Yahoo Tuning Groups Ultimate Backup tuning Problematic Mahler references please

(alternate subject heading:
anatomy of a grail-Mahler clinker)

hi Charles,

> From: "Charles Lucy" <lucy@harmonics.com>
> To: "tuninggroup" <tuning@yahoogroups.com>
> Sent: Friday, June 13, 2003 2:49 AM
> Subject: [tuning] Problematic Mahler references please
>
>
> I would be grateful if someone would point me to or
> send me the symphony, section and bar numbers, which
> they are finding problematic in Mahler's work.
>
> I would like to try to find out if and how LucyTuning
> could solve the problem sections.
>
> I have access to any of the Mahler scores, and plan
> to use Logic Audio with tuned samples.
>
> Midi files would be helpful, although I shall not
> be limited by 1/64th, panning, and track limit problems.
>
> I could unstuff the recently linked .rar, yet nothing
> on my system could actually read the resulting midi file.

here's one that to my ears was really bad:

Mahler, 7th Symphony, 1st movement, 2nd beat
of measure 79 (4th measure after rehearsal
number 10, just before the change of key-signature
to B-major), 1st and 2nd violins play G#, the
other instruments all play a B-major triad.

in Gene's grail-tuned MIDI-file:

measure 30, beat 2.000
time: 40.15 (minutes.seconds)

one violin part is on MIDI-channel 5, and the last
time that channel has a pitch-bend command before
this note is at [measure.beat.tick] 29.01.239.

the violin note, which is a G#, has a pitch-bend
on it of -1437 "cawapus", or -35.08300781 cents
deviation from 12edo.

there are a whole bunch of pitch-bend commands for
other channels at 30.1.239, which is 1 tick before
the chord at 30.2.000. but channel 5 doesn't have
one.

the other violin part plays this same G# on channel 2,
and there *is* at pitch-bend command for channel 2
at 31.1.239, with a value of -1077, which is
-26.29394531 cents deviation from 12edo.

two instruments are thus playing two tunings of
the same note, 8.7890625 cents apart.

however, (i assume it's because of the complicated
channel-swapping that takes place in trying to juggle
parts into the proper pitch-bends) there's also a
"program change" command on channel 2, on both
tracks 7 and 11, at 30.1.239, which causes that
other violin G# to be played on a trombone. (! and ?)

here's a print-out of everything that happens on
this chord:

("m.b.t." means "measure.beat.tick", 2 beats to
each measure, 240 ticks to each beat. "abs.tick"
= absolute tick value, i.e., the count of all
ticks from the beginning. "PrCh" = program change,
"ch" = MIDI-channel, "p" = patch, "Pb" = pitch-bend,
"v" after "Pb" = pitch-bend value where 4096 =
one 12edo semitone, "v" after "Par" is the value
of whatever controller is specified, "v" after "On"
is the velocity, "n" = MIDI-note number where 60 is
middle-C; and "On" command with a "v" of zero
indicates "note-off".)

m. b. t. abs.tick command and value

30 1 239 14159 PrCh ch=2 p=57
30 1 239 14159 PrCh ch=2 p=57
30 1 239 14159 Pb ch=3 v=7294
30 1 239 14159 Pb ch=2 v=7115
30 1 239 14159 Pb ch=6 v=7115
30 1 239 14159 Pb ch=7 v=7115
30 1 239 14159 Pb ch=11 v=7294
30 1 239 14159 Pb ch=8 v=7294
30 1 239 14159 Pb ch=9 v=7473
30 1 239 14159 Pb ch=13 v=7294
30 1 239 14159 Pb ch=12 v=7294
30 2 0 14160 On ch=7 n=75 v=28
30 2 0 14160 On ch=15 n=71 v=28
30 2 0 14160 PrCh ch=8 p=57
30 2 0 14160 Par ch=9 c=121 v=0
30 2 0 14160 PrCh ch=9 p=57
30 2 0 14160 On ch=13 n=66 v=28
30 2 0 14160 On ch=6 n=75 v=28
30 2 0 14160 PrCh ch=8 p=57
30 2 0 14160 On ch=16 n=71 v=28
30 2 0 14160 Par ch=9 c=121 v=0
30 2 0 14160 PrCh ch=9 p=57
30 2 0 14160 On ch=12 n=66 v=28
30 2 0 14160 Off ch=11 n=53 v=0
30 2 0 14160 PrCh ch=2 p=57
30 2 0 14160 On ch=11 n=54 v=30
30 2 0 14160 Par ch=1 c=121 v=0
30 2 0 14160 PrCh ch=1 p=45
30 2 0 14160 Par ch=3 c=121 v=0
30 2 0 14160 PrCh ch=3 p=45
30 2 0 14160 Par ch=1 c=7 v=127
30 2 0 14160 Par ch=1 c=10 v=38
30 2 0 14160 PrCh ch=1 p=60
30 2 0 14160 Par ch=6 c=121 v=0
30 2 0 14160 PrCh ch=6 p=45
30 2 0 14160 PrCh ch=3 p=48
30 2 0 14160 PrCh ch=3 p=45
30 2 0 14160 Par ch=8 c=121 v=0
30 2 0 14160 PrCh ch=8 p=45
30 2 0 14160 PrCh ch=3 p=48
30 2 0 14160 PrCh ch=3 p=45
30 2 0 14160 Par ch=4 c=10 v=93
30 2 0 14160 PrCh ch=4 p=71
30 2 0 14160 Par ch=6 c=7 v=100
30 2 0 14160 Par ch=6 c=10 v=58
30 2 0 14160 PrCh ch=6 p=68
30 2 0 14160 PrCh ch=3 p=48
30 2 0 14160 PrCh ch=2 p=45
30 2 0 14160 PrCh ch=9 p=45
30 2 0 14160 PrCh ch=2 p=48
30 2 0 14160 Par ch=1 c=7 v=100
30 2 0 14160 Par ch=1 c=10 v=35
30 2 0 14160 PrCh ch=1 p=73
30 2 0 14160 Par ch=3 c=7 v=127
30 2 0 14160 Par ch=3 c=10 v=38
30 2 0 14160 PrCh ch=3 p=60
30 2 0 14160 Par ch=7 c=7 v=100
30 2 0 14160 Par ch=7 c=10 v=35
30 2 0 14160 PrCh ch=7 p=73
30 2 0 14160 PrCh ch=8 p=48
30 2 0 14160 Par ch=9 c=7 v=100
30 2 0 14160 Par ch=9 c=10 v=35
30 2 0 14160 PrCh ch=9 p=73
30 2 0 14160 Par ch=4 c=121 v=0
30 2 0 14160 PrCh ch=4 p=48
30 2 0 14160 Par ch=6 c=121 v=0
30 2 0 14160 PrCh ch=6 p=48
30 2 0 14160 Par ch=8 c=7 v=127
30 2 0 14160 Par ch=8 c=10 v=51
30 2 0 14160 PrCh ch=8 p=56
30 2 0 14160 Par ch=1 c=121 v=0
30 2 0 14160 PrCh ch=1 p=43
30 2 0 14160 Par ch=6 c=7 v=100
30 2 0 14160 Par ch=6 c=10 v=93
30 2 0 14160 PrCh ch=6 p=71
30 2 0 14160 Par ch=3 c=121 v=0
30 2 0 14160 PrCh ch=3 p=48
30 2 0 14160 Par ch=7 c=10 v=58
30 2 0 14160 PrCh ch=7 p=68
30 2 0 14160 Par ch=2 c=7 v=127
30 2 0 14160 Par ch=2 c=10 v=68
30 2 0 14160 PrCh ch=2 p=57
30 2 0 14160 On ch=2 n=63 v=64
30 2 0 14160 Par ch=8 c=10 v=68
30 2 0 14160 PrCh ch=8 p=57
30 2 0 14160 On ch=8 n=54 v=64
30 2 0 14160 Par ch=9 c=7 v=127
30 2 0 14160 Par ch=9 c=10 v=68
30 2 0 14160 PrCh ch=9 p=57
30 2 0 14160 On ch=9 n=47 v=64
30 2 0 14160 Par ch=2 c=7 v=127
30 2 0 14160 Par ch=2 c=10 v=93
30 2 0 14160 PrCh ch=2 p=57
30 2 0 14160 On ch=5 n=80 v=116
30 2 0 14160 Par ch=7 c=7 v=127
30 2 0 14160 Par ch=7 c=10 v=93
30 2 0 14160 PrCh ch=7 p=57
30 2 0 14160 Par ch=2 c=10 v=12
30 2 0 14160 On ch=2 n=80 v=116
30 2 0 14160 On ch=3 n=66 v=106
30 2 0 14160 Par ch=2 c=7 v=127
30 2 0 14160 Par ch=2 c=10 v=93
30 2 0 14160 PrCh ch=2 p=57
30 2 0 14160 On ch=4 n=75 v=106
30 2 0 14160 Par ch=2 c=7 v=127
30 2 0 14160 Par ch=2 c=10 v=93
30 2 0 14160 PrCh ch=2 p=57
30 2 0 14160 On ch=4 n=63 v=106
30 2 0 14160 On ch=3 n=54 v=106
30 2 0 14160 Par ch=2 c=7 v=127
30 2 0 14160 Par ch=2 c=10 v=93
30 2 0 14160 PrCh ch=2 p=57
30 2 0 14160 On ch=1 n=35 v=64

1 B2 -719 (30.1.219)
2 G#6 -1077
2 D#5 -1077
3 F#5 -898
3 F#4 -898
4 D#6 -1077 (30.1.219)
4 D#5 -1077 (30.1.219)
5 G#6 -1437 (29.1.239)
6 D#6 -1077
7 D#6 -1077
8 F#4 -898
9 B3 -719
11 F#4 -898
12 F#5 -898
13 F#5 -898
15 B5 -719 (20.2.239)
16 B5 -719 (20.2.239)

(G#) 773.706
G# 764.917
F# 578.076
D# 273.706
B 1082.446

G#:(G#) 8.789
F#:(G#) 195.630
F#:G# 186.841
D#:(G#) 500.000
D#:G# 491.211
D#:F# 304.370
B:(G#) 891.260
B:G# 882.471
B:F# 695.630
B:D# 391.260

GRAIL:
1200.000
1086.869
1013.165
895.623
795.623
695.623
578.081
504.377
391.246
304.377
195.623
86.869

/tuning/topicId_44053.html#44053

AARGH! ... my long post on this snuck out before i
was finished with it. since the unfinished version
has the long MIDI print-out and i don't want to waste
bandwith, i've deleted everything from this version
that would simply repeat that post. what's in this
one is the polished analysis i wanted to end that
post with, and then i was going to append the MIDI
print-out at the end as an appendix.

(if you're viewing this on the Yahoo web interface,
use "Expand Messages" mode to format my tables properly.)

here's one chord that to my ears was really bad:

in Gene's grail-tuned MIDI-file:
/tuning/files/grail-Mahler/bd.mid

measure 30, beat 2.000
time: 40.15 (minutes.seconds)

here's a table cataloging the notes
and cawapu pitch-bend values for the
chord at 30.2.000 (measure.beat.tick is
given where the pitch-bend command occurs
significantly far before the note-on command) :

channel note pitch-bend in cawapus

it boils down to this chord:

note cents

(G#) 773.706
G# 764.917
F# 578.076
D# 273.706
B 1082.446

here is a list of all intervals in
this chord (8ve-reduced):

interval cents

G#:(G#) 8.789
F#:(G#) 195.630
F#:G# 186.841
D#:(G#) 500.000
D#:G# 491.211
D#:F# 304.370
B:(G#) 891.260
B:G# 882.471
B:F# 695.630
B:D# 391.260

Gene gave the grail tuning here:
/tuning/topicId_44053.html#44053

i can see from the cents-values i got for
Mahler's notes that Gene used "D" as the reference
note for his 12-tone grail scale:

note cents

(D 1200.000)
C#/Db 1086.869
B#/C 1013.165
B 895.623
A#/Bb 795.623
A 695.623
G#/Ab 578.081
G 504.377
F#/Gb 391.246
E#/F 304.377
E 195.623
D#/Eb 86.869
D 0.000

(pretty good detective work, eh Gene?)

i can also see from this that G# is supposed to be
578.081 cents as it is on channel 5, and not 586.870
cents, as it is on channel 2. apparently the error
was caused by Scala, and i'd guess it was simply because
there was too much MIDI data to process.

(Mahler symphonies are extremely data-intensive: in
addition to being incredibly long, his scores are also
very complex.)

so anyway, if we expunge the spurious G#, which i
labeled (G#) above, we get these intervals -- and
i've also given some close meantone approximations:

approximate meantone interval
interval cents meantone cents

F#:G# 186.841 2/5-c 186.7049701
D#:G# 491.211 +1/3-c 490.8762359
D#:F# 304.370 1/6-c 304.8881422
B:G# 882.471 1/3-c 884.358713
B:F# 695.630 2/7-c 695.8103467
B:D# 391.260 1/5-c 390.6149718

the one interval here which doesn't work as a
meantone interval is D#:G#, the "perfect 4th".
it's 6.833999135 cents *narrower* than a 4:3,
whereas all meantone "4ths" are wider than 4:3.

or, to look at it another way, we may consider the
grail scale to be a hodge-podge of various meantones,
so that the four notes of this chord would be derived
like this, where "D" is our reference of zero generators:

grail approximate meantone interval
note cents gen. cents meantone

D# 86.869 7 88.5943349 1/6-c
G# 578.081 6 579.4705708 1/4-c
F# 391.246 4 390.6149718 1/5-c
B 895.623 3 895.1118578 1/6-c

anyway, this analysis suffices to convince me that
what i'm hearing is essentially a meantone "major-6th"
tetrad, and the nasty-sounding "clinker" is simply the
result of Scala's inability to handle the deficiency
of available MIDI-channels and Manuel's method for
dealing with that.

it's not at all surprising to me that Scala had
difficulty with this -- quite the contrary: i think
the job it did overall in retuning these Mahler
excerpts is astounding!

given the liklihood of running into this channel
deficiency problem in doing MIDI Mahler, as i mentioned
before, i'd guess that many of the other poorly-tuned
notes in the 7th Symphony files result from the same
problem.

unfortunately, as i also mentioned earlier, in this
particular work Mahler was really at the edge
harmonically, and only the kind of careful analysis
like the one i've done here will reveal whether the
bad sound is from a Scala channel-deficiency error
or from a combination of notes that just don't work
in grail. and this one was already too much work for
*me* ... but of course, for Mahler (and particularly
for the 7th) it was worth it just this once. :)

-monz

Problematic Mahler references please

🔗Charles Lucy <lucy@harmonics.com>

🔗monz <monz@attglobal.net>

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗Manuel Op de Coul <manuel.op.de.coul@eon-benelux.com>

🔗monz <monz@attglobal.net>