<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>
<div><br></div><div>All best,</div><div><br></div><div>Brian Robison</div><div>Assistant Academic Specialist<br>Department of Music</div><div>Northeastern University<br>Boston MA 02115<br><br></div><div><a href="mailto:b.robison@neu.edu">b.robison@neu.edu</a><br>
<a href="mailto:brian.c.robison@gmail.com">brian.c.robison@gmail.com</a><br><br></div><div><br></div><div><br></div></div><div class="gmail_extra"><br><br><div class="gmail_quote">On Wed, Apr 23, 2014 at 7:35 AM, Marcel de Velde <span dir="ltr"><<a href="mailto:marcel@justintonation.com" target="_blank">marcel@justintonation.com</a>></span> wrote:<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<div text="#000000" bgcolor="#FFFFFF">
Hello Carson,<br>
<br>
I may not represent the group view here, but I have been studying
tuning and just intonation full time for about the past 8 years.<br>
I'll tell you my view on things.<br>
<br>
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.<br>
And our notation corresponds to this.
Gb-Db-Ab-Eb-Bb-F-C-G-D-A-E-B-F#- etc.<br>
We find a functional difference between for instance the intervals
C-Gb and C-F#.<br>
They are as different as for instance C-Eb and C-E even though Gb
and F# share the same key on the 12-tone equal tempered piano.<br>
We can tune for instance the C-E according to pure perfect fifths of
3/2, making C (1/1) - E (81/64), or detune it a little to for
instance C (1/1) - E (5/4).<br>
The result sounds acoustically a bit different, but we will still
interpret them both the same, as C-E. There is no functional
difference, no different interval indicated.<br>
The 5/4 as major third combined with 3/2 perfect fifths will however
give problems in actual music that cannot be overcome.<br>
As 5/4 cannot be made out of 4 * 3/2 divided by any number of
octaves, this means that for instance circle progressions and other
things do not work any more.<br>
I-vi-ii-V-I "breaks" in 5-limit and one must use unnatural comma
shifts, or "wolf fifths", or allow such progressions to comma drift
upon each repetition.<br>
Music is full of there sorts of things, and 95% or so of common
practice music will not function in 5-limit or any higher number of
overtones.<br>
This is why things like 1/4 comma meantone were invented which work
by flattening each perfect fifth by for instance a quarter Syntonic
comma so 4 flattened perfect fifths reduced by 2/1 octaves give a
5/4 major third. This will give the acoustic colouring of the 5/4
that is pleasing to so many, while keeping the chain of fifths
intact.<br>
<br>
Now in your question you try to relate the overtones to the chain of
fifths.<br>
Indeed we find that the 11th and 13th partial are almost in the
middle between 2 simple chain of fifths intervals.<br>
In relation to C (1/1) and reduced to the octave:<br>
F (4/3) perfect fourth at ~498 cents.<br>
F# (729/512) augmented fourth at ~612 cents.<br>
11th partial (11/8) at ~551 cents.<br>
So it's a little bit closer to F.<br>
However, there are also different intervals which are closer.<br>
Gb (1024/512) diminished fifth at ~588 cents.<br>
E# ( 177147/131072) augmented third at ~522 cents.<br>
And one can go on along the chain of fifths to indicate even more
remote intervals which are still closer in tuning to 11/8, like
C-Dx# and C-Abbb.<br>
However I doubt if these are possible to indicate to the brain in a
chord regardless of tuning. (melodically this may be possible with a
modulation / change of root)<br>
<br>
In the case of the 13th partial reduced to the octave (13/8) at ~841
cents we have:<br>
Ab (128/81) minor sixth at ~792 cents.<br>
A (27/16) major sixth at ~906 cents.<br>
G# ( 6561/4096) augmented fifth at ~816 cents.<br>
Bbb (32768/19683) diminished seventh at ~882 cents.<br>
<br>
However, we have more considerations than simply how close the
tuning is to an interval.<br>
The music itself can have a stronger influence on which interval we
perceive than even moderately large tuning differences of 40 or so
cents.<br>
What do we hear as the root / fundamental bass, what expectations
does the melody give, etc.<br>
Also the tuning of the other intervals matter.<br>
We can actually construct progressions where we de-tune intervals in
such a way that an interval closer to a minor third will still be
interpreted as a major third.<br>
Furthermore, under many practical circumstances precise tuning
information is largely lost. We go by the larger tuning differences
and what the music indicates in other ways.<br>
And lastly, it is even possible to use the partials in such a way
that we don't perceive them as a separate interval / tone but simply
as a part of the timbre of another tone.<br>
So I'm sorry, there is no simple answer to your question. Though I
hope that the above information is still of help in some way.<br>
<br>
As for blues.<br>
There is no need to invoke partials to explain blues.<br>
And the flat seventh character of the blues scale comes across as
such better when we see it tuned just according to the chain of
fifths:<br>
1/1 81/64 3/2 16/9. That 81/64 to 16/9 is ~588 cents.<br>
Similarly the minor third is quite low when combined with a major
third. 32/27 to 81/64 ~114 cents.<br>
These kind of characters come across better when tuned just
according to the chain of fifths.<br>
And it is more due to how it is used musically in blues that gives
it it's character.<br>
<br>
Kind regards,<br>
<br>
Marcel de Velde<br>
<br>
Zwolle, Netherlands<br>
<a href="mailto:marcel@justintonation.com" target="_blank">marcel@justintonation.com</a><br>
<br>
<br>
<br>
<blockquote type="cite"><div><div class="h5">
<div style="font-size:12pt;font-family:times new roman,new york,times,serif">
<p style>Hello Everyone,</p>
<p style> </p>
<p style>I'm a new
member of SMT. I am a composer/musician who studied music
theory at the University of Washington. I use the harmonic
overtone series in a lot of my compositional work and I have
encountered a variety of different partial interpretations for
specifically [with C as the fundamental] partials no. 10 and
12 - the pitches F or F# and A or Ab. </p>
<p style> </p>
<p style>C-C-G-C-E-G-Bb-C-D-E-[<b>F
or F#</b>]-G-[<b>Ab or A</b>]-Bb-B-C</p>
<p style> </p>
<p style>I have seen at
least three different interpretations. In Schoenberg's <i>Theory
of Harmony</i>, Schoenberg references the tones as F and A.
In <i>The Book Of Music edited by Gill Rowley</i> the
partials are listed as F# and A. And from internet research I
have seen the partials referenced as either F/F# and Ab. I
understand that the reason for the variation is most likely
related to the non tempered pitch of those partials and that
their pitch may lie somewhere between an F and F# and an Ab
and A (taking into account the non tempered frequency of all
the partials). I'm wondering if there is more consensus among
the theory group about whether in the above overtone series
[if arranged as scale with C as the root] C-D-E-?-G-?-Bb-B-C
as to the fourth and sixth degrees? </p>
<p style> </p>
<p style>The reason this
is important to me besides the compositional implications of
creating scales from overtone structure is a hypothesis/theory
I have regarding the jazz/blues scale and it's ability to
function with either major or minor diatonic tonalities. When
the above scale [which I call the overtone scale] is arranged
as the 5th mode:</p>
<p style> </p>
<p style>G-A-Bb-B-C-D-E-F#-G </p>
<p style> </p>
<p style>There is a
scale with both minor and major 3rd [a blue note] . . . and if
we use the partial variation with F we are ever closer to the
flat 7th character of the blues scale:</p>
<p style> </p>
<p style>G-Bb-C-C#-D-F-G</p>
<p style> </p>
<p style>This is my
explanation for why the blues scale works with both major and
minor modes. I'd be curious to get some feedback on my idea
and more specifically the partials above in question. </p>
<p style> </p>
<p style>Thanks,</p>
<p style>Carsonics</p>
</div>
<br>
<fieldset></fieldset>
<br>
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<br></blockquote></div><br><br clear="all"><div><br></div>-- <br>Brian Robison<br><br><a href="http://www.brianrobison.org">www.brianrobison.org</a>
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