Appreciate your thoughts Graham

As we discuss impacts of different tunings on different instruments, my=
=0Aappreciation for the very great interrelationship between "tuning" and=
=0A"timbre" deepens. Doing a bit of "free association", I recall working=
with a=0Agraduate student working with synthesized flute timbres based o=
n analysis of=0Arecorded flute notes played into a microphone (mono) and =
converted to 16 bit=0Asigned integer samples through a A/D converter at a=
40 KHz sampling rate.

Although for the particular note - a D4 - we were working with the fifth=
=0Apartial was very prominent, we didn't hear it distinctly as a tone in =
its own=0Aright within the overall sound of the flute D4. However, when =
I artificially=0Astrengthened that partial individually among the other p=
artials forming the=0Atotal sound, leaving the other partials as they had=
been (based on additive=0Aresynthesis of an analyzed flute note), we cou=
ld hear that partial's F#6 sound=0Aseparate from the overall sound. Then=
, if we listened for it, we could=0Awithout difficulty hear the 5th parti=
al's F#6 tone individually within the=0Aoriginal accurately resynthesized=
flute note and I believe within the=0Arecording of the original flute no=
te (I'm not sure we tested that, but in any=0Acase those two sounds were =
very close - nearly indistinguishable and that=0Abeing the case it would =
seem unlikely that if the fifth partial could be=0Adistinguished in the a=
dditively resynthesized sound, it would be=0Aindistinguishable within the=
original recorded sound).

Thus when we listen to a sound, depending on the mind set with which we l=
isten=0Ato it, we may hear - very clearly and fully - a "whole" or "gesta=
lt" sound, or=0Awe may hear a "composite" sound within which, along side =
the "gestalt", we=0Aperceive individual "component" sounds. I guess this=
isn't utterly different=0Ain essence from listening to a chord sung or p=
layed on a piano or other=0Amusical instrument - we easily hear the indiv=
idual notes of the chord, while=0Aat the same time we experience an effec=
t of the chord also as, in a way, a=0Asingle "gestalt". However in the c=
ase of the chord, we tend to be much more=0Aaware of the individual compo=
nents of the chord and don't habitually think of=0Athe chord as a single =
entity in the same way we would think of a flute note=0Awithin which we c=
an, it we try to do it, distinguish individual component=0Atones and hear=
them as distinct from the overall sound of the note, which we=0Anormally=
hear as a single entity.

Another example of this is the case of listening to a piano note, note pa=
ir,=0Aetc. There's a lot of beating going on - even if one stops all but=
one single=0Astring of a unison bank and the damper pedal is up so that =
all the other=0Astrings of the piano are mostly damped, frequently one ca=
n hear "false beats"=0Ain that single string. I'm not a piano tuner - I =
admire them and may become=0Aone - and when my piano tuner hits note pair=
s and tells me he is listening to=0Awhat, say, the fourth partial is doin=
g, I feel a sense of frustration because=0AI am not hearing perceptively =
what he is hearing. (Based on my experience=0Awith other things, I belie=
ve that if I made an effort - really applied myself=0Ato it - I could lea=
rn to hear the things he's listening for). The point is=0Athat the "soun=
d behind the sound" of a piano note, note pair, chord, etc. is a=0Acompos=
ite of a great many sounds which might be distinguished within the=0Aover=
all sound if one were to focus one's attention in such a way as to=0Adist=
inguish a particular one of the many component sounds.

What this leads me to is an explanation for the fact that a particular tu=
ning=0Amay sound reasonably good on one musical instrument while it may s=
ound=0Aterrible on another musical instrument. I'm thinking of my experi=
ence with=0Atwo pianos - an older one which I purchased second hand with =
a warm, not very=0Abright tone quality, on which I've found sixth comma M=
T temperament to sound=0Avery beautiful, if not harmonically clear, and a=
more "iron and steel" kind of=0AYamaha upright which I'm renting which h=
as a very bright tone quality with a=0Alot of sound in the high frequency=
region (I'd guess from 3 KHz up to 10 KHz=0Aor beyond), on which sixth c=
omma MT sounds harsh and strained and=0Adisappointing, although EQT sound=
s even harsher and "just awful" on that=0Apiano, which nevertheless has a=
very beautiful, pleasant, gentle sound in=0Aquarter comma MT. The effec=
t is so striking that one finds it hard to resist=0Abelieving that the Ya=
maha engineers did a lot of careful testing of their=0Apiano and designed=
it from the ground up as an instrument meant to be tuned to=0Aquarter co=
mma MT, never intending that it should be misused by tuning it to=0AEQT. =
One could go on speculating that in their inner deliberations, the=0Aeng=
ineers and management had come to the conclusion that EQT would be around=
=0Afor such a short while longer that they could safely leave it out of t=
heir=0Acalculations :)

It would seem that a tuning such as sixth comma MT, while it will pull th=
e=0Abeat frequencies down below the dissonance "threshold" in lower parts=
of the=0Aaudio spectrum so that an instrument without an abundance of hi=
gh harmonics,=0Abut with quite a lot of sound lower more in the middle of=
the audio spectrum,=0Amight benefit greatly as a result of its tuning be=
ing changed from EQT to=0Asixth comma MT, will, with a very bright instru=
ment having a lot of its sound=0Ain the high frequency region, leave the =
dissonance beat frequencies in that=0Ahigh frequency part of the audio sp=
ectrum still high enough to be in the Plomp=0Adissonance region for beati=
ng frequencies so that the piano still sounds=0Ashrill and harsh even in =
sixth comma MT.

There are quite a few considerations which suggest this explanation. The=
re is=0Aa quotation from around 1876 (I don't recall the source) to the e=
ffect that it=0A"takes a really modern piano to show up how bad EQT sound=
s". If the earlier=0Ainstruments were much less bright than the later on=
es, it could be that, even=0Ain EQT tuning, they produced much less sound=
in frequency ranges where the=0Adissonance beat rates were fast enough t=
o be in the unpleasant range - which=0Aalso could help to explain why EQT=
gained such widespread acceptance. We=0Ausually think of the guitar, pa=
rticularly a gut or nylon stringed one, as a=0Apleasingly melodious music=
al instrument, although until very recently, they=0Ahave been normally tu=
ned to EQT. If the harmonies are not the clearest and=0Apurest, still th=
e instrument has a very pleasing sound. Such nylon stringed=0Aguitars ha=
ve a mild not=96bright timbre and the dissonance beatings of EQT seem=0At=
o be below the dissonance threshold in the lower frequency ranges where m=
ost=0Aof the audio spectral energy of the guitar comes from.

In the case of the organ, however, particularly one with a bright timbre,=
the=0Adissonance beating of EQT will be very prominent. William Pole re=
marked on=0Athe change which retuning from a mean tone temperament (Would=
this likely have=0Abeen fifth comma MT?): "The modern practice of tuning=
all organs to equal=0Atemperament has been a fearful detriment to their =
QUALITY OF TONE. Under the=0Aold tuning an organ made harmonious and att=
ractive music, which it was a=0Apleasure to listen to, even though it mig=
ht be interrupted by a "wolf" now and=0Athen. Now, the harsh thirds, app=
lied to the whole instrument=0Aindiscriminately, give it a cacophonous an=
d repulsive effect, which people are=0Aglad enough to run away from." (f=
rom his Philosophy of Music 1879 edition, p.=0A153) Earlier he had writt=
en (regarding the equal tempered scale) "...The most=0Aimportant errors a=
re those of the (ital.) THIRDS, which are considerably=0Awrong; and it is=
undoubtedly the fact that the major third is an interval in=0Aregard to =
which, from its prominent place in the major triad (the chord of=0Anature=
), the ear is peculiarly sensitive. ON THE PIANOFORTE THIS IS NOT OF SO=
=0AMUCH CONSEQUENCE; but in the organ and harmonium, where the tones are=
=0Asustained, a moderately sensitive ear finds the equally=96tempered maj=
or third=0Avery harsh and disagreeable."

Pole finds that EQT doesn't have a seriously detrimental effect on the to=
ne=0Aquality of the piano, or he makes this concession re the piano in or=
der to=0Agive the impression that he is taking a fair, balanced approach =
in the face of=0Acriticism which he likely anticipates from advocates of =
EQT, who by 1879 in=0AEngland were increasingly coming to enjoy the taste=
of victory in their=0Aefforts to see the elegant, nifty 12 TET scale est=
ablished as the single=0Auniversal basis for music. He attributes this t=
o the fact that the piano=0Anotes decay away fairly rapidly. It seems to=
me that the pianos which he was=0Aused to hearing also had timbres which=
were much less bright than those of=0Asome of today's pianos.

I'd like to mention that I can count off at least ten people to whom I've=
=0Apresented contrasting examples of music played on the Yamaha upright i=
n EQT=0Aand quarter comma MT tuning who have very clearly and definitely =
indicated to=0Ame that they found the piano to sound "warmer" in quarter =
comma MT, to "sing"=0Ain that tuning. Some have said that the piano soun=
ds like a fine expensive=0Ainstrument in quarter comma MT while it sounds=
like a cheap piano when in EQT=0Atuning. One person writing anonymously=
in a listening research test which I=0Agave wrote: "I appreciate the sou=
nd of mean tone tuning; it's just different=0Aenough to be almost exotic.=
I think it's just beautiful." Although not all=0Apeople have agreed wi=
th me that there is a dramatic difference between the=0Asound of the pian=
o in EQT and in 1/4 comma MT, a great many people have - on=0Athe order o=
f half those who have heard the contrasting sounds - more than half=0Aof =
those with whom I've discussed the matter personally.

Getting to the matter of tuning and timbre of the piano, and of the "E=0A=
pluribus unum" phenomenon. When one strikes a note, say a G4, with the p=
edal=0Adown - i.e. damper off the other strings, leaving them free to vib=
rate along=0Awith the struck bank of three unisons in this case, a very g=
reat number of=0Aindividual tones are produced. First there are the sets=
of partials of each=0Aof the three G4 unisons. Following the striking o=
f these strings, perhaps=0Afrom 20 to 30 or more (a third of all the stri=
ngs of the piano) strings/sets=0Aof strings are set into vibration, the t=
ime courses (amplitude and to some=0Aextent - I think within a range of 2=
cents or so - frequency envelopes) of=0Atheir sounds, each being compose=
d of a set of partials, being individual to=0Athe particular string. Bel=
ow G4, the G3 string, the C3 string, the G2 string,=0Athe Eb2 string, and=
so on down will be set into vibration. This can be=0Ademonstrated by qu=
ietly pressing, say, the C3 note so that its individual=0Adamper is lifte=
d off the C3 string pair without these strings being set into=0Avibration=
, and then striking the G4 note and releasing the key so that the G4=0Ast=
rings are then stopped. One will continue to hear a reduced G4 tone unti=
l=0Aone releases the C3 key. Above G4, one will be able to hear tones of=
variable=0Aloudness depending on tuning when any key for a note whose fu=
ndamental=0Afrequency is close to the frequency of one of the G4 partials=
is depressed and=0Aheld down and then the G4 is struck and the key for G=
4 then released. Just=0Aplaying around with this roughly, I've found tha=
t when the tuned frequency for=0Athe upper string lies within about 5 to =
10 cents of the frequency of the lower=0Astring's partial corresponding t=
o that string, the upper string will begin to=0Avibrate. The closer its =
tuned frequency to the frequency of an upper partial=0Aof the lower strin=
g, the louder will be its sympathetic vibration sound.

With the piano tuned to quarter comma MT temperament and with my piano tu=
ner's=0Ahaving used some "octave stretching" - perhaps amounting to nearl=
y 50 cents=0Aover the piano's 7 octave range - less in the piano's middle=
range, more at=0Athe low and high ends, I find that there are strong sym=
pathetic vibration=0Aresponses for strings at one or more octaves above t=
he lower string and for=0Astrings at 2 or 3 octaves plus a third above th=
e lower string (eight notes Eb,=0ABb, F, ... to E - no detectable respons=
es for notes at "wolf" thirds above B,=0AF#, C#, and G#). The strings at=
1 and 2 octaves plus a fifth above a lower=0Anote vibrate sympatheticall=
y but not very strongly, which seems to result from=0Atheir being tuned (=
nominally) 5.4 cents flat from just. There are strong=0Aresponses for th=
e C# and G# strings 2 octaves and a seventh above Eb and Bb=0Arespectivel=
y when the latter are struck (nominally 3 cents flat from being=0Ajust 7/=
1 s above the lower notes). With the piano in 12 TET, I have sometimes=
=0Afound weak responses for strings two octaves and an EQT (nominally 13.=
7 cents=0Asharp from just) major third above lower strings, and sometimes=
these=0Aresponses have been too weak for me to detect.

Well, all this opens up a "world" of things happening in the piano when e=
ven=0Aone single note is struck. It occurs to me also that when strings =
are excited=0Ato vibrate in sympathy with a lower string, they in their t=
urn, albeit weakly,=0Awill exert some effect on the strings both above an=
d below them.

Even some of the physically low amplitude components of the overall sound=
-=0Adown 50 or 60 dB or more - could, depending on exactly where and wha=
t they=0Aare, have an appreciable effect on the piano's overall sound. T=
he pattern of=0Athis "cloud" of relatively low amplitude components could=
have the effect of=0Acontributing a delightful, difficult=96to=96describ=
e, "feel" to the piano's=0Aoverall sound or it could fail to have such a =
potentially achievable effect or=0Aeven detract from the pleasantness of =
the instrument's sound.

Your observations re 1/6 comma MT and 1/9 comma MT on the digital piano,=
=0AGraham, help to fill in this field of data out of which we're trying t=
o=0Adiscern underlying patterns. These patterns, to the extent they appl=
y=0Agenerally, in turn can provide us with new, more detailed, and more p=
owerful=0Aguidance towards creating really delightful music, gaining cont=
rol over those=0Aelusive "performance variables" which can, as if by magi=
c, if "all working=0Aright" make a performance sound great.

Dave Hill La Mesa, CA