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Comment by bloak | Hacker News Reader

It seems that no one objected to the (slightly off-topic) claim that "the vast majority of western music uses equal temperament". As I understand it, equal temperament is just a way of tuning keyboard instruments so that they sound the same in every key; a string quartet or a choir doesn't use equal temperament. (And some people claim that J. S. Bach, who insisted on tuning his own keyboards, didn't use equal temperament, either.)

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It's a way of tuning so that all semitone intervals are an equal [2^(1/12)] frequency ratio. The vast majority of western music, today, uses equal temperament. This includes most recorded performances of JS Bach's pieces.

It wasn't particularly common in Bach's time, though, and the math to do it 'properly' wasn't even known outside of China.

Today, though, it's everywhere. Modern Woodwinds are equal temperament due to the placement of the holes. To match that, the entire orchestra is in equal temperament, regardless of the requirements of the instrument.

Guitars are in equal temperament due to the placement of their frets -- to do otherwise would require frets that bend between strings.

In isolation, people will [attempt to] sing in equal temperament, because that's what 'all' accompaniment is like.

Barbershop quartets, acapella groups, and to some extent string quartets have a tendency to shift harmony notes toward simple fractions of the root note of the chord, on the fly, even as the overall melody runs in equal temperament. This isn't a different 'tuning', per se, but it is a thing.

Barbershop is notable for using the harmonic seventh, which doesn't exist in the standard 12 note scale. Its frequency is 7/4 times the frequency of the root, so a harmonic 7th above C is somewhere between A and B-flat.

https://en.wikipedia.org/wiki/Harmonic_seventh_chord

From that page: the harmonic seventh is '"sweeter in quality" than an "ordinary" minor seventh'. Well, as an ex- trumpet and trombone player,[0] what it sounds is out-of tune, and is generally avoided, although the out-of-tuneness can be compensated for by adjusting the trombone slide. It doesn't sound particularly bluesy to my ear. Sure, sliding around the flat 7 and flat 5 areas sound bluesy, but just that note as a melody note sounds very flat.

[0] Playing brass instruments is a matter of using your lip to find the various harmonics, and using the valves to flatten them by various amounts.

I don't think there's anything inherently wrong with natural harmonics in a melody. The opening and ending of Britten's Serenade for Tenor, Horn and Strings, Op. 31 uses them, and it sound good to me. Because it's notated as equal temperament, the score is ambiguous, and there are two ways of playing it:

https://www.youtube.com/watch?v=WxVnSkX4Fco (13th harmonic high note version)

https://www.youtube.com/watch?v=mkLyK-oSQ7A (14th harmonic high note version)

I suspect that brass players are unusually sensitive to deviations from equal temperament because they have to work so hard to overcome them if they want to play with other instruments (including other brass instruments of different sizes).

>I don't think there's anything inherently wrong with natural harmonics in a melody.

Not sure what you mean by 'natural harmonics', i.e. which ones you mean. I was just talking about how the Ab harmonic (on trombone/trumpet) sounds very flat. It's avoided because it sounds out of tune. I'm not sure what something being 'inherently wrong' would even mean. In music, if it sounds good, it is good.

>I suspect that brass players are unusually sensitive to deviations from equal temperament because they have to work so hard to overcome them if they want to play with other instruments

I don't know what you're referring to there - I've never had or even heard of that problem. And I hadn't noticed or heard, and don't believe, that 'brass players are unusually sensitive to deviations from equal temperament'.

By "natural harmonics" I mean notes at the resonant frequencies of the instrument. Several of them are obviously different from equal temperament, which means they will sound bad when played with other instruments. When brass players talk about "good intonation", they often mean adjusting these notes into equal temperament with valves/slides/embouchure/hand stopping. Because brass players actually have to pay attention to the tuning, I wouldn't be surprised if they were more sensitive to it than people who played fixed pitch instruments like piano. The Britten piece is notable for the parts where the horn player is instructed not to adjust the pitches to equal temperament, and because it's a solo it still sounds good.

.Guitars are in equal temperament due to the placement of their frets -- to do otherwise would require frets that bend between strings.

Interestingly enough, such a thing does exist.

http://www.truetemperament.com/

True temperament is meant to address guitar intonation problems regardless of the temperament. It's basically impossible to get a guitar intoned correctly over the fret board using straight frets because of the different string gauges. So it's not specifically meant for just intonation.

I would amend this to say that modern woodwinds are supposed to be equal temperament, but this is more aspirational than reality. Some instruments better than others, and in general they are all vastly improved over their 18th- and 19th-century ancestors, but a lot of the burden of making the pitches "equal" is left to the player.

(Source: I play bassoon, probably the worst of the lot.)

> It's a way of tuning so that all semitone intervals are an equal [2^(1/12)] frequency ratio

Or so I thought until I programmed an AVR. The F, I think it was, is terribly out of tune. I haven't found the wikipedia article again, that had the correct Frequencies noted in Hz, with F decidedly not in the scheme that you allege.

If you shift F away from that ratio, you're not doing equal temperament anymore. Which is fine. There are many different tuning systems [ https://en.wikipedia.org/wiki/Musical_tuning#Systems_for_the... ], and they all involve tradeoffs.

Equal temperament's benefit is its flexibility, but that doesn't make it 'better'.

Correct! Most live performed music does not use equal-temperament. Many keyboard instruments do not use equal-temperament either, especially organs/clavichords etc.

One of the interesting things about organ tunings is that because you can choose which pipes to perform with, different pipe-sets may be tuned according to slightly different needs on the same instrument. So, you might have one set of pipes that is well suited for equal-tempered, highly chromatic pieces. Another set of pipes may be intended for use with choirs, and another set still tuned to be ideal in an orchestral setting. However, the specific tuning of the instrument is usually maintained over the course of its life, which is part of why organs can be so distinct and characteristically themselves. Most organs are tuned by ear with tooling assists, and generally land in a Wohltemperiert that compromises between equal-temperament and pure 5ths.

Pure 5ths are are especially important on an organ, because many of the pipes produce highly sinusoidal fundamentals, making un-pure 5ths especially obvious and "out of tune" sounding. The complexity and bloom of the harmonics in a piano helps to mask these effects.

"Most live performed music does not use equal-temperament" - Such as? That claim doesn't sound right to me.

"a string quartet or a choir doesn't use equal temperament."

But they are still fairly deeply influenced by the fact all our ears are generally tuned to equal temperament, so I think it's still fair to say they use equal temperament + some local deviations, rather than some other tuning. Music that is "truly" not based on equal temperament sounds "wrong" to most people nowadays, or at least requires a significant adjustment period.

While they may be influenced by it, the serious choir I was in was adept at producing perfect harmonies rather than the slightly-off equal temperament. To say that 2 solid players can't produce a perfect fourth or fifth together due to this equal temp influence, that's incorrect.

The main issue comes when you have other instruments playing with you that are equal tempered. You will sound off if you sing or play with them, and you will sound off if you don't. That's one reason a capella music can sound really great, it's not slightly off but rather perfect intervals.

"To say that 2 solid players can't produce a perfect fourth or fifth together due to this equal temp influence, that's incorrect."

No, of course not. What I'm saying is the underlying tune is very likely still equal temperament. Probably one end of your perfect fifth is pinned to the equal temperament frequency, and the other end is tweaking just a bit to be the perfect fifth. That's still at least "influenced heavily" by equal temperament, if not simply "equal temperament with a couple tweaks". I've heard plenty of vocal/string works like this. I have not heard a lot of vocal works on a Pythagorean tuning or something, or something more exotic like shifting the base key of the tuning on the fly.

By contrast, historically, music was simply in another tuning. All of it, including vocal. It sounds strange to modern ears in a way that "equal temperament plus slight tweaks for a perfect 4th/5th" doesn't sound weird to anybody.

Close but not right. String players have to learn to place their fingers in locations that are consistent with equal temperament tuning, or they will sound of out key. It would be fine if a string quartet played on its own, but even then, most would play in ET not JT because otherwise everybody would complain it sounds funny.

I have a lovely blues album by a guy who plays a keyboard in JT. most people who hear it ask me to turn if off "because it sounds wrong" and that includes musicians! it sounds fine to me because I grew up listening to ragas and developed an appreciation for alternate tunings.

What is JT?

sorry, meant just intonation (JI): https://en.wikipedia.org/wiki/Just_intonation

it's the tuning system that was most commonly used before equal temperament in the west. It's attractive due to the geometry underlying the pitch ratios, but it's hard to work with if you have a bunch of different instruments that youy have to keep in tune with each other.

Just inTonation

> I have a lovely blues album by a guy who plays a keyboard in JT.

I would love to know what album this is; very interested in giving a listen.

I managed to dig this up from an 8 year old chat in FB Messenger(!!!) where I asked my friend about an album I heard in 1992. https://en.wikipedia.org/wiki/La_Monte_Young https://www.discogs.com/La-Monte-YoungForever-Bad-Blues-Band...

A choir doesn't need equal temperament because they have a continuous tuning versus a piano. A string quartet (and a trombone!) can do the same thing, they can adjust the tuning based on the instrument, the octave, and what everyone else is playing because they all have continuous tuning versus discrete tuning (I am a trombone player, so my individual instrument has its own quirks at different partials, but I can use the tuning slide to adjust and be in tune exactly).

For the record: I am a professional bassoon player. I have been working professionally for the last ten years in various orchestras in Sweden and germany.i currently hold the position as first bassoon in Norrköpings Symphony Orchestra.

Yes and no. It is true that we in orchestras "listen" and intonate in tune (with low major thirds, slightly high fifths and so on), but playing strictly in tune quickly becomes impractical.

If you play many harmonic sequences or modulations "in tune" and then return to you original key through a different path you will often end up nowhere near where you started. We all have the equal temperament as our base and even though we play one or two chords perfectly in tune we adapt tuning not to end up far from the standard equal temperament.

Then we have the problem of melodic intonation. If you play a melody with the intonation of the harmonic series you will sound _very_ low whenever you play a third.

In his lecture series on Bach, Robert Greenberg discusses temperament quite a bit and I found it fascinating. He relays all these descriptions that Bach had of different keys that are basically lost on us now as we cannot refer to the specific tunings he utilized (and thus cannot hear a lot of the music he wrote as he wrote it).

He also makes the claim that equal temperament became wide spread _because_ of the piano specifically - not just to sound the same in every key, but to sound the same on each piano. And so equal temperament would not have saturated European music until the early 19th century when the piano became ubiquitous. The reason being (as mentioned) that many other instruments can be tuned by the musician on the spot, whereas a piano requires some standardization.

https://en.m.wikipedia.org/wiki/The_Well-Tempered_Clavier at least is designed for well-temperament, which isn’t the same as equal temperament

The question of what temperament, exactly, Bach meant by "Well-Tempered" is a hotly contested question, with the majority assuming it is one of the Werkmeister variants, and a vocal minority insisting it was Bach's own custom temperament, with a couple of Bach scholars even hypothesizing that Bach encoded his temperament scheme into the decorative squiggle on the cover page of the original printing of the book.

But everyone agrees it wasn't equal temperament. The point of the book was to showcase the unique character of each key, uniqueness that is lost in equal temperament.

Have people listening recommendations to hear music without equal temperament? Having played the violin for over 30 years - and sung a bit of barbershop - this is the first time I've come across it, and I'd like to hear the difference to recognize it.

Here's a piece of Byzantine chant in the first mode: https://www.youtube.com/watch?v=bHpOiX2sO-s

Byzantine chant divides an octave into 72 comas. The intervals for the diatonic first mode are 10-8-12-12-10-8-12, although this changes when descending. For more information, see http://www.kelfar.net/orthodoxiaradio/Diatonic.html

Edit: The hard chromatic scale is pretty funky: http://www.kelfar.net/orthodoxiaradio/HChromatic.html

Arguably the most famous just intonation piece is La Monte Young's 5-hour The Well-Tuned Piano

Other just intonation or microtonal works:

Terry Riley - The Harp of New Albion

Glenn Branca's Symphonies #3 and #4

Lou Harrison - Piano Concerto

Karlheinz Stockhausen - Studie II (81-step microtonal scale)

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