Yahoo Tuning Groups Ultimate Backup tuning Request for historic tuning

--- In tuning@yahoogroups.com, "Jon Szanto" <jszanto@...> wrote:
>
> If one were to compose some music that would be a backdrop to
> Victorian England, and possible stretching into Edwardian times (let
> us just say from 1850 - 1915), what would be a plausible tuning other
> than 12tet?

I've got bad news. I don't think any other is very plausible on
fixed-pitch instruments unless you're talking pipe organs. They last a
long time and aren't so easy to retune, so there may have been a few
still around in England in 1/4-comma meantone in that period.

Except of course there's always the Great Highland Bagpipe. It's
_still_ holding out against the 12-equal tide. Hoorah.

-- Dave Keenan

🔗monz <monz@tonalsoft.com>

Hi Jon,

--- In tuning@yahoogroups.com, "Jon Szanto" <jszanto@...> wrote:
>
> If one were to compose some music that would be a backdrop
> to Victorian England, and possible stretching into Edwardian
> times (let us just say from 1850 - 1915), what would be a
> plausible tuning other than 12tet? One can think of early
> Elgar and various other composers, maybe even G&S. I may
> be writing something like this, and there is no reason to
> not use the opportunity to both explore (me), and enlighten
> (listeners).
>
> Try, if at all possible, to be succinct and as close to
> specs as possible (i.e. no 379 EDO treatises, etc) - give
> me your favorite choice, not an entire list. Bonus points
> if you can post data in .scl format or give me the name in
> the Scala tuning archives...

Darn, and the first tuning i thought of was 31920-edo!
... ok, just kidding.

Seriously, my choice would be 1/6-comma meantone.
I'm quite convinced by now that this was the standard
of intonation used in practice by orchestral musicians
during the 19th century and on into the first few
decades of the 20th -- more precisely, from c.1760-1930.

I don't have a .scl file of it handy, but over at the
Yahoo Tonescape Den Haag group i *have* posted
the whole set of 1/6-comma tunings for each tonic in
Tonescape .tuning format ... in case you're ready
to start composing with that. ;-)

If this helps, here's 1/6-comma meantone listed by
generator number. I've included all the notes you'd
need for any of the standard keys, from Cb-major on
the flat side (use generators -6 for Gbb to +24 for Ax)
to A#-minor on the sharp side (use generators -23 for
Gbb to +7 for Ax).

(use Options|Fixed Width Font to view correctly
on the stupid Yahoo web interface)

1/6-comma meantone

gen. .. cents

+ 24 . 1160.895
+ 23 .. 462.524
+ 22 .. 964.154
+ 21 .. 265.783
+ 20 .. 767.412
+ 19 ... 69.042
+ 18 .. 570.671
+ 17 . 1072.301
+ 16 .. 373.930
+ 15 .. 875.559
+ 14 .. 177.189
+ 13 .. 678.818
+ 12 . 1180.447
+ 11 .. 482.077
+ 10 .. 983.706
+ 09 .. 285.336
+ 08 .. 786.965
+ 07 ... 88.594
+ 06 .. 590.224
+ 05 . 1091.853
+ 04 .. 393.482
+ 03 .. 895.112
+ 02 .. 196.741
+ 01 .. 698.371
+ 00 .... 0.000
- 01 .. 501.629
- 02 . 1003.259
- 03 .. 304.888
- 04 .. 806.518
- 05 .. 108.147
- 06 .. 609.776
- 07 . 1111.406
- 08 .. 413.035
- 09 .. 914.664
- 10 .. 216.294
- 11 .. 717.923
- 12 ... 19.553
- 13 .. 521.182
- 14 . 1022.811
- 15 .. 324.441
- 16 .. 826.070
- 17 .. 127.699
- 18 .. 629.329
- 19 . 1130.958
- 20 .. 432.588
- 21 .. 934.217
- 22 .. 235.846
- 23 .. 737.476

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

🔗Jon Szanto <jszanto@cox.net>

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@...> wrote:
> I've got bad news. I don't think any other is very plausible on
> fixed-pitch instruments unless you're talking pipe organs.

Hey babe, it's a brand new (old) world. Don't *assume* I'm speaking of
writing for instruments that exist out here, think virtual. I'm emulating.

If it means anything, start from true Victorian-era music and take a
line from there to steampunk. And back.

Maybe I should put it this way, since imagination (and not truly
historical veracity) is the key: how about likely tunings as one
*entered* the Victorian era, before they all dropped away like dead
intonational flies?

Sorry for being cryptic, it isn't on purpose!

All hail Choob Master!!

Jon

🔗Charles Lucy <lucy@harmonics.com>

They would probably have been using 12edo, but if you want to use a meantone and have it be authentically English and in use in UK before that period, I have made it very easy for you.

Just go to:

http://www.lucytune.com/midi_and_keyboard/pitch_bend.html

and download the tuning codes for 49 different note assignments to LucyTune the most popular professional DAW's, in six different formats.

So you can then use a standard 12edo midi file and get the tuning adjusted by selecting which of the 49 options best suit your DAW and the sound that you want.

Charles Lucy lucy@lucytune.com

----- Promoting global harmony through LucyTuning -----

For information on LucyTuning go to: http://www.lucytune.com

LucyTuned Lullabies (from around the world):
http://www.lullabies.co.uk

Skype user = lucytune

On 24 Apr 2007, at 04:30, Dave Keenan wrote:

> --- In tuning@yahoogroups.com, "Jon Szanto" <jszanto@...> wrote:
> >
> > If one were to compose some music that would be a backdrop to
> > Victorian England, and possible stretching into Edwardian times (let
> > us just say from 1850 - 1915), what would be a plausible tuning > other
> > than 12tet?
>
> I've got bad news. I don't think any other is very plausible on
> fixed-pitch instruments unless you're talking pipe organs. They last a
> long time and aren't so easy to retune, so there may have been a few
> still around in England in 1/4-comma meantone in that period.
>
> Except of course there's always the Great Highland Bagpipe. It's
> _still_ holding out against the 12-equal tide. Hoorah.
>
> -- Dave Keenan
>
>
>

🔗Gene Ward Smith <genewardsmith@sbcglobal.net>

🔗Jon Szanto <jszanto@cox.net>

🔗monz <monz@tonalsoft.com>

Hi Jon,

--- In tuning@yahoogroups.com, "Jon Szanto" <jszanto@...> wrote:
>
> Gene,
>
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@>
> wrote:
> > In that case, Monz's suggestion of 1/6-comma meantone
> > is a good one.
>
> Thanks, I'll look into that...

I've made the Scale .scl file for you, using "A" as
the 1/1. Copy and paste everything between the horiztonal
lines below to a plain text file and save it with the name
i gave at the top or whatever other name makes sense to you.

-------------------------------------------------------
! 1-6-cmt_31-tone.scl
!

31
!
19.55257
88.59433
108.14690
177.18867
196.74124
216.29381
285.33557
304.88814
324.44071
393.48248
413.03505
482.07681
501.62938
521.18195
590.22371
609.77629
678.81805
698.37062
717.92319
786.96495
806.51752
826.07010
895.11186
914.66443
983.70619
1003.25876
1022.81133
1091.85310
1111.40567
1180.44743
2/1
---------------------------------------------------------

Since the pure .scl file doesn't have the note-names,
here's a list of them:

0: 1/1 A unison, perfect prime
1: 19.553 cents Bbb
2: 88.594 cents A#
3: 108.147 cents Bb
4: 177.189 cents B
5: 196.741 cents B
6: 216.294 cents Cb
7: 285.336 cents B#
8: 304.888 cents C
9: 324.441 cents C
10: 393.482 cents C#
11: 413.035 cents Db
12: 482.077 cents Cx
13: 501.629 cents D
14: 521.182 cents D
15: 590.224 cents D#
16: 609.776 cents Eb
17: 678.818 cents E
18: 698.371 cents E
19: 717.923 cents Fb
20: 786.965 cents E#
21: 806.518 cents F
22: 826.070 cents F
23: 895.112 cents F#
24: 914.664 cents Gb
25: 983.706 cents Fx
26: 1003.259 cents G
27: 1022.811 cents G
28: 1091.853 cents G#
29: 1111.406 cents Ab
30: 1180.447 cents Gx
31: 2/1 A octave

You'll be able to get Scala to show you this if you
choose the "Options" button and select "P31" notation,
and set "A" as the 1/1.

I personally much prefer playing with this in Tonescape,
but that's just me ... ;-)

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

🔗monz <monz@tonalsoft.com>

Hi Jon,

--- In tuning@yahoogroups.com, "monz" <monz@...> wrote:

> Since the pure .scl file doesn't have the note-names,
> here's a list of them:
>
> <snip>
>
> You'll be able to get Scala to show you this if you
> choose the "Options" button and select "P31" notation,
> and set "A" as the 1/1.

Oops, my bad ... of course you should use "P55" notation,
and the toolbar button is marked "Opts". Sorry about that.

I randomly chose a Tolerance of 0.18 and it worked fine.
Here's the correct list of note names:

0: 1/1 A unison, perfect prime
1: 19.553 cents Bbb
2: 88.594 cents A#
3: 108.147 cents Bb
4: 177.189 cents Ax
5: 196.741 cents B
6: 216.294 cents Cb
7: 285.336 cents B#
8: 304.888 cents C
9: 324.441 cents Dbb
10: 393.482 cents C#
11: 413.035 cents Db
12: 482.077 cents Cx
13: 501.629 cents D
14: 521.182 cents Ebb
15: 590.224 cents D#
16: 609.776 cents Eb
17: 678.818 cents Dx
18: 698.371 cents E
19: 717.923 cents Fb
20: 786.965 cents E#
21: 806.518 cents F
22: 826.070 cents Gbb
23: 895.112 cents F#
24: 914.664 cents Gb
25: 983.706 cents Fx
26: 1003.259 cents G
27: 1022.811 cents Abb
28: 1091.853 cents G#
29: 1111.406 cents Ab
30: 1180.447 cents Gx
31: 2/1 A octave

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

🔗monz <monz@tonalsoft.com>

🔗Tom Dent <stringph@gmail.com>

You are (for me) pretty darn cryptic. What would be the point of
supposedly historical tuning if you don't intend to use any other
historical method of music-making?

The historical method would be to take a 19th century piano, or not,
depending on whether you wanted it, get it tuned entirely by ear, take
string, woodwind and brass instruments likewise, put players behind
them and get them to use their ears.

The result would NOT be describable by any mathematical system short
of specifying the individual frequency of each separate note in the piece.

I happened to look at an article by the violinist Roentgen in a late
19th century German musicology journal - he was pointing out that even
in the absence of a keyboard people often didn't play pure thirds like
Helmholtz said they oughtta, and also people played different pitches
for the same nominal in different musical contexts.

Two examples: the first one was a perfect cadence prepared by a
suspension, C-B-C in the tenor over G-G-C in the bass. In that case he
said people commonly take a sharp leading note and G-B is impure. The
second was an imperfect cadence with G-C-B in the soprano over C-A-G
in the bass: in this case he said the final major third might well be
pure, as a point of rest.

So the tuning of each interval and each note *depends on the immediate
musical context*. Adaptive, but not always adaptive in the direction
of producing pure intervals. The easiest way to get that sort of
tuning is to use several musicians playing traditional instruments.

One thing I know is that Edward Elgar (and his father before him) did
a lot of piano tuning - that would have been in the 1860s onwards, and
probably some by-ear method of approximating 12ET, though one would
have to look at real historical evidence to see exactly what sort of
method. The big Jorgensen book has some evidence, though what he says
about Ellis' researches is seriously flawed (basically he massages the
numbers to fit his preconceptions of what a historical piano tuning
ought to have been) and his 'Broadwood' temperaments are pure fiction.

Try looking at 'Tuner's Guide #2' or 'Tuner's Guide #3' - based on
historical instructions from 1840 and basically quite close
approximations to 12ET.
http://rollingball.com/images/TunersGuide2.gif

Basically if you want something to sound 'Victorian' then I can't see
how temperament can be much of a factor. What you might like to
consider are: timbre, use of vibrato (less) or portamento (more) in
string playing, amount of octave stretch (less) in piano tuning,
dichords rather than trichords, rubato ...

(Or you could go for the gambit of a randomly out-of-tune piano, which
should suggest 'olden days' in that most old pianos are indeed
randomly out-of-tune due to neglect and decay... but you'd have to be
quite shameless.)

~~~T~~~

--- In tuning@yahoogroups.com, "Jon Szanto" <jszanto@...> wrote:
>
> --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@> wrote:
> > I've got bad news. I don't think any other is very plausible on
> > fixed-pitch instruments unless you're talking pipe organs.
>
> Hey babe, it's a brand new (old) world. Don't *assume* I'm speaking of
> writing for instruments that exist out here, think virtual. I'm
emulating.
>
> If it means anything, start from true Victorian-era music and take a
> line from there to steampunk. And back.
>
> Maybe I should put it this way, since imagination (and not truly
> historical veracity) is the key: how about likely tunings as one
> *entered* the Victorian era, before they all dropped away like dead
> intonational flies?
>
> Sorry for being cryptic, it isn't on purpose!
>
> All hail Choob Master!!
>
> Jon

🔗Tom Dent <stringph@gmail.com>

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:
>
> --- In tuning@yahoogroups.com, "Jon Szanto" <jszanto@> wrote:
> >
> > --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@> wrote:
> > > I've got bad news. I don't think any other is very plausible on
> > > fixed-pitch instruments unless you're talking pipe organs.
> >
> > Hey babe, it's a brand new (old) world. Don't *assume* I'm speaking of
> > writing for instruments that exist out here, think virtual. I'm
> emulating.
>
> In that case, Monz's suggestion of 1/6-comma meantone
> is a good one. Yse 55-et instead if that would be more
> convenient.
>

Wouldn't get you anywhere if you wanted to 'emulate' the expressively
adaptive aspect of tuning which is allowed by an artistically aware
choice of intervals anywhere between 5-limit and Pythagorean (which is
what Roentgen's article as a whole implies) and was almost certainly
used by string players and singers.

It's a myth that anyone, except players of fixed-pitch instruments,
ever 'succumbed to 12ET'. (A corollary of the range of choice in
intonation is that no-one 'succumbed' to 55ET either.)

Another article in the same journal is by Max Planck, who reports from
personal experience that unaccompanied choirs singing a particular
piece by Schuetz as purely as possible are subject to comma drift.
Draw your own conclusions.

~~~T~~~

🔗Carl Lumma <clumma@yahoo.com>

🔗monz <monz@tonalsoft.com>

Hi Tom,

--- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:
>
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@>
> wrote:
> >
> > In that case, Monz's suggestion of 1/6-comma meantone
> > is a good one. Yse 55-et instead if that would be more
> > convenient.
> >
>
> Wouldn't get you anywhere if you wanted to 'emulate' the
> expressively adaptive aspect of tuning which is allowed
> by an artistically aware choice of intervals anywhere
> between 5-limit and Pythagorean (which is what Roentgen's
> article as a whole implies) and was almost certainly
> used by string players and singers.
>
> It's a myth that anyone, except players of fixed-pitch
> instruments, ever 'succumbed to 12ET'. (A corollary of
> the range of choice in intonation is that no-one
> 'succumbed' to 55ET either.)
>
> Another article in the same journal is by Max Planck,
> who reports from personal experience that unaccompanied
> choirs singing a particular piece by Schuetz as purely
> as possible are subject to comma drift.
> Draw your own conclusions.

Everything you say is true. And for sure, any
_a capella_ choir singing music based on triadic harmony
and trying to make their intonation "pure" is going
to tend to drift downward in pitch -- it's a natural
result of moving from the II chord to the V chord in
a major key.

However, it is also true that orchestral musicians during
this period were often taught during their training that
the whole-tone was to be divided into 9 "commas", and
that there were two different sizes of semitones: the
chromatic-semitone of 4 commas, and the diatonic-semitone
of 5 commas. Assuming octave-equivalence and that the
octave is comprised of 5 whole-tones and 2 diatonic-semitones,
that is a total of (5*9)+(2*5) = 45+10 = 55 commas per
octave, which means 55-edo.

Our standard notational system uses a chain-of-5ths
that runs from Gbb to Ax, which is a total of 31 different
notes. So no composer during the "common-practice" period
ever used the entire 55-edo -- only at most a 31-tone
subset of it, and actually usually a far smaller subset.

I've discovered that in every Beethoven orchestral piece
that i've so far made into a Tonescape file, he used
a 15-tone set of notated pitches, with 3 pairs of
enharmonic equivalents along with the 9 other individual
notes -- and they all follow the same Lattice structure.
This leads me to believe that there's something to this.

And i wish to emphasize one phrase i wrote above:
"orchestral musicians during this period were often taught
during their training". As a trained musician -- but one
who learned 12-edo instead of 55-edo -- i can testify to
how ingrained this kind of thinking becomes. If musicians
during this period were taught 55-edo, then believe me,
that's what they tended to play.

Of course the "expressive intonation" was also taught,
and that would tend to bend some pitches toward the
pythagorean version of the notated pitch. So indeed
the intonational system would be quite messy and chaotic,
as you describe. But for this period, a 55-edo basis
is far preferred to 12-edo for orchestral instruments
(or their digital emulations).

In case you haven't seen it, i have a webpage about this:

http://tonalsoft.com/enc/number/55edo/55edo.htm

It's quite sloppy and badly needs to be edited, but
knowing your penchant for scholarship, i'd like to
direct you to the last part of it, which quotes Mozart's
actual teaching of intonation, and it is indeed meantone.
Altho Mozart himself never specified the 55-edo sizes
in this notebook, his father Leopold did teach exactly
that in his violin method.

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

🔗Jon Szanto <jszanto@cox.net>

Hi Tom,

--- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:
> You are (for me) pretty darn cryptic. What would be the point of
> supposedly historical tuning if you don't intend to use any other
> historical method of music-making?

Note the last line in my post:
> > Sorry for being cryptic, it isn't on purpose!

Hey, don't want to cause consternation. There are still a few people
around here who know me, and I'm sorry that my odd post was a problem
for you. I assure you I'm not up to no good (or that I'm actually up
to good)! The closest parallel I can think of is the "steampunk"
culture/aesthetic: if one could imagine that, at some juncture in the
early Victorian period, technology, society, and culture took a very
different course, what would be the end-products of this time? So I am
very much creating an imaginary musical situation, but one that would
branch out of an actual period in history. Therefore, I asked the
patient and knowledgeable staff of Ye Olde Tuning List for
recommendations on tunings that might be likely candidates as a
"jumping off point".

I could sure as hell just write stuff either in 12EDO, or just
completely at random throw a tuning in there that had no connection
whatsoever. But that doesn't interest me. Which means that:

> (Or you could go for the gambit of a randomly out-of-tune piano,
> which should suggest 'olden days' in that most old pianos are
> indeed randomly out-of-tune due to neglect and decay... but
> you'd have to be quite shameless.)

I'm not shameless. I just have a bit of a sense of humor, coupled with
a sense of adventure. And I was hoping maybe a couple souls could wrap
their head around that concept.

Cheers,
Jon

🔗Jon Szanto <jszanto@cox.net>

One last point,

--- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:
> It's a myth that anyone, except players of fixed-pitch instruments,
> ever 'succumbed to 12ET'.

Uh, since Carl decided to play "pile on" with that comment, I simply
threw out that wording to look at the end result of our slightly more
recent continuum: at one point, there were many tunings, and at some
point Western classical music (and popular, I suppose) boiled down to
pretty much only 12EDO. Hope that makes it more clear, it is a broad
generalization, but does (I believe) reflect the reality. It wasn't
meant as a strong statement of a historic event or movement.

🔗Charles Lucy <lucy@harmonics.com>

I see that Monz has used a different format for you:

Here would be the LucyTuned equivalents

0: 1/1 A unison, perfect prime
1: 54.084 cents Bbb
2: 68.451 cents A#
3: 122.535 cents Bb
4: 136.902 cents Ax
5: 190.986 cents B
6: 245.071 cents Cb
7: 259.436 cents B#
8: 313.521 cents C
9: 367.606 cents Dbb
10: 381.972 cents C#
11: 436.056 cents Db
12: 450.423 cents Cx
13: 504.507 cents D
14: 558.591 cents Ebb
15: 572.958 cents D#
16: 627.042 cents Eb
17: 641.409 cents Dx
18: 695.493 cents E
19: 749.577 cents Fb
20: 763.944 cents E#
21: 818.028 cents F
22: 872.113 cents Gbb
23: 886.479 cents F#
24: 940.563 cents Gb
25: 954.930 cents Fx
26: 1009.014 cents G
27: 1063.098 cents Abb
28: 1077.465 cents G#
29: 1131.549 cents Ab
30: 1145.916 cents Gx
31: 2/1 A octave

You will notice a wide divergence.

But then I suppose his choice will make more sense for your unpleasant "outta tune" intentions;-)

Charles Lucy lucy@lucytune.com

----- Promoting global harmony through LucyTuning -----

For information on LucyTuning go to: http://www.lucytune.com

LucyTuned Lullabies (from around the world):
http://www.lullabies.co.uk

Skype user = lucytune

On 24 Apr 2007, at 08:35, monz wrote:

> Hi Jon,
>
> --- In tuning@yahoogroups.com, "monz" <monz@...> wrote:
>
> > Since the pure .scl file doesn't have the note-names,
> > here's a list of them:
> >
> > <snip>
> >
> > You'll be able to get Scala to show you this if you
> > choose the "Options" button and select "P31" notation,
> > and set "A" as the 1/1.
>
> Oops, my bad ... of course you should use "P55" notation,
> and the toolbar button is marked "Opts". Sorry about that.
>
> I randomly chose a Tolerance of 0.18 and it worked fine.
> Here's the correct list of note names:
>
> 0: 1/1 A unison, perfect prime
> 1: 19.553 cents Bbb
> 2: 88.594 cents A#
> 3: 108.147 cents Bb
> 4: 177.189 cents Ax
> 5: 196.741 cents B
> 6: 216.294 cents Cb
> 7: 285.336 cents B#
> 8: 304.888 cents C
> 9: 324.441 cents Dbb
> 10: 393.482 cents C#
> 11: 413.035 cents Db
> 12: 482.077 cents Cx
> 13: 501.629 cents D
> 14: 521.182 cents Ebb
> 15: 590.224 cents D#
> 16: 609.776 cents Eb
> 17: 678.818 cents Dx
> 18: 698.371 cents E
> 19: 717.923 cents Fb
> 20: 786.965 cents E#
> 21: 806.518 cents F
> 22: 826.070 cents Gbb
> 23: 895.112 cents F#
> 24: 914.664 cents Gb
> 25: 983.706 cents Fx
> 26: 1003.259 cents G
> 27: 1022.811 cents Abb
> 28: 1091.853 cents G#
> 29: 1111.406 cents Ab
> 30: 1180.447 cents Gx
> 31: 2/1 A octave
>
>
>
>

🔗Jon Szanto <jszanto@cox.net>

🔗Gene Ward Smith <genewardsmith@sbcglobal.net>

🔗Carl Lumma <clumma@yahoo.com>

🔗Jon Szanto <jszanto@cox.net>

🔗monz <monz@tonalsoft.com>

--- In tuning@yahoogroups.com, "monz" <monz@...> wrote:
>
> Hi Tom,
>
> <snip>
>
> However, it is also true that orchestral musicians during
> this period were often taught during their training that
> the whole-tone was to be divided into 9 "commas", and
> that there were two different sizes of semitones: the
> chromatic-semitone of 4 commas, and the diatonic-semitone
> of 5 commas. Assuming octave-equivalence and that the
> octave is comprised of 5 whole-tones and 2 diatonic-semitones,
> that is a total of (5*9)+(2*5) = 45+10 = 55 commas per
> octave, which means 55-edo.
>
> <snip>
>
> In case you haven't seen it, i have a webpage about this:
>
> http://tonalsoft.com/enc/number/55edo/55edo.htm
>
> It's quite sloppy and badly needs to be edited, but
> knowing your penchant for scholarship, i'd like to
> direct you to the last part of it, which quotes Mozart's
> actual teaching of intonation, and it is indeed meantone.
> Altho Mozart himself never specified the 55-edo sizes
> in this notebook, his father Leopold did teach exactly
> that in his violin method.

I did just add some things to the part of that page which
quotes Attwood's [Mozart's student] notebook: an English
translation of Mozart's explanation of where the semitones
are in the major-scale, and English translations of all of
Mozart's Italian interval names in the table he gives, and
an expanded example illustrating his description of each one.

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

🔗Carl Lumma <clumma@yahoo.com>

🔗Jon Szanto <jszanto@cox.net>

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
> Because steampunk is all about what could have happened
> if technology had taken a different route. Typically
> steampunk universes don't feature technology as it
> actually existed in Victorian times, but rather, tech
> which is in some sense competitive or better than what
> we have today.

I see. Most of my readings have Victoriana as a definite jumping off
point, and when still situated in a somewhat period fashion, retain a
lot of those elements. I guess I am thinking of a branch of history,
yet only a few years (or, at best, decades) beyond the branch. This is
why I wanted to possibly retain a tuning that might have been in use
or just pre-dated the time, yet with other appendages that might have
developed 'otherwise'. Yeesh, cryptic again.

Anyhow, thanks for the suggestion, taking it under advisement.

Cheers,
Jon

🔗monz <monz@tonalsoft.com>

Hi Jon,

--- In tuning@yahoogroups.com, "Jon Szanto" <jszanto@...> wrote:
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <clumma@> wrote:
> > Because steampunk is all about what could have happened
> > if technology had taken a different route. Typically
> > steampunk universes don't feature technology as it
> > actually existed in Victorian times, but rather, tech
> > which is in some sense competitive or better than what
> > we have today.
>
> I see. Most of my readings have Victoriana as a definite
> jumping off point, and when still situated in a somewhat
> period fashion, retain a lot of those elements. I guess
> I am thinking of a branch of history, yet only a few years
> (or, at best, decades) beyond the branch. This is why
> I wanted to possibly retain a tuning that might have been
> in use or just pre-dated the time, yet with other appendages
> that might have developed 'otherwise'. Yeesh, cryptic again.
>
> Anyhow, thanks for the suggestion, taking it under advisement.

Wow, the syncronicity is amazing! -- i had just decided to
offer you a couple of Scala .scl files as alternatives to
the real 1/6-comma meantone, and now i read your post about
how your alternate vision of Victoriana is the whole point!

Anyways, here they are ...

First, "historically correct" approximation to 1/6-comma
meantone: 55-edo, which is what Mozart's father taught, with
9 commas per whole-tone and 5 commas per diatonic-semitone:

------------------------------------------------------
! 55edo_1-6-cmt_31-tone.scl
!

31
!
21.81818
87.27273
109.09091
174.54545
196.36364
218.18182
283.63636
305.45455
327.27273
392.72727
414.54546
480.00000
501.81818
523.63637
589.09091
610.90909
676.36363
698.18182
720.00000
785.45454
807.27273
829.09091
894.54545
916.36364
981.81818
1003.63636
1025.45455
1090.90909
1112.72727
1178.18182
2/1
----------------------------------------------------

Next, a really interesting tuning: 122-edo, which is a
much closer approximation to 1/6-comma meantone than 55-edo,
but which also offers a better mapping of prime-factor 5,
which means that you can also use it alternatively as an
approximation to 5-limit JI. The very-close-to-1/6-comma
meantone 5th is 71 degrees of 122, and the meantone mapping
of 5 (i.e., the major-3rd) is 40 degrees -- this mapping
tempers out the syntonic-comma and it really is thus a
meantone tuning. However, the "better" mapping of 5 is
39 degrees, which results in the syntonic-comma mapping
to 1 degree of 122-edo, thus this mapping behaves like JI.

Here's the .scl file for 122-edo as an approximation to
1/6-comma meantone ... compare these cents values with
those i gave in the .scl file for the real 1/6-comma meantone:

-------------------------------------------------------
! 122edo_1-6-cmt_31-tone.scl
!

31
!
19.67213
88.52459
108.19672
177.04918
196.72131
216.39344
285.24590
304.91803
324.59016
393.44262
413.11475
481.96722
501.63934
521.31147
590.16394
609.83606
678.68853
698.36066
718.03278
786.88525
806.55738
826.22950
895.08197
914.75410
983.60656
1003.27869
1022.95082
1091.80328
1111.47541
1180.32787
2/1
-------------------------------------------------------

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

🔗Carl Lumma <clumma@yahoo.com>

🔗Jon Szanto <jszanto@cox.net>

🔗Kraig Grady <kraiggrady@anaphoria.com>

I am always amazed at the difference in intonation practice even in my/our own life time.
If one listens to a recording from the 40's Orchestras have change very significantly.
Even Jazz, maybe for the worse.
Yesterday i listened to the earliest recording of Woody Herman and his herd playing the Ebony Concerto of Stravinsky
8/19/1946. It is the best version ever

Posted by: "Jon Szanto"

Cheers,
Jon
If you are saying that a performance in 1850 would "sound basically
the same tuning-wise as what we have today", well, hmmm, ok.
Nonetheless, while the tuning (as always) is just one component, it
seemed something interesting to look into. Which I've just done by
posting to the list.

Cheers,
Jon
--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/index.html>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main/index.asp> 88.9 FM Wed 8-9 pm Los Angeles

🔗threesixesinarow <CACCOLA@NET1PLUS.COM>

--- In tuning@yahoogroups.com, "Jon Szanto" <jszanto@...> wrote:
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <clumma@> wrote:
> > Because steampunk is all about what could have happened
> > if technology had taken a different route. Typically
> > steampunk universes don't feature technology as it
> > actually existed in Victorian times, but rather, tech
> > which is in some sense competitive or better than what
> > we have today.
>
> I see. Most of my readings have Victoriana as a definite
> jumping off point, and when still situated in a somewhat
> period fashion, retain a lot of those elements. I guess
> I am thinking of a branch of history, yet only a few years
> (or, at best, decades) beyond the branch. This is why I
> wanted to possibly retain a tuning that might have been
> in use or just pre-dated the time, yet with other
> appendages that might have developed 'otherwise'...

Earlier, but what about Farey's literal interpretation of
Broadwood's outline from the Monthly Magazine, dividing the
major semitone into 40 equal parts (reproduced in the
Edinburgh Encyclopedia): "'with your hammer,' says Mr.
Broadwood, 'lower down, or flatten C by the smallest
possible gradations, until it becomes unison with B ; with
a tolerably steady hand, and a few trials, you will be
enabled to enumerate forty gradations of sound, which I
call commas.'"

Clark

🔗Andreas Sparschuh <a_sparschuh@yahoo.com>

--- In tuning@yahoogroups.com, "Jon Szanto" <jszanto@...> wrote:
>
> If one were to compose some music that would be a backdrop to
> Victorian England....
Just try that modern trial of attempting to remake that style:

in 5ths:
-6: _ _ _ Ab 415 Hz < 416 208 204 102
-5: _ _ _ Eb 312 156 78
-4: _ _ _ Bb 234 117
-3: 351 > F_ 350 175
-2: 525 > C_ 524 262 131
-1: _ _ _ G_ 393 > 392 196 98
00: _ _ _ D_ 294 147
+1: 441 > A_ 440 220 110
+2: 330 > E_ 329 > 328 164 82
+3: _ _ _ B_ 246 123
+4: 369 > F# 368 184 92
+5: _ _ _ C# 276 138
+6: 414 > G# 415 Hz

yields recombined in ascending order:

+1: A3 220 Hz
-4: Bb 234
+3: B3 246
-2: C4 262 'middle-C'
+5: C# 276
00: D4 294
-5: Eb 312
+2: E4 329
-3: F4 350
+4: F# 368
-1: G4 393
+6: G# 415
+1: A4 440 Hz

> Bonus points if you can post data in .scl
> format or give me the name in the Scala tuning archives...
>
!neoVictorian.scl
!
middle-C4 = 262 Hz or A4 = 440 Hz
!
12
!
138/131 ! C#
147/131 ! D
156/131 ! Eb
329/262 ! E
415/262 ! F
393/262 ! F#
415/262 ! G
220/131 ! A
234/131 ! Bb
246/131 ! B
2/1
!
!

sharpnesses of the 3rds
on the empty violin strings:
1:G 2:D 3:A 4:E

1: G < B < < Eb < G.
absolute pitches:
G_ 393 = 131*3
5*131*3= 3*655 < 656*3 328*3 164*3 82*3 41*3 = B 123 < 124 62 31
5 * 31 = 155 < Eb 156 78 = 26*3
5*26*3 = 3*130 < 131*3 = G 393.

That results in the relative diesis 128/125 subdistribution:
G 656/655 B 69.333.../68.333... Eb 131/130 G.

2: D < F# < Bb < D.
abs:
D 147
5*147 = 735 < F# 736 368 ... 46 23
5* 23 = 115 < B 117 = 39*3
5*39*3= 3*195 < 196*3 98*3 49*3 = D 147.
rel:
D 736/735 F# 58.5/57.5 B 196/195 D.

3: A < C# < < F < A.
abs:
A 55
5* 55 = 275 < C# 276 139 69 < 70 35
5* 35 = 175 < F 176 88 44 22 11
5* 11 = A 55.
rel:
A 276/275 C# 70/69 F 176/175 A.

4: E < < G# < C < E.
abs:
E 329 < 330 165 < 166 83
5*83 = G# 415 < 416 208 ... 52 26
5*26 = 130 < C 131
5*131= 655 < E 658 329.
rel:
E 110.666../109.666.. G# (17/21+99)/(98+17/21) C 219.333../218.333.. E

~Cents approx. distribution of the 4 diesises
represented as 3rds sharpnesses:

1: G<3<B_<<<<<<<<<<<<25<<<<<<<<<<<Eb<<<<<<13<<<<<C.
2: D<2F#<<<<<<<<<<<<<<30<<<<<<<<<<<<<<Bb<<<<9<<<<G.
3: A<<<6<<C#<<<<<<<<<<<<25<<<<<<<<<<<F_<<<<10<<<<A.
4: E<<<<<<<16<<<<<<<G#<<<<<<<<17<<<<<C_<<<<<13<<<E.

slightly different from 12-EDO with all 3rds ~14Cents same sharp.

For those who like meantonic harmonic 7ths 7/4 Eb>C#
Attend:
7*Eb/C# is barely 92/91 ~18.9Cents sharp
-still yet used in Victorian era -
instead ~32.2C in 12-EDO.

have a lot of fun with that
A.S.

🔗Brad Lehman <bpl@umich.edu>

> The historical method would be to take a 19th century piano, or not,
> depending on whether you wanted it, get it tuned entirely by ear, take
> string, woodwind and brass instruments likewise, put players behind
> them and get them to use their ears.
> > The result would NOT be describable by any mathematical system short
> of specifying the individual frequency of each separate note in the
> piece.

I concur!

In this olden book from c1908 (IIRC - a cheap Dover paperback reprint that my local library has),
http://www.amazon.com/Piano-Tuning-Simple-Accurate-Amateurs/dp/0486232670

the author presses the model of equal temperament, done by ear, obviously...but an interesting remark (to me) is that he has a complaint against some of the other contemporary tuners. He says that some of them do too much favoring of the flat keys, and it's therefore not equal enough for him. [NB: His complaint is theoretical, not about the musical results or the usefulness of temperaments so nuanced.]

To me, this suggests that some of those Victorian piano tuners, *using their own good taste for their customers' repertoire*, were doing something sort of like:

- 1/6 to 1/8 comma 5ths among the naturals;

- having the sharps rise rapidly (maybe with several pure or nearly-pure 5ths starting somewhere around B-F#-C#ish);

- having the flats fall off with less tempering than that, around the region of C-F-Bb-Eb-Ab. Maybe something like 1/8 to 1/12 comma, in those several 5ths generating the flats.

I've been testing this notion, empirically, by playing a bunch of Grieg and Brahms and Joplin (et al) on our church's piano, which I've had set up in a similar temperament for the past two years. Tightest tempering is downtown in the naturals, and sharps rising quickly, and flats falling off less quickly. Sure enough, it makes the keys of 1 to 6 flats sound especially mellow and "favored", with a warm and rich sound. It's barely unequal enough that an equal-temperament polemicist might notice and then complain about it.

I noticed the same type of thing (vis-a-vis key character) by taking Peter Watchorn's harpsichord recording of the WTC
http://www.musicaomnia.org/bachharpsichord.asp
and burning myself a CD of only the preludes, rearranged to be in circle-of-5ths order. Whenever we get to the music in flats, going around the circle in either direction, the instrument sounds warmest and gentlest.

That circle of 5ths, in Heinichen's formulation from 1728:
http://www-personal.umich.edu/~bpl/larips/heinichen-circle.gif

Brad Lehman

🔗Tom Dent <stringph@gmail.com>

> In this olden book from c1908 (IIRC - a cheap Dover paperback reprint
> that my local library has),
>
http://www.amazon.com/Piano-Tuning-Simple-Accurate-Amateurs/dp/0486232670
>
> the author presses the model of equal temperament, done by ear,
> obviously...but an interesting remark (to me) is that he has a
complaint
> against some of the other contemporary tuners. He says that some of
> them do too much favoring of the flat keys,

hmm, you'd need to work out what 'favouring' means here.

Could be: flat keys have better *fifths*, because the tempering was
mostly used up in tuning through the naturals and sharps

Could be: flat keys have better thirds than *both* the central keys
and the sharps.

We need some context, it's suspicious when someone reads an apparently
vaguely worded historical source and interprets it in a way that just
happens to exactly fit their own favourite theory.

Using Amazon's sneak preview feature: the author says
'some tuners even now will try to favour the flat keys because they
are used more by the mass of players who play little but popular
music, which is mostly written in keys having flats in the signature.
(Is this true? You'd need to check with an expert in historical
American popular music.)

In any case, the obvious implication is that the unequal tuners, if
they knew which side their bread was buttered, made the flat keys the
*best*, which is nothing to do with the sort of tuning that Brad is
promoting.

A lot of Noel Coward is in E flat major, but I'm not sure that means
much...

~~~T~~~

🔗Brad Lehman <bpl@umich.edu>

> http://www.amazon.com/Piano-Tuning-Simple-Accurate-
Amateurs/dp/0486232670
> >
> > the author presses the model of equal temperament, done by ear,
> > obviously...but an interesting remark (to me) is that he has a
> complaint
> > against some of the other contemporary tuners. He says that some
of
> > them do too much favoring of the flat keys,
>
> hmm, you'd need to work out what 'favouring' means here.
>
> Could be: flat keys have better *fifths*, because the tempering was
> mostly used up in tuning through the naturals and sharps
>
> Could be: flat keys have better thirds than *both* the central keys
> and the sharps.

Good point. Could also be: that "favouring" to him meant that the
flat keys sounded MOST LIKE the character of equal temperament (his
ideal/standard).

Who's to say that "better thirds" [presumably *major* thirds, and
presumably "better" meaning "nearer to 5:4 pure"] would imply that
the whole "flat key" as a scale is better? Better for what?

What we do have -- whatever it means -- is that writer's complaint
that some of his contemporary tuners "favoured" the flats. It's
evidence of *something* unequal, at least; and perhaps evidence of
more, if we could only figure out his aesthetic sense and his
expectations.

So, what is it that you think that writer was complaining about, in
his quip against favouring the flat keys? Some screwball inside-out
(or rotated) system where the flat-generated 5ths got the most
tempering, and the natural 5ths got the least or none? Like anti-
Vallotti?

Brad Lehman

🔗Gene Ward Smith <genewardsmith@sbcglobal.net>

🔗Jon Szanto <jszanto@cox.net>

🔗Charles Lucy <lucy@harmonics.com>

The key which instruments are easiest to play seems to follow a general pattern influenced by their physical form:

Stringed instruments usually have sharp (key) open strings; e.g. guitar, violin family, bass, etc.
Keyboard layout tends to be easier to play for flat keys.

It is a matter of ergonomics.

Noel Coward prolly wrote on keyboards.

Charles Lucy lucy@lucytune.com

----- Promoting global harmony through LucyTuning -----

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On 25 Apr 2007, at 19:25, Tom Dent wrote:

>
>
> > In this olden book from c1908 (IIRC - a cheap Dover paperback > reprint
> > that my local library has),
> >
> http://www.amazon.com/Piano-Tuning-Simple-Accurate-Amateurs/dp/> 0486232670
> >
> > the author presses the model of equal temperament, done by ear,
> > obviously...but an interesting remark (to me) is that he has a
> complaint
> > against some of the other contemporary tuners. He says that some of
> > them do too much favoring of the flat keys,
>
> hmm, you'd need to work out what 'favouring' means here.
>
> Could be: flat keys have better *fifths*, because the tempering was
> mostly used up in tuning through the naturals and sharps
>
> Could be: flat keys have better thirds than *both* the central keys
> and the sharps.
>
>
> A lot of Noel Coward is in E flat major, but I'm not sure that means
> much...
>

Request for historic tuning

🔗Jon Szanto <jszanto@cox.net>

🔗Dave Keenan <d.keenan@bigpond.net.au>

🔗monz <monz@tonalsoft.com>

🔗Jon Szanto <jszanto@cox.net>

🔗Charles Lucy <lucy@harmonics.com>

🔗Gene Ward Smith <genewardsmith@sbcglobal.net>

🔗Jon Szanto <jszanto@cox.net>

🔗Jon Szanto <jszanto@cox.net>

🔗monz <monz@tonalsoft.com>

🔗monz <monz@tonalsoft.com>

🔗monz <monz@tonalsoft.com>

🔗Tom Dent <stringph@gmail.com>

🔗Tom Dent <stringph@gmail.com>

🔗Carl Lumma <clumma@yahoo.com>

🔗monz <monz@tonalsoft.com>

🔗Jon Szanto <jszanto@cox.net>

🔗Jon Szanto <jszanto@cox.net>

🔗Jon Szanto <jszanto@cox.net>

🔗Charles Lucy <lucy@harmonics.com>

🔗Jon Szanto <jszanto@cox.net>

🔗Gene Ward Smith <genewardsmith@sbcglobal.net>

🔗Carl Lumma <clumma@yahoo.com>

🔗Jon Szanto <jszanto@cox.net>

🔗monz <monz@tonalsoft.com>

🔗Carl Lumma <clumma@yahoo.com>

🔗Jon Szanto <jszanto@cox.net>

🔗monz <monz@tonalsoft.com>

🔗Carl Lumma <clumma@yahoo.com>

🔗Jon Szanto <jszanto@cox.net>

🔗Kraig Grady <kraiggrady@anaphoria.com>

🔗threesixesinarow <CACCOLA@NET1PLUS.COM>

🔗Andreas Sparschuh <a_sparschuh@yahoo.com>

🔗Brad Lehman <bpl@umich.edu>

🔗Tom Dent <stringph@gmail.com>

🔗Brad Lehman <bpl@umich.edu>

🔗Gene Ward Smith <genewardsmith@sbcglobal.net>

🔗Jon Szanto <jszanto@cox.net>

🔗Charles Lucy <lucy@harmonics.com>