get this information
about "5-limit fingering", etc.? Are brass instruments designed
at the factory to play 12-EDO or some other tuning? I never
questioned any of this, always assuming 12-EDO to be standard.

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

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--- In tuning@y..., klaus schmirler <KSchmir@z...> wrote:
> Paul Erlich schrieb:
> > , I don't
> > think the issue of fingerings is too relevant, because a valved-
brass
> > ensemble will make fine-tuning adjustments using their _lips_ and
not
> > their fingers, and any kind of JI in performance is a result of
the
> > combination of ears and lips . . . never fingers.
>
> No, Paul, the fingering does matter. There is no way (short of
> unhinging all resonance by half-valving) to lip down more than half
> (by whatever undetermined definition) the distance towards the next
> harmonic.

But Klaus, did you read the message? What retuning amounts would be
relevant in the discussion with Kami? Much smaller ones! It's unfair
of you to take this statement out of context. Of course fingering
matters . . . but the complexity of the chords Kami was reporting was
far in excess of what could be justified given the degree of
retunability by lipping.

> And with those chords typically being a bit higher up,
> this would be half the distance towards on of those unknown,
> *unusable* and *out of tune* higher prime harmonics. No way a
> trumpet will even risk that!

I think you may be misunderstanding something. Can you be more
specific and/or quantitative here?
>
> To make things seem even worse: the trumpet fingering has a tendency
> towards 3-limit. Typically the 2nd to 6th harmonics (plus octaves
> thereof) are used, but #9 seems to be employed occasionally, whereas
> #5 is another one of those *out of tune* notes.

Well that makes sense in a 12-tET world. I don't see how this is
relevant to my point to Kami, though.

Paul Erlich schrieb:
>
> --- In tuning@y..., klaus schmirler <KSchmir@z...> wrote:
> > Paul Erlich schrieb:
> > > , I don't
> > > think the issue of fingerings is too relevant, because a valved-
> brass
> > > ensemble will make fine-tuning adjustments using their _lips_ and
> not
> > > their fingers, and any kind of JI in performance is a result of
> the
> > > combination of ears and lips . . . never fingers.
> >
> > No, Paul, the fingering does matter. There is no way (short of
> > unhinging all resonance by half-valving) to lip down more than half
> > (by whatever undetermined definition) the distance towards the next
> > harmonic.
>
> But Klaus, did you read the message? What retuning amounts would be
> relevant in the discussion with Kami? Much smaller ones! It's unfair
> of you to take this statement out of context. Of course fingering
> matters . . . but the complexity of the chords Kami was reporting was
> far in excess of what could be justified given the degree of
> retunability by lipping.

True. I could lip down almost 80 cents from the sixth harmonic.
Going farther would need embouchure adjustments and does not feel
right. Could be practised, though. And it would be enough to adjust
a fingered 16/9 to a sounding 7/4.

>
> > And with those chords typically being a bit higher up,
> > this would be half the distance towards on of those unknown,
> > *unusable* and *out of tune* higher prime harmonics. No way a
> > trumpet will even risk that!
>
> I think you may be misunderstanding something. Can you be more
> specific and/or quantitative here?

The 7th harmonic would be right on target. However, trumpet players
avoid this, and lipping down from #8 would land them there (after
the tone broke: not nice). I expect more success if you
notate/finger a 6th instead of a minor 7th. But then, why should a
trumpet player squeeze up a note that is already 3-limit consonant
with that 10 underneath?

> >
> > To make things seem even worse: the trumpet fingering has a tendency
> > towards 3-limit. Typically the 2nd to 6th harmonics (plus octaves
> > thereof) are used, but #9 seems to be employed occasionally, whereas
> > #5 is another one of those *out of tune* notes.
>
> Well that makes sense in a 12-tET world. I don't see how this is
> relevant to my point to Kami, though.

O.K., this might actually not be specific for trumpet players. But
as Kami insinuated in another post, they learn their fingerings in
actual 3 limit (=in the lower register) and stick with it.

As Kami shows :o() (saying: gape!), anything seems to be possible if
you use all the harmonics and use the tuning slide(s) a lot. Voice
your chords with a good knowledge of the physics of the instrument
(and throw in a couple of C- and D-trumpets), and they seem to be as
flexible as trombones or strings. If you first brainwash the trumpet
players!

klaus

Klaus

--- In tuning@y..., klaus schmirler <KSchmir@z...> wrote:

> > > And with those chords typically being a bit higher up,
> > > this would be half the distance towards on of those unknown,
> > > *unusable* and *out of tune* higher prime harmonics. No way a
> > > trumpet will even risk that!
> >
> > I think you may be misunderstanding something. Can you be more
> > specific and/or quantitative here?
>
> The 7th harmonic would be right on target.

Klaus, it's the intervals formed against the other members of the
ensemble, not the absolute pitches, that matter in this context.

> But then, why should a
> trumpet player squeeze up a note that is already 3-limit consonant
> with that 10 underneath?

Not following you. What note is that?

From: "Paul Erlich" <paul@stretch-music.com>
>But Klaus, did you read the message? What retuning amounts would be
>relevant in the discussion with Kami? Much smaller ones! It's unfair
>of you to take this statement out of context. Of course fingering
>matters . . . but the complexity of the chords Kami was reporting was
>far in excess of what could be justified given the degree of
>retunability by lipping.

That is precisely why I first said:

>So, using 5-limit fingerings and without lip correction,
>if the C# is fingering 1-2 the intonation would be ...

IMO, most of the time, the diminished chord has its origin in equal temperament (multiples of 4) and the 6th chord is a meantone phenomena.
Sometimes, a diminished chord is 10:12:14:17 and a 6th chord is 14:18:21:24 or (insert your favorite harmonic serie fragment).

Asking a brass player to retune many notes by lipping would be like asking a guitar player to play Just Intonation on a 12-EDO guitar. Technically, it is possible to bend the notes, but it requires a lot, maybe too much, concentration.

Now, it the real world, many notes are lipped to 5-limit. Brass quintets do play in 5-limit, and, it all but the simplest tonalities, that requires some lipping.

Does dixieland music contain 7-limit intervals? Many the original music, but not the "commercial" music. Commercial meaning anything recorded during or after the big band era. When music became more complex harmonically, microtones were demoted to the role of occasional passing tones.

-Kami
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--- In tuning@y..., "Kami ROUSSEAU" <kamikulture@h...> wrote:

> Asking a brass player to retune many notes by lipping would be like
asking a
> guitar player to play Just Intonation on a 12-EDO guitar.

It happens all the time. An electric guitar player, using distortion,
starts on a perfect fourth, and then bends the lower note up,
creating a minor third. Is it a 12-tET minor third? No, the
distortion would make that rather painful . . . instead a just minor
third is the usual result. Do they know it? Usually not.

> Technically, it is
> possible to bend the notes, but it requires a lot, maybe too much,
> concentration.

I hear fine brass ensembles playing near-JI chords, regardless of
what key they're in. Lipping is clearly involved, no?
>
> Now, it the real world, many notes are lipped to 5-limit. Brass
quintets do
> play in 5-limit, and, it all but the simplest tonalities, that
requires some
> lipping.

Well that's what I'm saying!

I don't think it's a stretch to think 10:12:14:17 will similarly be a
goal, at least occasionally.
>
> Does dixieland music contain 7-limit intervals? Many the original
music, but
> not the "commercial" music. Commercial meaning anything recorded
during or
> after the big band era.

The same phenomenon seems to be present in gospel choir music.

> When music became more complex harmonically,
> microtones were demoted to the role of occasional passing tones.

Because the compositions were always noted in 12!

I wrote:
> True. I could lip down almost 80 cents from the sixth harmonic.
> Going farther would need embouchure adjustments and does not feel
> right. Could be practised, though. And it would be enough to adjust
> a fingered 16/9 to a sounding 7/4.

Especially when 7/4 is at 968.8 cents, not at 933.1 (that's 12/7). I
always mix these up. Which kind of takes the point out of

> notate/finger a 6th instead of a minor 7th. But then, why should a

Sorry!

Paul Erlich schrieb:

> Klaus, it's the intervals formed against the other members of the
> ensemble, not the absolute pitches, that matter in this context.

I assumed, as Kami did in his post of the ratios to be expected,
that 10:12 would be the 5th and 6th harmonic (the easiest solution).

> > But then, why should a
> > trumpet player squeeze up a note that is already 3-limit consonant
> > with that 10 underneath?
>
> Not following you. What note is that?

That would be A (transposing pitches; "10" of the cord is E on the
open horn). Fingered 1-2 and actually 27/20, but lipped to be 4/3.

This makes sense because my very own delusional 7/4 is at 933 cents
and pretty close to the 6th. (If your septimal seventh differs, good
for you. I just readjusted to reality, but I know I will mix up 7/6
and 8/7 again at the next opportunity.) Complete confession and a
bit of math for atonement: I was really thinking of 12/7. That minus
a 5/4 is 48/35, a fourth(?) at 547 cents. Doesn't make much
difference if you're lipping up or down.

klaus

--- In tuning@y..., klaus schmirler <KSchmir@z...> wrote:

/tuning/topicId_24481.html#24573

> As Kami shows :o() (saying: gape!), anything seems to be possible if
> you use all the harmonics and use the tuning slide(s) a lot. Voice
> your chords with a good knowledge of the physics of the instrument
> (and throw in a couple of C- and D-trumpets), and they seem to be as
> flexible as trombones or strings. If you first brainwash the trumpet
> players!
>
> klaus
>
> Klaus

Well, I found this surely to be the case with French Horn virtuoso
Francis Orval (now living back in Germany again). But, of course,
Orval had EXTENSIVE charts of ALL the harmonics that the horn could
produce and practiced all of them. Trombone players, of course,
don't have to do that...

________ ______ _____
Joseph Pehrson

--- In tuning@y..., klaus schmirler <KSchmir@z...> wrote:
> Paul Erlich schrieb:
>
> > Klaus, it's the intervals formed against the other members of the
> > ensemble, not the absolute pitches, that matter in this context.
>
> I assumed, as Kami did in his post of the ratios to be expected,
> that 10:12 would be the 5th and 6th harmonic (the easiest solution).
>
>
> > > But then, why should a
> > > trumpet player squeeze up a note that is already 3-limit consonant
> > > with that 10 underneath?
> >
> > Not following you. What note is that?
>
> That would be A (transposing pitches; "10" of the cord is E on the
> open horn). Fingered 1-2 and actually 27/20, but lipped to be 4/3.

First of all, one shouldn't assume that the fundamental "1" is C or any other pitch -- it could be
something far away from the scale system in use. Secondly, if the "10" of the chord is E, then
the chord is E-G-Bb-Db -- there's no A -- so I don't know where this is coming from.

Paul Erlich schrieb:

> First of all, one shouldn't assume that the fundamental "1" is C or any other pitch -- it could be
> something far away from the scale system in use.

Well, it _is_ assumed since the olden days when there weren't any
valves: classical horn parts were always written without any
accidentals "in the key of C" and were executed on an instrument
supplying the harmonic series of the actual key. Whatever the pitch,
the 5th partial was always "e". The same goes for trumpets, which
weren't notated much. However, when trumpets played together with
orchestras, they forced them to adapt to their "C" (which was D in
Bach's case).

When valves were introduced, this writing and naming convention was
kept for the open instrument, which could be in Bb, C, D, Eb, F (all
in use today to varying degrees) or anything alse. (Where the bass
clef is in use - with trombones and tubas outside of English brass
and Salvation Army bands - sounding pitch is written, and the
players use different fingerings depending on the instrument they
use.)

When Kami put the 10:12 on e and g, it was more than likely not an
arbitrary choice, but due to his decision to use the open horn for
the interval that is present within a brass player's range. For a
horn in F, they would be a and c, for a peck horn in Eb, g and bb.
But
they would always be the 5th and 6th partial.

> Secondly, if the "10" of the chord is E, then
> the chord is E-G-Bb-Db -- there's no A -- so I don't know where this is coming from.

The A would be the fingering (which was based on erroneous
presumptions on my part).

Klaus

--- In tuning@y..., klaus schmirler <KSchmir@z...> wrote:
> Paul Erlich schrieb:
>
> > First of all, one shouldn't assume that the fundamental "1" is C or any other pitch -- it could be
> > something far away from the scale system in use.
>
> Well, it _is_ assumed since the olden days when there weren't any
> valves: classical horn parts were always written without any
> accidentals "in the key of C" and were executed on an instrument
> supplying the harmonic series of the actual key.

Then you missed the whole point of this discussion. It was not about playing the 10th,
12th, 14th, and 17th harmonics of a C or of any other scale tone. The proportions
10:12:14:17 are to be understood _by themselves_, without reference to a fundamental,
whose relevance or lack thereof is merely incidental to the issue at hand. And it has
nothing to do with actually playing the 10th, 12th, 14th, and 17th resonances of a given
fingering. Rather, the typical scenario is four _different_ brass instruments, using four
_different_ fingerings, and the issue is whether or not they will tend or be able to use
lipping to bring such chords closer to JI proportions.

Paul Erlich schrieb:
>

> Then you missed the whole point of this discussion.

I was focussing on what would happen in a normal brass section.
Perhaps being lured into resistance by your wording (see below).

It was not about playing the 10th,
> 12th, 14th, and 17th harmonics of a C or of any other scale tone. The proportions
> 10:12:14:17 are to be understood _by themselves_, without reference to a fundamental,
> whose relevance or lack thereof is merely incidental to the issue at hand.

The fundamental is implied: 1. Otherwise spelling wouldn't matter
(see below) and you'd be moving in an equal tempered universe.
And didn't I make it clear that C is brass shorthand for the
partials 1, 2, 4, ..., G for 3, 6, 12, and E for 5 and 10? In all of
Kami's fingering variations, #12 was an open horn g. Written. The
pitch depends on the instrument used.

> And it has
> nothing to do with actually playing the 10th, 12th, 14th, and 17th resonances of a given
> fingering.

Would be hard on modern trumpets. In Bach's time they did it (with a
given tuning crook instead of a fingering). 5th, 6th and 7th are
possible.

> Rather, the typical scenario is four _different_ brass instruments,

not what "brass section" implied to me

using four
> _different_ fingerings, and the issue is whether or not they will tend or be able to use
> lipping to bring such chords closer to JI proportions.
>

Quite apart from "lipping", which I consider as a conscious
procedure, and probably depending on the acoustic environment, there
will be a certain amount of "physical attraction" between the tones,
and this will result in a tendency towards frequencies in simple
ratios. But the trumpet players will try to fight it, since moving
away from the center of the resonance will not only impair the tone
quality, but also the ability to nail the next note. The lead (for
whom this is the most crucial, and who has the hardest time anyway)
will adapt the least, the lowest voice the most. If the chord is
held for some time, everyone will try to adapt as little as possible
and consider the chord strenuous.

(Now adapting a different approach from Kami's, stopping all them
note name references :). Also a best case scenario.)

To a sophisticated player, the key signature and accidentals make
clear what the 10 in the chord is: the third of a short dominant 7
b9. If it is THE dominant (in which case Kami's spelling would be
quite confusing), it will be the 15/8 of the key scale. Either they
play it as a fifth partial (which also means that the 12 - second
degree of the scale - is on the third or sixth), or they know they
can and should relax a bit there. The 14 will be spelled like the
4th scale degree. You'll have to argue the player into lipping this
one down a lot or playing it in a "forbidden" way (7th partial) (I'm
of the 7-is-consonant-and-won't-do-for-a-dominant-7th conviction
myself). I won't say anything about the 17 (not much adjustment
needed - and it will somehow float with the other frequencies). Yes,
it is possible if the spelling makes sense and you analyse the chord
for the players (who all get to see only one note of the chord) -
and if it is voiced so that the top note can be played right on
center (which is probably true enough for the 17).

Klaus