re: Digest Number 330

unsubscribeunsubscribeunsubscribeunsubscribeunsubscribeunsubscribeunsubscribeunsubscri
beunsubscribeunsubscribeunsubscribeunsubscribeunsubscribeunsubscribeunsubscribeunsubsc
ribeunsubscribeunsubscribeunsubscribeunsubscribeunsubscribeunsubscribeunsubscribeunsub
scribeunsubscribeunsubscribeunsubscribeunsubscribeunsubscribeunsubscribeunsubscribeunsu
bscribeunsubscribeunsubscribeunsubscribeunsubscribeunsubscribeunsubscribeunsubscribeun
subscribeunsubscribeunsubscribeunsubscribeunsubscribeunsubscribeunsubscribeunsubscribe
unsubscribeunsubscribeunsubscribeunsubscribeunsubscribeunsubscribeunsubscribeunsubscri
beunsubscribeunsubscribeunsubscribeunsubscribeunsubscribeunsubscribeunsubscribeunsubsc
ribeunsubscribeunsubscribeunsubscribeunsubscribeunsubscribeunsubscribeunsubscribeunsub
scribeunsubscribeunsubscribeunsubscribeunsubscribeunsubscribeunsubscribeunsubscribeunsu
bscribeunsubscribeunsubscribeunsubscribeunsubscribeunsubscribeunsubscribeunsubscribeun
subscribeunsubscribeunsubscribeunsubscribeunsubscribeunsubscribeunsubscribeunsubscribe
unsubscribeunsubscribeunsubscribeunsubscribeunsubscribeunsubscribeunsubscribeunsubscri
beunsubscribeunsubscribeunsubscribeunsubscribeunsubscribeunsubscribeunsubscribeunsubsc
ribeunsubscribeunsubscribeunsubscribeunsubscribeunsubscribeunsubscribeunsubscribeunsub
scribeunsubscribeunsubscribeunsubscribeunsubscribeunsubscribeunsubscribeunsubscribeunsu
bscribeunsubscribeunsubscribeunsubscribeunsubscribeunsubscribeunsubscribeunsubscribeun
subscribeunsubscribeunsubscribeunsubscribeunsubscribeunsubscribeunsubscribeunsubscribe
unsubscribe
unsubscribe
unsubscribe

> ** Original Subject: [tuning] Digest Number 330
> ** Original Sender: tuning@onelist.com
> ** Original Date: 25 Sep 1999 08:50:04 -0000

> ** Original Message follows...

>
> > You do not need web access to participate. You may subscribe through
> email. Send an empty email to one of these addresses:
> tuning-subscribe@onelist.com - subscribe to the tuning list.
> tuning-unsubscribe@onelist.com - unsubscribe from the tuning list.
> tuning-digest@onelist.com - switch your subscription to digest mode.
> tuning-normal@onelist.com - switch your subscription to normal mode.
>
> ------------------------------------------------------------------------
>
> There are 21 messages in this issue.
>
> Topics in today's digest:
>
> 1. Re: Fokker periodicity blocks (Joe Monzo)
> From: Joe Monzo <monz@juno.com>
> 2. Re: sum tones and piano wire
> From: Clark <caccola@net1plus.com>
> 3. Re: sum tones and piano wire
> From: "John F. Sprague" <JSprague@dhcr.state.ny.us>
> 4. Re: sum tones and piano wire
> From: Clark <caccola@net1plus.com>
> 5. Re: sum tones and piano wire
> From: "John F. Sprague" <JSprague@dhcr.state.ny.us>
> 6. Re: sum tones and piano wire, (more)
> From: Clark <caccola@net1plus.com>
> 7. Re: Project Retune: my adaptive JI methods
> From: "John A. deLaubenfels" <jadl@idcomm.com>
> 8. minor chord
> From: "Xavier J.-P. CHARLES" <xcharles@club-internet.fr>
> 9. Elaine Walker's Zia kiks serious booty !
> From: "Drew Skyfyre" <drew_skyfyre@yahoo.com>
> 10. RE: minor chord
> From: "Paul H. Erlich" <PErlich@Acadian-Asset.com>
> 11. Re: resonators
> From: "John A. deLaubenfels" <jadl@idcomm.com>
> 12. Re: minor chord
> From: "Xavier J.-P. CHARLES" <xcharles@club-internet.fr>
> 13. RE: Re: resonators
> From: "Paul H. Erlich" <PErlich@Acadian-Asset.com>
> 14. RE: minor chord
> From: "Paul H. Erlich" <PErlich@Acadian-Asset.com>
> 15. RE: Re: resonators
> From: "Paul H. Erlich" <PErlich@Acadian-Asset.com>
> 16. Reply to Joe Monzo
> From: "Paul H. Erlich" <PErlich@Acadian-Asset.com>
> 17. RE: constant structures
> From: Carl Lumma <clumma@nni.com>
> 18. RE: sum tones and piano wire
> From: Carl Lumma <clumma@nni.com>
> 19. Re: Fokker periodicity blocks (Joe Monzo)
> From: Carl Lumma <clumma@nni.com>
> 20. symmetrical scales
> From: "D.Stearns" <stearns@capecod.net>
> 21. new lattice diagram on my Robert Johnson page
> From: Joe Monzo <monz@juno.com>
>
>
>
______________________________________________________________________
_________
>
______________________________________________________________________
_________
>
> Message: 1
> Date: Fri, 24 Sep 1999 08:20:45 -0400
> From: Joe Monzo <monz@juno.com>
> Subject: Re: Fokker periodicity blocks (Joe Monzo)
>
> > [Paul Erlich, TD 329.12]
> >
> >> Because he uses a triangular lattice, every ratio has an
> >> octave-equivalent representation that spans one rung.
> >> So his metric is simply the log of the odd limit of the
> >> ratio. Why log, I don't know.
> >
> > So that, for example, 9 is the same distance whether
> > considered on its own or as two steps of 3.
> >
> > <etc. - snip>
>
>
> Paul,
>
> I've been reading your postings on this thread with much
> interest, but since my name is part of the subject line,
> I just wanted it to be clear to everyone that it was
> Carl Lumma who wrote all the things (in TD 328.10) you
> quoted in your posting here.
>
>
> - 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 |
> --------------------------------------------------
>
> ___________________________________________________________________
> Get the Internet just the way you want it.
> Free software, free e-mail, and free Internet access for a month!
> Try Juno Web: http://dl.www.juno.com/dynoget/tagj.
>
>
>
______________________________________________________________________
_________
>
______________________________________________________________________
_________
>
> Message: 2
> Date: Fri, 24 Sep 1999 11:23:59 -0100
> From: Clark <caccola@net1plus.com>
> Subject: Re: sum tones and piano wire
>
> A few words on this subject. As Paul Erlich writes, the idea of inharmonicity is well
documented, and it is integral to the Electronic Tuning Devices now used by many piano
technicians.
>
> The design and manufacture of bass strings has improved greatly with computer scale
design programs, and in my opinion contradicts the notion that they have very little
fundamental (stand near a concert grand...); yes, they are not necessarily perfectly executed,
and the core wires probably aren't uniform, but these are not enough to make them
unmusical.
>
> When rescaling pianos, it is often useful to enter data from the original stringing. many of
these (now) 100 year old pianos have higher tension than modern practice prefers. My own
research has shown that the issues of scale design were known at least empirically by 1850.
The lower tension is not an issue of hard or soft wire, but one of string lengths, and changing
to the same size of modern wire does not damage the piano structurally.
>
> Returning to the subject of beating fundamentals, Acrosonics in particular often do not have
uniform trichord unison speaking lengths. This is a cost saving measure, and the unisons suffer
tremendously. The same effect has been seen as desirable. The two 9' pianos we have
(1960's Baldwin, 1890's Kimball) both have bridges notched at slight angles in the middle
tenor range. Steinway did this for a short period as well.
>
> _Beating_ can be heard on single strings as well. Many pianos intentionally have unmuted
end lengths - so-called "aliquots" - which often are untuned and uncontrolled. Another reason
for beating single strings is improper termination at the string ends, either from damage or
from poor work. Additionally, changes in bridge impedance, bass strings with loud
longitudinal mode vibrations all can lessen the overall sound of a piano.
>
> Clark
>
>
>
>
>
>
______________________________________________________________________
_________
>
______________________________________________________________________
_________
>
> Message: 3
> Date: Fri, 24 Sep 1999 11:46:36 -0400
> From: "John F. Sprague" <JSprague@dhcr.state.ny.us>
> Subject: Re: sum tones and piano wire
>
> Very interesting, thank you. When I toured the Kimball factory in southern Indiana about
ten years ago they had on display an old piano. I don't recall if it was 150 or 200 years old.
But we had quite a discussion about the lower tensile strength steel they had to use to restring
it to avoid damage. Apparently higher tensile strength steel had been developed later. It was
easy to hear that it had a softer, less brilliant tone quality. The difference was ascribed mainly
if not entirely to the strings. They also had a Bosendorfer, as the U. S. distributors, on which
it was fun try those extra low tones. I'll look this up again if not too difficult to find, but
clearly (perhaps mistakenly) recall that the low harmonics are stronger than the fundamental
on the lowest piano tones. A twelve foot concert grand should have stronger bass
fundamentals than a spinet.
>
> >>> Clark <caccola@net1plus.com> 09/24 8:23 AM >>>
> A few words on this subject. As Paul Erlich writes, the idea of inharmonicity is well
documented, and it is integral to the Electronic Tuning Devices now used by many piano
technicians.
>
> The design and manufacture of bass strings has improved greatly with computer scale
design programs, and in my opinion contradicts the notion that they have very little
fundamental (stand near a concert grand...); yes, they are not necessarily perfectly executed,
and the core wires probably aren't uniform, but these are not enough to make them
unmusical.
>
> When rescaling pianos, it is often useful to enter data from the original stringing. many of
these (now) 100 year old pianos have higher tension than modern practice prefers. My own
research has shown that the issues of scale design were known at least empirically by 1850.
The lower tension is not an issue of hard or soft wire, but one of string lengths, and changing
to the same size of modern wire does not damage the piano structurally.
>
> Returning to the subject of beating fundamentals, Acrosonics in particular often do not have
uniform trichord unison speaking lengths. This is a cost saving measure, and the unisons suffer
tremendously. The same effect has been seen as desirable. The two 9' pianos we have
(1960's Baldwin, 1890's Kimball) both have bridges notched at slight angles in the middle
tenor range. Steinway did this for a short period as well.
>
> _Beating_ can be heard on single strings as well. Many pianos intentionally have unmuted
end lengths - so-called "aliquots" - which often are untuned and uncontrolled. Another reason
for beating single strings is improper termination at the string ends, either from damage or
from poor work. Additionally, changes in bridge impedance, bass strings with loud
longitudinal mode vibrations all can lessen the overall sound of a piano.
>
> Clark
>
>
>
>
>
>
______________________________________________________________________
_________
>
______________________________________________________________________
_________
>
> Message: 4
> Date: Fri, 24 Sep 1999 13:13:13 -0100
> From: Clark <caccola@net1plus.com>
> Subject: Re: sum tones and piano wire
>
> John,
>
> We have a local _authority_ on antique pianos who maintains quite a collection. He is very
fond of telling us all about the practice of stringing with hard-drawn wire vs. soft-drawn wire,
embellished mostly with mythological piano pseudoscience (and now he _restrings_ with
quite as unauthentic stainless steel...).
>
> You are right, the difference in sound between hard and soft wire, yellow and red brass
wire, etc. is quite audible, but these pairs have approximately the same density, so I don't
understand (no, I do) why they at Kimball would think they were avoiding damage by
stringing with one instead of the other. The soft wire is still harder than the bearing pins, and
I've seen where it has sheared the bridge pins right off.
>
> I recall an article, perhaps in Scientific American, which featured microscopic photos of
music wire, comparing antique and modern drawing technology in terms of sound and
strength. Fractures in old wire were along the diameter of the wire where modern wire had
them along its length.
>
> Rosamond Harding's "The Piano-Forte" has a substantial appendix on the subject of
historical piano strings. Malcolm Rose, who draws several types of low tensile wire, has
compiled stringing data in "Historical Stringing Practices."
>
> Perhaps what further confuses the issue of bass string fundamentals is their inharmonicity.
The vogue of imparting high inharmonicity to their partials continues with scaling software, but
within the boundaries of length to an extent this can be countered. The 12' piano simply has
longer strings, and the harmonics are better related to the fundamental. Still there are a lot of
bad bass strings.
>
> Clark
>
>
>
>
______________________________________________________________________
_________
>
______________________________________________________________________
_________
>
> Message: 5
> Date: Fri, 24 Sep 1999 13:26:37 -0400
> From: "John F. Sprague" <JSprague@dhcr.state.ny.us>
> Subject: Re: sum tones and piano wire
>
> They had tried modern wire and damaged the wooden pin block, which they then had to
replace. I think that the old piano was something of a restoration job in any case. It looked
as good as new, unless the guide carefully pointed out what had been done.
> Ah, stainless steel. Reminds me of the early tape recorders used by the BBC, with thirty
inch reels. I wasn't there, but have seen pictures. After the war, wire recorders had a brief
popularity. I saw an old one sometime in the last ten years, but didn't buy it. As I recall,
there was no rust on the wire, indicating that it might also have been stainless.
>
> >>> Clark <caccola@net1plus.com> 09/24 10:13 AM >>>
> John,
>
> We have a local _authority_ on antique pianos who maintains quite a collection. He is very
fond of telling us all about the practice of stringing with hard-drawn wire vs. soft-drawn wire,
embellished mostly with mythological piano pseudoscience (and now he _restrings_ with
quite as unauthentic stainless steel...).
>
> You are right, the difference in sound between hard and soft wire, yellow and red brass
wire, etc. is quite audible, but these pairs have approximately the same density, so I don't
understand (no, I do) why they at Kimball would think they were avoiding damage by
stringing with one instead of the other. The soft wire is still harder than the bearing pins, and
I've seen where it has sheared the bridge pins right off.
>
> I recall an article, perhaps in Scientific American, which featured microscopic photos of
music wire, comparing antique and modern drawing technology in terms of sound and
strength. Fractures in old wire were along the diameter of the wire where modern wire had
them along its length.
>
> Rosamond Harding's "The Piano-Forte" has a substantial appendix on the subject of
historical piano strings. Malcolm Rose, who draws several types of low tensile wire, has
compiled stringing data in "Historical Stringing Practices."
>
> Perhaps what further confuses the issue of bass string fundamentals is their inharmonicity.
The vogue of imparting high inharmonicity to their partials continues with scaling software, but
within the boundaries of length to an extent this can be countered. The 12' piano simply has
longer strings, and the harmonics are better related to the fundamental. Still there are a lot of
bad bass strings.
>
> Clark
>
>
>
>
______________________________________________________________________
_________
>
______________________________________________________________________
_________
>
> Message: 6
> Date: Fri, 24 Sep 1999 13:24:57 -0100
> From: Clark <caccola@net1plus.com>
> Subject: Re: sum tones and piano wire, (more)
>
> One more note on bass string fundamentals.
>
> The back-length of bass strings is often ignored in favor of fitting long strings in small
pianos. In these cases, the short, stiff length of wire between the bridge and the hitch pin
impairs the motion of the soundboard and bridge assembly, essentially reducing their ability to
transmit the lower tones, ie fundamental. Additionally, it has been discussed on the Pianotech
list by Del Fandrich that the bass bridge apron adds a distorting (and so stiffening) force to
the soundboard, which serves further to reduce the tone of these fundamentals.
>
> Clark
>
>
>
>
______________________________________________________________________
_________
>
______________________________________________________________________
_________
>
> Message: 7
> Date: Fri, 24 Sep 1999 11:36:17 -0600
> From: "John A. deLaubenfels" <jadl@idcomm.com>
> Subject: Re: Project Retune: my adaptive JI methods
>
>
> [Paul Erlich, TD 329.15 - problems playing retuned files...]
>
> Paul, it sounds like you were streaming from the web. Please try
> downloading the files to your local drive before you play them. The
> sizes should be:
>
> 105613 be-ps-08z5.mid
> 101793 be-ps-08z7.mid
>
> If you don't get this number of bytes, I'll be glad to e-mail you the
> files. I actually have slightly more up-to-date retunings that aren't
> on the web site yet - I don't want to post everyone to death! If you DO
> get this number of bytes and still can't play the file, I'd say, try
> another player program. Are you running Win 95/98? Media Player works
> well.
>
> [Paul:]
> > I'd love to see your finite set of tunings and discuss other
> > possibilities with you.
>
> Sounds good! Clearly I haven't explored the possibilities in depth.
>
> > By the way, what do you think is the right tuning for the
> > half-diminished seventh chord: 1/7:1/6:1/5:1/4, or 5:6:7:9? I think I
> > would allow context to decide, and might have to slide between the two
> > in some situations.
>
> I've got to confess - I've never tuned it 1/7:1/6:1/5:1/4; that would
> of course be consistent with the "reverse dominant ninth" for which a
> new tuning file would be needed.
>
> The following are the current contents of the "just7.tun" file:
>
> #
> # just7.tun
> #
> # modification history:
> # 08-17-99 (jdl): new from just1.tun.
> #
> #
> #
> #
> # tuning:
> # cols 1-8 have mbu for +/- 1 semitone voice; halve for +/- 2 (usual):
> # (81.92 mbu/cent at this scale; 40.96 mbu/cent at +/- 2):
> #
> 0 # 0; the reference, "C"
> 0 # 1; has no known harmonic place in the scale...
> +320 # 2; 9/8 of C
> +1281 # 3; 6/5 of C
> -1121 # 4; 5/4 of C
> -160 # 5; 4/3 of C
> -801 # 6; 15/16 of 7
> +160 # 7; 3/2 of C
> +1121 # 8; 4/5 of 12
> -1281 # 9; 5/6 of C
> -2553 # A; 7/8 of C: 7-limit!!!
> -961 # B; 15/16 of C
>
>
>
> # interval goodness:
> # 6 as 15/16 of 7; 8 as 4/5 of 12:
> # interval starting at:
> # 0 1 2 3 4 5 6 7 8 9 10 11
> # interval 0:
> +8 -16 0 0 0 0 -16 0 -16 0 0 0
> # interval 1:
> -16 -16 +8 -16 +8 -16 0 -16 -128 -16 0 +16
> # interval 2:
> +8 -32 0 0 -8 +8 -128 0 -128 +8 0 -32
> # interval 3:
> 0 -32 -64 -16 +16 +8 -64 +4 -128 +8 -64 +8
> # interval 4:
> +32 -64 0 +16 -256 +16 -128 +24 +8 -64 0 -128
> # interval 5:
> 0 -256 +8 -8 0 -256 -8 +16 -256 -256 -256 0
> # interval 6 (must repeat identical groups of 6):
> -16 -32 -32 -32 +8 -16 -16 -32 -32 -32 +8 -16
>
> [end of file...]
>
> This is probably confusing as heck. The first section gives the actual
> tuning to use. Note 4 is tuned -1121 "Midi Bend Units" (mbu), which
> works out to -1121/81.92 = -13.68 cents, a more familiar number for
> adjusting E to sound well against C (-13.69 is theoretical, but anything
> finer than 1 mbu is unachievable with midi anyway...).
>
> The second section tells how "good" each resultant interval is. If we
> play, say, D and F together, that's interval 3 starting at 2, which
> shows -64: pythagorean tuning does not make a good minor third. On the
> other hand, E and G together are interval 3 starting at 4, which shows
> +16: it's tuned 5:6, which is very good.
>
> JdL
>
>
>
>
>
______________________________________________________________________
_________
>
______________________________________________________________________
_________
>
> Message: 8
> Date: Fri, 24 Sep 1999 22:40:19 +0200
> From: "Xavier J.-P. CHARLES" <xcharles@club-internet.fr>
> Subject: minor chord
>
> Paul H. Erlich wrote:
>
> > Helmholtz preferred 16:19:24 for its combination tones. What is the other
> > element? (To be, having the root of the chord octave-equivalent to the
> > fundamental of the harmonic series seems important).
> I did'nt know that Helmholtz had written 16-19-24 for minor chord. But I
> read in his "physiological theory..." something which involve that he
> prefered unconsciously 19/16 in place of 32/27. He was listening the
> third D-F to tune it on 32/27 by the means of combination tones.
> "The Pythagorean minor Third d''' / f''' has a1 for its combinational
> tone, which completes it into the chord d / f + a1, and this is not a
> perfectly correct minor chord. But as the incorrect Fifth a1 lies among
> the deep combinational tones and is very weak, the difference is
> scarcely perceptible. Moreover, practically almost impossible to tune
> the interval so precisely as to insure the combinational tone a1 in
> place of a."
> (in Dover edition, translated by Ellis, it's p. 335)
> For Helmholtz, a1 is one comma (81/80) below a. If he hear an a, it
> involve that the Fourth a - d is 4/3. Mathematically, the only solution
> is with 19/16 for the Third d - f. But, he didn't written this fraction.
>
>
> Paul H. Erlich wrote:
> >However, in Bach's time
> > 10:12:15 (nearly) would still have appeared on many instruments,
> I'm not an expert in temperaments, but when I learned some of them, I
> was a little surprise that author always spoke about major chord and
> nearly never of minor chord. And then, I looked the minor chord of usual
> tonality (c, d, f, g, a): I saw that minor chord were rarely 10/12/15.
> It was around 19/16 for half of them (exactly between 32/27 and the
> Third of the equal temperament), and one of ten was exactly 19/16.
>
> I try to play 19/16 on my violin. It's difficult but not impossible,
> with 2 high tones it's easier, then I prefere 19/16 than 6/5 for minor
> chord.
>
> One day, I realized that even if major chord is hard on a piano, minor
> chord is'nt so agressive. Then, mathematically, the Third of the piano
> is not far from 19/16.
>
> An other "proof" is bound to an hypothesis I developped in my "memoire
> de DEA" for explain the difference between tonality and modality. With a
> big simplification, it's because 16=2x2x2x2, therefore 16 is a tonic,
> that is impossible with the 5 of 6/5, or with the 27 of 32/27.
>
> Paul H. Erlich wrote:
> > Besides Helmholtz, Van Eck makes a point of the 16:19:24 chord in his book,
> > _J. S. Bach's Critique of Pure Music_.
> Thank you for this reference, honestly, I don't know anything of Van
> Eck. May you give me the year and the edition please?
>
>
> After this I must say that, even I admit 16-19-24 for minor chord do not
> involve that all chords named minor by traditionnal analysis are really
> minor chord. For example, the chord "d-f-a" in the tonality of C, may be
> a part of dominant chord, then a 6-7-9 chord. It really depend of the
> context, moreover, this problem is a big part of my futur thesis
> (1998-2003...).
>
> Xavier CHARLES
>
>
>
______________________________________________________________________
_________
>
______________________________________________________________________
_________
>
> Message: 9
> Date: Fri, 24 Sep 1999 19:18:41 +0530
> From: "Drew Skyfyre" <drew_skyfyre@yahoo.com>
> Subject: Elaine Walker's Zia kiks serious booty !
>
> Surfing along my merry way I noticed "Zia" pop up in the results of a search
> on Yahoo for microtonal synths. I remembered someone mentioning Zia on the
> list (Gary ?), so went over, found some mp3s. Yeah ! This is the kind of
> music that could push microtonality into the mainstream of popular music.
>
> http://www.pulserecords.com/zia/
>
>
> (oh, I shifted my new site, the one with my (non-microtonal) music to Xoom,
> so streaming now works & I have unlimited webspace. Yes!. The silly URL in
> my signature will take u there.)
>
> Oh & for the guitar players here, technology is great, Digitech's new RP-14D
> multi-fx floorboard has, get this, an SPDIF digital output ! and the list
> price is @ US$550 !
>
> - Drew
>
>
> --
> ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
> Drew Skyfyre songwriter, webmaster, happy human
>
> web : http://skyfyre.lookscool.com
>
> email : drew_skyfyre@yahoo.com
>
> Be young, be foolish, be happy !
> ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
>
>
> _________________________________________________________
>
> Do You Yahoo!?
>
> Get your free @yahoo.com address at http://mail.yahoo.com
>
>
>
>
______________________________________________________________________
_________
>
______________________________________________________________________
_________
>
> Message: 10
> Date: Fri, 24 Sep 1999 17:20:48 -0400
> From: "Paul H. Erlich" <PErlich@Acadian-Asset.com>
> Subject: RE: minor chord
>
> I wrote,
>
> >>However, in Bach's time
> >> 10:12:15 (nearly) would still have appeared on many instruments,
>
> Xavier wrote,
>
> >I'm not an expert in temperaments, but when I learned some of them, I
> >was a little surprise that author always spoke about major chord and
> >nearly never of minor chord. And then, I looked the minor chord of usual
> >tonality (c, d, f, g, a): I saw that minor chord were rarely 10/12/15.
> >It was around 19/16 for half of them (exactly between 32/27 and the
> >Third of the equal temperament), and one of ten was exactly 19/16.
>
> I don't think this is a fair analysis. Typically, temperaments from around
> Bach's time were symmetrical around the d-a fifth. So if you looked at (c,
> d, f, g, a) major, you should look at (b, d, e, g, a) minor. You should find
> that those minor chords are as close to 10:12:15 as the former major chords
> are to 4:5:6. Let me know if you don't find this to be true.
>
> >I did'nt know that Helmholtz had written 16-19-24 for minor chord. But I
> >read in his "physiological theory..." something which involve that he
> >prefered unconsciously 19/16 in place of 32/27. He was listening the
> >third D-F to tune it on 32/27 by the means of combination tones.
>
> That's what I meant. So your two elements are combination tones and . . .
> combination tones?
>
> >An other "proof" is bound to an hypothesis I developped in my "memoire
> >de DEA" for explain the difference between tonality and modality. With a
> >big simplification, it's because 16=2x2x2x2, therefore 16 is a tonic,
> >that is impossible with the 5 of 6/5, or with the 27 of 32/27.
>
> That's the same point I already made, that the root of the minor chord being
> octave-equivalent to the fundamental makes it more stable as a tonic.
>
> >Thank you for this reference, honestly, I don't know anything of Van
> >Eck. May you give me the year and the edition please?
>
> van Eck, C. L. Van Panthaleon. 1981. _J. S. Bach's Critique of Pure Music_.
> Princo, Culemborg, the Netherlands.
>
>
>
______________________________________________________________________
_________
>
______________________________________________________________________
_________
>
> Message: 11
> Date: Fri, 24 Sep 1999 15:45:48 -0600
> From: "John A. deLaubenfels" <jadl@idcomm.com>
> Subject: Re: resonators
>
>
> [me, TD 329.3:]
> >> If the resonator is linear in its response, we're guaranteed to get a
> >> sine wave out, at the same frequency as the sine wave in (though
> >> probably with amplitude and phase shifts). If the resonator is
> >> non-linear, there will potentially be additional frequencies present
> >> in the output, but they will all be overtones of the input sine wave.
>
> [Paul Erlich, TD 329.14:]
> > Right. Once again, non-linearities in the response lead to sum and
> > difference tones, which in the case of a single sine wave means
> > overtones of that sine wave. For air-cavity resonators, the
> > non-linearity of the air's response only becomes important at fatal
> > dB levels.
>
> I hope I'm not flogging a dead horse here, but way back in TD 322.2,
> Carl Lumma started this whole thing with:
>
> >> I doubt you'll wind up with sine tones, considering the parking-lot
> >> horns you'll be playing the thing thru...
>
> Parking lot horns could be expected to be highly non-linear: by tending
> to clip the sine wave in, they'd tend to add odd harmonics to the
> output. So Carl was right, yes? In a subsequent post, he made a
> statement that you and I agree was incorrect:
>
> [Carl Lumma, TD 323.1:]
> >> I've never been able to get a sine tones out of a cone speaker in a
> >> normal room. I don't know exactly why that is, but I suspect PA
> >> horns would be worse rather than better. I would guess that the
> >> bodies of the horns will resonate with their own harmonics, at least.
>
> Other than Carl's incorrect attribution of distortion to the harmonics
> of the horn, he was correct, yes?
>
> JdL
>
>
>
>
>
______________________________________________________________________
_________
>
______________________________________________________________________
_________
>
> Message: 12
> Date: Fri, 24 Sep 1999 23:52:09 +0200
> From: "Xavier J.-P. CHARLES" <xcharles@club-internet.fr>
> Subject: Re: minor chord
>
> Paul wrote:
>
> >
> > Xavier wrote,
> >
> > >I'm not an expert in temperaments, but when I learned some of them, I
> > >was a little surprise that author always spoke about major chord and
> > >nearly never of minor chord. And then, I looked the minor chord of usual
> > >tonality (c, d, f, g, a): I saw that minor chord were rarely 10/12/15.
> > >It was around 19/16 for half of them (exactly between 32/27 and the
> > >Third of the equal temperament), and one of ten was exactly 19/16.
> >
> > I don't think this is a fair analysis. Typically, temperaments from around
> > Bach's time were symmetrical around the d-a fifth. So if you looked at (c,
> > d, f, g, a) major, you should look at (b, d, e, g, a) minor. You should find
> > that those minor chords are as close to 10:12:15 as the former major chords
> > are to 4:5:6. Let me know if you don't find this to be true.
>
> I think you are right, I'm really not an expert in temperaments...,
> minor chords that I learned were essentially in a french book (LATTARD,
> Jean, Gammes et temperaments musicaux, ed. Masson, 1988). He had write
> (p. 54) : "9 minor thirds are cut by a syntonic comma (like fifths),
> but they seemed in tune."
> Did you read somewhere the same establishment for major chord?
>
> Xavier wrote
> > >I did'nt know that Helmholtz had written 16-19-24 for minor chord. But I
> > >read in his "physiological theory..." something which involve that he
> > >prefered unconsciously 19/16 in place of 32/27. He was listening the
> > >third D-F to tune it on 32/27 by the means of combination tones.
> Paul wrote
> > That's what I meant. So your two elements are combination tones and . . .
> > combination tones?
> Yes... but I did calculus of combination tones before reading the
> Helmholtz's theory. Then, for me, it's two elements.
>
> Xavier CHARLES
>
>
>
______________________________________________________________________
_________
>
______________________________________________________________________
_________
>
> Message: 13
> Date: Fri, 24 Sep 1999 17:59:16 -0400
> From: "Paul H. Erlich" <PErlich@Acadian-Asset.com>
> Subject: RE: Re: resonators
>
> >Other than Carl's incorrect attribution of distortion to the harmonics
> >of the horn, he was correct, yes?
>
> The horn could easily have a nonlinear response, so Carl was completely
> correct. It's not a case of a resonator responding nonlinearly, though.
>
>
>
______________________________________________________________________
_________
>
______________________________________________________________________
_________
>
> Message: 14
> Date: Fri, 24 Sep 1999 18:17:29 -0400
> From: "Paul H. Erlich" <PErlich@Acadian-Asset.com>
> Subject: RE: minor chord
>
> >I think you are right, I'm really not an expert in temperaments...,
> >minor chords that I learned were essentially in a french book (LATTARD,
> >Jean, Gammes et temper

Message truncated at 32K

>** --------- End Original Message ----------- **

>

AL

Modest Prophet
listen.to/modestprophet
www.mp3.com/modestprophet
ICQ# 27043492