Yahoo Tuning Groups Ultimate Backup tuning Ensemble tuning on "A"

Massimiliano wrote:
>Do you know about any reason why tuning of ensembles (at least
>symphonic orchestra) is made on the "A" note? I was not able to find
>exhaustive answers to this on the web (if there is one....) but there
>might be one, or at least clues for it. I have an idea in mind, but
>may be nonsense, since I don't know enough about music.

Salve Massimiliano!

Hi Max,

nowadays ensemble use A obviously because the tuning forks for the last 2
centuries, have been mostly in A. As for how historically A was selected, I
believe there is some explanation in Helmholtz-Ellis 1885, perhaps some
other friend here knows better.

I can say that the note A is indeed most convenient for tuning unequal
temperaments because it lies near to the symmetry axis of the Circle of
Fifths for most of them, including meantone with its typical wolf G#-Eb.

Thus if you start from A, then you have to tune as many fifths clockwise as
anticlockwise, thus minimising accumulation of error.
This is so for the tuning of a keyboard instrument.
But since this happens also for the intonation of all the instruments in an
ensemble following the keyboard's type of temperament (or trying to tune in
unisons or pure with it) it also implies that all the ensemble will enjoy a
reduction in tuning error if A is used as the initial tuning note.

Kind regards

Claudio

http://harps.braybaroque.ie/

🔗Carl Lumma <carl@...>

🔗Andreas Sparschuh <a_sparschuh@...>

--- In tuning@yahoogroups.com, "massimilianolabardi" <labardi@...> wrote:
>
> Do you know about any reason why tuning of ensembles (at least
> symphonic orchestra) is made on the "A" note?

Reviewed literature:
http://em.oxfordjournals.org/cgi/content/full/33/3/508
"This is hardly the kind of evidence that would have satisfied an
Ellis or a Mendel, who would have demanded proof that the organs
mentioned in 1640 were in fact those measured in 1885, and that their
pitch had not been altered at any time during the intervening 245 years."
http://muse.jhu.edu/journals/notes/v060/60.3marvin.pdf
http://www.newolde.com/haynes.htm
http://www.mcgee-flutes.com/eng_pitch.html

> I have an idea in mind, but
> may be nonsense, since I don't know enough about music.

Quest:
What's yours new idea about?

> an "why A is conventionally chosen at 440 Hz

http://drjazz.ca/musicians/pitchhistory.html
http://www.wam.hr/Arhiva/US/Cavanagh_440Hz.pdf

>or some other frequency"

http://www.the-compound.org/writing/tuningpre1750.pdf
http://www.the-compound.org/writing/classicaltuning.pdf

> but "why the A note is used and not E, or G, or C.....

/tuning/topicId_71935.html#72092
/tuning/topicId_71935.html#72121

Locally here in Heidelberg(Germany)
there had been some historically changes in the choice:

1.
http://tonalsoft.com/enc/p/pseudo-odo_dialogus.aspx
used 'G' := "GAMMA-ut"
2.
http://en.wikipedia.org/wiki/Arnolt_Schlick
used 'F'
3.
http://en.wikipedia.org/wiki/Sebastian_Virdung
used 'A'
4.
http://en.wikipedia.org/wiki/Salomon_de_Caus
http://de.wikipedia.org/wiki/Salomon_de_Caus
used 'C'
5.
Jacques Handschin
http://www.brainyhistory.com/events/1886/april_5_1886_61886.html
proposed in his "Toncharakter" center on "D":
.
..
...
....
3^-3 : F : 32/27
3^-2 : C : 16/9
3^-1 : G : 4/3
3^+0 : D : 1/1
3^+1 : A : 3/2
3^+2 : E : 9/8
3^+3 : B : 27/16
....
...
..
.

The fundamental orchestra-pitch depends
on the number of strings (4 or 5 ?) in the
http://en.wikipedia.org/wiki/Double_bass
"The lowest note of a double bass is an E1 (on standard four-string
basses) at approximately 41 Hz or a B0 (when five strings are used)
at approximately 31 Hz."

6.
with "E1"
7.
or "B0"
for the ensemble.

Key-instruments:
A0 ~27 Hz on standard 88-key Pianos,
but some
http://en.wikipedia.org/wiki/B%C3%B6sendorfer
grand-pianos begin an 6th lower from
C0 ~16 Hz alike the 97-key model: "Imperial".

A few dinosaur-organs contain even real 64-foot stops
as the:

http://en.wikipedia.org/wiki/Boardwalk_Hall_Auditorium_Organ
Wooden "Diaphone/Dulzian 64â² "
http://www.theatreorgans.com/atlcity/index2.htm
"The largest pipe in the organ and also the largest organ pipe in the
world is the low "C" of the 64 foot Diaphone Profunda. "
or
http://www.theatreorgans.com/sydney/
"...this is the ONLY organ in existance
that possesses a FULL LENGTH 64' REED!.. "

That both organs range down even to
C-1: ~8Hz
one octave underneath MIDI-specification.

But who needs that?
http://en.wikipedia.org/wiki/Infrasound
"Below 10 Hz it is possible to perceive the single cycles of the
sound, along with a sensation of pressure at the eardrums...
...Since it is not consciously perceived, it can make people feel
vaguely that supernatural events are taking place."

bye
A.S.

🔗massimilianolabardi <labardi@...>

🔗Daniel Forro <dan.for@...>

Solmization system has nothing to do with note names, here in Japan they use it also in music education with the same wrong presumption, that C = Do. In fact it's a relative system independent on the key. It has some advantages only for singers (learning intonation patterns, solfeggio, transposing) or simple music analysis. Because it's derived from diatonic major scale, it's problematic in minor, modality, diatonics with chromatic alterations, and generally in chromatics (nothing to say about microtonality).

Daniel Forro

On 17 Feb 2009, at 5:15 PM, massimilianolabardi wrote:
> ok, got it. Now the question could turn to "why the note A was
> called like that, and not e.g. the note C"? but I guess that latin
> lettering was introduced after different names (e.g. ut re mi...),
> when already A was used as a widespread standard for ensemble
> tuning, and then the chioce was to assign the first alphabet letter
> to such fundamental note....maybe.
>
> In Italian we have the following sentence that often starts
> beginner's music books: "Le note sono sette: do re mi fa sol la si"
> (Notes are seven: C D E F G A B)
>
> Cheers
>
> Max
>

🔗Killian-O'Callaghan Residence <gottharddanae@...>

Friends,

you cannot get away so cheaply with this one: Already the Greeks, Jews and
Sumers, used to notify with the letters meaning three
things:

a) pitch of musical sounds
b) weights
c) and phonems

What ever we are using, don't forget history as a reason.

So the greeks would have scales which they would start with Aleph,
descending with the evolvong alphabet in varied ways, look it up in the
books, there are a couple of them in those libraries on those campuses. Or
google the perfect immutable system etcpp

My 2 cents for today,

Gotthard

2009/2/17 Daniel Forro <dan.for@...>

> Solmization system has nothing to do with note names, here in Japan
> they use it also in music education with the same wrong presumption,
> that C = Do. In fact it's a relative system independent on the key.
> It has some advantages only for singers (learning intonation
> patterns, solfeggio, transposing) or simple music analysis. Because
> it's derived from diatonic major scale, it's problematic in minor,
> modality, diatonics with chromatic alterations, and generally in
> chromatics (nothing to say about microtonality).
>
> Daniel Forro
>
> On 17 Feb 2009, at 5:15 PM, massimilianolabardi wrote:
> > ok, got it. Now the question could turn to "why the note A was
> > called like that, and not e.g. the note C"? but I guess that latin
> > lettering was introduced after different names (e.g. ut re mi...),
> > when already A was used as a widespread standard for ensemble
> > tuning, and then the chioce was to assign the first alphabet letter
> > to such fundamental note....maybe.
> >
> > In Italian we have the following sentence that often starts
> > beginner's music books: "Le note sono sette: do re mi fa sol la si"
> > (Notes are seven: C D E F G A B)
> >
> > Cheers
> >
> > Max
> >
>
>
>

--
Gotthard

🔗massimilianolabardi <labardi@...>

> I can say that the note A is indeed most convenient for tuning
unequal
> temperaments because it lies near to the symmetry axis of the
Circle of
> Fifths for most of them, including meantone with its typical wolf
G#-Eb.
>
> Thus if you start from A, then you have to tune as many fifths
clockwise as
> anticlockwise, thus minimising accumulation of error.
> This is so for the tuning of a keyboard instrument.
> But since this happens also for the intonation of all the
instruments in an
> ensemble following the keyboard's type of temperament (or trying
to tune in
> unisons or pure with it) it also implies that all the ensemble
will enjoy a
> reduction in tuning error if A is used as the initial tuning note.

Grazie Claudio.

reduction of tuning error is the kind of thing I had in mind. I'll
try to go on with this (I mean - as a physicist - to make some
calculation and modeling...) to see what comes out, I'll let you
know.

Cheers,

Max

🔗Andreas Sparschuh <a_sparschuh@...>

--- In tuning@yahoogroups.com, "massimilianolabardi" <labardi@...> wrote:
> ...but I guess that latin
> lettering was introduced after different names (e.g. ut re mi...),
> when already A was used as a widespread standard for ensemble
> tuning, and then the chioce was to assign the first alphabet letter
> to such fundamental note....

Ciau Max,

the fundamental note in the traditional

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

theory begins historically with GAMMA-ut

GG=ut A=re B=mi C=fa D=sol E=la ....

http://www.medieval.org/emfaq/harmony/hex1.html

Here an pic of the earliest known usage, as far as i know:
http://tonalsoft.com/enc/p/pseudo-odo/paris-lat-7211_f107r-v_ps-Odo_dialogus_ch2.jpg
That refers to:
http://en.wikipedia.org/wiki/Ut_queant_laxis
which became later the origin of
http://en.wikipedia.org/wiki/Solf%C3%A8ge
History
http://www.neilhawes.com/sstheory/theory22.htm

> In Italian we have the following sentence that often starts
> beginner's music books:
> "Le note sono sette: do re mi fa sol la si"
> (Notes are seven: C D E F G A B)
>
http://www.neilhawes.com/sstheory/theory39.htm
explains that by:
'In Italy, the "ut" was changed to "do", being the first syllable of
"Dominus"...
# "si" was added later as the seventh note of the scale, being the
initial letters of the name at the end of the hymn (which in fact does
not use the seventh note of the scale because it was probably not part
of the normal scale at the time).
# "si" was much later changed to "te" by a Miss S. A. Glover and John
Curwen (1816-1880), a Congregational minister in England, so that each
degree of the scale would have a unique single letter abreviation used
for written notation. This was the start of the "movable doh" method
of teaching which lasted in the UK for a hundred years...."

But back to history:
http://www.huygens-fokker.org/docs/stevinsp.html
persisted in
"
...in certain diagrams he assigns the vocables

ut re mi fa sol la sa ut

to the letters

g a b c d e f g
"
http://www.xs4all.nl/~huygensf/doc/stevinsp.html
when considering 12-EDO.

Even Isaac Newton still starts in 1664 from the usual root
G=0=53
in
http://societymusictheory.org/mto/issues/mto.93.0.3/mto.93.0.3.lindley7.gif
when drawing something near
http://en.wikipedia.org/wiki/53_equal_temperament#History

bye
A.S.

🔗Daniel Wolf <djwolf@...>

🔗Andreas Sparschuh <a_sparschuh@...>

--- In tuning@yahoogroups.com, "Daniel Wolf" <djwolf@...> wrote:
>
>... ensemble tuning note is a convention of the particular ensemble.
> Wind bands â" with most instruments in flat keys â" tune to Bb,
> orchestras tune to A,
> which is an open string for all the string instruments, relatively
> stable for the oboe and relative adjustable for the flute.
> In addition, when an orchestral or chamber group plays with a piano,
> the pianist conventional plays an a minor triad as a control for the
> temperament.
>
General instructions by
http://www.midwestclinic.com/clinicianmaterials/2005/thomas_oneal.pdf
Discussions
http://www.menc.org/forums/viewtopic.php?pid=860
http://www.wikihow.com/Tune-a-Clarinet
http://www.emich.edu/music/wpnew/clarinettune.html
http://www.freepatentsonline.com/EP1465151.html
http://www.jennifercluff.com/begtune.htm
http://www.public.asu.edu/~jqerics/double_horn.htm
http://www.jazz-o-matic.com/JOMMedia/contestEntries/JoelShifflet/tuning.html
&ct.
The situation is compareable to:
http://en.wikipedia.org/wiki/Gamelan
"The precise tuning used differs from ensemble to ensemble, and give
each ensemble its own particular flavour. The intervals between notes
in a scale are very close to identical for different instruments
within each gamelan, but the intervals vary from one gamelan to the
next...."

bye
A.S.

🔗Daniel Wolf <djwolf@...>

🔗Andreas Sparschuh <a_sparschuh@...>

🔗Daniel Wolf <djwolf@...>

> No, it not's comparable at all.
Why not?

In a western band or orchestral environment, there are clearly a number of factors involved in intonation, but among them are, at very least, the principle that individual instruments tune flexibly, in real time, but also with reference to standards for individual pitches as well as temperament (in some cases, particularly when the ensemble includes members with absolute pitch), pay attention to the quality of unison and chordal tuning, and, at times, use variable intonation as an expressive device. In other words, individuals are expected to contribute to the intonation of the ensemble as a whole, and are expected to discern the contextually appropriate intonation, be it precisely following one model or another (i.e. 12-tet in some cases, beatless triads and seventh chords in others).

In contrast, with the Javanese gamelan, if we may first distinguish those ensembles which are either understood to be out of tune or to have fallen out of tune with themselves (there are many; one of the best examples is Kyai Kanyut Mesem, which is a lovely old heirloom gamelan, but seriously out of tune, yet the complete tuning is described in MGG!) and those musicians who are relatively indifferent intonational precision (there are also many) from the gamelan ensembles and musicians recognized for their intonation. A gamelan in good tune may have copied a famous orginal (although the degree of accuracy will vary, in some cases, sharing the tuning with only one pitch of the original is sufficient) or be a unique tuning. The general principle, however, is to create a complete gestalt, if you will, beginning with a few fixed references, for example the gong (for both pitch and internal beating rate) or the kethuk, or pitch 6 of a well-known gamelan, typically that of RRI Solo, and then continuing to the gamelan as a whole. The gender is tuned next, as it is the fixed pitch instrument which plays a significant number of dyads, and does so that it plays well in all three pathet (= usually translated as mode but here actually more like key, with the tuning of the gender analogous to a temperament designed to play a scale type well and charcateristically in more than one transposition with a minimal number of keys). Additional fixed pitch instruments are gradually added, again paying attention to the general gestalt, continuously rechecking. Some pitches or some instruments are deliberately raised or lowered so as to be better heard in a dense ensemble texture and unisons between instruments are frequently (but not always) tuned so as to beat, typically at a rate similar to the internal beating of the gong, which in turn is close to the prevailing tempo of the irama system. This beating of near-unisons is done chiefly by the louder instruments, the demungs and sarons which frequently come in pairs, for an increase in volume, brilliance, and a more lively tone, somewhat akin to the criteria used to justify vibrato in western playing, but this is, due to the permance of the metal, not an optional expressive feature but a built-in feature. Finally, in performance, the variably-pitched instruments (voices, rebab (spike fiddle) and suling (fipple flute)) have, by nature, great flexibility in intonation, but they must remain recognizeably within the general tuning environment of the gamelan as well as the specific pathetan. While in most cases, this is restricted to ornamentation, miring or "minir" pitches (which are between those in the gamelan), and some strategic use of sharp or flat playing so as to project through the ensemble, there are several leading, usually mature, musicians who are noted for the individuality ("embat") of their intonation and tone quality and often play with and against the intonation of the ensemble for expression or color or general liveliness.

As Lou Harrison liked to point out, the orchestra is ensembled from musicians who own and bring their individual instruments with them while the gamelan is, at its best, tuned together as a single instrument which musicians gather to play. There is one more critical difference, and that has to do with the substance of the instruments. Western orchestras are, for the greatest part, composed of instruments with simple harmonic spectra, thus reinforcing considerable uniformity in intonation. The harmonic series is almost always available, in some form, as a point of reference or even background radiation. In contrast, the spectra of the idiophones in a gamelan is wildly variable (and can be dramatically changed by the slightest alterations in the shape of any of the single sounding bodies). This variability permits a wider amount a variation in tuning than would be tolerable among western instruments and, I daresay, is one of the important factors in allowing the laras and pathet systems to have flowered.

Daniel Wolf

🔗massimilianolabardi <labardi@...>

Ciao Claudio,

I have simply calculated the average deviation (Y) - that is,
difference in cents between corresponding grades - over the whole
diatonic major scale in JI and in 12-TET. If I assume the frequency
of C in JI equal to the frequency of C in 12-TET, that means, C is
mistuned by 0 cents between the two scales, I get

Y(0) = Sum[Abs[c[JI_i]-c[12-TET_i]]]

where c[JI_i] is the value in cents of the i-th grade of the
diatonic scale in JI, and c[12-TET_i] the same for 12-TET, and the
sum is made over all i grades.

If you now calculate the same for a given mistune X in cents, you get

Y(X) = Sum[Abs[c[JI_i]-c[12-TET_i]-X]]

The plot of Y (average error over all scale grades) vs X (detuning
of Cs between the two scales) you get a minimum about 0 cents, but
not exactly on it.

The plot is uploaded as "accordatura.gif" in Tuning List file
folder "Max".

Actually, there is a plateau from -2 to -12 cents. It means all
detunings (of Cs) within such interval lead to minimization of
error. The conclusion drawn here is that it would be convenient to
tune an 12-TET instrument together with a JI instrument on the II,
IV, V and VII grade.

This does not seem to tell anything. the conventional A is the VI
grade, so it is not even comprised in the group of best candidates...
so, to me this was enough, it is evidently not worth to keep up this
hypothesis too much....

The first time I have done this, was to understand how it would be
better to tune a 17-TET instrument with a 12-TET one (assuming the
17-TET diatonic major scale to be C=0, D=3, E=6, F=7, G=10, A=13,
B=16 grades of the 17-TET chromatic scale). The result was
strikingly that A was the most convenient grade to tune on... so I
was encouraged to try different scales. But probably was just a
result by chance!

Thanks

Max

--- In tuning@yahoogroups.com, "massimilianolabardi" <labardi@...>
wrote:
>
>
> > I can say that the note A is indeed most convenient for tuning
> unequal
> > temperaments because it lies near to the symmetry axis of the
> Circle of
> > Fifths for most of them, including meantone with its typical
wolf
> G#-Eb.
> >
> > Thus if you start from A, then you have to tune as many fifths
> clockwise as
> > anticlockwise, thus minimising accumulation of error.
> > This is so for the tuning of a keyboard instrument.
> > But since this happens also for the intonation of all the
> instruments in an
> > ensemble following the keyboard's type of temperament (or trying
> to tune in
> > unisons or pure with it) it also implies that all the ensemble
> will enjoy a
> > reduction in tuning error if A is used as the initial tuning
note.
>
>
> Grazie Claudio.
>
> reduction of tuning error is the kind of thing I had in mind. I'll
> try to go on with this (I mean - as a physicist - to make some
> calculation and modeling...) to see what comes out, I'll let you
> know.
>
> Cheers,
>
> Max
>

🔗massimilianolabardi <labardi@...>

🔗Cornell III, Howard M <howard.m.cornell.iii@...>

🔗Claudio Di Veroli <dvc@...>

Ciao Max,

There is a misunderstanding here.
Let me see how I can tell you in a few words a complex thing without
incurring in so many things that are under discussion.
1. Using A as a tuning fork arose historically for non-Just, regular or
irregular, fixed-note temperaments used by keyboards AND woodwinds AND open
strings of violins and cellos etc.
2. Even when violin fingering adjusts for Just intonation (and mostly for
250 years they have adjusted for Pythagoren i.e. in the opposite direction),
this was NOT playing in JI at all: quite a different thing as we all know.
3. Historically it can be shown that JI was hardly evern in use:
- Around 1490 musicians were discussing whether or not to adopt Ramos
Pythagorean-Just.
- Around 1520 most musicians were already giving meantone per granted, while
a few were still using medieval Pythagorean.
4. JI was known to be impractical because of the wolf fifths.
5. Then came the idea of using more than 12 pitches per octave: Vicentino
for meantone, Salinas for JI.
6. That was end of 16th century: meantone reigned supreme, the proposals by
Vicentino, Salinas and many followers were always a minimal part of the
instruments built and the music written. According to some researchers
(including Barbieri with his huge recent treatise on Enharmonic Keyboards)
its use was very much limited historically and only second-rate composers
ever wrote fitting music for Vicentino's ET31 or for Salinas's
JI+alternative notes.
7. It is nowadays different, since we can today write modern music and
program modern instruments to circumvent the JI limitations.
8. I never said that A was the best tuning reference for this modern use of
JI: it is not.
9. By the way, the advantage of using A is of a few Cents, while the
differences between JI and other temperaments are usually of the order of
the S.c., over 20 Cents.
So obviously the same tuning fork cannot apply.

Kind regards,

Claudio

🔗massimilianolabardi <labardi@...>

Ok Claudio. Thanks a lot for your very clear explanations. I can add
that I didn't mean to say that one should play in some temperament
or in others, or that people uses to play in one way or the other.
(I would prefer not to get into this kind of debates... frankly, I
have no title at all to get into the issues presently under debate
on tuning list!) I just meant "If one had to tune a JI instrument
with an equal-tempered one to play together"... but this was just
a "working" hypothesis...

Cheers

Max

--- In tuning@yahoogroups.com, "Claudio Di Veroli" <dvc@...> wrote:
>
> Ciao Max,
>
> There is a misunderstanding here.
> Let me see how I can tell you in a few words a complex thing
without
> incurring in so many things that are under discussion.
> 1. Using A as a tuning fork arose historically for non-Just,
regular or
> irregular, fixed-note temperaments used by keyboards AND woodwinds
AND open
> strings of violins and cellos etc.
> 2. Even when violin fingering adjusts for Just intonation (and
mostly for
> 250 years they have adjusted for Pythagoren i.e. in the opposite
direction),
> this was NOT playing in JI at all: quite a different thing as we
all know.
> 3. Historically it can be shown that JI was hardly evern in use:
> - Around 1490 musicians were discussing whether or not to adopt
Ramos
> Pythagorean-Just.
> - Around 1520 most musicians were already giving meantone per
granted, while
> a few were still using medieval Pythagorean.
> 4. JI was known to be impractical because of the wolf fifths.
> 5. Then came the idea of using more than 12 pitches per octave:
Vicentino
> for meantone, Salinas for JI.
> 6. That was end of 16th century: meantone reigned supreme, the
proposals by
> Vicentino, Salinas and many followers were always a minimal part
of the
> instruments built and the music written. According to some
researchers
> (including Barbieri with his huge recent treatise on Enharmonic
Keyboards)
> its use was very much limited historically and only second-rate
composers
> ever wrote fitting music for Vicentino's ET31 or for Salinas's
> JI+alternative notes.
> 7. It is nowadays different, since we can today write modern music
and
> program modern instruments to circumvent the JI limitations.
> 8. I never said that A was the best tuning reference for this
modern use of
> JI: it is not.
> 9. By the way, the advantage of using A is of a few Cents, while
the
> differences between JI and other temperaments are usually of the
order of
> the S.c., over 20 Cents.
> So obviously the same tuning fork cannot apply.
>
> Kind regards,
>
> Claudio
>

🔗Claudio Di Veroli <dvc@...>

🔗Andreas Sparschuh <a_sparschuh@...>

--- In tuning@yahoogroups.com, "Cornell III, Howard M"
<howard.m.cornell.iii@...> wrote/asked:
>
>
> So, what do you get for Y when you assume the 12-TET
>

Hi Howard & Max,
when demanding 12-TET you'll recieve the common usual:
http://en.wikipedia.org/wiki/Piano_key_frequencies

>
>and the JI A's are 440 Hz?
>

In that case for instance something near to:
An ~JI~ circle consisting
of a dozen partially epimoric flattend tempered 5ths,
that octaved 7-times downwards

A_1: 55 110 220 440Hz
E_2: 165
B_4: 495
F#_6: 1485
C#_7: 2227 4454 (<4455)
G#_5: 835 1670 3340 6680 (<6681)
Eb_4: 313 626 1252 2504 (<2505)
Bb_5: 939
F_-1: 11 22 44 88 176 352 704 1408 2816 (<2817)
C_1: 33
G_2: 99
D_2: 37 74 148 296 (<297)
A_1: 55 110 (<111)

That includes an epimoric distribution of the
http://en.wikipedia.org/wiki/Schisma
within the accidentials

32805/32768 = (4455/4454)(6681/6680)(2505/2504)(2817/2816)

into 4 superparticular subfactors,
Also it contains an analogous bisection of the Syntonic-Comma

81/80 = (297/296)(111/110)

Line up the pitches in ascending in order to yield the scale:

c' 264 tenor-C_5
#' 278.375
d' 295
#' 313
e' 330
f' 352
#' 371.25
g' 396
#' 417.5
a' 440
#' 469.5
b' 495
c" 524 sopran-C_6

or consider instead of the absolute pitch-frequences
the relative
http://www.xs4all.nl/~huygensf/scala/scl_format.html
ratios

! Ensemble_almost_JI.scl
!
epimoric Ensemble ~JI @ A4=440Hz by Andreas Sparschuh
12
!
2227/2112 ! (135/128)(4454/4455)
37/33 ! (9/8)(296/297) = (10/9)(111/110)
313/264 ! (32/27)(2817/2816)
5/4
4/3
45/32
3/2
835/524
5/3
939/524 ! (16/9)(2817/2816)
15/8
2/1
!
!

have a lot of fun when playing in that as 'Ensemble-tuning'
bye
A.S.