Yahoo Tuning Groups Ultimate Backup tuning Howling and Growling Wolves

The new 55-tone scale of mine has 3 growling dogs at 707 cents.

Oz.
----- Original Message -----
From: Afmmjr@aol.com
To: tuning@yahoogroups.com
Sent: 24 Ekim 2007 Çarşamba 19:29
Subject: [tuning] Howling and Growling Wolves

Since we have been dancing with wolves of late, maybe this is a good time for some consensus building.

It seems that each meantone member (except ET) has a single wolf, a sharped fifth. This wolf "howls."
If the fifth were to be way flat, such is in a simple just intonation scale, 680 cents "growling" wolves would emerge. I would like to secure this language.

Staying with fifths for the present, how much higher than just constitutes a howling fifth?
How much lower than just constitutes a growling fifth?
Whatever limits we impose may be more of a modern choosing from a modern aesthetic (ET or microtonal), or more from implications more emic, available commentary from the musical period (hopefully unembelished by a third party).

While we could continue with goats, etc., it is the fifths that determine functionality in modulation more than any other intervals. And these intervals are commented upon, as with Schlick.

quarter comma meantone = 1 wolf at 737 cents
sixth comma meantone = 1 wolf at 722 cents
Werckmeister IV = 2 dogs at 708 and 714
Werckmeister V = 2 dogs at 690 and 708 (one growling and one barking)
Werckmeister VI = 2 barking dogs at 706 and 707
Kirnberger II = 2 growling dogs at 691
Kirnberger III = 1 growling dog at 601.5

This should be fun. Johnny

🔗Afmmjr@aol.com

🔗Charles Lucy <lucy@harmonics.com>

I find nothing at all strange about your wolves and goats from a meantone perspective.

The sharp fifth is 8 steps of fifths from the tonic, (#V = 4L) C to G# and hence one would expect it to be more dissonant than any of the intervals having less steps between their notes.

The corresponding interval in the opposite direction is the flattened second; i.e. (bIV = L+2s) C to Fb

the mirror image, or complement is equally dissonant.

Db-Cb-Gb-Db-Ab-Eb-Bb-F-C-G-D-A-E-B-F#-C#-G#

So there are two equally dissonant wolves, or the second is the reflection of the first in still water on a moonlit night. (a la Robbie Burns?)

Charles Lucy lucy@lucytune.com

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On 24 Oct 2007, at 18:01, Afmmjr@aol.com wrote:

> Thanks, Oz, for the admission. Of course, Margo might simply want > to consider this a tame poodle. I on the other hand would only > suggest that the dogs are barking rather than growling. :) Johnny
>
> The new 55-tone scale of mine has 3 growling dogs at 707 cents.
>
> Oz.
>
>
>
>
>
>
> See what's new at AOL.com and Make AOL Your Homepage.
>
>

🔗Charles Lucy <lucy@harmonics.com>

🔗Ozan Yarman <ozanyarman@ozanyarman.com>

🔗Joe <tamahome02000@yahoo.com>

🔗Paul Poletti <paul@polettipiano.com>

--- In tuning@yahoogroups.com, Afmmjr@... wrote:

> It seems that each meantone member (except ET) has a single wolf, a
sharped
> fifth.

Depends on whether or not you consider that the term "meantone" refers
only to *regular* meantone schemes. And in any event, if you want to
include ET as a memeber of the meantone family, you should also
include the theoretically possible though historically absent 1/10 and
1/11 comma versins, which also have no unpleasant fifth to speak of.
>
> Staying with fifths for the present, how much higher than just
constitutes a
> howling fifth?
> How much lower than just constitutes a growling fifth?

What little can be derived from the historical use/literature would
imply that tempering is tempering regardless of up or down. Thus
deviation from pure is the only factor.

> Werckmeister IV = 2 dogs at 708 and 714
> Werckmeister V = 2 dogs at 690 and 708 (one growling and one barking)

I don't where you are getting your data. Werckmeister IV (1691
nomenclature I assume) is a -/+ 1/3 comma temperament, thus it only
has two sizes of tempered fifths, one at 694,135 cents and the other
at 709,775. Your 708 is close enough for jazz, though at almost 2
cents off it cold be better. But where is the 714? Even assuming you
have miscalculated the 709,8 as 708, the error doesn't explain the
deviation.

Likewise, Werckmeister V (1691 only) is a -/+ 1/4 comma temperament,
thus it also only has two sizes of tempered fifths, one at 696,09
cents and the other at 707,82. Where lies the fifth so narrow as 690?

> Kirnberger III = 1 growling dog at 601.5

Kirnberger III (by this I assume you meant the Forkel letter 1/4 S.
comma C-G-D-A-E) has no such fifth.

I would posit that before reaching any sort of agreement about
creative names, the primary step is to do the numbers correctly.

And while I would hate to further spoil this doggie fest, I would
point out that the first (as far as I know) use of the term "wolf" to
describe an interval is Preatorius, who uses it in reference to the
minor third f-ab (g#). Interesting question, that... who started using
it in reference to fifths, and when?

Ciao,

🔗monz <monz@tonalsoft.com>

Hi Paul,

--- In tuning@yahoogroups.com, "Paul Poletti" <paul@...> wrote:
>
> And in any event, if you want to include ET as a memeber
> of the meantone family, you should also include the
> theoretically possible though historically absent 1/10
> and 1/11 comma versins, which also have no unpleasant
> fifth to speak of.

While i think you're correct that no-one has ever
actually written about a tuning called 1/11-comma
meantone, this is worth mentioning:

EDOs approximate fraction-of-a-comma meantones to
varying degrees -- for example:

* at the mediocre end, 55-edo and 31-edo are fair
(but still not remarkably close) approximations to
1/6-comma and 1/4-comma respectively,

* at the other end, 19-edo and 43-edo are very close
approximations to 1/3-comma and 1/5-comma respectively.

But 12-edo is *incredibly* close to 1/11-comma meantone.
So much so, that even within Tonescape's precise tuning
tolerances, i can't make it temper 5-limit JI into
1/11-comma meantone and give separate pitches for the
enharmonic pairs. The only way i was able to do it was
to artificially set up what i call "699.99-cent meantone".

The 1/11-Comma Meantone "5th" 2,3,5-monzo [-7/11 7/11, 1/11>
= ~1.498306976 ratio = ~699.9998836 cents.

The difference between the notes of an enharmonic pair
in 1/11-comma meantone is only ~0.001396448 (~1/716) cent.

The difference between the "5th"s of 12-edo and 1/11-comma
meantone is ~0.000116371 (~1/8593) cent.

The calculations can all be seen on my webpage:
http://tonalsoft.com/enc/number/12edo.aspx

-monz
http://tonalsoft.com
Tonescape microtonal music software

🔗Paul Poletti <paul@polettipiano.com>

🔗Brad Lehman <bpl@umich.edu>

> > And in any event, if you want to include ET as a memeber
> > of the meantone family, you should also include the
> > theoretically possible though historically absent 1/10
> > and 1/11 comma versins, which also have no unpleasant
> > fifth to speak of.
>
> While i think you're correct that no-one has ever
> actually written about a tuning called 1/11-comma
> meantone, this is worth mentioning:

Well...Murray Barbour on pages 43-44 wrote that Romieu mentioned 1/10
comma, and that Marpurg included 1/10 comma in his 1776 publication.

On page 83 Barbour wrote: "Since the syntonic comma is much easier to
form than the ditonic, it is easy to see why it should have been
preferred as the quantity to be divided. However, since the ratio of
the two commas is about 11:12, an excellent approximation for equal
temperament can be made by tempering the fifths by 1/11 syntonic
comma." And here he footnotes out to Marpurg, p.177, for that
observation.

I wrote about 1/11 SC myself on page 4 of my main article:
"The geometric difference between the PC and the SC is called the
schisma. It is very nearly the same size as either 1/12 PC or 1/11
SC. (...) For all practical purposes the 1/12 PC temperaments are 1/11
SC temperaments, as these two small portions have very nearly the same
size."

And my file of "data charts" that is part of the article has a page
about equal temperament, giving a row of -1/11 SC all the way across
all twelve 5ths. Download from Oxford's server via this link:
http://www-personal.umich.edu/~bpl/larips/outline.html
where it says: "[Download/Read "Supplementary Data" four PDF files]"

Incidentally, that link also leads to a set of six "Music Clips
associated with this paper": various harpsichord and organ
performances by me, for free download from their server. About half
an hour of music to go with the analyses in the article.

=====

Apropos of the canine nomenclature discussion, are my detractors ready
to stop calling the A#-F 704 cent interval a "wolf" anymore? That
interval is so gentle and harmless, it doesn't have any fangs or
claws, or even gonads or a bladder. My old boyhood poodle was
feistier than that. I would suggest "prairie dog" for 704 cents, but
they're members of the squirrel family, not canines. Genus "Cynomys",
a cool word.

Brad Lehman

🔗Brad Lehman <bpl@umich.edu>

🔗Paul Poletti <paul@polettipiano.com>

🔗Tom Dent <stringph@gmail.com>

🔗Afmmjr@aol.com

🔗Gene Ward Smith <genewardsmith@sbcglobal.net>

🔗Afmmjr@aol.com

Candidates for Canidea
--- In _tuning@yahoogroups.com_
(/tuning/post?postID=dUbNNSm4H1PBUyFXKZBFOJEEPFSaOy_0noiazHohoKq1TddxMp9Y8YIvn1nZuTwZ3vQ
hNQpfi0pwUrYM) , Afmmjr@... wrote:
> It seems that each meantone member (except ET) has a single wolf, a
sharped
> fifth.

Paul: Depends on whether or not you consider that the term "meantone" refers
only to *regular* meantone schemes.
Johnny: Sounds good, especially if regular meantone means not a “modified
meantone.”
Paul: And in any event, if you want to
include ET as a memeber of the meantone family, you should also
include the theoretically possible though historically absent 1/10 and
1/11 comma versins, which also have no unpleasant fifth to speak of.
>
> Staying with fifths for the present, how much higher than just
constitutes a
> howling fifth?
> How much lower than just constitutes a growling fifth?

What little can be derived from the historical use/literature would
imply that tempering is tempering regardless of up or down. Thus
deviation from pure is the only factor.

Johnny: Is this the question raised by our friend in Slovenia? Wasn’t he
tackling the issue by saying there is a difference whether one tunes in a
different direction? I am agreeing with this. It is interesting that there is no
distinction in the “literature” that points to this. But Paul is wrong to
state “scientifically” “Thus deviation from pure is the only factor.” It
is another issue worth exploring on the List, perhaps appropriate for
microtonalists who might be in different listening positions than our ancestors.

> Werckmeister IV = 2 dogs at 708 and 714
> Werckmeister V = 2 dogs at 690 and 708 (one growling and one barking)

Paul: I don't where you are getting your data. Werckmeister IV (1691
nomenclature I assume) is a -/+ 1/3 comma temperament, thus it only
has two sizes of tempered fifths, one at 694,135 cents and the other
at 709,775. Your 708 is close enough for jazz, though at almost 2
cents off it cold be better. But where is the 714? Even assuming you
have miscalculated the 709,8 as 708, the error doesn't explain the
deviation.

Johnny: A good friend has been assisting me with the number crunching. The
numbers I gave him for Werckmeister IV C major scale are:
0 81 195 295 393 498 590 693 781 891 1003 1088
If I was wrong in these, please let me know. The 714 is G# to Ab, and the
708 is Eb to A#. Though I hadn’t mentioned it, there is the C to G fifth of
693 cents.

Paul: Likewise, Werckmeister V (1691 only) is a -/+ 1/4 comma temperament,
thus it also only has two sizes of tempered fifths, one at 696,09
cents and the other at 707,82. Where lies the fifth so narrow as 690?

Johnny: The 690 fifth is F# to Db in WV.

> Kirnberger III = 1 growling dog at 601.5

Kirnberger III (by this I assume you meant the Forkel letter 1/4 S.
comma C-G-D-A-E) has no such fifth.
Johnny: Yes, I became aware of this from my friend because I sent him a
copy of what I sent to the list. It is not 601.5 – a typo – but 690.5 cents.

Paul: I would posit that before reaching any sort of agreement about
creative names, the primary step is to do the numbers correctly.
And while I would hate to further spoil this doggie fest, I would
point out that the first (as far as I know) use of the term "wolf" to
describe an interval is Preatorius, who uses it in reference to the
minor third f-ab (g#). Interesting question, that... who started using
it in reference to fifths, and when?

Ciao,

P
Johnny: Yes, who indeed sicced the wolves on the fifths. Thank you for all
help in getting the numbers right.
Choos

************************************** See what's new at http://www.aol.com

🔗Gene Ward Smith <genewardsmith@sbcglobal.net>

🔗Paul Poletti <paul@polettipiano.com>

--- In tuning@yahoogroups.com, Afmmjr@... wrote:
>

> Johnny: A good friend has been assisting me with the number
crunching. The
> numbers I gave him for Werckmeister IV C major scale are:
> 0 81 195 295 393 498 590 693 781 891 1003 1088

Funny, I never knew the C MAJOR scale had so many notes in it.

;-)

> If I was wrong in these, please let me know. The 714 is G# to Ab,
and the
> 708 is Eb to A#. Though I hadnât mentioned it, there is the C to
G fifth of
> 693 cents.

The correct numbers, calculated as fifth ratios to 13 decimal places
and then converted to cents, are as follows:
(chromatic ascending C to C, reading down)
0,00
82,41
196,09
294,14
392,18
498,05
588,27
694,14
784,36
890,23
1003,91
1086,32
1200,00

Fifth sizes are as follows:
(circle of fifths, ascending/clockwise, reading down, C-G repeated at
end of list)
694,14
701,96
694,14
701,96
694,14
701,96
694,14
701,96
709,78
709,78
694,14
701,96
694,13

If you want more decimal places, let me know. Tis but a click of the
formatting menu.
>
> Paul: Likewise, Werckmeister V (1691 only) is a -/+ 1/4 comma
temperament,
> thus it also only has two sizes of tempered fifths, one at 696,09
> cents and the other at 707,82. Where lies the fifth so narrow as 690?
>
> Johnny: The 690 fifth is F# to Db in WV.

Ain't no such critter.

Werckmeister V
(chromatic ascending C to C, reading down)
0,00
96,09
203,91
300,00
396,09
503,91
600,00
701,96
792,18
900,00
1001,96
1098,04
1200,00

(circle of fifths, ascending/clockwise, reading down, C-G repeated at
end of list)
701,96
701,96
696,09
696,09
701,96
701,96
696,09
696,09
707,82
701,96
701,96
696,09
701,96

> > Kirnberger III = 1 growling dog at 601.5
>
> Kirnberger III (by this I assume you meant the Forkel letter 1/4 S.
> comma C-G-D-A-E) has no such fifth.
> Johnny: Yes, I became aware of this from my friend because I sent
him a
> copy of what I sent to the list. It is not 601.5 â" a typo â" but
690.5 cents.

Nope, even that one, like Baby Bear's chair, porridge, and bed, is too
small as well.

Kirnberger "III"

(chromatic ascending C to C, reading down)
0,00
90,22
193,16
294,13
386,31
498,04
590,22
696,58
792,18
889,74
996,09
1088,27
1200,00

(circle of fifths, ascending/clockwise, reading down, C-G repeated at
end of list)

696,58
696,58
696,58
696,58
701,96
701,96
700,00
701,96
701,96
701,96
701,96
701,96
696,58
>
> Thank you for all
> help in getting the numbers right.

Glad to be of service.

Ciao,

🔗Afmmjr@aol.com

🔗Tom Dent <stringph@gmail.com>

Achtung! A word to the wise. The whole mathematical content of
Werckmeister 1691, so far as it relates to the 'good' temperaments,
has already been translated, calculated and documented here:

http://en.wikipedia.org/wiki/Werckmeister_temperament

A page which I had a nontrivial part in formatting and correcting.

I can't answer for Paul, but the fifths are easy to calculate from the
usual numbers:

Pure fifth = 701.955

Pythagorean comma = 23.46

Werckmeister says explicitly what fraction of a PC has to be added to
or subtracted from each fifth. Indeed the sizes of tempered fifths
*define* the tuning.

If you take the usual approximation of 702 and 24 then it becomes even
easier. WIV has pure fifths at 702, 1/3 PC flat fifths at 694, and 1/3
PC sharp fifths at 710. Both of the latter, in my opinion, qualify as
Wolverines.

I think, given the faulty arithmetic of his sources, we can be
grateful that Johnny *hasn't* performed in 'WIV' or 'WV'.

~~~T~~~

--- In tuning@yahoogroups.com, Afmmjr@... wrote:
>
>
> Thank you Paul, so very much. Did you deduce these numbers or did you
> acquire them from someone or somewhere?
>
> choos, J
>
> --- In _tuning@yahoogroups.com_
>
(/tuning/post?postID=aDcY4ODIeu6ms3cqTs77Csezh9b03Dsn-vNVfgup-tyIU-dlfY6Wxx9SyBvBt34P56d
> YmqwLHaf6uNAorFgnHQ) , Afmmjr@ wrote:
> >
>
> > Johnny: A good friend has been assisting me with the number
> crunching. The
> > numbers I gave him for Werckmeister IV C major scale are:
> > 0 81 195 295 393 498 590 693 781 891 1003 1088
>
> Funny, I never knew the C MAJOR scale had so many notes in it.
>
> ;-)
>

🔗monz <monz@tonalsoft.com>

🔗Andreas Sparschuh <a_sparschuh@yahoo.com>

--- In tuning@yahoogroups.com, "Paul Poletti" <paul@...> wrote:
>
> RE: folks who object to your 704 cent fifth. Sometimes I think these
> types forget that it is the 702 cent fifth which is the natural state
> of affairs, and not the 700 cent version. Thus they see a number like
> 704 and they panic, failing to realize that it is merely the negative
> universe version of an ET fifth.
But the 'Mensur' of modern romantic pianos
with thick strong strings is optimized for
12-edo with ~700Cent 5ths due to an additional
increment by inharmonitciy of ~2Cents
so that ~702C = ~700C + 2C

The ratio of length:diameter of a string is
intensionally so desiged that the 12-edo error
and inharmonicity do compensate for 5ths 3:2
by canceling each others out.

http://en.wikipedia.org/wiki/Inharmonicity
http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=JASMAN0000760000S1000S22000004&idtype=cvips&gifs=yes
http://en.wikipedia.org/wiki/Piano_acoustics
http://www.postpiano.com/support/updates/tech/Tuning.htm
http://www.amarilli.co.uk/piano/theory/paradigm.asp
http://www.acoustics.auckland.ac.nz/research/research_files/keane_nzas04.pdf
http://www.math.niu.edu/~rusin/uses-math/music/tuning.biblio
that makes -when considering inharmonicity- for
'Rosetta-Stone'd "dimished-6th" wolf
~706Cents = ~704Cents + 2 Cents.
Hence Brad's ~704Cents dackhel-wolf fit well
to piano-strings with negative inharmonicity.
Have Brad's instruments really negative string-diameters?

> And since when did anybody ever
> complain about the aural quality of the FIFTHS in ET?
>
http://anaphoria.com/mjm1.pdf
pdf.
p.20
Janko:
http://en.wikipedia.org/wiki/Paul_von_Janko
http://en.wikipedia.org/wiki/Janko_keyboard
"...the 5ths must be better than the one found in 12-tone equal
temperament"
p.21 in the pdf:
Partch:
http://en.wikipedia.org/wiki/Harry_Partch
footnote 37
...even 2-Cents is an excessive alteration: Ref:
"A heared 2-Cents discrepancy is a sensible difference in
simutaneous soundings"
For this reason P. opposes 12-edo.

me too!

A.S.

🔗Paul Poletti <paul@polettipiano.com>

--- In tuning@yahoogroups.com, "Andreas Sparschuh" <a_sparschuh@...>
wrote:
>
> --- In tuning@yahoogroups.com, "Paul Poletti" <paul@> wrote:
> >

> But the 'Mensur' of modern romantic pianos
> with thick strong strings is optimized for
> 12-edo with ~700Cent 5ths due to an additional
> increment by inharmonitciy of ~2Cents
> so that ~702C = ~700C + 2C
>
> The ratio of length:diameter of a string is
> intensionally so desiged that the 12-edo error
> and inharmonicity do compensate for 5ths 3:2
> by canceling each others out.

Bullkrap!!!!

I'm sorry, but this is the biggest load of junk to come down the pike
in a very long time. There is no such thing a "the" mensur of modern
pianos, nor are they (al of the different variants) "optimized" for
any size of fifth. The vast majority of modern writing about piano
scales is complete and utter nonsense, almost everything you can find
in even the best acoustics works is written in total ignorance of the
actual history of the development of piano design as evident in the
surviving instruments themselves. So many times I have a good laugh at
reading yet another "learned" tract going on about some perfect design
to achieve some intricate balance of whatever, and I think to myself,
these guys haven't even taken the time to actually go look at all the
instruments. I personally know of one modern organologist who was
adding to the dung pile by basing his work on that of another previous
pile of dung, and who, when I personally gave him a list of a number
of important and prominent instruments he should go LOOK AT which
disproved the whole lot, choose rather to ignore and publish anyway,
with the footnote that I had mentioned perhaps there are "some"
instruments which don't display this aspect.

Piano scaling comes from harpsichord scaling, and like many
harpsichord scales of the Germanic tradition, the scale is stretched
non-Pythagorean going up merely to take advantage of the fact that
smaller diameters of premodern steel wire were relatively stronger
than larger diameters (proportional to cross sectional area), meaning
you can get away with longer strings which ring better and have less
internal damping and inharmonicity problems when you get way up in the
treble. There essentaily has been no change in scaling since about
1820 or so, and that is essentially the same as harpsi scaling in the
17th century. So much for "optimized for thick strings and ET". What
aload dingo's kidneys! All the nonsense you can read in modern books
comes from people who didn't understand the origins of the traditional
design, with a good dose of claptrap about constant tension (which NO
piano, modern nor antique, has) thrown in, thanks mostly to Hipkins.

> http://en.wikipedia.org/wiki/Inharmonicity
>
http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=JASMAN0000760000S1000S22000004&idtype=cvips&gifs=yes
> http://en.wikipedia.org/wiki/Piano_acoustics
> http://www.postpiano.com/support/updates/tech/Tuning.htm
> http://www.amarilli.co.uk/piano/theory/paradigm.asp
>
http://www.acoustics.auckland.ac.nz/research/research_files/keane_nzas04.pdf
> http://www.math.niu.edu/~rusin/uses-math/music/tuning.biblio

Yeah, I've read most of this well-intentioned though seriously
misguided stuff. It all sounds good, unless you know how instruments
really were made, and what real builders like Blüthner said about why
they did what they did, for example:

Nur in den oberen Oktaven bestimmt man die Saitenlängen annährend so,
als wären alle Saiten gleich dick and gleich gespannt, d. h. man
reduziert die Saitenlänge beim Aufsteigen um eine Oktave auf die
Hälfte. Wie schon erwähnt, verfährt man aber in der Regel nicht genau
nach diesem Prinzipe. . . .sucht man nämlich im allgemeinen die Mensur
im Diskant zu vergrössern, soweit die Beschaffenheit der Saiten dies
erlaubt, um denselben mehr Elastizität und den Tönen mehr Stärke und
Gesang zu geben.

(Only in the upper octaves one determines the string lengths more or
less as though all strings were of equal diameter and at equal
tension, that is, for ever octave higher one reduces the string length
by half. As already mentioned, one usaually doesn't proceed following
this principle exactly . . . one generally attempts to increase the
scale in the treble as much as allowed by the quality of th

🔗Ozan Yarman <ozanyarman@ozanyarman.com>

Gosh, I'm so relieved that any piano can accomodate any temperament no
matter what the size of the fifth!

Thanks Paul,

Oz.

----- Original Message -----
From: "Paul Poletti" <paul@polettipiano.com>
To: <tuning@yahoogroups.com>
Sent: 28 Ekim 2007 Pazar 2:19
Subject: [tuning] ~704 detuned 5th was: Re: 12-edo and 1/11-comma meantone
(was: Candidates....

--- In tuning@yahoogroups.com, "Andreas Sparschuh" <a_sparschuh@...>
wrote:
>
> --- In tuning@yahoogroups.com, "Paul Poletti" <paul@> wrote:
> >

Bullkrap!!!!

> http://en.wikipedia.org/wiki/Inharmonicity
>
http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=JASMAN0
000760000S1000S22000004&idtype=cvips&gifs=yes
> http://en.wikipedia.org/wiki/Piano_acoustics
> http://www.postpiano.com/support/updates/tech/Tuning.htm
> http://www.amarilli.co.uk/piano/theory/paradigm.asp
>
http://www.acoustics.auckland.ac.nz/research/research_files/keane_nzas04.pdf
> http://www.math.niu.edu/~rusin/uses-math/music/tuning.biblio

Yeah, I've read most of this well-intentioned though seriously
misguided stuff. It all sounds good, unless you know how instruments
really were made, and what real builders like Blï¿½thner said about why
they did what they did, for example:

Nur in den oberen Oktaven bestimmt man die Saitenlï¿½ngen annï¿½hrend so,
als wï¿½ren alle Saiten gleich dick and gleich gespannt, d. h. man
reduziert die Saitenlï¿½nge beim Aufsteigen um eine Oktave auf die
Hï¿½lfte. Wie schon erwï¿½hnt, verfï¿½hrt man aber in der Regel nicht genau
nach diesem Prinzipe. . . .sucht man nï¿½mlich im allgemeinen die Mensur
im Diskant zu vergrï¿½ssern, soweit die Beschaffenheit der Saiten dies
erlaubt, um denselben mehr Elastizitï¿½t und den Tï¿½nen mehr Stï¿½rke und
Gesang zu geben.

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🔗Paul Poletti <paul@polettipiano.com>

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> Gosh, I'm so relieved that any piano can accomodate any temperament no
> matter what the size of the fifth!
>
Did I say that? No, I said that that temperament was NOT the deciding
factor in piano design. And that there is no generally observable
standard in modern piano scaling. Nor is there any consistency in the
inharmonicity of modern pianos. Go ask any modern piano tuner.

BTW, quite a bit of my reply got clipped by the web interface. Here?s
the whole of the translation of Blüthner's text:

(Only in the upper octaves one determines the string lengths more or
less as though all strings were of equal diameter and at equal
tension, that is, for ever octave higher one reduces the string length
by half. As already mentioned, one usaully doesn't proceed following
this principle exactly . . . one generally attempts to increase the
scale in the treble as much as allowed by the quality of the wire in
order to give the strings more elasticity and to make a fuller and
more singing tone.)

Lehrbuch des Pianofortebaus, 1872

Modern piano scaling is the same as 19th century piano scaling which
is essentially the same as 17th century harpsichord scaling of the
German school. If you want to know why it is the way it is, read my
published work:

Beyond Pythagoras: Ancient Techniques for Designing Musical Instrument
Scales, in Keyboard Instruments - Flexibility of Sound and Expression,
Proceedings of the harmoniques International Congress, Lausanne 2002,
Peter Lang 2004 ISBN3-03910-244-3

I'm sorry to react so strongly, but this is my field of expertise, and
it really drives me around the bend when this klaptrap is brought up,
elegant theories concocted by people who have never got their hands
dirty touching a real instrument. This stuff always sounds good unless
you know the details of historical instrument construction and scale
design. I've got the length and diameter indications of every string
for a vast number of instruments (close to 200), from early
harpsichords all the way up to a number of big and large modern
pianos, all analyzed for deviation from just scaling, stress/strain,
closeness to breaking, inharmonicty, etc etc etc. That combined with
almost thirty years of making and restoring harpsichords and pianos
means that I am intimately aware of the acoustical and mechanical
problems instruments makers were dealing with, not some imagined quest
for some imagined perfect balance between yet another set of esoteric
variables that some physicist or acoustician has dreamed up from
looking at but one limited aspect of a very complex picture.

Ciao,

🔗Ozan Yarman <ozanyarman@ozanyarman.com>

So, let me get this right:

"Temperament is not the deciding factor in piano design" = "Any temperament
is equally fine for a piano"?

Oz.

----- Original Message -----
From: "Paul Poletti" <paul@polettipiano.com>
To: <tuning@yahoogroups.com>
Sent: 28 Ekim 2007 Pazar 2:57
Subject: [tuning] ~704 detuned 5th was: Re: 12-edo and 1/11-comma meantone
(was: Candidates....

BTW, quite a bit of my reply got clipped by the web interface. Here?s
the whole of the translation of Blï¿½thner's text:

(Only in the upper octaves one determines the string lengths more or
less as though all strings were of equal diameter and at equal
tension, that is, for ever octave higher one reduces the string length
by half. As already mentioned, one usaully doesn't proceed following
this principle exactly . . . one generally attempts to increase the
scale in the treble as much as allowed by the quality of the wire in
order to give the strings more elasticity and to make a fuller and
more singing tone.)

Lehrbuch des Pianofortebaus, 1872

Ciao,

🔗Paul Poletti <paul@polettipiano.com>

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> So, let me get this right:
>
> "Temperament is not the deciding factor in piano design" = "Any
temperament
> is equally fine for a piano"?
>
Man, are you slow, Oz! I already told you once that this was an
invalid conclusion. Look, explaining all the details of piano design
in this respect would take far more time than I have, and first you
should go do a bunch of basic preparatory work on materials strength,
Young's modulus, stress/strain curves, plastic/elastic extension
regions, etc etc etc, which I doubt you are interested in. This is if
you want to really understand everything in modern intellectual terms.
Old makers of course didn't understand it in the same way, but
understand it they did because they HAD to. They were building
instruments at many different pitch levels and pusing their wire to
the limits. This means if you made a mistake in one direction, the
instrument sounded dull and false, and if you made a mistake in the
other direction, the strings broke. Their is documentary evidence that
both did indeed occasionally happen.

Now, specifically, about temperament. The totality of an instruments
scale is the result of three REGULAR aspects: (1) the so-called string
band, which is an even distribution across the instrument of the
choirs of strings which matches the regular distribution of the
keyboard and action. Until the introduction of the overstrung design
in 1857 (and for a long time thereafter for builders who continued
making straight strung instruments, as many did), this is a set of
parallel equally spaced lines. (2) A spline curve, which intersects
the string band. This produces a regular proportional change in string
length from note to note which in no way mirrors the IRREGULAR
proportional changes from note to note required to produce anything
other than equal temperament. This is true for ALL instruments, no
matter what time period we are discussing. Granted, the interruptions
in the regularity of both caused by the layout of the modern
overstrung frame make this hard to see, but if you actually climb
inside such a monster and measure the length of EVERY string and then
compare them to stringing scales stretching back for several
centuries, you will find that there is no real difference, except for
the progressive lengthening of the entire scale throughout the 19th
century as every harder steels became available. (3) The reduction in
diameter, which almost always follows a regular distribution, that is,
the steps between gauge changes are regular.

The problem with these elegant theories of balance between scaling and
inharmonicity is that the coefficient of inharmoncity is NOT constant
over the entire scale. It is highest in the upper octaves, dropping to
very low in the middle octaves, and then rising again for the tenor.
The bass bridge is a completely different world because you can design
wound strings to have a wide range of elasticity, so you can leave the
bass bridge out of the discussion entirely. Now I would like you or
anyone to explain to me how the intersection of three regular
progressions can in some way add up to compensate for a factor which
is highly irregular.

Beyond all that is the inconvenient truth that other aspects of the
instruments design (soundboard compliance, ribbing, downbearing, after
and forelength, etc etc etc) can also cause inharmonicity to vary from
region to region, even from note to note.

Now, as to which temperament sounds "better" on a modern piano, htat
is a matter of personal preference. The biggest problem with this
concept is the lumping together of the truly vast variation of designs
and the resultant acoustical objects under the heading "the modern
piano". If you think there is any sort of consistency in the presence
of inharmonicity among modern pianos, then you are in for a big
surprise. How strange that the makers of all advanced modern
electronic tuning devices and software, like the Rayburn Cyber Tuner,
go to great lengths to allow the device to analyze the inharmonicty
for EVERY note on each individual piano so that the tuner can decide
how to program the stretching of EACH octave (differently) in order to
attempt to compensate. If we were to believe Andreas, this was all
resolved by the scaling of "the" modern piano. Poor stupid piano
tuners, they go to so much work for nothing!

Frankly, I think that any EDO which stays away from near harmonic
proportions is the best way to tune a modern piano, because when there
is constant rapid beating, you don't hear the large variation in
interval quality over the range of the instrument caused by the large
variation in inharmonicty. But that is only my preference.

Now, if that doesn't clear it up for you Oz, let me frame it in
another way. The fact that cars are not designed specifically for one
particular size of person does not mean that ANY size of person fits
equally well in any given car. Do you see where your insistence upon
drawing a connection is false?

Ciao,

🔗threesixesinarow <CACCOLA@NET1PLUS.COM>

🔗Ozan Yarman <ozanyarman@ozanyarman.com>

----- Original Message -----
From: "Paul Poletti" <paul@polettipiano.com>
To: <tuning@yahoogroups.com>
Sent: 28 Ekim 2007 Pazar 8:57
Subject: [tuning] ~704 detuned 5th was: Re: 12-edo and 1/11-comma meantone
(was: Candidates....

> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
> >
> > So, let me get this right:
> >
> > "Temperament is not the deciding factor in piano design" = "Any
> temperament
> > is equally fine for a piano"?
> >
> Man, are you slow, Oz!

Better slow than overcome by sorrow.

I already told you once that this was an
> invalid conclusion.

You did? Maybe it was not expressed in those exact terms.

Look, explaining all the details of piano design
> in this respect would take far more time than I have, and first you
> should go do a bunch of basic preparatory work on materials strength,
> Young's modulus, stress/strain curves, plastic/elastic extension
> regions, etc etc etc, which I doubt you are interested in.

My interest lies elsewhere at the moment.

This is if
> you want to really understand everything in modern intellectual terms.

I want to understand in abstract terms first.

> Old makers of course didn't understand it in the same way, but
> understand it they did because they HAD to. They were building
> instruments at many different pitch levels and pusing their wire to
> the limits. This means if you made a mistake in one direction, the
> instrument sounded dull and false, and if you made a mistake in the
> other direction, the strings broke. Their is documentary evidence that
> both did indeed occasionally happen.
>

This is very informative. Thanks.

> Now, specifically, about temperament. The totality of an instruments
> scale is the result of three REGULAR aspects: (1) the so-called string
> band, which is an even distribution across the instrument of the
> choirs of strings which matches the regular distribution of the
> keyboard and action. Until the introduction of the overstrung design
> in 1857 (and for a long time thereafter for builders who continued
> making straight strung instruments, as many did), this is a set of
> parallel equally spaced lines.

I recall overstringing means that the bass strings cross over the middle
strings. I have an idea how it may affect piano design.

(2) A spline curve, which intersects
> the string band. This produces a regular proportional change in string
> length from note to note which in no way mirrors the IRREGULAR
> proportional changes from note to note required to produce anything
> other than equal temperament.

I cannot project this sentence onto my mind. Can you not rephrase it?

This is true for ALL instruments, no
> matter what time period we are discussing. Granted, the interruptions
> in the regularity of both caused by the layout of the modern
> overstrung frame make this hard to see, but if you actually climb
> inside such a monster and measure the length of EVERY string and then
> compare them to stringing scales stretching back for several
> centuries, you will find that there is no real difference, except for
> the progressive lengthening of the entire scale throughout the 19th
> century as every harder steels became available.

So, barring the overstringing, nothing has changed fundamentally over the
centuries in regards to the average proportions of the keyboard instruments.

(3) The reduction in
> diameter, which almost always follows a regular distribution, that is,
> the steps between gauge changes are regular.
>

How regular? Can you show by an example?

> The problem with these elegant theories of balance between scaling and
> inharmonicity is that the coefficient of inharmoncity is NOT constant
> over the entire scale.

That is to say, octaves are not widened by the same amount throughout the
compass of the instrument when compensating for inharmonicity.

It is highest in the upper octaves, dropping to
> very low in the middle octaves, and then rising again for the tenor.

I see.

> The bass bridge is a completely different world because you can design
> wound strings to have a wide range of elasticity, so you can leave the
> bass bridge out of the discussion entirely.

I see.

Now I would like you or
> anyone to explain to me how the intersection of three regular
> progressions can in some way add up to compensate for a factor which
> is highly irregular.
>

I dare not suggest anything in that direction.

> Beyond all that is the inconvenient truth that other aspects of the
> instruments design (soundboard compliance, ribbing, downbearing, after
> and forelength, etc etc etc) can also cause inharmonicity to vary from
> region to region, even from note to note.
>

So much so, that anybody designing a stringed keyboard instrument for a
particular temperament is nil?

> Now, as to which temperament sounds "better" on a modern piano, htat
> is a matter of personal preference. The biggest problem with this
> concept is the lumping together of the truly vast variation of designs
> and the resultant acoustical objects under the heading "the modern
> piano".

I can see the problem.

If you think there is any sort of consistency in the presence
> of inharmonicity among modern pianos, then you are in for a big
> surprise.

Actually, I am not surprised at all that inharmonicity varies considerably
from fortepiano to fortepiano.

How strange that the makers of all advanced modern
> electronic tuning devices and software, like the Rayburn Cyber Tuner,
> go to great lengths to allow the device to analyze the inharmonicty
> for EVERY note on each individual piano so that the tuner can decide
> how to program the stretching of EACH octave (differently) in order to
> attempt to compensate.

Fascinating.

If we were to believe Andreas, this was all
> resolved by the scaling of "the" modern piano. Poor stupid piano
> tuners, they go to so much work for nothing!
>

I can understand your frustration.

> Frankly, I think that any EDO which stays away from near harmonic
> proportions is the best way to tune a modern piano, because when there
> is constant rapid beating, you don't hear the large variation in
> interval quality over the range of the instrument caused by the large
> variation in inharmonicty. But that is only my preference.
>

Insteresting. But still, one can implement a custom-tailored temperament for
a given piano which bodes well with harmonic proportions?

> Now, if that doesn't clear it up for you Oz,

It clears up matters alright.

let me frame it in
> another way. The fact that cars are not designed specifically for one
> particular size of person does not mean that ANY size of person fits
> equally well in any given car. Do you see where your insistence upon
> drawing a connection is false?
>

My "insistence", was rather based on the fact that any temperament might be
expected to work just as fine as 12-EDO on "modern pianos".

> Ciao,
>
> P
>

Oz.