Resultant/Tartini Tones

hazmat · Heavyweight Member Joined: 23 Mar 2003 Posts: 669

For eveyone that's interested in reading more on resultant or Tartini tones, I have a short list of books you should check out. I spent about half an hour at the music library and went through about 25 books to find these.

In short (very short) resultant tones are broken down into difference and summation tones. Difference tones would be the frequency of the higher pitch minus the frequency of the lower pitch. So if you played 440hz (A) and 660hz (E) the difference tone would be 660-440=220hz (A).
The summation tone would be 440+660=1100 (C#). The summation tone is harder to pick out because it is in the overtone series.

"The difference tone is generally ascribed to the German organist Sorge (1740) and the Italian violinist Tartini (1754)" - Campbell and Greated

The hardest time making resultant tones is when you are using tempered intonation. So if you are playing with a piano is will be much harder. Here is a chart of tempered frequencies http://www.phy.mtu.edu/faculty/info/suits/notefreqs.html

Books:

Backus, John. The Acousical Foundations of Music. New York: W.W. Norton and Company, Inc., 1977

Campbell, Murray and Clive Greated. The Musician's Guide to Acoustics. New York: Schirmer Books, 1988

Jeans, Sir James. Science and Music. Cambridge (Eng.): The University Press, 1961

White, Harvey E. and Donald H. White. Physics and Music: The Science of Musical Sound. Philadelphia: Saunders College Publication, 1980

Billy B · Posted: Sun Nov 21, 2004 11:01 pm Post subject:

Bill Adam told me s story about a visiting name conductor who stopped to listen to Adam's brass choir playing Come Sweet Death. As the last chord died away he commented that the third of the chord was much too loud. No one was playing the third, it was a resultant tone!
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Derek Reaban · Posted: Mon Nov 22, 2004 7:42 am Post subject:

Bill,

Great story! I can certainly relate to this story after hearing Manny and Mike Thompson play some standard excerpts in Denver at ITG. It was amazing how strong the resultants were that those two were able to develop. Literally as if there was another player on stage playing the notes!
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tpter1 · Heavyweight Member Joined: 17 Jun 2004 Posts: 1194

Great topic... very interesting research.

If you have a Dr. Beat db88 you can practice resultant tones of the difference tone varitey by setting the tuner function in the "3" octave setting: buzzing a 2nd line g (concert F...I do this on a Bb, and so think it as a G) produces a resultant tone, for example when the tuner is set to concert A#3. Use of this in lip slurs, scale studies and long tones really helps develop listening skills! (If you do it too long it develops into some serious brain damage

).
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"Character is the backbone of human culture, and music is the flowering of human character". -Confucious

trpt.hick · Posted: Mon Nov 22, 2004 9:17 am Post subject:

Let's not confuse "difference" or "resultant" tones (same thing) with "Tartini" tones (not the same thing).

hazmat · Heavyweight Member Joined: 23 Mar 2003 Posts: 669

Derek Reaban · Posted: Mon Nov 22, 2004 11:46 am Post subject:

Matt,

You must not have seen the message that I posted in a topic called 10 Question Music Quiz. Here is the text related to Tartini Tones:

mcamilleri · Posted: Mon Nov 22, 2004 4:20 pm Post subject:

All these resultant or Tartini tones are strongest when played with similar instruments. The rich and strong harmonic series of the trumpet lends itself well to creating these, as the resultant tones also have a rich harmonic series, which makes it easier for the ear to hear them as separate tones.

There is another really interesting physco-acoustic effect. You can create the same resultant tones by playing one tone in the left ear, and a different tone in the right ear. There are no acoustic resultant tones, but the brain combines them and creates is own internal resultants. If you have a keyboard with control of stereo panning and headphones you can check it out for yourself. It is really wierd. The resultant tones are also not limited to the audible frequency range. It may be possible for some people that have high or low frequency hearing loss to still hear these tones in the head.

It is also possible to "hear" into the infra sound range also like this. Tune the difference to 8-12 Hz and chill out to the alpha beat...

Michael
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hazmat · Heavyweight Member Joined: 23 Mar 2003 Posts: 669

hazmat · Heavyweight Member Joined: 23 Mar 2003 Posts: 669

mcamilleri · Posted: Mon Nov 22, 2004 6:36 pm Post subject:

Yeah, get the beat frequency down into the delta and theta range and start counting those sheep.

Makes you wonder what a very carefully out of tune ensemble could do to an audience

. I wonder if some of the emotional impact of an orchestral performance is due to infra-sonic difference tones? Just thinking out loud.

Michael
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trpt.hick · Posted: Mon Nov 22, 2004 9:32 pm Post subject:

Matt:

It's great that you are doing some research on your own. This is always the best method of learning and retaining information.

The Groves dictionaries are good sources but are often quite general. Some of the articles go WAY back. As newer research is done, updated articles will replace the old ones. Dr. Ed Tarr has rewritten many of the trumpet related articles which were too general and even inaccurate.

The best sources on acoustics are the newer books SPECIFICALLY on acoustics. There are even several that deal with brass only. A few of the better brass acoustics authors include Apel, Cardwell, Schilke, and Benade.

DH

hazmat · Heavyweight Member Joined: 23 Mar 2003 Posts: 669

Thanks Mr. Hickman. As you can tell, all the books I checked out were a little older. I guess I'mm have to check out some of the newer books.

Thanks,

Matt

Coltssop01 · Posted: Tue Nov 23, 2004 6:19 am Post subject:

Cool...I'll have to check out some of those newer books. I thought about taking the acoustics class here, but I think I would've been annoyed since it required only basic algebra or something (I used to be an engineer, and give me calculus any day!)

Derek Reaban · Posted: Tue Nov 23, 2004 9:16 am Post subject:

Matt,

I had a lesson yesterday and we spent some time playing different intervals and listening for the Tartini Tone. We started with the Major 3rd based on the above example in A Major. The resultant was very clear, and after several times playing it my instructor could find the Tartini Tone in the sound. I had more of a general impression that I heard a Major chord (E-A-C#), but couldn’t isolate the Tartini Tone. That’s a challenge for me.

I thought this was interesting related to Resultants and Tartini Tones. Before the lesson, I quickly ran some numbers to show what we needed to be listening for when playing different intervals.

Major 3rd: A – C#, Resultant = 550 – 440 = 110 (A), Tartini Tone = 2(440) – 550 = 330 (E)
Perfect 4th: E – A, Resultant = 440 – 330 = 110 (A), Tartini Tone = 2(330) – 440 = 220 (A)
Perfect 5th: A – E, Resultant = 660 – 440 = 220 (A), Tartini Tone = 2(440) – 660 = 220 (A)
Octave: A – A, Resultant = 880 – 440 = 440 (A), Tartini Tone = 2(440) – 880 = 0

Notice that the Tartini Tone is masked by the resultant tone on the Perfect 5th (they are the same for this particular interval). It is enhancing the resultant tone on the Perfect 4th, up one octave from the resultant, and one octave below the top played note. So there is at least one case (interval) where Tartini Tones and Resultants are the same.

I recently received the book Kinkaidiana as a gift, and in this book he has a piece entitled Trio for Two flutes. For those of you that attend church, it’s the Holy, Holy, Holy tune. It’s written in such a way to ring the resultants so strongly that it sounds like a third player is covering the “bass” line, and he has actually notated what pitches should be heard as the resultants. While the Tartini Tones weren’t shown, they also play a part in what we were hearing. I really enjoyed the chord that was a top line F whole note for 1st trumpet and a 3rd space C half note (ringing the F two octaves below) for 2nd trumpet with the 2nd part moving up to the 4th space Eb for the other half note. This caused the resultant F to drop down an octave!
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Tempe Winds / Symphony of the Southwest

ken_fung · Posted: Tue Nov 23, 2004 9:32 am Post subject:

mcamilleri · Posted: Tue Nov 23, 2004 1:04 pm Post subject:

You can buy prerecorded tapes or CDs that do this either with tones, or with normal music (they take a mono track, and re-record it with another channel at 8-12 hz lower frequency). It sounds like normal music, but causes the brain to generate the 8-12 hz frequency internally. Recordings are availalble for alpha, theta, delta brain wave states, or to encourage sleep. Don't use them while driving!

If you want to do it yourself, you can use a tone generator on a computer, or if you have fine tune function on a keyboard you could use that.

Regarding sleep disturbance, there are some good websites around with advice. Send me an email to remind me and I will send you some links tomorrow. It is fairly easy to fix most sleep problems within a few weeks. Just saying "it takes ages for me to fall asleep" sets up your subconscious mind to disturb your sleep. Strange but true...

Michael
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