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Equal temperament vs other tunings


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#16 Gordon Shumway

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Posted 26 February 2019 - 14:57

Innate sense of harmony? Hmm. The ancient Greeks, we are told, thought that the major third was dissonant (do I mean discordant?). And Ptolemy knew the JI major third was 5/4, but the Pythagoreans couldn't get 5/4 out of 2 and 3/2, so they never bothered with it, lol!

I'm told Suk's serenade for strings requires certain passages to be played with JI so that different parts of the orchestra harmonise with each other in different ways. I should imagine a singer can do it with the right accompaniment, although it might be harder for them than for a violinist who always has to fudge between their JI open strings and whatever ET piece they are playing.

When I was 12 I had a friend who had perfect pitch. He wasn't musical - they just had a piano in the house, so I've always assumed it was just an eidetic memory thing.

Pavarotti apparently had it and insisted on using it, but as a result there are recordings where he is so much sharper than his accompaniment that I can't listen to them.


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#17 Eureka

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Posted 26 February 2019 - 15:28

So are violin strings normally tuned to just intonation even when they play with fixed-pitch instruments in ET? Why don't they tune to ET for that?


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#18 Gordon Shumway

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Posted 26 February 2019 - 15:40

If violin strings are always tuned to perfect fifths, that's JI, but you'll need an experienced violinist to tell you more. It may be that some violinists tune to a piano, but that might affect their muscle memory. Or it may be that the tiny number of cents they will be out are more than compensated for by the vibrato.


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#19 elemimele

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Posted 26 February 2019 - 17:04

for innate sense of harmony, see the thing I posted the other day where someone went looking at scale-systems used across the world in a multitude of cultures, finding that the scales most commonly used are those whose intervals approximate most nearly to just intervals. Might be true.

How do singers sing? Someone must have measured it (what people do isn't necessarily what they think they're doing - if I remember How Equal Temperament... properly), but I suspect it will depend on context. A jump from Do to Soh in a melody is very different to singing a fifth against another part. Singing to a totally stable ocatve note, I'm quite certain anyone would pitch their voice to avoid beats. Singing to a fifth, I'd guess most people would do the same - unless they're a piano tuner and automatically know how rapid a beat to expect! A third - I'm  not sure; we're so used to the sound of an equally-tempered third, maybe we'd try for the same overall sound?? I'm no expert on all this - Eureka, you need someone who's made a study of this.

Here, by the way, is Elam Rotem's early music sources site. If you use the "Tags", you'll find three that deal with temperament. I strongly recommend you have a good listen to what he has to say:

https://www.earlymus...ces.com/youtube


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#20 Eureka

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Posted 26 February 2019 - 17:43

Ah yes that website looks very useful - thank you! I will start watching. 

 

Yes I guess I'm wondering if I'm "not necessarily doing what I think I'm doing". For some reason I really like the idea that I might sometimes be singing in just intonation unwittingly - I think because it seems 'purer'. Also I'm wondering if that might be one reason why I like hearing a cappella singing - maybe it's the ratios?! Sounds like there's not an easy answer, but that's very helpful for me to know in itself - ie it's not just something that's obvious.

 

As for absolute pitch, I'm now very glad I didn't know anyone with that when I was younger - sounds a bit stressful. In fact I'm not sure I'd even heard of it back then. 


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#21 SingingPython

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Posted 26 February 2019 - 22:20

Regarding string instruments - I came across something a while back that said (rather unequivocally so unlikely to be 100% correct!) that most orchestral string players tune the G to D string fifth a little small to even things up a bit.  I did find it interesting as I was aware of tuning A to E and D to A with more "confidence" on my violin, and have subsequently confirmed that I like to tune my G string sharp.

 

My youngest has absolute pitch and, also being ridiculously bright, his first experiences of tranposition in choir were very hard work.  I remember talking with him age 9 and finding out that he was looking at a note, applying the transposition and then singing the result.  For every note in a piece ... We had a chat about following the line of a tune on the page after that!


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#22 Cyrilla

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Posted 26 February 2019 - 23:38

Elemimele - certainly when singing unaccompanied, using solfa, you become very aware that not every e.g. major 2nd is the same.   La-ti is very big compared with so-la, for example.

 

Likewise, not all perfect 5ths are the same - and sometimes a note will change its pitch according to a harmony note.   If one person sings a sustained 're' with the la below it - and the la person then sings a so instead, you can often hear (and feel, if you're the singer) the re change.   This isn't done consciously - it just happens because the supporting note is different.

 

Kod├íly wrote a book of tuning exercises called 'Let Us Sing Correctly', which start with the intervals in the overtone series.   Zsuzsanna Kontra has written 'Let Us Try to Sing Correctly' (lol) in which she analyses each exercise.

 

Fascinating stuff.

 

Or should I just get out more??

 

unsure.png 


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#23 Gordon Shumway

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Posted 27 February 2019 - 10:08

...when singing unaccompanied, using solfa, you become very aware that not every e.g. major 2nd is the same.   La-ti is very big compared with so-la, for example....

 

Yes, I've noticed this type of thing on the violin. I'm glad I never used tape on the neck to tell me where to put my fingers. I just play a note and adjust to what sounds right. I start a practice session with slow scales and every note is an experiment to begin with - some of them can take an age to get right. On the other hand, there doesn't seem to be a problem with fretted instruments, so maybe I'm just not understanding something.

 

Getting the Corelli sarabande (in E minor) exactly right can be tricky, the temptation is to make the B on the A string close to the A, i.e. comparatively flat, so that the jump from the B to the open E string makes the E sound horribly sharp.


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#24 elemimele

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Posted 27 February 2019 - 13:42

No, Cyrilla: if you do decide get out more, do please carry on coming in to write such useful and interesting posts! I love Zsuzsanna Kontra's choice of title alone, and will try to see if I can get a look at them!


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#25 Eureka

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Posted 28 February 2019 - 10:04

Oooh this is all VERY interesting - thank you! I love the way musicians might subconsciously change the tuning on violin and with the voice as described above. Actually I guess that could apply to most instruments (but not piano or hmmm....xylophone? That sort of thing?)

 

Generally I think it's fascinating what we might be doing without realizing it. Apart from tuning to the 'tuning note' at the start of a rehearsal I didn't think about tuning at all when I was younger...but I must have been making minute changes all the time to stay in tune on the flute, without realizing what I was doing. I thought I was just pressing the buttons and therefore the right note came out...I'm glad my subconscious brain knew what to do at least.

 

I had a watch of a few of the early music sources videos, which are great and very clear. I guess the closest they got to my question was when they asked "Did a cappella singers in the renaissance sing in just intonation?" After some interesting analysis the answer was "We don't know!"

 

Also cleared up my misunderstanding about what just intonation was - I thought it was just another temperament, but it's not.    


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#26 kenm

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Posted 24 March 2019 - 01:47

... or temperaments that, while not equal, have their commas distributed sufficiently evenly that all keys can be used. Many modern organs are tuned to good, unequal temperaments (names such as Werckmeister, Kirnberger, Valotti etc.); there are lots of YouTube clips comparing how these temperaments sound. "Well-tempered" might actually be what Bach wanted (how are we to know, so many years later?), but there are so many options, and a great deal of argument. It all gives me brain-strain.

I thought of a way that might give some insight into what temperament JSB had in mind with the 48: analyse all the chords in each piece and see what pairs of notes are avoided.  I couldn't face doing this myself, but if someone has produced a version of the 48 in MIDI or MusicXML, it could be done by a computer program.


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#27 Tenor Viol

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Posted 24 March 2019 - 13:23

One of the modern challenges with people - especially those who have been exposed to less theory - is explaining that the tuning meter / app may not be right... Whilst ET has its use and its place, it is also a problem. Most tuners/apps are set to ET by default and most people are unaware of that and of the issues it can present. 

The app I use you can select the temperament and I use one for tuning stringed instruments, which provides purer 5ths.

The major third in ET is evil - it is way too wide and to all intents and purposes is out-of-tune. But, we're used to hearing it so we now think it's 'normal'.

On the Bach WTC - that was written for a 'well-tempered' not an 'equally tempered' keyboard... We know Bach had his own way of tuning harpsichords - unfortunately, he left no written records of it... 


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#28 kenm

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Posted 24 March 2019 - 16:57

The major third in ET is evil - it is way too wide and to all intents and purposes is out-of-tune. But, we're used to hearing it so we now think it's 'normal'.

It sounds normal to me on the piano, but not on brass, blown wind or bowed strings.  Near the end of a thread about music theory on the General forum, I try to explain why, but ISTR a passage in Helmholz's book. "On the sensations of tone as a physiological basis for the theory of music", that discusses the changes in piano design and construction that make ET12 work on the later 19th C. piano.  See the list of references at the bottom of

https://en.wikipedia...n_von_Helmholtz

The book by Sethares that I mention in that post builds on Helmholz's work, referencing his own and other people's observations and measurements in the perception of consonance and dissonance.


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#29 elemimele

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Posted 25 March 2019 - 14:55

found it! Here's the reference I mentioned earlier:

https://www.ncbi.nlm...les/PMC2779864/

If you're into computerised studies, this is a look at a very wide range of scales and tunings used across multiple cultures, across the whole globe, trying to establish whether we as humans favour scales with just intervals or not. Conclusion: no matter what culture you come from, what instruments you're used to, and what strange scale or temperament you use, the chances are it favours justly harmonic intervals to a good extent. It's a decent read, and an example of something that would have been hard to do, only a very short time ago.


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#30 SingingPython

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Posted 25 March 2019 - 15:08

kenm your suggestion of analysing chords in the WTC and looking for any that are avoided, sounds like a project my youngest would really enjoy - I might pass the idea on to him!


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