Yahoo Tuning Groups Ultimate Backup tuning music theory reference site

Chris wrote:

____________________________

>this looks to be a very complete music theory site, at least for old music
which is only as far as I've gone through.
>an excellent series of links with explanatory text.
> http://www.dolmetsc <http://www.dolmetsch.com/theoryintro.htm>
h.com/theoryintro.htm

Yes, but perhaps with a few caveats. I found puzzling some of the Musical
Temperaments tables, "Temperament and Pitch Calculator" by Dr. Brian Blood
http://www.dolmetsch.com/musictheory27t.htm

- It covers several hundreds of 12-note temperaments! Perhaps too many?
Quite few are purported to be historical but are actually modern concoctions
with no possible claim at historical authenticity, e.g. "# 471 :
Aron-Neidhardt equal-beating well-temperament (Sc)"

- I also find it puzzling that, for each temperament, different values are
shown in over 10 rows, including circle of fifths in fractions, but the two
all-important values: fifths and major thirds in cents (or else their
deviations from purity) are not shown.

- As for accuracy of the values, I tested a few temperaments, pasting the
offsets into my spreadsheet for automatic conversion to Circle of Fifths,
and double-checking with my own offsets:

* "#311 Pythagorean-Mean Semitones" and "# 416 Werckmeister I(III)" are
absolutely correct.

* His interpretation of accidentals in "#323 Rameau's Modified Meantone
(Temp.Ord.)" is quite debatable, but the core of 4 pure major thirds is
correct.

* Schlick's temperament is given in no less than 9 modern
interpretations! Yet one which was once thought to be quite accurate,
Hussman, is not included). The last of Schlick's ones reads "Temperament #
357 : Schlick modified Meantone (Po p.35) (DH)": duly analysed, it has
ten(10) equally-tempered fifths by a 1/6 P.c. , closing the circle with a
slightly large fifth and a wolf. I cannot see by any stretch of imagination
how Schlick's description can be interpreted in that way.

* Finally in "#176: Lambert Chaumont" both the Fifths and the Major
thirds circles are zig-zags, alternating very good with very bad values.
E.g., the fifth F-C was flat by 15.6 Cents! This should be is a meantone
fifth! Looking into the values, I found that 3 notes have differences of
quite a few Cents (thus much beyond any discrepancy due to personal
interpretation) with Lambert Chaumont : Eb, Bb and B.

____________________________

>and especially this right now.
>http://www.medieval <http://www.medieval.org/emfaq/harmony/triad.html>
.org/emfaq/harmony/triad.html

A very good recommendation Chris! These are the excellent and very thorough
writings of medieval scholar Margo Schulter, which I recommend in my recent
book.

Kind regards

Claudio

http://temper.braybaroque.ie/

🔗Danny Wier <dawiertx@...>

From: "vaisvil" <chrisvaisvil@...>

> this looks to be a very complete music theory site, at least for old > music which is only as far as I've gone through.
>
> an excellent series of links with explanatory text.
>
> http://www.dolmetsch.com/theoryintro.htm

One of my favorite websites. And they do cover quarter-tone accidentals on page 7 "Small Intervals"; they show the ones I use as the basis of my own 72-equal notation; it's found on page 7, the page titled "Small Intervals", and it does have some links at the bottom, but none to

And thanks for reminding me to do some early music research.

On an aside, I randomly found this page:

http://www.tmdk.itu.edu.tr/n.pdf

The author, Istanbul-based musician and professor Dr. Nail Yavuzoglu (who worked on Tarkan's self-titled album), combines Tartini-Couper accidentals with arrows to notate 53-tone Pythagorean. The TC accidentals raise and lower notes by 2, 5, 7 and 9 commas, while arrows alter them by one. Except quarter-tone and three quarter-tone accidentals with arrows aren't to be found in Euterpe or any other fonts I've found so far...

~D.

🔗Andreas Sparschuh <a_sparschuh@...>

--- In tuning@yahoogroups.com, "Claudio Di Veroli" <dvc@...> wrote:

> http://www.dolmetsch.com/musictheory27t.htm
>
> - I also find it puzzling that,...
> ... fifths and major thirds in cents (or else their
> deviations from purity) are not shown.
>
> - As for accuracy of the values,
> I tested a few temperaments,... by
> .... double-checking with my own offsets:
>
> * "#311 Pythagorean-Mean Semitones" and
> * "# 416 Werckmeister I(III)" are
> absolutely correct.

or try to check it against my own
http://www.strukturbildung.de/Andreas.Sparschuh/Mainz_1999.jpg
The precise results should all be turn out as integral,
when translated back to the original:

"Temperament # 382 : Sparschuh (L e&c) (DH)" @ a'=420Hz

Frequency in Hz.:
orig. vs. Dolmetsch's re-calculation

250 c' ~249.99
264 #' ~263.99
280 d' ~279.99
297 #' ~296.98
314 e ~313.99
333.5 ~333.49 f
352 # =352.00 first exact match
374 g' ~373.98
396 #' ~395.99
420 a' =420.00 per definition = pseudo Neo-'Baroque pitch' + 5Hz
445 bb =445.00 second exact match
470 h' ~469.99
500 c" ~499.99

Result/Conclusion:
All in all there's there appears a tiny tendency
to got somewhat more flattend pitches than the original.

Next topic:
> * Schlick's temperament is given in no less than 9 modern
> interpretations!
> Yet one which was once thought to be quite accurate,
> Hussman, is
unfortunately
> not included).
> The last of Schlick's ones reads "Temperament #
> 357 : Schlick modified Meantone (Po p.35) (DH)":
> duly analysed, it has ten(10)
> equally-tempered fifths by a 1/6 P.c. ,
> closing the circle with a
> slightly large fifth and a wolf.
That both defects appear i.m.h.o. ahistorically.

> I cannot see by any stretch of imagination
> how Schlick's description can be interpreted in that way.
Agreed.
Hence better try for that the well-approved German source:
http://www.groenewald-berlin.de/Inhaltsverzeichnis.html
especially there

#15 Wilhelm Dupont's (1935) interpretation, in Vogel (1975)
http://groenewald-berlin.de/ttg/TTG_T015.html

#28 Helmut K.H. Lange's (1968) interpretation
http://groenewald-berlin.de/ttg/TTG_T028.html

#27 Schlick - Barbour (1/6 pyth. Komma)
http://groenewald-berlin.de/ttg/TTG_T027.html

#45 Rolf Drescher, Berlin, (1980)
http://groenewald-berlin.de/ttg/TTG_T045.html

#49 Franz Josef Ratte: Acta Organologica, Band 21, (1990)
http://groenewald-berlin.de/ttg/TTG_T049.html

#92 Manfred Tessmer, Acta Organologica, Band 25, (1994)
http://groenewald-berlin.de/ttg/TTG_T092.html

or:
http://www.pianolit.com/tuning/left.php?orderBy1=name&orderBy2=name&orderBy3=name
http://www.pianolit.com/tuning/main.php?tuning_id=21
http://www.pianolit.com/tuning/main.php?tuning_id=93
http://www.pianolit.com/tuning/main.php?tuning_id=156
http://www.pianolit.com/tuning/main.php?tuning_id=157

Quest:
Does anybody here in that group knows about more
other interpretations of so called
"Schlick (1511) "-tunings ?

Attend:
In the year after the next
there will be the penta-centenary of
http://en.wikipedia.org/wiki/Arnolt_Schlick
's writing:
* Spiegel der Orgelmacher und Organisten
("Mirror of Organ Makers and Organ Players", Speyer, 1511)

I intend to celebrate that 500ths anniversary by an
-as-complete-as-possible-
critial overview about the different interpretations
over the last few centuries.

bye
A.S.

🔗Claudio Di Veroli <dvc@...>

Thanks Andreas,

Will check the versions you quote as a check. As you probably know, there is
a full re-appraisal in the 2nd edition of my new book, collating Barbour,
Hussman, opinions by Barber and, most importantly, what Schlick actually
wrote, and as a final result a new reconstruction of the temperament which
should be accurate to less than +/- 1 Cent.

Will keep you informed about any significant discrepancy I find with the
sources you quote.

Kind regards,

Claudio

http://temper.braybaroque.ie/

_____

From: tuning@yahoogroups.com [mailto:tuning@yahoogroups.com] On Behalf Of
Andreas Sparschuh
Sent: 24 April 2009 20:13
To: tuning@yahoogroups.com
Subject: [tuning] Schlick in Re: music theory reference site

--- In tuning@yahoogroups. <mailto:tuning%40yahoogroups.com> com, "Claudio
Di Veroli" <dvc@...> wrote:

> http://www.dolmetsc <http://www.dolmetsch.com/musictheory27t.htm>
h.com/musictheory27t.htm
>
> - I also find it puzzling that,...
> ... fifths and major thirds in cents (or else their
> deviations from purity) are not shown.
>
> - As for accuracy of the values,
> I tested a few temperaments,... by
> .... double-checking with my own offsets:
>
> * "#311 Pythagorean-Mean Semitones" and
> * "# 416 Werckmeister I(III)" are
> absolutely correct.

or try to check it against my own
http://www.struktur
<http://www.strukturbildung.de/Andreas.Sparschuh/Mainz_1999.jpg>
bildung.de/Andreas.Sparschuh/Mainz_1999.jpg
The precise results should all be turn out as integral,
when translated back to the original:

"Temperament # 382 : Sparschuh (L e&c) (DH)" @ a'=420Hz

Frequency in Hz.:
orig. vs. Dolmetsch's re-calculation

Result/Conclusion:
All in all there's there appears a tiny tendency
to got somewhat more flattend pitches than the original.

> I cannot see by any stretch of imagination
> how Schlick's description can be interpreted in that way.
Agreed.
Hence better try for that the well-approved German source:
http://www.groenewa
<http://www.groenewald-berlin.de/Inhaltsverzeichnis.html>
ld-berlin.de/Inhaltsverzeichnis.html
especially there

#15 Wilhelm Dupont's (1935) interpretation, in Vogel (1975)
http://groenewald- <http://groenewald-berlin.de/ttg/TTG_T015.html>
berlin.de/ttg/TTG_T015.html

#28 Helmut K.H. Lange's (1968) interpretation
http://groenewald- <http://groenewald-berlin.de/ttg/TTG_T028.html>
berlin.de/ttg/TTG_T028.html

#27 Schlick - Barbour (1/6 pyth. Komma)
http://groenewald- <http://groenewald-berlin.de/ttg/TTG_T027.html>
berlin.de/ttg/TTG_T027.html

#45 Rolf Drescher, Berlin, (1980)
http://groenewald- <http://groenewald-berlin.de/ttg/TTG_T045.html>
berlin.de/ttg/TTG_T045.html

#49 Franz Josef Ratte: Acta Organologica, Band 21, (1990)
http://groenewald- <http://groenewald-berlin.de/ttg/TTG_T049.html>
berlin.de/ttg/TTG_T049.html

#92 Manfred Tessmer, Acta Organologica, Band 25, (1994)
http://groenewald- <http://groenewald-berlin.de/ttg/TTG_T092.html>
berlin.de/ttg/TTG_T092.html

Quest:
Does anybody here in that group knows about more
other interpretations of so called
"Schlick (1511) "-tunings ?

Attend:
In the year after the next
there will be the penta-centenary of
http://en.wikipedia <http://en.wikipedia.org/wiki/Arnolt_Schlick>
.org/wiki/Arnolt_Schlick
's writing:
* Spiegel der Orgelmacher und Organisten
("Mirror of Organ Makers and Organ Players", Speyer, 1511)

I intend to celebrate that 500ths anniversary by an
-as-complete-as-possible-
critial overview about the different interpretations
over the last few centuries.

bye
A.S.

🔗a_sparschuh <a_sparschuh@...>

> > /tuning/topicId_83189.html#83193
> > Schlick's temperament
> > is given in no less than 9 modern interpretations!

--- In tuning@yahoogroups.com, "Claudio Di Veroli" <dvc@...> wrote:
> As you probably know, there is a full re-appraisal in the 2nd
> edition of my new book, collating Barbour, Hussman,
> opinions by Barber and, most importantly, what Schlick actually
> wrote, and as a final result a new reconstruction of the
> temperament which should be accurate to less than +/- 1 Cent.

Here comes my own recent interpretation of Schlick's
'Eleven-eyes' instructions in his chapter 8:
"The tuning of the organ"
by using Werckmeister's "septenarian" style:
http://en.wikipedia.org/wiki/Werckmeister_temperament#Werckmeister_IV_.28VI.29:_the_Septenarius_tunings

when assuming the technical-term "11-eys" could mean as concept

-'-'-'-°-°-°-"-"-"-"-"-

concrete an running chain of 5ths in order from left to right:

F'C'G'D°A°E°B"F#"C#"G#"Eb"Bb

in detail elaborated by the following beating-plan at full length,
now in top-->down direction of the 5ths:

F(87.5g"/9)<[87.6b"'/45]<(87.7c'/3)<[87.8e"'/15]<87.9F<[88a'/5=440/5]
'
C : [260=G#*5] < (262.5=g"/3) < 263.1c' = middle_C4
'
G : [195=EEb*5] < 196.875=g 393.75=g' 787.5=g" 1575=g'''
'
D : 6D=2.3 5D4.6 4D9.2 ... 294.4d'[585.5=Bb*5<] d"588.8 <(590.625=g*3)
°
A : (4D*3=27.6>)3A27.5 a220(>219b"'/9 438<439e"'/3 <)440(<441.6d'*3)
°
E : (328.5=b"/3 b"'/3=657 <) 658.5e" e"'1317 (:= 439*3)
°
B : (FFF#/3=7.7 ... 985.6>) 985.5=b" (:= 328.5*3)
"
F# : [5D*5=23 >] 23.1=FFF# [< 23.42=Bb/5] ... f#'=369.6
"
C# : C#=69.3 c#138.6 [> 137.5=AAA*5 AA*5=275 <] 277.2=c#'
"
G# : 4G#13 3G#26 GG#52 G#104 [>105.24=c"/5]...g#'416 [>411.5625=E*5]
"
Eb : EEb39 Eb78 eb156 [< 157.5=g"/5] eb'312 [> 307.96875=BB/5]
"
Bb :(F/3=29.3 f/3=58.6 f'/3=117.2 >) 117.1Bb (>117EEb*3)[>117.76=d"/5]

That dozen pitch-classes show also the beating-plan of all
twelve 5ths and some of the 3rds. That procedure awakens the 11-eyes
F'C'G'D°A°E°B"F#"C#"G#"Eb"Bb chain concrete into alive.
For retaining that easier in mind, read that instruction, more concise, as mnemonic sequence, with only one single entry for each pitch-class:

F 87.9
'
c' 263.1 middle_C
'
g" 787.5
'
6D 2.3
°
AAA 27.5 lowest piano key 440Hz/16
°
E 328.5
°
B 985.5
"
FFF# 23.1
"
CC# 69.3
"
5G# 6.5
"
EEEb 19.5
"
Bb 117.1

That yields in chromatic ascending order as resulting scala file:

! Sp11eys440Hz.scl
Sparschuh's rational '11-eyes' interpretation of Arnolt Schlick (1511)
12
!
! @ middle c' 263.1 Hz
2772/2631 ! #' 277.2
2944/2631 ! d' 294.4
3120/2631 ! #' 312
6585/5262 ! e' 329.25 := 658.5/2
3516/2631 ! f' 351.6
3696/2631 ! #' 369.6
7875/5262 ! g' 393.25 := 787.5/2
4160/2631 ! #' 416
4400/2631 ! a' 440 Hz absolute pitch reference from tuning fork
4684/2631 ! #' 468.4
9855/5262 ! b' 492.75 := 985.5/2
2/1 ! tenor c" 526.3
!
!

Attend the synchronous beating 3rds an 5ths
in the three most frequently favourite used major triads
F-a-C-e-G-b-D
in the harmonic-cadence of C-major tonality,
that Schlick demands to temper less,
especially in that three relevant 3rds: F-a, C-e and G-b,
instead of privilegeing the older Pythagorean chain of 5ths
F_C_G_D_A_E_B.

That sounds and work fine even on modern pianos
i.m.h.o. even more apt than the stupid 12-edo,
that usually results in: "Tears in my ears!"

Also be aware, key-change results quite strong
http://de.wikipedia.org/wiki/Tonartencharakter
http://eo.wikipedia.org/wiki/Tonalkaraktero
Sorry, that there is not yet any english entry of that.
But just try that one simply out, and conclude yourself
how well that tuning fits into yours own ears.
Have a lot of fun...

Quest:
Are there any other new suggestions for
http://en.wikipedia.org/wiki/Arnolt_Schlick
http://de.wikipedia.org/wiki/Arnolt_Schlick
's really remarkable temperament half an millenium ago,
when celebrating in the next year
the occasion of his penta-centennial jubilee?

bye
A.S.

music theory reference site

🔗vaisvil <chrisvaisvil@...>

🔗Carl Lumma <carl@...>

🔗Chris Vaisvil <chrisvaisvil@...>

🔗Claudio Di Veroli <dvc@...>

🔗Danny Wier <dawiertx@...>

🔗Andreas Sparschuh <a_sparschuh@...>

🔗Andreas Sparschuh <a_sparschuh@...>

🔗Andreas Sparschuh <a_sparschuh@...>

🔗Claudio Di Veroli <dvc@...>

🔗a_sparschuh <a_sparschuh@...>