Sixth comma meantone temperament: "per comune opinione perfettissimo"

I've been playing my piano which was retuned from quarter comma meantone=
=0Atemperament to sixth comma MT last week and want to put down some impr=
essions=0Awhile they're fresh. A year ago, I had my other piano - an old=
er one with a=0Awarm, not bright tone quality retuned from equal temperam=
ent to sixth comma MT=0Atemperament. As I played that piano over the nex=
t days and weeks, my initial=0Asense of amazement that a piano, of all in=
struments, could sound so pleasingly=0Aharmonious grew even greater. The=
change in tuning did wonders for that=0Apiano's overall resonance, givin=
g it an almost awe-inspiring "big" sound. The=0Afact that I'd never seen=
or really seriously imagined a "change of heart" in a=0Apiano of this na=
ture before contributed to the overall impression.

Despite the overall reduction in sharpness of the major thirds from about=
13.5=0Acents to a little over 7 cents (I'm sure there were deviations fr=
om target of=0A1, 2, and even three cents here and there), the sharpness =
of the thirds in=0Asixth comma MT was prominent in its overall sound. Th=
e harmonies were warmer,=0Abut had a mild "impressionistic" vagueness whi=
ch I associate with 12 TET=0Aharmonies. I had a desire to hear a piano t=
uned with the sharpness of the=0Athirds reduced even more and later began=
working with a rented piano tuned for=0Aa brief time to 5/24 comma MT (t=
hirds 3 and a half cents sharp) and then,=0Abecause even in that tuning t=
he sharpness of some of the thirds sometimes drew=0Aattention, quarter co=
mma MT temperament. The increasing flatness of the=0Afifths which was ne=
eded to get the thirds down to just was so gradual that I=0Adidn't notice=
it at all until reaching the full quarter comma temperament.

Now, my rented Yamaha upright with a very bright tone quality - capable o=
f=0Asounding loud and harsh - has been retuned in the other direction fro=
m quarter=0Acomma MT to sixth comma MT. My first impressions of the chan=
ge are a slight=0Asense of disappointment. To me, overall the piano does=
n't sound quite as=0Asmooth and harmonious as it did in quarter comma. I=
n fact, it almost sounds=0Aas though it had been put into equal temperame=
nt - but the wolves - with=0Athirds now only 28 cents sharp rather than 4=
0 cents sharp remove any doubt as=0Ato the fact that it's not in equal te=
mperament.

When I play pieces, trying to get them to sound really nice and harmoniou=
s, I=0Afeel some frustration. Getting a good balance with the melody not=
es clear and=0Athe full harmonies continuously present is more difficult =
- at times upper=0Anotes which are thirds above the root will surge too l=
oud, or else they will=0Abe unexpectedly drowned out by lower notes. The=
harmonies overall don't sound=0Aas smooth and pleasant.

However, in one piece - Long, long Ago - which I play with some 7th and 9=
th=0Achords marking important points in the piece - the sixth comma MT pe=
rformances=0Areally sound better and more musical than the quarter comma =
ones. To me,=0Athere didn't seem to be anything out of place at all in u=
sing a just 5/4 for=0Awhat might be intended as a 9/7 in playing such a c=
hord in quarter comma MT -=0Aafter all, it's a twelve=96note=96per=96octa=
ve instrument. But these chords have a=0Acertain sweetness and flexible =
musicality in the sixth comma MT - the sense of=0Athe different harmony o=
f the ninth chord as contrasted with that of a major=0Atriad - really com=
ing through - which isn't there in the quarter comma=0Arecordings. Thus =
it seems that widening a 5/4 third by only 7 cents can make=0Ait a lot ea=
sier to "hear" it as something like a 9/7. It may be that 12 TET=0Agives=
this same effect and that for many people who are less put=96off by the=
=0Adissonant (and for most contexts too=96sharp) thirds, the improved "re=
alism" of=0Aseventh and ninth chords in 12 TET outweighs its drawbacks.

There's another thing about the sixth comma MT which distinguishes it cle=
arly=0Afrom both quarter comma MT and 12 TET. This is the quite noticeab=
le pulsating=0Aeffect, a quakiness or shakiness, which seems to be presen=
t most of the time -=0Aa wa=96wa=96wa=96wa=96wa kind of sound going on wi=
th a pulsation rate of about 2 to 4=0Aor 5 waves per second. I believe t=
his is an effect of the reinforcement of=0Athe beating of the fifths, whi=
ch are flat by about one part in 480, and the=0Amajor thirds, which are s=
harp by exactly twice that amount - one part in 240.=0AWith the bright po=
werful Yamaha, this pulsating is quite noticeable, but it=0Ahadn't caught=
my attention (although it was present) with the other piano last=0Asumme=
r.

It is possible - maybe there are writings about this - that one of the=0A=
"fathers" of the piano, Gottfried Silbermann, has his name attached to th=
is=0Atemperament - the Silbermann temperament - because he wanted to give=
his=0Ainstrument a natural vibrato and could best achieve this effect by=
this=0Aparticular temperament. An Italian writer on music described thi=
s temperament=0Aas "temperamento per comune opinione perfettissimo" in a =
work published in=0A1786.

Later today my piano tuner is coming again to put the piano into 12 TET a=
nd=0AI'll have a chance to see if that causes the piano to seem appreciab=
ly=0Adifferent than it does now in sixth comma MT, which now seems to me =
almost=0Alike 12 TET already. Maybe I should enjoy the short time I have=
before he=0Acomes!

Just a couple additional observations: The major semitones are wide from =
a=0Ajust 16/15 in quarter comma by 5.4 cents, but they are narrow from 16=
/15 by=0A3.6 cents in sixth comma MT - a difference of 9 cents. The whol=
e tones are=0Avery slightly wider (by 3.6 cents) in sixth comma MT, and t=
his also affects=0Athe overall impression.=0A

>All-
> Here is a page that makes mystical claims for the 7/4.
>http://www.primasounds.com/seventh.html

This is a really neat page, with very pretty music. More "info" is at
http://www.primasounds.com/lostchrd.html and
http://www.primasounds.com/mega.html. The flavor of the "theory" is sort
of a cross between Danielou and Lucy. The text is a little bit ambiguous
as to the exact tuning. Can anyone decipher it from the .wav or .mid
files at the site? My guess is that it is based on a chain of four 7/4s:

Ratio Cents
1/1 0
2401/2048 275
343/256 506
49/32 738
7/4 969

(although the page does suggest that "very little tempering" is used to
adjust these frequencies for some reason). This resembles some Javanese
and/or African scales, doesn't it? The third mode has a meantone-like
fifth above the tonic:

Ratio Cents
1/1 0
8/7 231
64/49 462
512/343 694
7/4 969

Paul H. Erlich wrote:
> > Here is a page that makes mystical claims for the 7/4.
> >http://www.primasounds.com/seventh.html

Ever since I discovered 10TET's decent approximation to 7:4 (10TET
was my first microtonal tuning), I've found 7:4 a very nifty-sounding
interval. But I really don't see any call for mysticizing it.

But I should probably check out the web page first - not knock it
until I try it, so to speak.

------------------------------

End of TUNING Digest 1450
*************************

Paul Erlich wrote:

>The text is a little bit ambiguous
>as to the exact tuning. Can anyone decipher it from the .wav or .mid
>files at the site? My guess is that it is based on a chain of four 7/4s:

>Ratio Cents
>1/1 0
>2401/2048 275
>343/256 506
>49/32 738
>7/4 969

Theory is apparently explained at http://www.primasounds.com/prima.html,
but I can't retireve the page. Maybe this is like the instructions to
Mornington Crescent (to choose an analogy most people won't understand).

>(although the page does suggest that "very little tempering" is used to
>adjust these frequencies for some reason).

With tuning to exact 7/4s, intervals between adjacent notes will be 8/7,
except for one that is 44 cents sharper. Tempering would be to make it
more like 5-equal. Analysing one of the .au files, this seems to be the
case. I make the scale this:

1 8 64 7 2
- - -- x - -
1 7 49 4 1

(They should look like fractions if you're in monospaced mode.)

The note x is tempered midway between the two adjacent notes. So, those
intervals are 22 cents sharp of 8/7. I measured this accurately enough
that it can't be 5-equal.

It is particularly difficult to count the cycles of the tempered note, but
I think I've got it right now. The answer I get is spot on to the nearest
millioctave. It may be they've done something clever like play the two
just notes together.

Gary Morrison wrote:

> Ever since I discovered 10TET's decent approximation to 7:4 (10TET
>was my first microtonal tuning), I've found 7:4 a very nifty-sounding
>interval. But I really don't see any call for mysticizing it.

To quote from the site:

>The frequency and harmonics of the acoustic seventh interval are
>dissonant with all of the other basic fractions. For this reason it is
>said to have no place in Music.

With friends like that does it really need enemies?

Graham Breed
gbreed@cix.co.uk www.cix.co.uk/~gbreed

In reference to you posting to Tuning Digest #1450:

>With tuning to exact 7/4s, intervals between adjacent notes will be 8/7,
except for one that is 44 cents sharper. Tempering would be to make it
more like 5-equal. Analysing one of the .au files, this seems to be the
case. I make the scale this:

1 8 64 7 2
- - -- x - -
1 7 49 4 1

>(They should look like fractions if you're in monospaced mode.)

>The note x is tempered midway between the two adjacent notes. So, those
intervals are 22 cents sharp of 8/7. I measured this accurately enough
that it can't be 5-equal.

---------------------->
According to "Chance and Choice: a compendium of ancient and modern wisdom
revealing the meaning and significance of the Myth of Science" by Arnold
Keyserling and Ralph Losey, [1993] 1994, ISBN 1-883185-52-1, page 76:

The Primatonic Scale (9 octaves x 5 notes = 45 audible notes) can be
represented by the following chart:

: A E I O U A
: |------|-------|-------|-------|-------|
: | | | | | |
:1.0 1.14 1.31 1.49 1.75 2.0

Which by my calulations relate to the ratios: E (8/7), I (21/16), O (73/49? or
perhaps [pure speculation ] 7 * Log of [7 to the base 2] reduced by "1"
octave, i.e. to 1.49345) and U (7/4). All of which convert to, in cents,
respectively: E (231.174), I (470.781), O (694.379), and U (968.826).

And on page 77 says "Note that the vowel scale designation is arbitrary, was
made before the discoveries of Tomatis, and does not correspond with Tomatis
vowel/chakra alignments."

There is now a book on "PrimaSounds.: The Discovery of Chakra Music" by Arnold
Keyserling and Ralph Losey available at
. It appears to contain
material in part from their CD booklets and their book "Choice and Chance".

This scale (page 75) "opens hearing to the inner Universe and in most ancient
civilations this music was held sacred. the music is fractal, based on zero,
the fourth dimension and the Strange attractor. It has no melodies, rhythms or
other forms or order found in other music. It sounds almost completely chaotic,
unpredictable, yet there is a fractal link to your own being which makes the
sounds soothing and leaves you serene. Being attuned to the primal energies of
the soul it has the power to throw you into the zero dimension, to open you to
the healing influences of the Strange attractor."

The book fully discusses the subjects of Music in pages 69-74 and PrimaSounds
in pages 75-86.

In "Laws of Wisdom: An Introduction to the Natural Laws of Human Potential" by
Ralph Losey, Esq, essentially the other book is quoted as a small extract
concerning PrimaSounds.

Three CDs (which I also have) are available (via the website) which well
demonstrate the use a PrimaSounds:

"Life Tuning with Prima Sounds: The Discovery of Chakra Music" by Arnold
Keyserling and Ralph Losey (1993)

"Primasounds" by Ralph Losey (1994)

"Gate Keeper with PrimaSounds" by Ralph Losey and the School of Wisdom (1998)
<--------------------

-------------
Benjamin Tubb
AIM: brtubb
ICQ: 650264
brtubb@cybertron.com
http://home.cybertron.com/~brtubb

The Music of Stephen Collins Foster (1826-1864)
http://www.geocities.com/Nashville/9958/

Benjamin Tubb wrote:

>The Primatonic Scale (9 octaves x 5 notes = 45 audible notes) can be
>represented by the following chart:

>: A E I O U A
>: |------|-------|-------|-------|-------|
>: | | | | | |
>:1.0 1.14 1.31 1.49 1.75 2.0

>Which by my calulations relate to the ratios: E (8/7), I (21/16), O
(73/49? or
>perhaps [pure speculation ] 7 * Log of [7 to the base 2] reduced by
"1"
>octave, i.e. to 1.49345) and U (7/4). All of which convert to, in cents,
>respectively: E (231.174), I (470.781), O (694.379), and U (968.826).

>And on page 77 says "Note that the vowel scale designation is arbitrary,
was
>made before the discoveries of Tomatis, and does not correspond with
Tomatis
>vowel/chakra alignments."

My results are as follows:

samples per 100 cycles| relative freq | pitch | my theory
2031 | | |
1781 | 1.140 | 0.190 | 0.193
1557 | 1.304 | 0.383 | 0.385
1345 | 1.510 | 0.595 | 0.596
1162 | 1.748 | 0.806 | 0.807
1013 | 2.005 | 1.004 | 1.000

Pitches are given in octaves rather than cents so you can compare with
5-equal: 0.0, 0.2, 0.4, 0.6, 0.8, 1.0

The O given by Keyserling and Losey looks like (8/7)^3=512/343=1.493.
This may be correct: there seem to be some fluctuations on the note I'm
measuring here. Sometimes, 10 cycles can be as few as 134 samples but
around 138 is more common. This is how I originally measured it, but it
is flat even of 512/343, so I measured again and got this result that was
either a fluke or miscounting. The given value of I is also consistent
with (8/7)^2=64/49=1.306.

If the scale is untempered, the interval O-U is 8 cents sharp of a 7/6.

Graham Breed
gbreed@cix.co.uk www.cix.co.uk/~gbreed/