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what exactly is equal temperament and how it relates


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deleted_user_680e93b
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PostPosted: Tue Sep 11, 2018 7:42 am    Post subject: what exactly is equal temperament and how it relates Reply with quote

What is equal temperament and how it relates to using a tuner with a trumpet.
Or should the tuner i'm using be set to equal temperament or some other setting when in use it to check pitch ?
This isn't about if you use or don't use a tuner, but what settings to you have it set to if you use one.


thanks

tom
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kehaulani
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PostPosted: Tue Sep 11, 2018 8:59 am    Post subject: Reply with quote

If I'm not mistaking, tuners are set up to equal (well-) temperament. It's what you'd find on a keyboard.

Acoustically, scales are built on a combination of the overtone series-notes which have some notes flatter/sharper than found on the piano (natural vs. well temperament). Try playing an 11th and see if it's a true interval of a fourth from the tonic or if it's naturally sharp.

That means that to play on the keyboard, all scales have to be "tempered" and not "natural" or you wouldn't be able to play in remote keys and have all keys with the same proportional acoustic interval between pitches. Playing a modulation on a "naturally" tuned keyboard would be very squirelly if it's a more remote modulation.

If you want to play a true western-music scale a la violin, better to use your ear than a tuner.


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deanoaks
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PostPosted: Tue Sep 11, 2018 9:42 am    Post subject: Reply with quote

Equal temperament is the perfect compromise used to tune pianos everywhere. It places every half step or semi-tone equal distance from one another which allows every key to be functional but objectively sound the same.
Brass players typically tune with "just temperament" where at the beginning of the tune everybody is tuned to A=440, but as the piece goes on, the tonal center very well could change depending on harmonies used. Most seen in Bach or other composers heavily using minor 7ths chords (as a minor seventh is almost a quarter tone flat to be "in tune")
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trompette229
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PostPosted: Tue Sep 11, 2018 9:48 am    Post subject: Reply with quote

This can be a long discussion but the short of it is, yes, tuners are set to equal temperament and while most tuner apps can be set to different systems virtually all of them use equal temperament as their default.

If you are working on pitch and knowing your instrument, the tuner is a great place to start. "Just" intonation is used when tuning chords in different keys. It requires altering certain chord tones (most commonly 3rds) to play a resonant "in tune" sounding chord within different keys. If you hear a great sounding chord in a brass ensemble, they are using "just intonation" whether they know it or not!
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trickg
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PostPosted: Tue Sep 11, 2018 11:08 am    Post subject: Reply with quote

I never worried too much about it, or at least I never made a point to use a tuner regularly in the practice room. For a short while, I used a clip-on tuner on my bell while playing with the wedding band, but that was a different kind of thing due to the fact that in the early days with that band, monitoring was hit-or-miss, (we used in-ears, but I was still beholden to the sound man, prior to getting control of my own mix with a digital mixer) and volume was a consideration.

Ultimately with a wind instrument, you have to use your ear to adjust to whatever the pitch center happens to be for whatever the note happens to be, and you "tune" in a general way rather than trying to lock into the fixed intonation of an electronic tuner.
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Andy Del
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PostPosted: Tue Sep 11, 2018 4:32 pm    Post subject: Reply with quote

It's getting close, but not quite accurate. Equal temperament is exactly that, equal tempering of all semitones across the range of an instrument and the default of most tuners.

Pianos are sort of tuned this way, although if measured, you will notice that the high end is stretched slightly sharp, so we don't hear it flat.

Other temperaments, such as mean tone, just, werckmeister, Vallotti, and various French temperaments vary, usually so one key or another will sound more pure. The exact differences? I really have no idea. I just trust the instrument tuner and my ears!

We had a piano at college which was tuned to 'mean tone' tempering in the studio of a recorder prof. He would demonstrate the difference, often via Bach chorales. It is quite stunning how brilliant and pure a D major chorale sounds as opposed to F# minor! When a buddy of mine retuned a chamber organ to Werckmeister III for a recital, I found myself all at sea for a while, but it turned out quite well, and sounded rather nice.

Using our ears will help so much more than one realises. Even kids can do this - tell them to listen, explain that note X must be a little lower to sound good, and note Y a little higher. All of a sudden, the harmonies start to ring instead of grind!

So when using a tuner, it is for a reference pitch only. We are all roughly at A=440 (or 442, which helps strings sound ever so much nicer) and then go and play, using our ears to maintain some harmonic tunefulness. A tuner will be useless after about 30 seconds. I have watched this happen in the pit for a long time.

cheers

andy
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JoseLindE4
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PostPosted: Tue Sep 11, 2018 5:23 pm    Post subject: Reply with quote

Equal temperament is the agreement that ALL notes will be equally out of tune.

Just to clear up a misconception, well temperament is not the same as equal temperament. The question of tuning is a complex problem. Broadly, the problem is that if you start stacking beatless pure intervals that actually sound in tune, they don't add up to other beatless pure intervals. If you're math-minded, Wikipedia gives a pretty mathy summary (see the article on the comma).

Tuning systems are a much bigger issue for fixed pitch instruments such as the piano since wind and string players can adjust the pitch on the fly. Essentially, no matter what system you use for fixed pitch instruments, you run into problems. If you make all of your fifths pure, your thirds end up really high and you end up with a wolf fifth which sounds extra rough. Even if you decided to make all intervals justly tuned (pure intervals with simple ratios) to C, it would only work in relation to the note C.

Some tuning systems work pretty well (better than equal temperament, but still not entirely just) in a handful of keys but as you venture further around the circle of fifths the intervals move further and further from just (pure).

Various tuning systems exist to distribute the difference of the problem intervals throughout the system so as to fix problem intervals and problem keys.

So-called well-temperament, which references a number of tuning systems, was known for making all major and minor keys playable. This doesn't mean that they sounded the same like a modern piano. Each particular key had its own sound. If you study Bach's Well-Tempered Clavier, you'll notice that his treatment of different keys takes this into account. Certain intervals are either highlighted or hidden.

Equal temperament is the decision to equally divide the octave, so each note is the same distance from its neighbor. This makes each key essentially sound the same, which is useful for the way we think of music, but it comes at the cost of pure, beatless intervals.

Quality wind and string players tend to play in some intuitive hybrid of equal temperament with some justly tuned intervals, although some string players will intentionally play the 7th scale degree high. They do this so that it pulls more strongly up to the 1st scale degree but it can come at the cost of a just interval. The 7th scale degree often needs to be flat from equal temperament to be in tune and they want to play it sharp from equal temperament.

A tuning system and the intervals it favors or doesn't is intimately connected with the musical characteristics of a time period. If you trace music from the 5ths of medieval organum to the contenance angloise (3rds and 6ths) of the late medieval period, to the music of Bach, to the upper extensions and colors we use today, you see that tuning systems favor the intervals that are commonly used.

I recommend playing slow scales against a drone pitch, singing solfege with a piano, and lots of listening.

If you're interested in the subject, there are some good demonstrations available on youtube.


Link



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Seymor B Fudd
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PostPosted: Wed Sep 12, 2018 1:17 am    Post subject: Reply with quote

JoseLindE4 wrote:
Equal temperament is the agreement that ALL notes will be equally out of tune.............................................................................
.............................................................................................................


Thanks a lot for a most enlightening post!
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Andy Del
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PostPosted: Wed Sep 12, 2018 4:08 am    Post subject: Reply with quote

Same here...
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delano
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PostPosted: Wed Sep 12, 2018 4:26 am    Post subject: Reply with quote

In Holland somebody developed a new tuning system called divine 9. The A is 427 herz in this system and it's certainly not equal temperement:

https://www.youtube.com/watch?time_continue=57&v=mP3u_Do2IT8

The theory:

http://divine9music.com/divine-9-music-frequencies/?lang=en

and the music:

https://www.youtube.com/watch?v=wgACzmcQ0uI&list=PLM_nkcQbER2FW0O5hxzG4AeXWufpEvdaz


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deleted_user_48e5f31
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PostPosted: Wed Sep 12, 2018 4:27 am    Post subject: Reply with quote

Deleted by dfcoleman

Last edited by deleted_user_48e5f31 on Tue Jan 05, 2021 7:26 am; edited 1 time in total
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mm55
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PostPosted: Wed Sep 12, 2018 4:57 am    Post subject: Reply with quote

JoseLindE4 wrote:
Equal temperament is the agreement that ALL notes will be equally out of tune.
That's nonsense. Equal temperament is the agreement that all semitones will be the same size. That's the most common modern definition of "in tune".
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deleted_user_680e93b
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PostPosted: Wed Sep 12, 2018 5:55 am    Post subject: Reply with quote

Thank you all, for the education. Lots of stuff to check out, very much appreciated.

tom
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scottfsmith
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PostPosted: Wed Sep 12, 2018 5:58 am    Post subject: Reply with quote

mm55 wrote:
JoseLindE4 wrote:
Equal temperament is the agreement that ALL notes will be equally out of tune.
That's nonsense. Equal temperament is the agreement that all semitones will be the same size. That's the most common modern definition of "in tune".


Your response reminds me of when the Indiana state legislature tried to pass a law setting pi to 3.2. Just as pi has an inherent meaning in terms of a circle and square, "in tune" has meaning beyond the scale, its about frequency ratios.
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LSOfanboy
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PostPosted: Wed Sep 12, 2018 6:02 am    Post subject: Reply with quote

mm55 wrote:
JoseLindE4 wrote:
Equal temperament is the agreement that ALL notes will be equally out of tune.
That's nonsense. Equal temperament is the agreement that all semitones will be the same size. That's the most common modern definition of "in tune".


Hi,

Careful. I think JoseLindE4 was right on the money there.

Make sure you read the entire post before commenting, that statement is anything but 'nonsense'.

Please can we all show some respect for our fellow posters. This has been a really informative and interesting thread, let's not start getting confrontational.

All the best
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cheiden
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PostPosted: Wed Sep 12, 2018 6:28 am    Post subject: Reply with quote

Andy Del wrote:
It's getting close, but not quite accurate. Equal temperament is exactly that, equal tempering of all semitones across the range of an instrument and the default of most tuners.

Pianos are sort of tuned this way, although if measured, you will notice that the high end is stretched slightly sharp, so we don't hear it flat.

When I studied piano repair we were taught that the reason for stretching the upper octaves sharp was due to what is called inharmonicity, that the ascending partials from a struck string are not mathematically simple ratios as one would presume.
https://en.wikipedia.org/wiki/Inharmonicity

In order to get the best tuning you had to listen not only to the beats between fundamentals but also the beats that exists between certain partials. It hurts my head to remember how hard I worked on this and still never got particularly good at it.
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mm55
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PostPosted: Wed Sep 12, 2018 6:46 am    Post subject: Reply with quote

LSOfanboy wrote:

Careful. ... Make sure you read the entire post before commenting


Thanks for that condescending response.

Equal-tempered major thirds are considered in tune in most western and popular music of the twentieth and twenty-first centuries. So called "pure" intervals of simple integer ratios, especially the major third, are out of tune in many, perhaps most, modern contexts. Beating is normal. Claiming that all equal-tempered notes are "equally out of tune" uses a definition of intonation that is obsolete in many contexts, and there's no reason to remain in the old-fashioned world if you're not playing old-fashioned music. A major third with a simple 5/4 frequency ratio sounds grossly out of tune on a piano, to me, to most piano players, and to any qualified piano tuner.

We don't have to be tied to simplistic definitions of "in tune". The reason we use twelve-tone equal temperament is so no note need be out of tune, unlike the Pythagorean definitions, which kept harmonic and tonal vocabulary limited because so many intervals in that system were badly out of tune and unuseable.

Twelve-tone equal temperament is the agreement that the definition of "in tune" is based on all semitones having the same frequency ratio, rather than having a limited number of intervals with arbitrarily simple frequency ratios.

Just intonation is the agreement that most intervals will be badly out of tune so a few favored intervals can sound especially sweet, and we'll limit ourselves to the simple sweetness. That seems as valid as JoseLindE4's definition of 12TET, and much more relevant to anyone who plays in ensembles with keyboards, giutars, vibes, harps, or synthesizers.

Major thirds with a frequency ratio of 1.25 sound nicely in tune in a Gabrieli brass quintet, but they can sound badly out of tune in a jazz combo with a piano, where the definition of a major third is a ratio of about 1.26.

Here in the twenty-first century, 12TET is the default, but more old-fashioned tunings as well as newer more innovative tunings are definitely appropriate in specific contexts.
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LSOfanboy
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PostPosted: Wed Sep 12, 2018 8:22 am    Post subject: Reply with quote

mm55 wrote:
LSOfanboy wrote:

Careful. ... Make sure you read the entire post before commenting


Thanks for that condescending response.

Equal-tempered major thirds are considered in tune in most western and popular music of the twentieth and twenty-first centuries. So called "pure" intervals of simple integer ratios, especially the major third, are out of tune in many, perhaps most, modern contexts. Beating is normal. Claiming that all equal-tempered notes are "equally out of tune" uses a definition of intonation that is obsolete in many contexts, and there's no reason to remain in the old-fashioned world if you're not playing old-fashioned music. A major third with a simple 5/4 frequency ratio sounds grossly out of tune on a piano, to me, to most piano players, and to any qualified piano tuner.

We don't have to be tied to simplistic definitions of "in tune". The reason we use twelve-tone equal temperament is so no note need be out of tune, unlike the Pythagorean definitions, which kept harmonic and tonal vocabulary limited because so many intervals in that system were badly out of tune and unuseable.

Twelve-tone equal temperament is the agreement that the definition of "in tune" is based on all semitones having the same frequency ratio, rather than having a limited number of intervals with arbitrarily simple frequency ratios.

Just intonation is the agreement that most intervals will be badly out of tune so a few favored intervals can sound especially sweet, and we'll limit ourselves to the simple sweetness. That seems as valid as JoseLindE4's definition of 12TET, and much more relevant to anyone who plays in ensembles with keyboards, giutars, vibes, harps, or synthesizers.

Major thirds with a frequency ratio of 1.25 sound nicely in tune in a Gabrieli brass quintet, but they can sound badly out of tune in a jazz combo with a piano, where the definition of a major third is a ratio of about 1.26.

Here in the twenty-first century, 12TET is the default, but more old-fashioned tunings as well as newer more innovative tunings are definitely appropriate in specific contexts.


Hi,

My post was never intended to be condescending or cause offence.

It did work well though in provoking the correct response from you. The above reply was a great post, filled with knowledge and thought; which, of course, should have been your first reply to JoseLindE4 instead of the short, (in my opinion) incorrect and confrontational post you started with.

I also feel at liberty to point out that your lengthier post actually made acknowledgement that the debate can be approached from both sides, and different musicians in different contexts require different tunings. In many ways it served far more to contradict your own original post than anyone else's.

Thanks for your contribution, it is valuable and informative (well, the second one was...).

All the best
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trickg
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PostPosted: Wed Sep 12, 2018 8:37 am    Post subject: Reply with quote

Although this is an interesting discussion from an academic standpoint, is there really any kind of practical use for the knowledge, especially when trying to actively play trumpet while utilizing a tuner?

We don't play trumpet that way - at least no one I know does. Every now and again it might be a good idea to check things because we can train our ears to hear the pitch high or low, and in that case a tuner would come in handy to try to get us back toward a "better" pitch and center, but it has no practical bearing when thinking about it from a temperament point of view while playing in an ensemble because that's not how we approach it - we push or pull the pitch so that it matches what's around us so that the chords sound right, and we use our ears for that.
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mm55
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PostPosted: Wed Sep 12, 2018 9:44 am    Post subject: Reply with quote

The knowledge of various intonation schemes can be useful to a player for things like setting up a horn, characterizing its intonation on various notes, if that interests you. It can also help with evaluating how high or low on the slots you're playing. But in practice, it's rarely useful to use a tuner while playing.

As JoseLindE4 wrote, experienced players know what they want the intonation to sound like. An understanding of temperaments can inform that experience, but I don't think it's absolutely necessary. The major 7 leading tone can be sharper than both 12TET and 5-limit, and still sound entirely correct; not out-of-tune. A sharp 4 can be way sharp at the same time as a flat 6 is way flat, if your brass quintet encounters an Italian Sixth chord.

But you don't really have to think about any of that, and you'll still do fine. If your tuner has a choice, the default is 12TET. If your tuner has no choice, it's already 12TET. You shouldn't have to use other temperaments unless you know of a specific reason to do so.

Specifying a special temperament is usually more applicable to tuning stringed instruments and keyboards for styles of music, new, old, or non-western, that use something other than 12TET.
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