Checks his strings for true intervals at the fifth

English translation: uses harmonics to make sure his strings are tuned a true fifth apart

GLOSSARY ENTRY (DERIVED FROM QUESTION BELOW)
English term or phrase:Checks his strings for true intervals at the fifth
Selected answer:uses harmonics to make sure his strings are tuned a true fifth apart
Entered by: Charles Davis

05:56 Dec 1, 2015
English language (monolingual) [PRO]
Art/Literary - Music / String music
English term or phrase: Checks his strings for true intervals at the fifth
Not a string player - what kind of action does this represent?
Lincoln Hui
Hong Kong
Local time: 15:31
uses harmonics to make sure his strings are tuned a true fifth apart
Explanation:
I think this is probably referring to a violin, whose strings are tuned at intervals of a fifth: G-D-A-E (going upwards). The viola and the cello are also tuned in fifths, so the same principles apply, though the double bass is tuned in fourths, and the guitar mostly in fourths, with one minor third (G to E). However, the same method can be adapted to ensure true tuning on these instruments too.

Anyway, you tune a violin by tuning the A string to a reference tone at 440 Hz (from a tuning fork, an electrical tuning device or the oboe in an orchestra). Then you tune the other strings by ear (or with an electrical tuning device) at intervals of a perfect fifth.

Here's where it starts getting complicated. A true fifth is a pure fifth in the tuning system known as just temperament, which violinists use. It means that the ratio of frequencies is 2:3. So if A is 440 Hz, the E a true fifth above it is 660 Hz. Notes a true octave apart have frequency ratios of 1:2, so the next A above that E is 880 Hz.

However, the trouble is that if you keep going up in fifths until you reach an A (in other words, you play the so-called circle of fifths), as follows:
A-E-B-F#-C#-G#-D#-A#-E#(=F)-C-G-D-A,
you find when you get to the end, playing true fifths, that the frequency of the last A is not a perfect multiple of the first A, as it should be; it is a little higher.

To solve this problem, a different tuning system called equal temperament is used for instruments like the piano. It means that intervals are very slightly different from (less than) the true (just) interval; every adjacent interval is the same and it means every key is in tune. The octaves are true octaves, because if they are not it really will sound out of tune. This means that if you tune a violin to a piano it will be very slightly out of tune, because the fifths on the piano are not true fifths. The A above middle C is 440 Hz (or should be), and the A above that is 880, but the E between them is tuned on the piano not to 660, as on a violin, but to 659.255 Hz.

Violin players (like other string players) have a method of checking that adjacent strings really are tuned a true fifth apart: using harmonics. If the A string is tuned to 440 Hz, then a string of the same thickness and tension exactly half as long will produce the A an octave above, 880 Hz, and a string a third as long will produce the E above that, at 1320 Hz. These are known as the first and second harmonics, and you can produce them by touching rather than damping the string at these points and bowing it. The point is that the harmonics are perfect intervals; the second harmonic gives you a perfect fifth.

Therefore if you play the second harmonic on the A string and the first harmonic on the E string, they should be exactly the same: 1320 Hz (3 x 440 = 2 x 660). And you can hear whether they are; if they are not, there will be a kind of beat or vibration. You adjust the tuning of the E until this disappears, and voilà: a true fifth. That, in essence, is how violinists check for true intervals at the fifth.

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Note added at 2 hrs (2015-12-01 08:14:16 GMT)
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I meant to say that the harmonics are true or just intervals, and the second harmonic gives you a true fifth.

--------------------------------------------------
Note added at 3 hrs (2015-12-01 09:50:22 GMT)
--------------------------------------------------

Further to my comment on Sheila's answer: if it's about the guitar, then "at the fifth" probably does mean "at the fifth fret". I thought it was the violin because I found the phrase in an article about a violinist (and nowhere else). But actually "true intervals" makes me feel that it's more likely to be about a violin or some other (fretless) string instrument, because "true", applied to intervals, is a technical term, with the sense I've explained; properly used, it doesn't just mean "well-tuned". I think it would be odd to use it in relation to the guitar.

--------------------------------------------------
Note added at 4 hrs (2015-12-01 10:20:07 GMT)
--------------------------------------------------

A small mistake in my main explanation: the "half-length" and "one-third-length" positions are the first and second overtones, but the second and third harmonics (the first harmonic is the fundamental tone).

"At the fifth": this is a normal expression in string-players' language for the position of the (third) harmonic:

"Figure 4.13. A stopped harmonic at the fifth above.
Stopped harmonics fall into a span of an octave, so they can be divided into harmonics at the octave, fifth, fourth, and major and minor third"
Patricia & Allen Strange, The Contemporary Violin: Extended Performance Technique, 120.
https://books.google.es/books?id=HZtGs5_z4zIC&pg=PA120&lpg=P...

--------------------------------------------------
Note added at 4 hrs (2015-12-01 10:47:16 GMT)
--------------------------------------------------

And by the way, here's a forum for string players talking about checking tuning with harmonics, and one of them mentions harmonics "at the fifth":
http://www.abrsm.org/forum/index.php?showtopic=34208

--------------------------------------------------
Note added at 10 hrs (2015-12-01 15:58:42 GMT)
--------------------------------------------------

Hi Lincoln. Well, the fifth position puts you a fifth (interval) higher than the first position, but I don't think playing in the fifth position would particularly help you check the tuning for true intervals.

--------------------------------------------------
Note added at 12 hrs (2015-12-01 18:23:17 GMT)
--------------------------------------------------

Hi again, Lincoln. One more note: I thought you might be interested to know that my son, who is studying the violin, has just got home and I've asked him about this. He confirms what I have said about checking tuning with harmonics, and in fact he tells me that Spanish violinists use the verb "quintar" for this, which literally means "to fifth".
Selected response from:

Charles Davis
Spain
Local time: 09:31
Grading comment
4 KudoZ points were awarded for this answer



SUMMARY OF ALL EXPLANATIONS PROVIDED
4 +2uses harmonics to make sure his strings are tuned a true fifth apart
Charles Davis
3checks his instrument's tuning at the fifth fret
Sheila Wilson


  

Answers


2 hrs   confidence: Answerer confidence 3/5Answerer confidence 3/5
checks his strings for true intervals at the fifth
checks his instrument's tuning at the fifth fret


Explanation:
I couldn't possibly disagree with the full answer already proposed by Charles. However, the use of "at" worries me. My husband's a pro musician who plays the guitar and he and others check their instruments' tuning at the fifth fret, apart from one string where they move up to the fourth fret..

--------------------------------------------------
Note added at 3 hrs (2015-12-01 08:59:10 GMT)
--------------------------------------------------

The verb used also leads me to believe this is the right answer. He isn't using this method to tune the instrument (you can use it, but there are better ones), but rather to check its tuning. Before the invention of built-in tuners, guitarists used to do this regularly as a quick check between numbers.

Sheila Wilson
Spain
Local time: 08:31
Native speaker of: Native in EnglishEnglish
PRO pts in category: 4

Peer comments on this answer (and responses from the answerer)
neutral  Charles Davis: If it is about the guitar, this could be it; guitarists certainly do this. (Actually they use harmonics too; my brother is one.) I took "at" to mean "at the interval of". You can't do it on a fretless instrument, of course.
51 mins
  -> As you say, we really need more information. And I can't argue the toss - my husband's the one with the technical insight, I just listen and enjoy :)
Login to enter a peer comment (or grade)

2 hrs   confidence: Answerer confidence 4/5Answerer confidence 4/5 peer agreement (net): +2
checks his strings for true intervals at the fifth
uses harmonics to make sure his strings are tuned a true fifth apart


Explanation:
I think this is probably referring to a violin, whose strings are tuned at intervals of a fifth: G-D-A-E (going upwards). The viola and the cello are also tuned in fifths, so the same principles apply, though the double bass is tuned in fourths, and the guitar mostly in fourths, with one minor third (G to E). However, the same method can be adapted to ensure true tuning on these instruments too.

Anyway, you tune a violin by tuning the A string to a reference tone at 440 Hz (from a tuning fork, an electrical tuning device or the oboe in an orchestra). Then you tune the other strings by ear (or with an electrical tuning device) at intervals of a perfect fifth.

Here's where it starts getting complicated. A true fifth is a pure fifth in the tuning system known as just temperament, which violinists use. It means that the ratio of frequencies is 2:3. So if A is 440 Hz, the E a true fifth above it is 660 Hz. Notes a true octave apart have frequency ratios of 1:2, so the next A above that E is 880 Hz.

However, the trouble is that if you keep going up in fifths until you reach an A (in other words, you play the so-called circle of fifths), as follows:
A-E-B-F#-C#-G#-D#-A#-E#(=F)-C-G-D-A,
you find when you get to the end, playing true fifths, that the frequency of the last A is not a perfect multiple of the first A, as it should be; it is a little higher.

To solve this problem, a different tuning system called equal temperament is used for instruments like the piano. It means that intervals are very slightly different from (less than) the true (just) interval; every adjacent interval is the same and it means every key is in tune. The octaves are true octaves, because if they are not it really will sound out of tune. This means that if you tune a violin to a piano it will be very slightly out of tune, because the fifths on the piano are not true fifths. The A above middle C is 440 Hz (or should be), and the A above that is 880, but the E between them is tuned on the piano not to 660, as on a violin, but to 659.255 Hz.

Violin players (like other string players) have a method of checking that adjacent strings really are tuned a true fifth apart: using harmonics. If the A string is tuned to 440 Hz, then a string of the same thickness and tension exactly half as long will produce the A an octave above, 880 Hz, and a string a third as long will produce the E above that, at 1320 Hz. These are known as the first and second harmonics, and you can produce them by touching rather than damping the string at these points and bowing it. The point is that the harmonics are perfect intervals; the second harmonic gives you a perfect fifth.

Therefore if you play the second harmonic on the A string and the first harmonic on the E string, they should be exactly the same: 1320 Hz (3 x 440 = 2 x 660). And you can hear whether they are; if they are not, there will be a kind of beat or vibration. You adjust the tuning of the E until this disappears, and voilà: a true fifth. That, in essence, is how violinists check for true intervals at the fifth.

--------------------------------------------------
Note added at 2 hrs (2015-12-01 08:14:16 GMT)
--------------------------------------------------

I meant to say that the harmonics are true or just intervals, and the second harmonic gives you a true fifth.

--------------------------------------------------
Note added at 3 hrs (2015-12-01 09:50:22 GMT)
--------------------------------------------------

Further to my comment on Sheila's answer: if it's about the guitar, then "at the fifth" probably does mean "at the fifth fret". I thought it was the violin because I found the phrase in an article about a violinist (and nowhere else). But actually "true intervals" makes me feel that it's more likely to be about a violin or some other (fretless) string instrument, because "true", applied to intervals, is a technical term, with the sense I've explained; properly used, it doesn't just mean "well-tuned". I think it would be odd to use it in relation to the guitar.

--------------------------------------------------
Note added at 4 hrs (2015-12-01 10:20:07 GMT)
--------------------------------------------------

A small mistake in my main explanation: the "half-length" and "one-third-length" positions are the first and second overtones, but the second and third harmonics (the first harmonic is the fundamental tone).

"At the fifth": this is a normal expression in string-players' language for the position of the (third) harmonic:

"Figure 4.13. A stopped harmonic at the fifth above.
Stopped harmonics fall into a span of an octave, so they can be divided into harmonics at the octave, fifth, fourth, and major and minor third"
Patricia & Allen Strange, The Contemporary Violin: Extended Performance Technique, 120.
https://books.google.es/books?id=HZtGs5_z4zIC&pg=PA120&lpg=P...

--------------------------------------------------
Note added at 4 hrs (2015-12-01 10:47:16 GMT)
--------------------------------------------------

And by the way, here's a forum for string players talking about checking tuning with harmonics, and one of them mentions harmonics "at the fifth":
http://www.abrsm.org/forum/index.php?showtopic=34208

--------------------------------------------------
Note added at 10 hrs (2015-12-01 15:58:42 GMT)
--------------------------------------------------

Hi Lincoln. Well, the fifth position puts you a fifth (interval) higher than the first position, but I don't think playing in the fifth position would particularly help you check the tuning for true intervals.

--------------------------------------------------
Note added at 12 hrs (2015-12-01 18:23:17 GMT)
--------------------------------------------------

Hi again, Lincoln. One more note: I thought you might be interested to know that my son, who is studying the violin, has just got home and I've asked him about this. He confirms what I have said about checking tuning with harmonics, and in fact he tells me that Spanish violinists use the verb "quintar" for this, which literally means "to fifth".

Charles Davis
Spain
Local time: 09:31
Specializes in field
Native speaker of: Native in EnglishEnglish
PRO pts in category: 24
Notes to answerer
Asker: It is the violin, and I believe you have more than answered the question. I had at some point pondered whether it was a reference to the "fifth position".


Peer comments on this answer (and responses from the answerer)
agree  Henk Sanderson
8 mins
  -> Thanks, Henk!

agree  airmailrpl: I am impressed
2 hrs
  -> Thank you very much!
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