Pianotech

Expand all | Collapse all

Using difference tones to tune?

  • 1.  Using difference tones to tune?

    Registered Piano Technician
    Posted 10-24-2021 20:18
    Hi Everyone,

    Does anyone use "difference tones" to help tune octave 5?  Maybe perhaps other ranges in the piano too?

    Interested in other's experience with them. One major writer said they were not helpful and I wrote them off a while ago but as I continue to listen/search for resonance and try to tune a P12 tuning the difference tones seem to line up very cleanly (oct 5ish). And better than that they seem to add a ton of resonance.

    Daniel


    ------------------------------
    Daniel Achten
    Chattanooga TN
    423-760-2458
    ------------------------------


  • 2.  RE: Using difference tones to tune?

    Posted 10-25-2021 00:59
    Let's supppse D4 and A5 is the P12 we are using: A5 is 880Hz and D4 is somewhere around 293.3Hz. This difference tone you speak of would be 880-293.3=586.7Hz. 586.7Hz would be D5. So by what I understand you are saying is that you are using a P12 (D4A5) to tune the note in the middle of the outer two notes (D5)??? If that's the case I'm certain it'd be incredibly hard to hear or feel over all the partials in that same area.

    I typically use difference tones between A0-A1. Say B0 is 30Hz and B1 is 60Hz. 60-30=30...so in this scenario our difference tone is at the same frequency as B0...30Hz. Thus B0 and the difference tone between B0 and B1 octave (played together) is in-tune.

    But if we lower B0 to 28Hz then when you play B0 and B1 together you get 60-28=32Hz. In this case the difference tone is 32Hz which you will hear OR feel as fighting/beating against B0 at 4 beats per second. Thus B0 and the difference tone between B0 and B1 octave (played together) is out-of-tune.

    ------------------------------
    Cobrun Sells
    cobrun94@yahoo.com
    ------------------------------



  • 3.  RE: Using difference tones to tune?

    Registered Piano Technician
    Posted 10-25-2021 18:09
    Define "difference tones" please.

    Pwg

    ------------------------------
    Peter Grey
    Stratham NH
    603-686-2395
    pianodoctor57@gmail.com
    ------------------------------



  • 4.  RE: Using difference tones to tune?

    Registered Piano Technician
    Posted 10-25-2021 21:10
    Hi Peter,

    I am assuming you know what they are since you have been at this a while longer than myself and maybe just asking for clarification for the thread? In any case, its been a few years since I have read what they are mathematically or physically. But here is my layman explanation: 

    When playing an interval like A5/D5 5th the two frequencies interact in a way that produce the appearance of a lower note, namely a frequency that corresponds to D4. That's a 12th below the upper note of the interval. This is not a true frequency produced from a string but somehow the vibration created by the difference between the A5 and D5. Hence the name "difference tone".  

    To our ear, however, they sound like any other frequency. And they can have beat speeds which change just like listening to any partial. 

    Is that a good explanation? 

    The easiest place to hear them seems to be in the 5th octave and in the bass. However, today I was following them from C6/G6 5th down to the single strings in the bass. I followed the 4ths as well. 

    Daniel

    ------------------------------
    Daniel Achten
    Chattanooga TN
    423-760-2458
    ------------------------------



  • 5.  RE: Using difference tones to tune?

    Registered Piano Technician
    Posted 10-25-2021 21:23
    Oops! Sorry, I made a typo in the explanation. 

    The 5th should read D5/A5! Which produces a  difference tone frequency that corresponds to D4. 

    Daniel



    ------------------------------
    Daniel Achten
    Chattanooga TN
    423-760-2458
    ------------------------------



  • 6.  RE: Using difference tones to tune?

    Posted 10-25-2021 22:22
    So you have D4 tuned and A5 tuned as P12 to D4. Then you fiddle around with D5?

    I like it. I'll have to try to see if I can hear it.

    What about when you get to A4 A5 and E6? Do you then fiddle with A5 so it resonates well between A4E6, even though you've already tuned A5 to D4 as P12? (Hypothetically speaking)

    Also,

    What I mean by "feel" is that I can feel B0 and B0 difference tone in my chest (because it is so low in frequency it's actually throwing my body back and forth!) I also "put my ear across the room." What I mean is I listen to the low octaves while tuning them as if my ears are 20ft away across the room where low frequencies have time to develop and become full bodied...I learned this when I had tuned a 28" marching bass drum's 1st partial to A#1 and up close it sounded alright but listening to it played while I was way up in the bleachers and the drum was on field just BLEW me away as I realized the drum sounded and felt much much bigger and fully developed up in the stands than standing right bext to it.

    ------------------------------
    Cobrun Sells
    cobrun94@yahoo.com
    ------------------------------



  • 7.  RE: Using difference tones to tune?

    Registered Piano Technician
    Posted 10-25-2021 23:19
    Cobrun, 

    Ah! I made some typos in those posts and tried to correct after they were posted! Blame it on me putting my many children to bed while working on this. It's late and I am usually using my phone for everything instead of a computer. I have made a mess of this thread!

    But to try and clarify, the main typo has to do with what notes I am playing and tuning. I meant to say D4 and D5 are tuned and I am working on A5. So the 5th I am playing is D5/A5 and I hear a difference tone corresponding to D4. If you keep that in mind I think my other post will make sense. 

    As for A4, A5 and E6; A4 and A5 will have been tuned already and I will be working on E6. Looking for the difference tone to clean up and then resonance to pop. Then do my checks. The P12 check (M6/M17) for A4/E6 should be perfect. 

    Interesting way to listen to the bass as you describe. I used to know an electric bass player who said the quietest place to stand was about 4 feet in front of his amplifier. He said the actual bass waves were so big he could stand under them and they would go over his head! Also, I am a guitar player and we talk about our amplifiers having "throw". The speakers throw the sound out and away from the amp. The soundboard acting like a speaker might have "throw". 

    Daniel

    ------------------------------
    Daniel Achten
    Chattanooga TN
    423-760-2458
    ------------------------------



  • 8.  RE: Using difference tones to tune?

    Registered Piano Technician
    Posted 10-26-2021 11:12
    Well, I have a theory (which may or may not go over so well)...however I need more information. One question is: Do these difference tones occur only at frequencies below the highest pitch of the interval being played, or are they occurring even above the intervals entirely?

    Pwg

    ------------------------------
    Peter Grey
    Stratham NH
    603-686-2395
    pianodoctor57@gmail.com
    ------------------------------



  • 9.  RE: Using difference tones to tune?

    Registered Piano Technician
    Posted 10-26-2021 11:37
    Peter, 

    the Difference tone is always lower then either note being played. 

    So When playing a fifth, such as D5/A5, the difference tone corresponds to D4. A 12h below the upper note. But below both notes

    When playing a fourth, such as D5/G5,  The difference tone corresponds to G3.  Two octaves below the upper note but below both notes. 

     Dan Levitan is one person who wrote about difference tones. It's in his book that he published. 

    Daniel

    ------------------------------
    Daniel Achten
    Chattanooga TN
    423-760-2458
    ------------------------------



  • 10.  RE: Using difference tones to tune?

    Registered Piano Technician
    Posted 10-26-2021 13:37
    A difference tone is the difference between the upper tone and the lower tone. Subtract the frequency of the lower tone from the frequency of the higher tone and the result is the difference tone. Below about 20 Hz we hear them as beats and use them in setting temperament by using the difference tone generated by the closely matched upper partials. Above about 20 Hz we hear them as tones. 

    Using Daniels example:
    A5 (880) - D5 (587.330) = 292.67, or about D4 (293.665).

    Using it in setting a temperament, the 5th partial of F3 and the 4th partial of A3 meet at A5 providing a difference tone of about 7 bps.


    ------------------------------
    Geoff Sykes, RPT
    Los Angeles CA
    ------------------------------



  • 11.  RE: Using difference tones to tune?

    Registered Piano Technician
    Posted 10-26-2021 16:38
    Geoff,

     Thank you for that explanation and your comments. 

     Could you elaborate on how we use them for setting a temperament?

    I've been experimenting with that the last few days and I found it useful for both setting the temperament and hearing  resonance  within the temperament.  When tuning fourths and fifths I listen and check for the normal beats beats etc. But I also listen below to the difference tones as they become more present and resonant. 

     I'm curious how you were using them, or what you mean. 

    Daniel

    ------------------------------
    Daniel Achten
    Chattanooga TN
    423-760-2458
    ------------------------------



  • 12.  RE: Using difference tones to tune?

    Posted 10-26-2021 17:03
    For our purposes, the difference tone is the fundamental of the overtone series in which the two notes would appear.
    Example:
    C1, C2, G3, C4, E4, G4, A#4, C5
    Pick any two adjacent notes above C1, and they can generate C1 as a difference tone.
    Because there is a strong physiological and neurological component in the perception of difference tones, perceptions may vary from person to person.
    When I was younger, some pianos had strong difference tones from fourths in the mid-range, perhaps because I was furiously pounding out fourths and fifths.
    18th century flute and recorder duets with many thirds, fourths and fifths in octaves 4 and 5, often generate very clear difference tones which take the shape of a bass voice, so much so that I have wondered if the effect was intentional, though again I have found that not everyone hears them as clearly as me.

    ------------------------------
    Ed Sutton
    ed440@me.com
    (980) 254-7413
    ------------------------------



  • 13.  RE: Using difference tones to tune?

    Posted 10-26-2021 17:22
    What Geoff means is that we see it in the temperament...we see it everywhere two notes are played. When we play F3A3 we hear A5 partial from both F3 and A3. Both A5's are beating roughly 7 beats-per-second against each other. Instead of calling them beats-per-second we could also call them Hertz...7Hz.

    ------------------------------
    Cobrun Sells
    cobrun94@yahoo.com
    ------------------------------



  • 14.  RE: Using difference tones to tune?

    Registered Piano Technician
    Posted 10-26-2021 17:52
    Daniel --

    In your example you are listening to the difference tone obtained off the the fundamental, or P1, of A5 and D5. Here's the math.

    A5 (880) - D5 (587.330) = 292.67 Hz, or about D4 (293.665 Hz)

    When setting a temperament, using my example, you are not using the fundamental, or P1, of either F3 or A3. Here's the math if you were to use P1:

    A3 (220) - F3 (174.614) = 45.386 Hz, or about halfway between F1 and F#1. Not a very useful difference tone.

    You are, however, still using a difference tone in setting a temperament, only instead of listening to the P1 of F3 and A3 you are listening the the comparison of the 5th partial of F3 and the 4th partial of A3 where they meet at A5.

    4th partial of A4 is 880 Hz
    5th partial of F3 is 873.071 Hz

    880 - 873.071 = 6.929 Hz, or a difference tone of about 7 bps, which is what were listening for when setting a temperament.

    Does this help?


    ------------------------------
    Geoff Sykes, RPT
    Los Angeles CA
    ------------------------------



  • 15.  RE: Using difference tones to tune?

    Registered Piano Technician
    Posted 10-26-2021 19:05
    Geoff,

    I see. My understanding was that difference tones were different than the tones we listen to above the interval (partials), as in your F3/A3 example. I thought the term only referred to the fantom fundamental produced as in the 4th and 5th I have been talking about. The difference being that the upper difference tones as you speak of are created by real partials interacting which creates a beat. While what I thought were difference tones are not really pitches below the interval but the appearance of a pitch below produced by the difference of the two notes of the interval. 

    I can hear these notes below as pitches which I can then control the beat speed of those pitches while the pitch of those fantom notes stays the same. (Prob a better way to say that!)  Yet they are obviously not real pitches because neither individual note of the interval is capable of producing the low pitch. 

    Like Ed S. I hear them in the midrange as well as in the bass and up through mid 6th octave. But I don't usually need to bag them to hear them. Sometimes ;)

    What I am discovering in this endeavor is that my awareness of them is helping control the quality of resonance so that from note to note the resonance is the same. Sort of like how we might listen to the quality of the unison. As the unison suddenly increases in presence or perceive volume we have found the sweet spot. And then make all the unisons sound/feel the same or have the same quality. So with the 5ths and 4ths in the temperament and all throughout up to where I loose track of them in the 6th octave. 

    Daniel 


    ------------------------------
    Daniel Achten
    Chattanooga TN
    423-760-2458
    ------------------------------



  • 16.  RE: Using difference tones to tune?

    Registered Piano Technician
    Posted 10-26-2021 20:14
    > I see. My understanding was that difference tones were different than the tones we listen to above the interval (partials), as in your F3/A3 example.

    Well, yes and no. What you are listening to in the F3/A3 example is not A5. It is the difference between the F3 P5 and the A4 P4 at A5. You are not actually listening to A5. You're listening to the difference tone that the F3 P4 frequency and the A4 P5 frequency produces when they combine at the A5 freqency. That resulting difference tone is WAY below any note on the piano, at about 7 Hz, or 7 bps. Remember, when a frequency is below about 20 Hz we hear it as a beat. When it is above about 20 Hz we start hearing it as a tone. The fact that it does not represent a tone that the piano strings themselves are actually producing, it is, nevertheless, a very real tone. Not a phantom. And what you are doing with it I find very interesting. In fact until you brought it up I was not aware of the term difference tone. I enjoyed researching what it is, how it is created, and now you, coming up with a way to actually use it. Cool!


    ------------------------------
    Geoff Sykes, RPT
    Los Angeles CA
    ------------------------------



  • 17.  RE: Using difference tones to tune?

    Posted 10-26-2021 20:54
    So on Audacity software (Windows I think) I generated two waves (I must have created sine waves or triangle waves...I don't remember):

    1000Hz
    700Hz

    I thought to myself "there is no way that two random tones could be harmonious." These two tones just don't line up, as far as upper partials go (with sine waves these two tones could barely produce upper partials):

    700
    1400
    2100
    2800
    3500
    4200
    4900
    5600
    6300
    7000

    1000
    2000
    3000
    4000
    5000
    6000
    7000

    So they meet at 7000Hz, but MAN that is a 10:7 interval where as we are familiar with 3:2 5:4 4:2 etc.

    But it wasn't the upper partials I was interested in...

    It was the difference tone I was curious about.

    What I learned was AMAZING:

    1000Hz-700Hz=300Hz

    So 300Hz was the difference tone which when I listened into my computer speakers I could definitely hear.

    But wait, there's more:

    1000
    700
    300

    700-300=400

    So now I found that there was a 2nd difference tone which was 400Hz.

    1000-400=600

    And yet another difference tone: 600Hz

    400-300=100

    300-100=200

    1000-200=800

    800-300=500

    Pretty soon I learned that by just generating 2 sine waves (1000Hz 700Hz) I was able, when I listened very very closely and quietly to my speakers I could hear 10 notes playing all at once FROM JUST TWO TONES.

    And the best part?!? 100Hz was the true fundamental or true 1st partial. I had just created a whole harmonic series by just generating 2 tones (1000Hz and 700Hz)

    ------------------------------
    Cobrun Sells
    cobrun94@yahoo.com
    ------------------------------



  • 18.  RE: Using difference tones to tune?

    Registered Piano Technician
    Posted 10-26-2021 22:47
    This is all quite interesting. 

    Physically speaking though we do not "hear" with our ears. Our ears collect information and our brain interprets it, basically manufacturing the sounds we recognize. So really we hear with our brain. It's all a VERY complicated process which testifies to the massive complexity of the brain. 

    Anyway, my theory is that what is being "heard" as difference tones is in fact being ultimately generated in our brains. (Ed Sutton aluded to this in his comments). Some people "hear" many individual partials clearly (separately) when a note is played, whereas others (I think most) hear a combination of them which makes up their interpretation of the "sound"of that note. We tuners train our brains to isolate specific partials that we use to tune (most clients cannot hear these without our actually "ghosting" the interval for them to isolate it. They hear the complete combination of these partials which their brain condenses into a specific tone. 

    According to Cobrun's math (as I see it) one could "isolate" a nearly infinite number of "difference tones" between two notes. Then, with effort, one can "hear" these tones. I believe this is the brain doing this. Do they exist? Yes, but are they usefully perceptible?  That is something I cannot answer with certainty. 

    I know that when I am tuning, I am highly receptive to singular partials needed for tuning because I know where they are and my brain is trained to listen to them (and the beating between them). However, after I am done tuning (and esp if I give my ears a rest for a few minutes) and I now start PLAYING the piano, I do not hear things the same way as when I was tuning. I now hear the combinations and the full tonal expression that these combinations are producing. IOW I now hear MUSIC rather than specific partials. 

    The fact that some of these (if not all of them [we've had at least two different definitions of "difference tones"]) occur below the frequency of either tone in a two note interval, argues that this phenomenon is in fact "psychological" rather than physical. Our brain is capable of doing some amazing things, and as we know, no two people "hear" things exactly the same. And, some simply cannot hear certain things...period. Additionally, some people "see" different colors when they "hear" different tones. It's all VERY complicated. 

    I'll probably get some blowback on this. I'm not saying these tones don't exist. I'm saying that it has to do with a very complicated mechanism we call "hearing" which is not fully understood even. 

    Pwg

    ------------------------------
    Peter Grey
    Stratham NH
    603-686-2395
    pianodoctor57@gmail.com
    ------------------------------



  • 19.  RE: Using difference tones to tune?

    Posted 10-26-2021 23:35
    In a "pure" situation, a band pass filter will not recognize a difference tone. Loudspeakers, however, may produce an objective difference tone. To get an idea of the complexity of the experience, see this: http://www.faculty.ucr.edu/~eschwitz/SchwitzPapers/TitchDemo030417.htm

    ------------------------------
    Ed Sutton
    ed440@me.com
    (980) 254-7413
    ------------------------------



  • 20.  RE: Using difference tones to tune?

    Registered Piano Technician
    Posted 10-27-2021 02:00
    Fascinating. I could plainly hear the difference tone in those tests but when I used a spectrum analyzer the difference tone did not show up.

    ------------------------------
    Geoff Sykes, RPT
    Los Angeles CA
    ------------------------------



  • 21.  RE: Using difference tones to tune?

    Registered Piano Technician
    Posted 10-27-2021 13:51
    Peter and everyone,

    all these theories and examples are interesting to say the least. 

    Here is another idea. I don't know the mathematical or physics difference between sine wave, triangle waves and the different ways to generate them etc., so my theory may hold no water. 

    Peter suggested it's in the mind. The empirical evidence suggests maybe it's somehow in the piano strings interaction.

    but it's actually an effect of the waves on the ear drum itself?  When I'm listening while tuning I hear the partials and the fundamental of each note outside of me coming from the piano, if you could think of sound coming from a direction. But when I listen and feel the lower difference tones  I feel and hear them as pressure in the lower and back part of my eardrum.  As though the sound were coming from inside my ears rather than from the piano. 

    Daniel

    ------------------------------
    Daniel Achten
    Chattanooga TN
    423-760-2458
    ------------------------------



  • 22.  RE: Using difference tones to tune?

    Registered Piano Technician
    Posted 10-27-2021 14:07
    If Peter is correct that it's in our mind rather than in the empirical world, here are two examples from my own experience that might support that.  When I was a kid I would wander around the neighborhood playing with friends or go to the next neighborhood over to play with friends over there and my mom had an extremely loud whistle. She would whistle for me when it was time to come home and eat dinner. She did this so often that when I was in my 20s there were times where I could still hear her whistling for me lol.  It was clearly psychological!  

    Also, Correct me if I'm wrong but isn't tinnitus of the ear a psychological effect as well!  Isn't the brain psychologically trying to fill in frequencies that the eardrum can no longer produce? 

    Daniel

    ------------------------------
    Daniel Achten
    Chattanooga TN
    423-760-2458
    ------------------------------



  • 23.  RE: Using difference tones to tune?

    Registered Piano Technician
    Posted 10-27-2021 16:02
    We are getting out into the weeds here. Daniel, there's more to hearing than the ear drum, i.e. middle and inner ear; and then "listening" as the signals work their way through the brain. Locating the sound physically I think is at least partially a subjective experience, as well as "seeing", "tasting" etc. sound. One thing I've learned, unfortunately due to a bit of asymmetrical hearing loss is that the binaural aspect plays a big part in the synesthetic aspects. None of which are as vivid for me as they once were.

    One way to test whether a perceived pitch is acoustic or psychoacoustic is to see if it can be produced via "ghosting". If it's acoustic (a pressure wave) it should be possible to ghost the pitch if there's a string that's close to the frequency, if not then it's the result of our faculties of perception at work. Maybe.

    In practical terms, I think ultimately we are utilizing all of these phenomena in the practice of aural tuning, but we are making decisions in a very short time and it's not necessarily productive to try to figure it out in real time. Automatic pilot works much better. I don't count beats, I listen to the tempo.

    Btw, I'm not sure that optimizing resonance and finding the optimal pitch for a given string are always the same thing. As stated above, there are many resonating frequencies, which should be prioritized and is it always the same? Again, I suspect some of these issues are best left to intuition or we'd never finish a tuning.
    You don't mention whether your tests are with single strings or unmuted unisons.

    One of the glorious aspects of piano tuning is that we have all this time to ponder these things while we're doink doink doinking away. Resonance and Harmony are universal qualities, it's a blessing to have this field with which to examine them.

    ------------------------------
    Steven Rosenthal
    Honolulu HI
    808-521-7129
    ------------------------------



  • 24.  RE: Using difference tones to tune?

    Registered Piano Technician
    Posted 10-27-2021 19:54
    So in view there are only two choices: they are either real (i.e. physically generated), or they are not (and are therefore a product of our "interpretation" of the data). 

    Supposing that they are "real", is it possible that they are generated by the STRUCTURE (somehow) in conjunction with the string vibrations? I find it interesting that the loudspeakers also seem to generate this effect. In both cases we are dealing with sound pressure waves coming from a standing source. Perhaps the effect of the air movement has an effect on our physiology to such an extent that we perceive these "extra-vibrational" tones...? 

    I don't know and am simply speculating. What I do know for a fact though is that ALL sounds (of any kind), if separated into their partial components, all sound the same (that is all the partials separately). What we perceive (and identify as a specific sound) is in fact a combination of these partials in varying intensities (amplitudes) to such a degree that we can identify it as a "sound" (such as a cats meow, or a dog's bark, or a musical tone). This was demonstrated in a class in Lancaster, PA a few years ago by Keith Kopp. It was a real eye opener (or ear opener as the case may be). 

    Does anyone know who was the originator of the term "difference tone"? Hiw long has this been around?

    Pwg

    ------------------------------
    Peter Grey
    Stratham NH
    603-686-2395
    pianodoctor57@gmail.com
    ------------------------------



  • 25.  RE: Using difference tones to tune?

    Posted 10-27-2021 20:23
    They are called difference tones I suppose because that's what the mathematical term is for subtraction; difference:
    Addition; sum
    Subtraction; difference
    Multiplication; product
    Division; quotient

    Since we are subtracting frquencues from each other the outcome is a difference...difference tone. I've heard them called natural beat, sub-tone, resultant tone, difference tone, undertone, phantom note, ghost note.

    Technically speaking I would suppose that they do exist in actuality. It's called wave interference.

    "Wave interference is the phenomenon that occurs when two waves meet while traveling along the same medium. The interference of waves causes the medium to take on a shape that results from the net effect of the two individual waves upon the particles of the medium." (Good old wikipedia)

    If I drop a stone in a pond and drop another one close by both of the waves created by both stones will interfere with each other adding and subtracting to the overall amplitude and shape of the waves. The same is happening with air molecules as sound's pressure waves travel through it. If a tuba 5ft to your left plays C2 and another tuba 5ft to your right plays G2 both of those tubas' notes sound separate. But from 100ft away where the soundwaves have sufficient distance to develop a difference tone would exist at C1, not just in our ears or brains but in the compression and decompression of the air molecules between the 100ft-distant observer and the tubas.





    ------------------------------
    Cobrun Sells
    cobrun94@yahoo.com
    ------------------------------



  • 26.  RE: Using difference tones to tune?

    Posted 10-26-2021 12:27
    What we're talking about is the resultant notes, used by organists to simulate a 32ft pedal note.

    Because these tones are 1/3 frequency of the higher note tuning with them alone will be less accurate as 1 beat per second out in the top note will result in 1 beat per 3 seconds out in the lower.

    However for anyone  conscious of these sounds equal temperament produces a sound 1/4 tone sharp on major thirds which is why I loathe such.

    In unequal temperaments the difference tones go to reinforce the resonance of the lower harmonic notes and amplify the harmonics of the lower fundamental. 

    On another thread I posted a YouTube video of a concert last Saturday with both a 1869 Broadwood and 20th century repertoire on a "modern" instrument. The solidity of the tuning and coincidence of scale notes to harmonics, fundamentals and difference notes on that recording is apparent.

    Best wishes 

    David P 





  • 27.  RE: Using difference tones to tune?

    Registered Piano Technician
    Posted 10-25-2021 21:49
    Hi Cobrun, 

    Here is the way I am using them. It's a little different than the scenario you suggested. 

    The intervals I am using are a 5th and a 4th. 

    So if I was playing D5/A5 5th I would hear a difference tone that corresponded to D4. D4 and A5 will have already been tuned and I would be working on D5 as I tune up through the treble. While tuning the D5 I listen to the 5th, 4th, octave and 12th below it. If I have to I also listen to M10 chromatically. I use the M6/M17 beat speed test for the D5 to try for a P12. Always making sure the octave is not over stretched. 

    What i I have noticed is that the difference tone beat speed from the D5/A5 which matches the D4 is very clean (no perceivable beat) while the 12th checks out as perfect. 

    More importantly, the increase in resonance/presence happens when this difference tone is clean with no perceivable beat speed. All other checks check out. 

    The sustain of this difference tone also seems to be related to how clean it is. 

    I hear it all over the piano now. I thought it was just in then 5th octave but the resonance that I have used to tune the bass is exactly this. 

    Your example of using difference tones to tune A0-A1 is very interesting. I'll have to try that. I have simple
    Been switching to octaves and 12ths down there while listening and feeing for resonance. Also, checking where the 6/3 octave check is. (Except for 9'). 

    Its also interesting that you mentioned "feeling". I feel the beat speeds in my key hand (left hand) and in the tuning hammer (right hand) while tuning through the the base too. I also feel the different pressures on the ear drum as they move around depending on beat speed and resonance all throughout the piano. Sometimes I am sitting just right to sort of jig the piano with my waist as I sit and can feel the whole piano come alive right when I find the resonance. 

    All this "come alive" seems to correspond with the clean difference tones I am mentioning. 

    Daniel 


    ------------------------------
    Daniel Achten
    Chattanooga TN
    423-760-2458
    ------------------------------



  • 28.  RE: Using difference tones to tune?

    Registered Piano Technician
    Posted 10-27-2021 20:29
    https://en.wikipedia.org/wiki/Combination_tone

    ------------------------------
    William Ballard RPT
    WBPS
    Saxtons River VT
    802-869-9107

    "Our lives contain a thousand springs
    and dies if one be gone
    Strange that a harp of a thousand strings
    should keep in tune so long."
    ...........Dr. Watts, "The Continental Harmony,1774
    +++++++++++++++++++++
    ------------------------------



  • 29.  RE: Using difference tones to tune?

    Member
    Posted 10-28-2021 15:02
    Back when I was into ham radio I learned about the "superheterodyne receiver," which relied on difference frequencies.  The frequency of the signal received over the air (the "radio frequency" or "RF") was too high to amplify and process efficiently, so the electronics would convert the frequency down to an intermediate frequency (the "IF").  This is done by generating tunable local oscillator signal that is offset from the desired frequency by exactly the IF frequency.  The generated signal and the RF signal are combined in a non-linear fashion so that a real (not just a psychological) difference frequency is generated.  The sum frequency is also generated, but that is filtered out by a narrow band-pass filter in the IF section of the receiver.  The advantage of this method is that the IF section (usually 455 kHz for AM radios) can be fixed-tuned, to process only that one frequency.  The circuit that did the non-linear mixing of the RF and the local oscillator was called (unsurprisingly) a mixer circuit.  It usually involved diodes to chop the RF using the local oscillator as the knife to do the chopping.  The point is, these two signals did not just peacefully coexist together.  In this way a mixer in a superheterodyne receiver is very different from the kind of mixer used in high-end recording studios.  In those kinds of mixers, the various audio inputs are combined in a (hopefully) very linear way.  The result is that signals combined in an ideal audio mixer board do not generate any (real) difference tones.

    So, what happens when tones from various piano strings are combined in the soundboard?  Well, if things are working properly, that mixing is linear.  That is, the signals add together without affecting each other in any way.  But things are not always ideal.  Sometimes there is a loose connection somewhere in the piano.  In the extreme case it might even produce an audible buzz.  But in the less extreme case it might just produce some non-linear interaction between signals, causing difference frequencies (and sum frequencies).  This is real, not psychological.  The sum and difference frequencies produced this way would even show up on a spectrum analyzer.  The non-linear interaction might be amplitude dependent.  That is, below a certain sound level, everything is linear.  That loose screw does not rub at all.  But above a certain threshold, non-linearity kicks in and real difference tones are generated.  There can even be non-linear interaction within the structures of the human ear, although they would probably be noticeable only near the levels where actual hearing damage could occur.  People who use hearing aids may also hear real difference tones when the sound levels exceed the linear range of the hearing aid circuitry.

    Here's an experiment.  Try to engineer something that will buzz on the soundboard - maybe a paper clip or something made out of paper.  Then play various pairs of notes.  You will probably hear difference tones that you did not hear without that device touching the soundboard.

    ------------------------------
    Robert Scott
    Real-Time Specialties (TuneLab)
    fixthatpiano@yahoo.com
    Hopkins MN
    ------------------------------