[Smt-talk] Fwd: Re: a la mode
Ildar Khannanov
solfeggio7 at yahoo.com
Tue Dec 3 19:01:22 PST 2013
Dear Marcel and the List,
this seemed to be an interesting topic (returning to and revisiting the old one, of course). I suggest creating a panel at the upcoming EUROMAC 2014 in Leven. I know (from the recent Congress of the Russian society for theory of music) the names of at least two more scholars, working in this area, Pyotr Tchernobrivets from St. Petersburg and Franck Edrzejewsky from Paris. We could organize a truly international panel On Tuning in Composition Today. Here is the wiki discussion room, prepared by the organizing committee of the EUROMAC 2014: http://groups.google.com/group/euromac-2014/topics
Of course, the topic can be extended to the manipulation of partials and harmonics in a synthesized sound.
Best wishes,
Ildar Khannanov
Peabody Conservatory
Member of the Organizational Committee
EUROMAC2014
solfeggio7 at yahoo.com
On Tuesday, December 3, 2013 8:01 PM, Marcel de Velde <marcel at justintonation.com> wrote:
Dear Ildar,
Aah, now I get what you mean! I thought we were talking about
merely tuning the diatonic scales in Pythagorean on the piano.
But no, of course, you are right. One can only tune 12 notes per
octave on a standard piano (though pianos have been built that
have 24 tones).
So a piano tuned to Pythagorean is very limiting in what one can
play in it!
For this reason I work with virtual pianos, sampled pianos on my
computer. I can tune them to any enharmonic and am no longer
limited to 12 tones per octave.
The Fauré piece I linked to below has more than 12 tones per
octave and all of them are tuned to perfect Pythagorean. (try to
spot the places where an A# is followed by a Bb)
What is often misunderstood is that Pythagorean is not a
temperament for 12-tones.
And for instance the "wolf fifth" is not a fifth at all.
If you tune your piano to Pythagorean, even for only 12 tones
per octave, then there is not an out of tune interval there.
But if one tries to use the diminished sixth, which is tuned
perfect, as a perfect fifth then this diminished sixth will
sound like a horribly out of tune perfect fifth of course.
There is no enharmonic equivalence in Pythagorean tuning. So for
instance an Ab is tuned differently than a G#, and one had
better know some music theory to use it correctly / play in
tune.
The optimal tuning for a piano if one wants to be able to play
everything on it is 12-tone equal temperament like we use
standard today.
I'll be the last person to propose a change for that.
Kind regards,
Marcel de Velde
Zwolle, Netherlands
marcel at justintonation.com
Dear Marcel,
>
>
>if you managed to tune piano to Pythagorean fifth without destroying other intervals you deserve a Nobel Prize in music theory.
>
>
>It is commonly known that 12 perfect fifths do not fit into 7 octaves (the overshooting is Pythagorean comma). Let us say, you have tuned your middle octave as follows: C-G-D-A-E-B (in a zigzag fashion). Your B will be higher than the equally tuned B exactly 5/12 of Pythagorean comma.
>
>
>You will have to detune your fifths (shrink them) and they will stop being Pythagorean perfect fifths. For ever. You can do two things: leave four fifth Pythagorean and sacrifice one of the fifth (say, supertonic to submediant) by detuning it 5/12 of the P. comma. That fifth will start howling like a wolf! And this fifth will not be able to serve as the basis for the tonic triad, if you would like to modulate to the key of supertonic. And in general, you will be able to play only in this key (on the condition of avoiding the supertonic triad). Or, you can detune each fifth to two beatings per second, and detune each fourth to one beating per second. All your fifth and fourth will be miserably out of tune, but you will receive a system of equal temperament. And a badly tuned instrument.
>
>
>Of course, hundreds of theorists before us had a dream of perfect tuning because, if the fifth is perfect, the two tones create resonance. Violinists like it, singers cannot live without it. The equally tuned piano, on the other hand, marks the end of Western music (at least, such is the opinion of Phillip Gosset). The piano makers put three strings for a note, in order to compensate for the dull and uninteresting sound of equally tempered intervals. Still, circonium is no match for diamonds (ask any woman!).
>
>
>Best,
>
>
>Ildar Khannanov
>Peabody Institute
>solfeggio7 at yahoo.com
>
>
>
>On Tuesday, December 3, 2013 6:14 PM, Marcel de Velde mailto:marcel at justintonation.com wrote:
>
>Dear Ildar,
>
>That is very odd.
>Indeed the fifths are perfectly tuned when the
beating stops and the interval sounds perfectly
stable.
>And 4/3 fourth down should work as well in
theory, though probably a bit harder to get
perfect by ear.
>It should work the way you describe. I'm not an
expert in piano tuning at all but I did tune a
piano this way myself once and it worked
perfectly.
>Though I was surprised by the great amount of
detail needed, the smallest movement of the
tuning wrench had an enormous effect on the
tuning, I spent about a full day tuning the
piano.
>I tuned first the middle octave by adding fifths
and reducing them by an octave when needed. Then
I tuned the other octaves based on this middle
octave.
>I may not give a perfect result as the overtones
of the piano become slightly inharmonic
especially for the lower keys which gives a
slight streching relative to the lower keys I
belief. But audibly the piano I tuned this way
was tuned to Pythagorean correct enough (and I
know Pythagorean tuning very well).
>I've read reports of others who have tuned this
way as well with good results.
>I can't tell what went wrong in your case, but
please don't blame Pythagoras ;-)
>Perhaps someone more experienced with piano
tuning can explain what may have gone wrong.
>
>As for the 5/4 major third vs the 81/64
Pythagorean major third.
>This is the stuff of great debates.
>The 5/4 major third gives what most people
(including me) find a very pleasurable sound.
Same goes for 7/4 for a minor seventh.
>They are similar to the 3/2 major third in the
way that it has the lowest harmonic overtone
relation and therefore gives a very "synchronous
buzzing" sound.
>But is it in tune? I personally, after about 7
years (I lost count) of research, think it is
not. At least not in the strict sense of "in
tune".
>I think the 5/4 is a coloration of the major
third. This is not always wrong, and as I said
it is a very pleasant sounding coloration. And I
see good reason to prefer it to a perfectly "in
tune" 81/64 major third in many situations.
>But "in tune", or "just intoned" had a deeper
meaning than simply a pleasant sound. It is to
tune according to how we internally "understand"
the interval.
>And we internally categorize pitches according
to a chain of fifths and octaves.
>I can give many demonstrations of this but that
would make this an email the size of a book
perhaps haha.
>One very simple example is to tune a circle
progression. For instance I-vi-ii-V-I or
I-IV-ii-V-I.
>A very simple natural diatonic progression. To
use 3/2 for perfect fifths, 5/4 for major thirds
and 6/5 for minor thirds will not correspond at
all to how we interpret this progression.
>As all the notes are linked by a perfect fifth
somewhere in this progression, and since 4
perfect fifths make an 81/64 and not a 5/4,
there is no mathematical solution that will
allow one to tune this progression without some
very unnatural modifications.
>One will have to either allow a "wolf fifth"
which sound horrible and makes no sense.
Unacceptable in this progression.
>Or one will have to allow a "comma shift",
meaning a (possibly held) note will all of a
sudden become a different note a comma higher.
Sounds horrible and makes no sense either.
Unacceptable.
>Or one will have to allow the whole progression
to "comma drift", which means it ends up a
(Syntonic) comma lower every time it repeats.
Sounds strange, makes no sense, and for many
other progressions this does not work.
>Another example: try tuning a big chord like
F-A-C-E-G-B-D-F to 5-limit "just intonation".
Won't work without wolves.
>5-limit or higher limit "just intonation" was
nice to theorize about, but it has no practical
place in music as for 90%+ of common practice
music it is not mathematically possible, and it
clearly does not correspond to how we perceive
music.
>Many people think pure "just intonation" is
impossible. I think it is Pythagorean.
>One can however tune the above things with the
pleasant coloration of the 5/4 major third if
one gives up the pure 3/2 fifth, then one gets
1/4 comma meantone.
>But 1/4 comma meantone performs very badly the
more chromatic the music gets. It is pleasant
for harpsichord playing renaissance music, both
because of the music and because of the harsh
harsichord timbre which can use the sweetening
effect of 5/4 very well. But for for instance
late romantic or modern music it is much worse
performing.
>Here an example of an enharmonic progression in
1/4 comma meantone vs Pythagorean. Notice how
the Ab goes down to G# in 1/4 comma meantone and
the Ab goes up to G# in Pythagorean.
>http://www.youtube.com/watch?v=pr7PTxGnI1I
>And here an example of a sampled piano tuned to
Pythagorean (so perhaps try again on your own
piano as well ;-)
>http://www.youtube.com/watch?v=JgLz5qYdM88
>
>As for the chromatic tetrachord singing. Listen
to Arabic / Turkish / Persian maqam music. They
do make these distinctions.
>In some Turkish music theory it is even
described as such. For instance the Rast
tetrachord is for instance D E Gb G and they
sing it! (though not reliably so, there's great
variety in practice)
>
>Kind regards,
>
>Marcel de Velde
>Zwolle, Netherlands
>marcel at justintonation.com
>
>
>
>
>
>Dear Marcel,
>>
>>
>>I have tried just that. I decided to save on tuning and do it myself. I bought a tuning fork (some 100USD), took one evening off and started tuning. When are the two strings tuned perfectly at a fifth? When the beating stops. You will feel how two notes blend with each other, creating a beautiful sound, almost like a single note sounding. It made me so happy. So, I tuned the notes in the first octave, going by fifth up and fourth down (they are the same, just inversions, am I right?). However, when I listened to an octave--it did not sound tuned, at all. The more notes I tuned by Pythagorean perfect fifth, the more the notes were running away from me, like rabbits. I got very angry at Pythagoras! So much for the diatonic scale tuned by fifth! And, check the major thirds then--they will be also out of tune, definitely not expected 5/4 ratio. And if you stack the fifth from the Do in the bottom of the keyboard until you have reached another Do, the two
Do's will be 1/5 of a semitone apart.
>>
>>
>>The resume: Pythagorean slogans are like Communist Party slogans: they may sound good but digress significantly from reality. Just as the joke of Archytas the Pythagorean, which everyone seemed to buy: the three types of tetrachord. Was he a practical musician? Where did he get these three from? No answer. Please, find me a person who can sing effortlessly a chromatic tetrachord after the enharmonic tetrachord. From Mi down to Ti. Try to hit that C double flat after the D sharp.
>>
>>
>>Best wishes,
>>
>>
>>Ildar Khannanov
>>Peabody Conservatory
>>solfeggio7 at yahoo.com
>>
>>
>>
>>
>>
>>On Tuesday, December 3, 2013 4:33 PM, Marcel de Velde mailto:marcel at justintonation.com wrote:
>>
>>Dear Ildar,
>>
>>You wrote:
>>
>>
>>
>>>
>>>
>>>As for the mathematical toys, such as a stack of fifth--since Pythagoras some inquisitive scientists are trying to harness music with the rules of high school math. If you believe that diatonic is the product of the stack of fifth, take a tuning fork and tune your piano by perfect fifth. Gook luck! In Greece there has been a controversy (canoncs vs harmonics), but practical musicians (including Aristoxenus and his father) did not adopt Pythagorean views. They were too abstract and impractical.
>>>
>>
>>I can assure you that the chain of
fifths (and octaves) is not a mere
"mathematical toy".
>>The math may be easy, primary
school level will do, but the
consequences profound and
fundamental.
>>Our notation system is based on
the chain of fifths, and most of
our music theory along with it.
>>The chain of fifths is what makes
a diminished fourth a different
interval from the major third etc,
and at the same time gives no "2
different major thirds"
>>And the reason this all works so
perfectly is that the chain of
fifths corresponds to how the
human brain quantizes the pitch
space / how we automatically
categorize intervals.
>>Tune the fifths and octaves
perfect and you get Pythagorean
tuning.
>>I will not get into a further
debate on tuning as it is probably
to unrelated to the topic of this
thread, but I will say that it is
not merely an old controversy in
Greece but that Pythagorean is
also still practiced today
naturally by violin, singers,
trombone etc when playing solo
(both taught and automatically
done so). And was the default
tuning system for polyphonic music
in the west until replaced by 1/4
comma meantone and other meantone
tunings. And the 12-tone equal
tempered tuning system that we use
today for fixed pitch instruments
is very close to Pythagorean
tuning, it is hard to hear the
difference with Pythagorean as
long as one follows the enharmonic
notation correctly (don't play a
diminished sixth as if it is a
perfect fifth, or augmented second
when there should be a minor third
etc)
>>
>>It is very easy to tune the
diatonic system based on perfect
fifths on a piano. Tuning fork is
not even needed as it can be done
by ear with ease.
>>Lets start with F tune perfect
fifths above it and reduce them by
perfect octaves when needed and
one gets:
>>F-C-G-D-A-E-B, or C D E F G A B C
when going up in steps from C.
Containing all the strict diatonic
scales. A chain of 6 perfect
fifths linking 7 tones like
described.
>>Tune one fifth extra and you get a
chromatic interval, F-F#. And one
can continue adding fifths till
one gets D#-F a diminished third.
>>Makes good sense to call these the
chromatic intervals, from 7 to 11
fifths. So the chromatic scale
covers 12 tones linked by perfect
fifths.
>>If we add one more fifth we get E#
- F, which are enharmonically
related. So a chain of 12 fifths
and upwards are the enharmonic
intervals.
>>To me this is the best description
there is.
>>It also allows the following
clarification which corresponds to
how we perceive music.
>>Something like the harmonic minor
scale is by this definition a
chromatic scale.
>>However, one can use it
melodically in such a way that the
melody only moves by diatonic
intervals within this scale.
>>So the augmented second is not
used as a melodic step. This is
the most common use of this scale
in western music so one can still
speak of diatonically based music
in a way.
>>
>>Kind regards,
>>
>>Marcel de Velde
>>Zwolle, Netherlands
>>marcel at justintonation.com
>>
>>
>
>
>
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