The centuries-old struggle to play in tune

http://www.slate.com/id/2250793/

by brianmckenzie • 16 years ago

84 32 16 years ago

RevRal4• 16 years ago

Single page: http://www.slate.com/id/2250793/pagenum/all/

BrandonM4• 16 years ago

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.)

aristus• 16 years ago

I hear you, but I think it's more protest/irony than information. Page-breaking is a cheap trick to inflate page views, borne of the same low cunning that gives us items priced at $2.98 instead of $3.

When I'm reading HN on a phone or other high-latency environment I appreciate saving the extra roundtrip.

RevRal4• 16 years ago

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.

brianmckenzie• 16 years ago

Sorry, that was an oversight on my part.

btilly• 16 years ago

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...

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

cgs• 16 years ago

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

jws• 16 years ago

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• 16 years ago

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.

sswam2• 16 years ago

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.

sswam2• 16 years ago

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• 16 years ago

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?

BrandonM4• 16 years ago

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.

chancho2• 16 years ago

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

humbledrone• 16 years ago

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/

chancho2• 16 years ago

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.)

hernan7• 16 years ago

Not MIDI, but CV: Ondes Martenot / The French Connection

http://en.wikipedia.org/wiki/Ondes_Martenot

demallien• 16 years ago

I went to a concert based around that instrument last year in Paris - it's a very weird sound.

najirama• 16 years ago

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.

klipt3• 16 years ago

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.

ars2• 16 years ago

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.

ericbb• 16 years ago

If you are mathematically inclined, this might help. It's how I, as a non-musician, came to understand tuning a little.

Equal temperament uses frequencies that are scaled by powers of the twelfth root of 2. Moving up one semitone is the same as multiplying the frequency by 2^(1/12). If you look at this table

http://en.wikipedia.org/wiki/Equal_temperament#Comparison_to...

you can see how the resulting values approximate certain ratios. Ratios matter because two tones that are related by a simple ratio will tend to have greater harmonic relationship and be more 'consonant'.

Other tunings emphasize different ratios and give up the equal spacing of notes -- equal spacing when plotted by frequency on a logarithmic scale.

loup-vaillant2• 16 years ago

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... 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).

ars2• 16 years ago

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?

gjm11• 16 years ago

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.

The centuries-old struggle to play in tune

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