
The centuries-old struggle to play in tune - brianmckenzie
http://www.slate.com/id/2250793/
======
btilly
Random note. One of my favorite instruments is the wire-strung Celtic harp. It
was killed by several things. First of all it didn't include the sharps and
the flats. Secondly it has a 10-30 second sustain. Because of those two
factors it sounds better in the older tunings. Because of those two factors it
sounds horrible playing more complex modern music.

A lot of the old Irish fiddle music was actually originally intended for the
harp. If you want to know what it sounds like, I highly recommend Patrick
Ball. [http://www.amazon.com/Celtic-Harp-Vol-Turlough-
OCarolan/dp/B...](http://www.amazon.com/Celtic-Harp-Vol-Turlough-
OCarolan/dp/B0000007SD/ref=sr_1_1)

(I don't know what tuning he is using. I strongly suspect equal temperment.)

~~~
cgs
Also in the Celtic vein: uilleann pipes. Anything played in the key of D with
drones sounds fantastic, since it is tuned using just temperament:
<http://www.youtube.com/watch?v=FW0foorxhDk>

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BrandonM
That was a great article. It used multimedia wonderfully, was intriguing, had
a subtly-humorous tone, told an interesting narrative, and most importantly it
taught me something I knew absolutely nothing about in the meantime.

This is what Hacker News is all about, in my opinion.

------
jws
For bonus difficulty: Single strings of the low and high end of pianos aren't
even in tune with themselves. All those little terms that in Physics 101 you
said "…and those approach zero so cross them out" come back and make the
higher harmonics and lower harmonics not match. Pity the poor bass player
attempting to choose his pitch for his note. [wikipedia:stretched tuning]

I generally tell pianists to keep their left hand out of my octave and no one
will get hurt.

~~~
warfangle
You know, I've tried to jam with bands as a non-fretted player. It's tough -
especially since I haven't played with fretted/keyboard instruments in about
12 years (switched from duet recitals to chamber/symphonic).

It's really frustrating to try and figure out the precise notes - but I can
improvise fairly well on my own or with another string. I definitely need to
train my ear better, but knowing that there's this interval problem now -
it'll probably help, because I know that there's something I'm going to have
to adjust for.

------
RevRal
Single page: <http://www.slate.com/id/2250793/pagenum/all/>

~~~
BrandonM
Do we really need these for every multi-page article? I mean, on this one in
particular you read down to the bottom of the first page and see:

    
    
      1 | 2 | 3 | 4 | SINGLE PAGE
    

Clicking SINGLE PAGE even puts us at the correct position in the single-paged
article! When I saw the link though, I couldn't help laughing to myself and
thinking, "I should be one of those karma dudes who posts 'Single Page:' as a
comment." Then I checked out the comment thread and here it is.

Who votes these up? Don't we all know by now that clicking the "Print this
article" or "Single page" link on a multi-page article will transport us to
that magical single page?

(In case you're wondering, I didn't vote the parent down.)

~~~
RevRal
I'd prefer that the submitters submit the full page stories or printer
friendly versions as the submission. Posting the single page link in the
comments is friendly. I also check the comments on HN before clicking the
submission link, as there is often a full page link, which always makes me
happy. (The comments also tell me whether if I should take the time to
actually check the submission out)

I kind of had the feeling that someone is jumping to the karma conclusion.
Woe. Woe, I dare to say.

\----

Addendum:

Oh, and if I said I didn't appreciate the karma, I'd be lying. The +3 boost
this is giving me puts me at 660, and I'm annoyed when my karma isn't
divisible by 5. (I'm serious)

Otherwise I don't really care. In fact, I often post riskier comments if my
overall karma isn't divisible by 5. If I was at 901, and someone somewhere
downvoted me to 900, it would make me happy.

So please don't screw up my karma, you'll make me sad.

~~~
BrandonM
The "karma" comment was a joke, one that had the possibility of having some
truth to it. I didn't assume any ill will :)

\---

Addendum: I do appreciate that "divisible by 5" quirk you mentioned :).

My quirk seems to be that I don't really consider my comments complete until
I've reread and edited them something like 5-10 times. I thinks that's why it
makes me kind of sad when my shortest comments (e.g.
<http://news.ycombinator.com/item?id=1283979> and
<http://news.ycombinator.com/item?id=1219118>) are the ones that get the most
upvotes... I spend so little time on those comments, as compared to one like
<http://news.ycombinator.com/item?id=1284130>.

~~~
RevRal
It's fine.

I also remembered that I hate touching my mouse, and I prefer to keep my ring
finger on "page down" when reading on a computer. Having to physically lift my
hand, move it to the mouse, find the cursor on the screen, aim it at "next
page" or whatever then click, and if I misfire... start over. This really
breaks my flow and is quite disruptive.

I know I'm not the only one who cares about stuff like this.

------
klipt
I was interested in this a few years ago, and one of the sites I found back
then was Xentonality:

<http://eceserv0.ece.wisc.edu/~sethares/xentone.html>

It includes music featuring some really intriguing concepts. For example,
"Three Ears" isn't played in a fixed scale at all - instead the tuning is
tweaked on the fly "for maximum consonance". The result is weirdly
fascinating.

------
najirama
Wow - I've always run away from harpsichord recordings because they're usually
so stringent and cold; but the harpsichord samples in this article are so very
rich and warm.

I don't know if its the tunings or something in the recording/mix process;
nevertheless I'm going to seek out the cd recordings - thanks for sharing.

------
ars
I feel sad that I simply can not hear this.

I've read about this (temperament) many times, and I still have no idea what
they are talking about, and I assume it's because I just can't hear the
difference.

I'm not tone deaf, but I guess I'm not very good at tones.

~~~
loup-vaillant
Virtually no untrained ear can hear the difference. It's perfectly normal.
Now, if you really have no clue, I can give you a mathematical intuition, so
your brain understand what your ear can't hear.

(1) Axiom: We hear at a logarithmic scale. What we perceive to be a
_difference_ (or interval) between 2 notes is actually a _ratio_ of
frequencies. (I think biology may explain this axiom.)

(2) Axiom: Say you hear 2 notes, of frequencies f1 and f2 respectively. When
the f1/f2 ratio is a simple rational number (like 2) or (3/2), it sounds good.
When the ratio is more complicated (like 19/17), it sounds worse. (Physics can
explain that axiom.)

(3) Definition: when the f1/f2 ratio is 2, we call that an octave. The 3/2
ratio is a fifth. The 4/3 ratio is a fourth. As a side note these ratio were
basically the only ones that were used. They didn't really used thirds or
sixths, probably because of their more complicated ratios, which may have
sounded bad to their ears. [1]

(4) Theorem: There is no way in hell you can make an octave out of fifths
(they won't perfectly tune together). Informal proof: this is because you
can't find any (i,n) ∈ ℤ², such that (3/2)ⁱ = 2ⁿ. As a side note, you can come
relatively close: (3/2)¹² = 129,75 which is close to 2⁷.

So, a mathematical impossibility prevents you to perfectly tune the two most
basic intervals ever. Ouch. We have to compromise, then. We can sacrifice a
few chords (which if played will cause severe ear damage); or cheating a
little bit on every ratio, so no chord sounds outright wrong, nor exactly
right; or we can try to find a middle ground between these two extremes.

The "sacrifice" strategies was originally favoured. They sounded better, but
restrained what you could play. Now, we favour the "cheating a little"
strategy (also called "equal temperament"). They give you more liberty, but
sounds rather dull on old music meant to be played with an old fashioned
tuning (to trained ears, at least :-).

Hope this helped.

[1]: [http://pipolitics.com/video-streaming/kaamelott-
saison-2-epi...](http://pipolitics.com/video-streaming/kaamelott-
saison-2-episode-20-la-quinte-juste.html) is an excellent joke on the topic.
(This is a flash video in French, unfortunately. I hope you understand it, or
can find a friend who does).

~~~
ars
Thanks it does help. So the actual note doesn't matter? Just the ratio of the
notes when played together?

What about the ratio of two notes played on after the other? Is that very
important too?

Could you make a piano with multiple keys each tuned to match a particular
ratio better?

~~~
loup-vaillant
The actual note doesn't matter at all. Just the ratio. We do have a reference
note, but this is only for convenience. (Indeed, the reference note in Europe
progressively changed, from 415Hz to 440Hz).

I'm not sure the ratio of two notes played one after the other really counts
by itself. However in many instruments, two consecutive notes will tend to
overlap (piano, for instance). Also, many instruments (especially those with
strings, like claviers and violins), resonate better when the note you play
has a "good" ratio with the natural notes of the instruments, even if you
don't play them! Some instruments were even designed around this principle. So
you have to maintain a good ratio with respect to these "base" note at all
times.

In practice, the ratio of two notes played one after another is indeed
important.

I'm not sure I understand your last question. Actually, you can change the
tune of a piano. So, the optimization you speak of is possible even on a
modern piano. Just re-tune it.

A final note about why "simple ratios" sound better: When you make a string
resonate, it doesn't do only one note. It does its base frequency (say f), and
many others (every multiple of f). So, in a piano, when you play a G at 100Hz,
it also plays at 200Hz (a G), 300Hz (a D), 400Hz (a G) etc. Note that there
exist actual keys whose main frequencies are 200Hz, 300Hz, 400Hz and so on.
They will resonate, which will make the sound richer, louder.

The problem with equal temperament is that the only ratio which is really
respected is the octave (2 to 1). In such a case, the D I mentioned above
won't be _quite_ at 300Hz, and won't resonate well. So equal temperament
became practical only when instruments became loud enough to make up for the
loss in resonance.

------
gjm11
For information about the temperament used in Watchorn's recording of the
_Well-Tempered Clavier_ , based on an examination of (I kid you not) the
spirally ornaments on the title page of Bach's manuscript, see
<http://www.larips.com/> . (Why "larips"? Well, you see, the analysis begins
by looking at that title-page upside down, and "larips" is "spiral" backwards.
Again, I kid you not.)

It sounds pretty good, actually, but so do plenty of other temperaments.

------
chancho
Wanted: midi keyboard controller with a 1-axis touch control surface on every
key. I will be your first pre-order.

~~~
humbledrone
Isn't this already supported in most modern MIDI keyboards in the form of
Aftertouch? If that's not what you're looking for, you could always get one of
these:

    
    
        http://www.cerlsoundgroup.org/Continuum/

~~~
chancho
That's exactly what I was thinking of. Thanks.

(Of course, at >$3000 I'm not actually going to buy one. Just geek out over
it.)

------
sswam
I have done some work on this. I think the best way to tune a system for
playing diatonic music is to ensure that the major and minor chords on tonic,
dominant and sub-dominant are perfectly tuned in harmony. This sets exact
frequencies for every note of the 12 except for the diminished dominant, which
is not used much except in modulation or more atonal music. This tuning gives
very good sounding harmonies. If the tune modulates, the best thing to do is
to change the tuning of all the notes to match the new key. You might also
shift the pitch of the new key note to its equal-tempered value, or to the
value in the original "base" key, to which your piece will probably be
returning. This will give excellent sounding music. Even the chromatic scales
sound really brilliant with proper harmonic tuning like this, if you listen to
a random segment of a chromatic scale, you can get a feel for where the tonic
note is! equal-tempered scales just don't give that. I have written a simple
computer-keyboard app that implements this tuning and modulation, it not
complete, a work in progress.

~~~
sswam
this system does keep every key sounding the same, for me that is a desirable
quality. Some variety of harmonies might be used to achieve different feels.
The key of the system is that it is designed for an electronic synthesizer - a
different tuning can be used for any piece or key within a piece, and the
tuning can be varied at modulation.

~~~
dmoney
_a different tuning can be used for any piece or key within a piece, and the
tuning can be varied at modulation_

How hard is it to vary tunings with existing synthesizers?

