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Dear Martin, Brian and list,<br>
<br>
Sorry for my very late reply.<br>
I was distracted for a while (by something in music theory) and only
now handling my emails.<br>
<br>
Martin, you wrote:<br>
<blockquote cite="mid:BB5492F110B040CE983C6DDC001362AE@Martin2014"
type="cite">
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<div>Hallo Marcel and others,</div>
<div> </div>
<div>You wrote:</div>
<div> </div>
<div>“We are from birth hard-wired to "quantize" the interval
space by a chain of perfect fifths and octaves.<br>
That is, we identify unique intervals according to this
"algorithm". Music is built upon this.”</div>
<div> </div>
<div>You are right about the octave. Today there is a biology
of the octave. But there is no biology of the fifth. From
our knowledge of the auditory brain that we have today – as
little as that may be – it seems unlikely that we will ever
see a biology of the fifth.</div>
<div> </div>
<div>Many humans can learn the chain of fifths as something
apparently natural. But the main reason may be that in
harmonic sound spectra the group of fifth-related partials
is the second strongest group after the group of
octave-related partials.</div>
<div> <br>
</div>
</div>
</div>
</blockquote>
<br>
I think it is amazing you have found a biology of the octave.<br>
And I think the field of the neurobiology of music holds all the
promises for the future.<br>
But, while I'm not an expert in the field, the things I've read so
far make me believe that it is likely a very distant future where
this field can say things about how we actually quantize the pitch
space and internally represent melody and harmony as we perceive
them in music.<br>
I see many things come out of research into the auditory cortex and
auditory midbrain that point clearly to pitch detection from
harmonics and things like that. But this is primarily the field of
timbre and it seems to me of a certain aspect of the "colour" of
intervals and chords and related things.<br>
In my opinion this is not the same as the intervals of music. These
are 2 very distinct things.<br>
Again, I am not an expert in neurobiology, but it seems to me the
field currently has a hard time distinguishing the two?<br>
So far I've not read any evidence that the "musical processing" of
the intervals of melody and harmony even takes place in the auditory
cortex or auditory midbrain.<br>
<br>
What I can tell you and which is my field of expertise is that there
is most certainly a quantization of the pitch space based on octaves
and perfect fifths.<br>
And that it is this very quantization that distinguishes intervals
from others and is the very foundation for melody and harmony in
music. From my own research I consider this proven.<br>
And while I can't guarantee the following, it seems very likely to
me this is (or comes naturally from) a system we're born with. There
are many things which indicate this, one of them is that we simply
do not have a functional difference between 5/4 and 81/64 as a major
third (even though we can perceive the difference under good
circumstances). The consonant major triad in our music is proven to
me to be pure and functional as 81/64. If this is not the place for
a 5/4, then what would be? And how would we distinguish this
functionally? It is certainly not in western music. And I've
searched in world music but find no good reason to see it there
either.<br>
<br>
I can give you this audio example as well:<br>
<a class="moz-txt-link-freetext" href="http://youtu.be/FNGZE8GHvtE">http://youtu.be/FNGZE8GHvtE</a><br>
It is an accessible but still clear tuning demonstration thanks to
the chromatic nature of the music and remote intervals in some of
the chords.<br>
As you can hopefully tell the Pythagorean (3/2 fifths) version is
perfectly in tune and shows the "radical" nature of the Tristan
chord. (don't mind the not perfect sampled piano timbre though)<br>
For those with good ears you can hear, especially in comparison,
that the 12-tone equal temperament is slightly out of tune.<br>
The more one flattens or stretches the fifths the more out of tune
the music becomes. Where flattening gives a "sweeter" timbral effect
and stretching gives a "harsher" timbral effect in general (this
effect is harmonics related it seems to me).<br>
In the quarter comma meantone version the major thirds are all 5/4,
and the fifths fairly flat.<br>
To put it in a 5-limit or higher limit rational intonation system
(often wrongly called 5-limit "just intonation"), would sound in
ways similar to the quarter comma meantone version, and in other
ways worse as it will give either many comma shifts (this means a
note will suddenly while being held shift up or down a Syntonic
comma of 22 cents, sounds horribly unnatural and out of tune), and /
or "wolf fifths" that are famous for their out of tune "howl", and /
or comma drifting where the whole music shifts up and down by commas
like a drunken sailor.<br>
There is NO solution to these problems of 5-limit or higher limit
rational intonation. And roughly 95% of classical music will give
these sorts of problems, that cannot be overcome.<br>
5-limit rational intonation and similar tuning systems were a nice
theoretical toy for earlier theorists, but they simply do not match
at all how we perceive music in practice.<br>
I have spent many years researching this full-time and retuned
several hundred of short classical pieces to many systems thought of
as "just intonation" at some point. (all unpublished, though I plan
on writing a book with a new and improved theory of harmony ;-) )<br>
I believe I am the only person to have undertaken such a thorough
practical test for tuning systems (and it is only since the coming
of computers that such a thing is possible in such scale and with
such precision and repeatability). And my conclusion is very clear.
Western classical music functions according to the chain of fifths
and octaves, and nothing else.<br>
The 5/4 major third is nothing but a colouration of the 81/64 just
major third. And has proven to be the biggest trap for music
theorists of the past (and tuning enthusiasts of the present as
well).<br>
<br>
I also think that Pythagorean tuning can have a positive effect in
education and further research in music theory. As it is possible to
hear the enharmonic difference.<br>
I am currently researching how to harmonize the more exotic maqam
modes. Something which would be much more difficult to do on an
equal tempered instrument.<br>
<br>
<br>
Brian, you wrote:<br>
<blockquote
cite="mid:CAAFr0zVfjCGeaDaOj_U_S+QN8R8Lxz1zMnYEfzxnoion+bSn3w@mail.gmail.com"
type="cite">
<div dir="ltr">I'm generally inclined to agree that European
classical melodic thinking tends toward Pythagorean tuning.
However, one should take care not to extend this notion to other
repertoires without empirical support.
<div>
<br>
</div>
<div>A couple of years ago, I played along with Blind Willie
Johnson's classic recording "Dark was the night, cold was the
ground," using a slide guitar with the fingerboard marked
according to Harry Partch's 43-one system of 11-limit just
intonation. Johnson's flattened version of scale degree 3 very
clearly and consistently represents a 6/5 relation (i.e., a
5-limit "minor third") to the tonic pitch, not 32/27.</div>
<div><br>
</div>
<div>Yes, this recording represents just one data point, but
it's precisely the sort of information that one ought to
accumulate before making any broad claims about what blues
musicians were or weren't (or are or aren't) trying to do.</div>
<br>
</div>
</blockquote>
<br>
I've analysed music from all over the world.<br>
Indian music, Arabic / Persian / Turkish maqam music from various
regions (they differ in tuning practice per region), African music
including Pygmy music, etc. And also american blues.<br>
Where possible and practical (not that often due to strong pitch
variations of the human voice etc often making good stable pitch
detection difficult) I've analysed music with Melodyne DNA (direct
note access), which allows one to analyse the pitches of individual
voices in recordings of polyphonic music.<br>
All music fits the Pythagorean system perfectly. With two
exceptions. Some maqam practice I'm not sure yet how to analyse.<br>
In some regions a maqam like Rast for instance fits Pythagorean
logic perfectly in tuning, C-D-Fb-F (and some Persian regions
practice it as C-D-D#-F), but some other regions play that Fb up to
a Pythagorean comma lower which would in theory make it C-D-Gbbb-F.
I'm not sure how to see this, is it an exaggeration of the Fb to
make it more distinct from an E? Or is it indeed indicating another
distinct interval to our brain, a Gbbb? Very remote. I can't figure
it out yet. And while I can harmonize a C-D-Fb-F (which to do
naturally requires quite a different way of harmonizing than we do
in the west btw), I have great trouble making sense of how to
harmonize something like C-D-Gbbb-F.. perhaps use that Gbbb only as
a nonchord tone? And even then, I'm not sure I'm hearing it as a
Gbbb or as a very low "coloured" Fb.<br>
The other music that has trouble fitting Pythagorean logic is
Indonesian gamelan music. Their tuning is all over the place and
differs from village to village. No doubt this has to do with the
bell like inharmonic overtones of their instruments and percussive
way of playing. I'm not too worried about this one.<br>
<br>
As for blues. There are a lot of augmented seconds etc in use in
blues as well.<br>
So while, as you say one song isn't much sampling material, it's
quite possible that the interval you're describing is expressing an
augmented second instead of a minor third.<br>
The just tuning for the augmented second is 19683/16384 which is
~318 cents. A 6/5 is ~316 cents, an almost imperceptible difference.<br>
Also don't trust the spelling in the blues scores or theory books.
There are many spelling errors there. We can't apply some of the
"rules" we've found for classical music to blues as it often
"functions" quite differently.<br>
Take for instance the "Hendrix chord" / "purple haze chord" which is
often described as an dominant 7 #9. It is not, that's most
definitely a minor tenth instead of a augmented ninth, etc.<br>
<br>
<br>
Sorry for not only the late but also the long reply.<br>
I can't help it with this subject :) Though I think the subject
deserves it..<br>
<br>
Kind regards,<br>
<br>
Marcel de Velde<br>
<a class="moz-txt-link-abbreviated" href="mailto:marcel@justintonation.com">marcel@justintonation.com</a><br>
Zwolle, Netherlands<br>
<br>
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