Yahoo Tuning Groups Ultimate Backup tuning High third

>John, since you're a microtonal (xenharmonic?) vocalist,

I've never said or thought either of those things. I just do my best to
sing in tune.

>and that webpage is concerning Johnson's microtonal vocals,
>I'd like to point out to both of you one of the most surprising
>things I found after doing my analysis:
>
>At the end of the very first line of the song (on the word
>'man' in 'I'm a drunken hearted man...'), Johnson sings
>a note which is the '3rd' of the tonic D-major chord.
>It begins quite a bit below the 12-tET (12-EDO?) '3rd',
>then rises quite far above it.
>
>What surprised me was that the ending pitch is *clearly*
>far higher than the Pythagorean '3rd' [= 81/64 = ~408 cents].
>
>I hear it as starting out approximately 14 cents below
>2^(4/12) [= 400 cents] and rising to ~27 cents above.
>
>The starting pitch is quite clearly implying a 5/4
>[= ~386 cents], and I interpreted the ending pitch rationally
>as a 32/25 [= ~427 cents].
>
>I considered 9/7 [= ~435 cents] as the ending pitch, but
>when I tuned the MIDI track up to that, it sounded too high
>and did not (to my ears) accurately reflect Johnson's vocal.
>
>I settled on 32/25 because my criteria, aside from closeness
>in pitch, was lowness of prime/integer limit, and those were
>the smallest ratio-numbers which fit.

Thanks for bringing this to my attention. I will tune my guitar so that I
can hear 32/25. Note the following:

(9/7) / (32/25) = 225/224 = 1.00446

1200*(log(225/224)/log(2)) = 7.71

So the two intervals vary by less than one half of one percent, just under
8 cents.

John Link

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>From: Joe Monzo <monz@juno.com>
>
>At the end of the very first line of the song (on the word
>'man' in 'I'm a drunken hearted man...'), Johnson sings
>a note which is the '3rd' of the tonic D-major chord.
>It begins quite a bit below the 12-tET (12-EDO?) '3rd',
>then rises quite far above it.

My recollection is that Mick Jagger did a similar thing with "You can't..".
Does anybody have the recording handy to check?

John Link

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In early November of 1999 I wrote:

>How about a new topic? Does anybody know anything about the tuning of
>horns in cars, trucks, and trains? How about written sources? My
>experience is as follows:
>
>Cars: usually two horns, tuned 2:3, 3:4, 4:5, 5:6

But now I'm not so sure about the 4:5. In the last few days I think I've
been hearing 7:9 for at least some of the major thirds. Please listen to
the horns in your neighborhood and tell me what you think you hear.

John Link

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🔗Kraig Grady <kraiggrady@xxxxxxxxx.xxxx>

John!
yes i have heard what seems to be a 9/7. I have heard trains play 7/9/11
too. It seems you would want to have a more dissonant interval to cut through
the masking of the ambient noise. Here I noticed that they change the siren
patterns here depending on the time of day!

John Link wrote:

>
> But now I'm not so sure about the 4:5. In the last few days I think I've
> been hearing 7:9 for at least some of the major thirds. Please listen to
> the horns in your neighborhood and tell me what you think you hear.
>
> John Link
>
> ****************************************************************************
>
> Watch for the CD "Live at Saint Peter's" by the JOHN LINK VOCAL QUINTET,
> featuring original compositions as well as arrangements of instrumental
> music by Brahe and Taylor, Chick Corea, Miles Davis, Claude Debussy, Bill
> Evans, Ennio and Andrea Morricone, Modeste Mussorgsky, Erik Satie, and Earl
> Zindars.
>
> ****************************************************************************
>
> Check out WWW.DUESBERG.COM for information that could make the difference
> between life and death for you or someone you know.
>
> ****************************************************************************
>
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http://www.anaphoria.com

🔗johnlink@xxxx.xxxxxxxxxxxxxx)

>From: Kraig Grady <kraiggrady@anaphoria.com>
>
>John!
>yes i have heard what seems to be a 9/7 [from cars]. I have heard trains
>play 7/9/11
>too. It seems you would want to have a more dissonant interval to cut through
>the masking of the ambient noise. Here I noticed that they change the siren
>patterns here depending on the time of day!

And maybe a more dissonant major third to make sure that the third is heard
distinct from the root and still locked in tune with it, as in Mick
Jagger's "You can't.."?

John Link

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🔗Herman Miller <hmiller@xx.xxxx>

🔗Paul H. Erlich <PErlich@xxxxxxxxxxxxx.xxxx>

🔗John Link <johnlink@con2.com>

I've been following the posts about the high third and unfortunately with
my ancient equipment the samples that Joe put up play on my computer but
they all sound the same, since there is no sliding up of the third! That's
why I haven't put in my two cents about my impressions. Based on what
everybody else has reported, if the 9/7 is actually as high as Joe has it
then it is probably the case that my guitar experiment wasn't quite right,
maybe due to old strings with inharmonic overtones. Tonight I did the
guitar experiment again and used my tuning meter to measure the number of
cents in the interval between 5/4 and 9/7 and between 9/7 and 4/3.

Here are my results:

9/7 to 4/3 = 65 cents

4/5 to 9/7 = 50 cents

According to my copy of Helmholtz the numbers should be 63 and 49. So I
conclude that I have correctly tuned 9/7 on my guitar. The triad that I
formed including the 9/7 clearly does not sound like a suspended chord.

John Link

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🔗Gerald Eskelin <stg3music@earthlink.net>

To my post:
>
>> [Jerry Eskelin, TD 499.22]
>> BTW, You [Paul Erlich] still haven't responded to my
>> "off the wall" suggestion that the shift in tuning may
>> have to do with the combination of overtones (or undertones)
>> in the tonic and dominant fundamentals. Might that have any
>> relation to this discussion. (If that is a naive notion,
>> just say so and I'll forget it.)

Joe Monzo offered:
>
> Actually, Jerry, Paul did respond to this idea.
>
>> [Paul Erlich, TD 493.7]
>> I don't think it's remotely possible for one to acoustically
>> "lock" into the 81/64 over a 1/1 root and 3/2 fifth. That's
>> why I suggested 24/19 -- it's still a long shot, but may be
>> within the realm of possibility due to the common overtone.
>
> This idea of 'sharing overtones' was also at the root of
> my suggestion that 81/64 might be the 'high 3rd', but Paul
> showed that I was fallaciously using prime-limit thinking
> here.

Thanks, Monz. I'm still not totally tuned in to "number-ese," so I didn't
recognize it as such. I still don't have a vivid take on this answer, but I
get the drift that it isn't practical. So, that's that.

>> [Jerry Eskelin TD 499.8]
>> I just played the MIDI posted a few days ago (young9.mid)
>> which sustains 7:8:9:12 and I sang a perfect fifth above 7
>> (14:21 as in the chord you described earlier; 14:18:21,
>> I believe) and the result sounded very much like the singers'
>> "high third" to me. Since John Link's guitar version also
>> sounded very "good" to me, I think the 7:9 theory moves to
>> the top of the list of possibilities.
>
> Whoa, hold on there!
>
> This file
> http://www.ixpres.com/interval/td/monzo/young9.mid
> actually contains the complete chord
> mentioned by Daniel Wolf [TD 493.17], 32:48:56:63:72.
> That's the 4:6:7:9 drone, with the 63/32 'pseudo-octave'
> which is an 8:9 above 7/4, added in as the sung pitch.
>
> With the vibrato your MIDI setup is producing, you probably
> didn't notice the 'off' 32:63 'octave', hearing it instead
> as 1:2, and apparently you're hearing the '6' as a '12'
> (i.e., an 'octave' too high). Those two mishearings would
> give the 7:8:9:12 you mention.
>
> But the presence of 63/32 in the chord would certainly help
> your sung 21/16 'lock', as can be readily seen from the
> lattice:
>
>
> 63/32 ---------- 9/8
> / /
> / /
> 21/16 ---------- 3/2
> / /
> / /
> 7/4 ----------- 1/1
>
>
> The 4:6:7:9 describes the pitches 1/1 - 3/2 - 7/4 - 9/8.

All I know is that when I sang the 2:3 fifth above the seventh partial, I
was experiencing a perfectly tuned major triad with high third and added 6th
and 9th (for example, Bb-C-D-F-G) The "original" root (C) was inaudible to
me in a low octave so it was easy to hear the Bb as the root.

I'm sure your numbers are significant, Monz, but I'm focussing here on the
7:9 third. Did I misunderstand that the 7:9 was present? Bottom line: If
that was the 7:9 third, it sounds very close to what I have been calling the
"high third." Also, I believe John Link has redone his guitar work on the
7:9 and will be reporting on that presently.

Also I'm not totally discounting (as discussed with Paul) that the
impression of the "high third" might be illusionary. I want to do some more
"live" experiments this week with my college singers. I'll report anything
of interest.
>
>> [Jerry Eskelin, TD 499.27]
>>> http://www.ixpres.com/interval/td/monzo/high3rd.mid
>>
>> Thanks, Monz. I now have been able to open "high3rd2.mid"
>> and agree that the last item is very sharp. (I'm still
>> confused about the number of items in your various versions.
>> Was the first one titled "high3rd.mid? If so, did it
>> include the 7:9 third? Actually, this is probably academic
>> at this point. Let's just drop it. I'll work on getting
>> this one to play.
>> <snip>
>> With the same title (high3rd.mid)? I assume yes, since at
>> that time I had not yet heard "high3rd2.mid." On the other
>> hand, "high3rd2.mid" also has seven items. Am I confused???
>> Yes, I'm confused. But take heart in the fact that it is
>> not the first time I've been confused. :-)
>
>
> Now I'm confused! I never created a file named 'high3rd2.mid'!
> I suppose it's possible that my FTP program added that '2'
> without my noticing it.

> The URL given above is the only filename I ever intended to
> use for this experiment, and it should contain 7 different
> versions of the 'high 3rd':

Now that I remember it happening before with multiple downloads, I think
that my computer adds the next number automatically when more than one of
the same file is introduced to the finder. I'll trash the early ones and
perhaps that will allow the latest version to open.

No more confusion--at least about that.

Thanks,

Jerry

🔗Joe Monzo <monz@juno.com>

>> [me, monz, TD 501.7]
>> This file
>> http://www.ixpres.com/interval/td/monzo/young9.mid
>> actually contains the complete chord
>> mentioned by Daniel Wolf [TD 493.17], 32:48:56:63:72.
>> That's the 4:6:7:9 drone, with the 63/32 'pseudo-octave'
>> which is an 8:9 above 7/4, added in as the sung pitch.
>>
>> With the vibrato your MIDI setup is producing, you probably
>> didn't notice the 'off' 32:63 'octave', hearing it instead
>> as 1:2, and apparently you're hearing the '6' as a '12'
>> (i.e., an 'octave' too high). Those two mishearings would
>> give the 7:8:9:12 you mention.
>>
>> But the presence of 63/32 in the chord would certainly help
>> your sung 21/16 'lock', as can be readily seen from the
>> lattice:
>>
>>
>> 63/32 ---------- 9/8
>> / /
>> / /
>> 21/16 ---------- 3/2
>> / /
>> / /
>> 7/4 ----------- 1/1
>>
>>
>> The 4:6:7:9 describes the pitches 1/1 - 3/2 - 7/4 - 9/8.
>
>
> [Jerry Eskelin, TD 502.9]
> All I know is that when I sang the 2:3 fifth above the
> seventh partial, I was experiencing a perfectly tuned major
> triad with high third and added 6th and 9th (for example,
> Bb-C-D-F-G) The "original" root (C) was inaudible to me
> in a low octave so it was easy to hear the Bb as the root.

OK, that all sounds reasonable. What I was trying to show
you with the lattice was that, to an extent, even if you *do*
hear the 'original root' (C 1/1) clearly, the relationships
among the higher notes in the chord would make it easy for
you to 'lock' onto the '2:3 fifth above the seventh partial',
which would be F 21/16. Because 63/32 is present in the
chord, you get the same 8:9:12 proportions between
Bb 7/4 - C 63/32 - F 21/16 that you get between
C 1/1 - D 9/8 - G 3/2.

>
> I'm sure your numbers are significant, Monz, but I'm
> focussing here on the 7:9 third. Did I misunderstand that
> the 7:9 was present?

No, you understand correctly. The 7:9 third is most
definitely present as the top interval in the drone: 4:6:7:9.

If you sang the F 21/16 correctly, which as I show above
you probably did, because it's easy to hear, then you most
certainly did hear the 14:18:21 'major triad with high 3rd'.

> Bottom line: If that was the 7:9 third, it sounds very close
> to what I have been calling the "high third."

OK. But if you're hearing 7:9 as the 'high 3rd' here, you
should also be hearing it as the 'high 3rd' in my MIDI-file
of your experiment, because it's exactly the same interval!

I suggest that the context is playing tricks on you here.

> [me, monz]
>> http://www.ixpres.com/interval/td/monzo/high3rd.mid
>>
>> The URL given above is the only filename I ever intended to
>> use for this experiment, and it should contain 7 different
>> versions of the 'high 3rd':
>
> [Jerry]
> Now that I remember it happening before with multiple
> downloads, I think that my computer adds the next number
> automatically when more than one of the same file is
> introduced to the finder.

Yes, that typically happens, at least in Windows.

> I'll trash the early ones and perhaps that will allow the
> latest version to open.

My suggestion - trash all of them and download it anew,
just once. That way you'll be sure to have the latest
version I uploaded. At least we'll be certain that we're
discussing the same file.

-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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🔗John Link <johnlink@con2.com>

>From: Robert C Valentine <bval@iil.intel.com>
>
>Its a little difficult for me, since I don't know what the
>'high third lock' is supposed to be, but am just hoping I'll
>recognize it if it bites me on the...

How about trying the 1:9/7:3/2:9/5:9/4 (i.e., 1/9:1/7:1/6:1/5:1/4) dominant
9th chord that I recently posted? Jerry said he thinks that 9/7 is the high
third he hears from singers, based on his listening over the phone to my
guitar tuned with a 9/7 third.

John Link

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🔗Paul H. Erlich <PErlich@Acadian-Asset.com>

John Link wrote,

>How about trying the 1:9/7:3/2:9/5:9/4 (i.e., 1/9:1/7:1/6:1/5:1/4) dominant
>9th chord that I recently posted?

I posted at length about this chord a few years ago (I've spent a lot of
time listening to it -- have you?). I compared it to a microscope slide
cover -- those really thin squares of glass. When handled with the slightest
bit of force, it breaks. That's because combinational tones, which are very
sensitive to the volume of a chord, ruin a utonal chord (work out the math
if you're not convinced). On the other hand, an otonal dominant 9th,
4:5:6:7:9, sounds really good when played loud, since the combinational
tones all reinforce the fundamental (two octaves below the fundamental,
actually).

I've found that the acoustic guitar is the best timbre for utonal chords.
Something about the strings vibrating sympathetically with one another must
provide an extra reinforcement for that common overtone. On a synth, with
any harmonic timbre, and played moderately loudly, most utonal chords tend
to be heard as out-of-tune otonal chords.

🔗Paul H. Erlich <PErlich@Acadian-Asset.com>

I have a suggestion that will help show that the 7:9 major third, which
sounds like it's "from Mars" when the lower third in a major triad, sounds
positively wonderful as the seventh and ninth of a dominant chord. I often
perform this demonstration (or a close approximation) on my meantone piano
and my 22-tET guitar. Hopefully, Joe Monzo or someone else will help create
a MIDI file that will once and for all dispell all doubts that these
intervals are really one and the same. I strongly encourage the rest of you
to go over to your synth and try it yourself. Report back to us on what you
hear. Everyone's been strangely silent on this issue!

First, use 7:9 in a major triad, 7:9:10.5 (aka 14:18:21). Hold this for a
while. Then drop out the upper voice, and introduce three lower voices,
forming a 4:5:6:7:9 with the 7:9 held constant. Voila! The interval that was
once so dissonant is now quite consonant. What's going on here? Just another
demonstration that context is everything. If the ear can understand the 7:9
as the seventh and ninth partials of a clear fundamental, it is hearing
something it is very familiar with. Almost every instrumental timbre has
seventh and ninth partials -- though they normally go by unnoticed, they can
be clearly heard if one focuses one's attention on them. However, in the
triad 14:18:21, the numbers are too high to unambiguously represent familiar
partials of a fundamental at 1, 2, 4, 8, or 16 (which would correspond to
the _second_ of this chord). The ear (actually the brain's central pitch
processor) is confused -- it thinks it might be hearing a 4:5:6, or maybe
7:9:11, or maybe 5:6:7; 14:18:21 might even enter in as a weak contender if
it's in a high enough register. This confusion corresponds to a high degree
of what I call "harmonic entropy", which is an important component of what
we call dissonance.

🔗Herman Miller <hmiller@io.com>

On Mon, 31 Jan 2000 17:22:13 -0500, "Paul H. Erlich"
<PErlich@Acadian-Asset.com> wrote:

>First, use 7:9 in a major triad, 7:9:10.5 (aka 14:18:21). Hold this for a
>while. Then drop out the upper voice, and introduce three lower voices,
>forming a 4:5:6:7:9 with the 7:9 held constant. Voila! The interval that was
>once so dissonant is now quite consonant. What's going on here? Just another
>demonstration that context is everything.

How true. I've heard a similar effect with the 9:11, and even the 8:11
(which by itself isn't exactly the most consonant interval). Even more
amazing is the effect I noticed a while back with the 1/4-comma meantone
"wolf fifth", which sounds *very* dissonant by itself, but blends right in
as the (approximate) 21:32 of a 12:18:21:32 chord! The only sense I can
make of this is that it's "really" a 4:6:7 chord with an added 4th (i.e.,
an 8/3 above the root), which resolves nicely down to a 4:6:7:10. Except
for the 21:32 itself, the other intervals of the 12:18:21:32 chord are all
consonant or nearly so (2:3, 4:7, 3:8, 6:7, and 9:16).

--
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🔗Christopher J. Chapman <christopher.chapman@conexant.com>

Hi Folks,

I'll admit that I've gotten a little lost trying to keep track of the
paths taken during the "High Thirds" discussion, but if it would help
(and hasn't been done already), I'd be willing to generate .WAV (or
.AIFF, .MP3, or whatever) files of the chords in question using either
pure sine waves or tones with harmonics that are simple sums of sine
waves (just tell me how many harmonics you want and what decay). That
way there should be no problem with vibrato on differing interpretations
of General MIDI, etc.

If this would be of use, here's what I need to know:

* what ratios (e.g., 4:5:6, 7:9:11, etc.)
* pure sine vs. harmonics
* if harmonics, then how many and what decay
(e.g. 8 harmonics, decay of 0.88 times previous amplitude)
* what format? (I know I can generate raw PCM, .WAV, .AIFF, and .MP3)
* what base frequency? (A=440 Hz?, C=261.6 Hz?, what?)

Cheers,
Christopher
christopher.chapman@conexant.com

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