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What are the 2:1, 4:2 and 6:3 octaves? Why are they important?

  • 1.  What are the 2:1, 4:2 and 6:3 octaves? Why are they important?

    Posted 07-25-2019 14:11
    2:1, 4:2 and 6:3 octaves have been mentioned by some members of Pianotech. What are these octaves and why are they important?

    Are the following basic descriptions correct?

    C1 is the 1st harmonic. C2 is the 2nd harmonic. Therefore, the ratio of C1-C2 is 2:1. C1-C2 is a 2:1 octave.

    C2 is the 2nd harmonic. C3 is the 4th harmonic. Therefore, the ratio of C2-C3 is 4:2. C2-C3 is a 4:2 octave.

    G2 is the 3rd harmonic. G3 is the 6th harmonic. Therefore, the ratio of G2-G3 is 6:3. G2-G3 is a 6:3 octave.


    Summary:

    C1-C2 = 2:1 octave.

    C2-C3 = 4:2 octave.

    G2-G3 = 6:3 octave.

    ------------------------------
    Roshan Kakiya
    ------------------------------


  • 2.  RE: What are the 2:1, 4:2 and 6:3 octaves? Why are they important?

    Registered Piano Technician
    Posted 07-25-2019 14:49


    Here's a graphic explanation:





  • 3.  RE: What are the 2:1, 4:2 and 6:3 octaves? Why are they important?

    Registered Piano Technician
    Posted 07-25-2019 14:53
    Okay, I'll try again:







    ------------------------------
    Richard West
    Oro Valley AZ
    520-395-0916
    440richard@gmail.com
    ------------------------------



  • 4.  RE: What are the 2:1, 4:2 and 6:3 octaves? Why are they important?

    Registered Piano Technician
    Posted 07-25-2019 14:56
    One more time  See attachments.

    ------------------------------
    Richard West
    Oro Valley AZ
    520-395-0916
    440richard@gmail.com
    ------------------------------



  • 5.  RE: What are the 2:1, 4:2 and 6:3 octaves? Why are they important?

    Registered Piano Technician
    Posted 07-25-2019 15:11
    Along with Richard's graphics, I'll throw in some verbiage.

    I THINK you're associating the ratios with the fundamental note being tuned, but they are harmonics you are listening to in the octave you are tuning, not different octaves elsewhere. (If I've misunderstood you, I apologize in advance.)   If you are tuning C3 to C4, and you listen to the harmonic above C3, this matches the fundamental of C4. That's a 2:1 octave. If you are tuning the SAME octave, C3 to C4, but you listen to the 4th and 2nd harmonics respectively, you are comparing where they meet at C5. If you are tuning the SAME octave, C3 to C4, but you listen to the 6th and 3rd harmonics respectively, you are comparing where they meet at G5. Does that make sense? I wanted to explain more of the "what" while Richard is explaining more of the "how".

    ------------------------------
    Maggie Jusiel
    Athens, WV
    (304)952-8615
    mags@timandmaggie.net
    ------------------------------



  • 6.  RE: What are the 2:1, 4:2 and 6:3 octaves? Why are they important?

    Posted 07-25-2019 16:05
    Margaret, thank you for providing an explanation. You have clearly understood the examples that I have provided in my original post. I have indeed associated the ratios with the fundamental note.


    The following examples are based on the explanation that you have provided:

    C1-C2 is the octave that is being tuned.

    C1-C2 is a 2:1 octave if the 2nd harmonic of C1 (C2) coincides with the 1st harmonic of C2 (C2).

    C1-C2 is a 4:2 octave if the 4th harmonic of C1 (C3) coincides with the 2nd harmonic of C2 (C3).

    C1-C2 is a 6:3 octave if the 6th harmonic of C1 (G3) coincides with the 3rd harmonic of C2 (G3).

    ------------------------------
    Roshan Kakiya
    ------------------------------



  • 7.  RE: What are the 2:1, 4:2 and 6:3 octaves? Why are they important?

    Registered Piano Technician
    Posted 07-25-2019 17:36
    You've got it! Richard & several others here can give you great explanations of how they work in pianos & how to use them. (Plus other resources like books, etc.) I wanted to make sure you understood exactly what you just reiterated so their explanations would make sense. ;-)

    ------------------------------
    Maggie Jusiel
    Athens, WV
    (304)952-8615
    mags@timandmaggie.net
    ------------------------------



  • 8.  RE: What are the 2:1, 4:2 and 6:3 octaves? Why are they important?

    Registered Piano Technician
    Posted 07-25-2019 15:47
    I'll expand on what Maggie said: Strings under tension have a predictable harmonic series. The main sound coming out of a string is the first partial or fundamental. But there are literally an infinite number of upper partials. As tuners we only use the lowest few. We can tune an octave because the second partial of the lower note is very close in frequency to the fundamental of the upper note of the the octave. But inharmonicity creates partials that are inharmonic. Therefore we can never completely make the octave pure and without beats. We have to choose what set of partials we like best.

    If we tune the octave and then use the 2:1 test to check our octave, we want the 10th and 17th to beat at the same speed. Then we know that set of partials is pure. After having done that, we could listen to the test for the partials at the 4:2 level. The 10th would be slower than the 3rd indicating that the octave is not pure at the 4:2 level. We could retune the octave and then use the 4:2 octave test to make the 4:2 set of partials beat the same speed, but then the 2:1 would now be beating. That is by using the 4:2 set of partials we've widened the octave a little. Now we'll hear that the 2:1 test will show that the 17th is beating faster than the 10th.

    All of tuning is matching partials. If the strings had no inharmonicity the coincidental partials of octaves would coincide perfectly and create totally beatless/pure octaves at every pair of coincident partials. But the piano has inharmonicity. Therefore if the 2:1 set of coincidental partials is the same frequency, the 4:2 set of coincidental partials will not be the same frequency. Because of inharmonicity, the 4th partial of the lower note shows a greater influence of inharmonicity making the frequency of that 4th partial higher than the 2nd partial of the upper note of the octave. 

    The 6:3 partials will differ even more, because the inharmonicity pushes the upper partials even higher. By using the various tests, you can widen an octave in a controlled fashion. Piano technicians prefer the 4:2  test. And if they want a little more stretch, they make the 10th slightly faster than the third, which widens the octave just a little bit. 

    There are lots of similar aural tests that help technicians determine interval width using various coincidental upper partials. 

    Richard West





  • 9.  RE: What are the 2:1, 4:2 and 6:3 octaves? Why are they important?

    Posted 07-25-2019 16:13
    Richard, thank you for providing attachments and further explanations.

    ------------------------------
    Roshan Kakiya
    ------------------------------



  • 10.  RE: What are the 2:1, 4:2 and 6:3 octaves? Why are they important?

    Registered Piano Technician
    Posted 07-25-2019 17:08
    "The Craft of Piano Tuning" by Daniel Levitan is the best book I know to explain this concept and many others tuning theory related. I highly recommend it if you have more than a passing interest in this topic

    ------------------------------
    Daniel DeBiasio
    Brooklyn, NY
    646.801.8863
    ------------------------------



  • 11.  RE: What are the 2:1, 4:2 and 6:3 octaves? Why are they important?

    Registered Piano Technician
    Posted 07-25-2019 17:44
    I second what Daniel has written!

    Alan

    ------------------------------
    Alan Eder, RPT
    Herb Alpert School of Music
    California Institute of the Arts
    Valencia, CA
    661.904.6483
    ------------------------------



  • 12.  RE: What are the 2:1, 4:2 and 6:3 octaves? Why are they important?

    Registered Piano Technician
    Posted 07-25-2019 19:53
    So, Alan, is Levitan's book the one you use to teach your piano technician students/interns?

    And Fred, have you used Baldassin's book in teaching? 

    And to both of you, do you assign parts and then go over that assignment or do you basically tell the student to read the material cover to cover and then go from there? In other words how much of your own time do you spend helping students with the written materials? Can you trust that the student will be able to understand the book without taking your personal time to offer further support?

    Richard West








  • 13.  RE: What are the 2:1, 4:2 and 6:3 octaves? Why are they important?

    Registered Piano Technician
    Posted 07-25-2019 20:56
    Richard,
    I do not teach tuning.
    Fred Sturm
    fssturm@unm.edu
    www.artoftuning.com
    http://fredsturm.net
    "Tradition is not the worship of ashes, but the preservation of fire." -Gustav Mahler






  • 14.  RE: What are the 2:1, 4:2 and 6:3 octaves? Why are they important?

    Registered Piano Technician
    Posted 07-27-2019 09:57
    (NOTE: This response is intended for the entire list. Please let me know if it goes out only to you, Richard.)

    Richard,

    You attended my "Shop Help" class at National four years ago. You may recall my referring to the education that my assistants get as a "Combat Apprenticeship." This means that Maintaining the Pianos is our Prime Directive, and the vast majority of what they learn will be in the order presented by the needs of the pianos in our care (i. e., no syllabus or curriculum as such). Yes, this leaves holes in one's training, but as I have bragged about previously, several folks who started out with me have achieved at a very high level in our field.

    Although I strongly encourage the development of aural tuning skills (and PTG membership, and becoming an RPT), I do not teach aural tuning of Equal Temperament per se on a regular basis. We do have special sessions on it, as time and interest allow (if they are really interested, and I have the time!). I do teach some aural skill as part of ETD instruction, since I have witnessed what can happen without them (wrong page, wrong octave, wrong note, corrupt tuning file, inappropriate pitch correction functioning, etc.). So even in the course of becoming an ETD tuner (which is the most efficient use of my time, from my employers perspective), tuning unisons by ear and learning to listen to octaves and fifths are essential.

    Somewhat ironically, we really dig into the fine points of aural tuning when we have to execute tuning systems other than ET. We tackle these tasks entirely aurally (and often get a different, better result than when we enter the unequal temperament into a gizmo and then press the magic button!). In this context, they learn about coincident partials and the like.

    Virtually all of my student assistants at CalArts are music majors, and so are familiar with the language of intervals and partials. Anyone who comes to study with me is required to learn that language. I will tell someone something once, but after that, it is their responsibility to shed with the written sources readily available in our library and online to make sure that they internalized what they need to. I recommend several books, including Dan's, as well as certain videos. I am always available to discuss something they have read, seen or heard about, and still don't understand, but I will not spoon-feed them repeatedly. They know that's the deal.

    If they don't understand Levitan's exceedingly well-written text, we can discuss that ideas that elude them, but I do not walk them through it. As you may have gathered, I only teach those who are highly motivated. I am not being paid the premium that would be necessary to hold the hands of those who are not. (Nor would I be particularly interested in doing so, at any price.)

    To your greater pursuit, if I understand it correctly... There isn't one book or one approach that is the best to use. It depends on the strengths and weaknesses of both student and teacher, and their chemistry together.

    And just for the record, Baldassin's excellent book is also in our library (as is every other text concerning piano technology that I've been able to get my hands on!). I encourage my students to read them all, as I have done over the years.

    Alan


    ------------------------------
    Alan Eder, RPT
    Herb Alpert School of Music
    California Institute of the Arts
    Valencia, CA
    661.904.6483
    ------------------------------



  • 15.  RE: What are the 2:1, 4:2 and 6:3 octaves? Why are they important?

    Registered Piano Technician
    Posted 07-27-2019 12:48
    Alan,

    As far as I can tell, your message went out to the Pianotech list. If we get some responses, we'll know for sure. And you have a good memory. I enjoyed your "Shop Help" class and I was flattered when I walked into the room and you said, "Well, we can get started now. Richard West is here!"

    I have several responses to your post. I've decided to start another thread, so check out "The geography of aural tuning" and let me know what you think. That goes for anyone with comments to help enlighten the journey.

    Richard West

    ------------------------------
    Richard West
    Oro Valley AZ
    520-395-0916
    440richard@gmail.com
    ------------------------------



  • 16.  RE: What are the 2:1, 4:2 and 6:3 octaves? Why are they important?

    Registered Piano Technician
    Posted 07-25-2019 18:49
    Also, On Pitch by Rick Baldassin covers this sort of thing thoroughly, with both aural and ETD methods.

    ------------------------------
    Fred Sturm
    University of New Mexico
    fssturm@unm.edu
    http://fredsturm.net
    http://www.artoftuning.com
    "We either make ourselves happy or miserable. The amount of work is the same." - Carlos Casteneda
    ------------------------------



  • 17.  RE: What are the 2:1, 4:2 and 6:3 octaves? Why are they important?

    Registered Piano Technician
    Posted 07-26-2019 11:49
    So, Roshan, how does this knowledge affect your life? your investigations/research? your previous knowledge of how temperament works for pianos?

    Richard West

     






  • 18.  RE: What are the 2:1, 4:2 and 6:3 octaves? Why are they important?

    Posted 07-26-2019 13:12
    This knowledge has highlighted to me that a universal solution for inharmonicity could solve most, if not all, the practical problems of tuning. Inharmonicity seems to be the final piece of the puzzle.

    A universal solution could lie herein:

    "All of tuning is matching partials" (quote by Richard West).


    Has a universal solution for inharmonicity been discovered?


    ------------------------------
    Roshan Kakiya
    ------------------------------



  • 19.  RE: What are the 2:1, 4:2 and 6:3 octaves? Why are they important?

    Posted 07-26-2019 13:42

    >Has a universal solution for inharmonicity been discovered?

    ------------------------------
    Roshan Kakiya
    ------------------------------

    Within the Vertituner program are many Styles to handle stretch. They use multiple partials in differing percentages and beat rates for each octave. There really is no "One Way" to tune a piano. It is highly subjective. Temperament is only one apsect, how you choose to stretch it is another.


    ------------------------------
    Regards,

    Jon Page
    mailto:jonpage@pianocapecod.com
    http://www.pianocapecod.com
    ------------------------------



  • 20.  RE: What are the 2:1, 4:2 and 6:3 octaves? Why are they important?

    Registered Piano Technician
    Posted 07-26-2019 13:44
    Since inharmonicity varies with the scaling of pianos, there can be no truly universal solution. There are many possible approaches to the problem. Here's an interesting one: http://piano-tuner.org/entropy The partials of each note are measured, and the tuning is adjusted to achieve minimum entropy, which translates as achieving the greatest degree of order. The partials are read as produced by the instrument, so inharmonicity is included in the calculations.

    Bernard Stopper's Onlypure software does some kind of universal treatment of inharmonicity, to the extent I understand how it works. It is set up so that you can start on any note of the piano, and tune in any order. Hence, the partial spectrum of each note must be compared with some kind of background universal spectrum, and then adjusted for tuning to fit into that pattern to the greatest extent possible. Something like that, anyway. Bernard is not very forthcoming on how it actually works, but it does produce good results.

    Fred Sturm
    University of New Mexico
    fssturm@unm.edu
    http://fredsturm.net
    www.artoftuning.com
    "Practice makes permanent. (Only perfect practice makes perfect)."






  • 21.  RE: What are the 2:1, 4:2 and 6:3 octaves? Why are they important?

    Posted 07-26-2019 14:52
    I think the following solution could be useful:

    Imitate the specific Railsback curve for each piano by using a different width of equal temperament for each of the 7 consecutive octaves, for example, C1-C2-C3-C4-C5-C6-C7-C8.

    An example of a Railsback curve:

    https://en.m.wikipedia.org/wiki/Piano_acoustics#/media/File%3ARailsback2.png

    In the 7th octave, the difference between C7 and C8 is about +20 cents. Therefore, if C7 is the reference, C8 should be about 20 cents sharper than C7.

    A semitone can be created for C7-C8, the octave, by dividing 1220 cents by 12:

    1220 cents / 12 = 101.67 cents.


    C7-C8 could be tuned as follows:

    C7 = 0.00 cents (the reference).

    C#7 = 101.67 cents.

    D7 = 203.33 cents.

    D#7 = 305.00 cents.

    E7 = 406.67 cents.

    F7 = 508.33 cents.

    F#7 = 610.00 cents.

    G7 = 711.67 cents.

    G#7 = 813.33 cents.

    A7 = 915.00 cents.

    A#7 = 1016.67 cents.

    B7 = 1118.33 cents.

    C8 = 1220.00 cents.


    This method can be applied to any Railsback curve.

    ------------------------------
    Roshan Kakiya
    ------------------------------



  • 22.  RE: What are the 2:1, 4:2 and 6:3 octaves? Why are they important?

    Posted 07-26-2019 15:29
    The Railsback curve isn't God.

    Often I depart from it.

    Best wishes

    David P

    --
    - - - - - - - - - - - - - - - - - - - - - - - -
    David Pinnegar, B.Sc., A.R.C.S.
    - - - - - - - - - - - - - - - - - - - - - - - -
    +44 1342 850594





  • 23.  RE: What are the 2:1, 4:2 and 6:3 octaves? Why are they important?

    Posted 07-26-2019 16:48
    I think you should actually try tuning a piano. The extremes are stretched according to the partials you selected throughout the scale. I know of two pianos where the 2P of C7 is + 60 cents. Even the triple Octave (8:1) depends on the 8P of C5 (which is sometimes +60 cents) for C8. So choosing the appropriate Partials is important. Pianos are tuned via partials and not mathematical equations.

    Every piano's Partial structure is different. A tuning on one piano will not match the tuning on another piano, note for note in stretch. Which is why when tuning with an ETD, the better piano is tuned first and then that file is used to tune the other for note match. A compromise is always made when tuning.

    ------------------------------
    Regards,

    Jon Page
    mailto:jonpage@pianocapecod.com
    http://www.pianocapecod.com
    ------------------------------



  • 24.  RE: What are the 2:1, 4:2 and 6:3 octaves? Why are they important?

    Registered Piano Technician
    Posted 07-26-2019 17:09
    I'm going to interject again. Richard can correct me if I don't explain something right. We need to back up again to understand a concept. If you think of inharmonicity as a static thing, you'll never gain understanding of it. If you ever think you've gained full understanding of it, you'll know you've missed something. Here's a basic aspect I'd like to share. The more stiff a sounding body, the more altered (or less pure, mathematical ratio wise) its harmonic series can be. Harpsichords don't have as much inharmonicity as pianos, and pianos don't have as much inharmonicity as marimbas. Piano wire is pretty stiff, and the harmonic series above each fundamental note gets gradually sharper as it goes up. This is why we have a "tuning curve" as you noted: the bass is lowered so their harmonics match the fundamentals of the middle section, and the higher treble is raised so their fundamental pitches match the harmonics of the notes below them. BUT, the amount of inharmonicity is different in different pianos. If you're looking to find a single way to finely tune all pianos, you won't find it. That's why everyone is explaining what to listen to. If you like up one pair of coincident partials, the others won't line up exactly. Choosing which coincident partials to listen to is what determines the size of the octave. Not only do we have the stiffness of wire affecting all these things, but also the evenness of the wire, the hardness of the hammer, the angle of the hammer, the level of the hammer & strings, the placements of the bridges, the fit of the bridge pins, etc. Two "identical" pianos can be different. The "universal solution" to inharmonicity is to manipulate the tuning based on listening to coincident partials. ETD's will "listen" to each piano differently and develop unique tuning curves for each piano.

    I hope this is helpful and not too dumbed down. Get the book recommended and explore more. Everyone here has given you really good information. Back up and bit and try to understand these concepts before you get too far into the math. The math won't mean much if you're missing a "gut" understanding, if that makes sense. I'm speaking from personal experience. ;-)

    ------------------------------
    Maggie Jusiel
    Athens, WV
    (304)952-8615
    mags@timandmaggie.net
    ------------------------------



  • 25.  RE: What are the 2:1, 4:2 and 6:3 octaves? Why are they important?

    Posted 07-26-2019 18:02
    Attached are tuning curves for a Bosendorfer upright 160. The Railsback curve really jumps at the break in the tenor. But after I've tuned the instrument no jump is greatly discernable at the break at all.

    Best wishes

    David P

    ------------------------------
    David Pinnegar BSc ARCS
    Curator and House Tuner - Hammerwood Park, East Grinstead, Sussex UK
    antespam@gmail.com

    Seminar 6th May 2019 - http://hammerwood.mistral.co.uk/tuning-seminar.pdf "The Importance of Tuning for Better Performance"
    ------------------------------



  • 26.  RE: What are the 2:1, 4:2 and 6:3 octaves? Why are they important?

    Posted 07-26-2019 18:27
    Margaret,

    The method that I have mentioned can be applied to any Railsback curve since it is very flexible. I know that each piano can have its own specific Railsback curve.

    ------------------------------
    Roshan Kakiya
    ------------------------------



  • 27.  RE: What are the 2:1, 4:2 and 6:3 octaves? Why are they important?

    Registered Piano Technician
    Posted 07-26-2019 18:31
    Ok. Sorry. Just checking. Everyone else here knows lots more than me. ;-)

    ------------------------------
    Maggie Jusiel
    Athens, WV
    (304)952-8615
    mags@timandmaggie.net
    ------------------------------



  • 28.  RE: What are the 2:1, 4:2 and 6:3 octaves? Why are they important?

    Posted 07-27-2019 10:41
    Roshan-
    How about telling us a few things about yourself?
    Have you ever tuned a piano? A piano with strings, not a digital program?
    What books or sources about piano tuning have you read?
    What is your motivation for your studies, proposals and questions?
    Have you considered joining PTG?

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



  • 29.  RE: What are the 2:1, 4:2 and 6:3 octaves? Why are they important?

    Registered Piano Technician
    Posted 07-25-2019 21:08
    Roshan,
    You mention the C1/C2 octave. In the bass, the best way to listen is usually ghosting partials. Hold down C1/C2 - either press the notes down silently, or play them very softly. Then play the note corresponding to each partial in turn, a firm staccato blow. This will excite the corresponding partial of each note, and you will be able to hear beats (if any) at that partial level. 2:1 won't be very useful, and 4:2 is unlikely to have a noticeable beat. So play G3 to hear the 6:3 relationship (whether it is synchronized - you won't be able to tell which is sharp or flat of the other, just whether or not there is a beat). Then play C4 to hear 8:4. E4 to hear 10:5. G4 to hear 12:6. 

    In all likelihood (unless it is a concert grand), at some point there will be quite noticeable beating. Beware to listen at the pitch level of the note you have ghosted, as there could also be a noticeable beat an octave higher (around twice as fast).

    Generally speaking, a 6:3 octave is a good starting point for the bass of any piano. Using the m3/M6 test (C1D#1/D#1C2), they should beat the same. (Ghost G3 to focus your ear on where that beat is). Usually the interval should be slightly expanded at that coincident partial, so the m3 should beat slightly slower than the M6.

    You might also want to check larger intervals, like the double octave (C1C3), double octave 5th (C1G3), triple octave (C1C4). Depending on the size of the piano, you might want to favor the largest of these intervals (largest pianos), or somewhere in between (small pianos).

    In the mid range, the tests and ideas Richard West wrote about apply more.

    ------------------------------
    Fred Sturm
    University of New Mexico
    fssturm@unm.edu
    http://fredsturm.net
    http://www.artoftuning.com
    "We either make ourselves happy or miserable. The amount of work is the same." - Carlos Casteneda
    ------------------------------



  • 30.  RE: What are the 2:1, 4:2 and 6:3 octaves? Why are they important?

    Posted 07-26-2019 14:06
    Fred's concept of ghosting partials is great and I hadn't considered it a technique as a tool before.

    Is specific handling of partials using these methods unique to equal temperament? Or do they have relevance to unequal temperaments? Is evenness something we have to worry about only in Equal Temperament?

    Best wishes

    David P 

    --
    - - - - - - - - - - - - - - - - - - - - - - - -
    David Pinnegar, B.Sc., A.R.C.S.
    - - - - - - - - - - - - - - - - - - - - - - - -
    +44 1342 850594





  • 31.  RE: What are the 2:1, 4:2 and 6:3 octaves? Why are they important?

    Registered Piano Technician
    Posted 07-25-2019 19:10
    The relationships are not ratios, but coincident partial pairs. Any single octave has all of the relationships you list. Tracking these relationships is necessary in tuning octaves between strings with differing inharmonicity. In the math model these relationships are identical, but they will differ on real pianos. One can be pure, another might be contracted, and one expanded, all at the same time.

    Sent from my iPhone




  • 32.  RE: What are the 2:1, 4:2 and 6:3 octaves? Why are they important?

    Registered Piano Technician
    Posted 07-27-2019 03:13
    The Tao of piano tuning.

         "If you think of inharmonicity as a static thing, you'll never gain understanding of it. If you ever think you've gained full understanding of it, you'll know you've missed something." – Jusiel

    Quite!

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



  • 33.  RE: What are the 2:1, 4:2 and 6:3 octaves? Why are they important?

    Registered Piano Technician
    Posted 07-27-2019 07:19
    This may not be the place, but, what octave stretch does a perfect 12th tuning give? 2.5-1, 4.25-2,

    ------------------------------
    Larry Messerly, RPT
    Bringing Harmony to Homes
    www.lacrossepianotuning.com
    ljmesserly@gmail.com
    928-899-7292
    ------------------------------



  • 34.  RE: What are the 2:1, 4:2 and 6:3 octaves? Why are they important?

    Registered Piano Technician
    Posted 07-27-2019 11:39
    Since Mr. Railsback has been mentioned, it might be interesting to describe the research that went into his famous curve. In 1937, Railsback got hold of a very early version of a "chromatic stroboscope," the instrument that was fairly shortly thereafter commercialized as the Conn Stroboscope. He set about to more or less replicate the work of Alexander Ellis in the late 19th century, measuring what piano tuners actually produced to see whether or not it was really ET. 

    The set up was four grands and three uprights of various models, each tuned by four different piano tuners (28 tunings in all). These tunings were measured - at the fundamental or first partial - and analyzed. Railsback published an article about that. He also noticed that the bass was considerably flat, while the treble was sharp. He published a second paper about that the following year, going into that phenomenon of "stretch," opining that the bass stretch was probably due at least in part to inharmonicity, while the treble was a conscious effort not to "flat the notes" (he had presumably interviewed his tuners).

    He compiled his data in data point charts, and drew a nice smooth curve to show the average trend, though the curves for the actual tunings were quite jagged. IOW, the curve is an idealized average, which was unlikely to correspond to any actual tuning until the makers of the stroboscope in its various iterations gave it in chart form to purchasers of their devices, and those purchasers followed them (blindly and deafly?).

    The thing is that we don't tune fundamentals, other than the reference pitch (A4, C5, whatever). Particularly in the bass, we have no idea where the fundamental is. We are always tuning by matching partials, whether we think we are or not. In the high treble, we are often matching the fundamental of the note being tuned to a compromise of several partials of notes below.

    In any case, Railsback's archaic (80-year-old) work was the beginning of the modern electronics based scientific study of tuning, with the factor of inharmonicity thrown into the mix. It has long been superseded by more extensive and complex studies, published or not. Al Sanderson, for instance, did an enormous amount of measurement of actual tuning during the process of developing both the PTG tuning test and the software for his Sight-o-Tuner and Accutuner. It would be interesting to get hold of that data, if it has been saved in any form. Anybody know anything about that?
    Regards,
    Fred Sturm
    "The true sign of intelligence is not knowledge, but imagination." - Einstein






  • 35.  RE: What are the 2:1, 4:2 and 6:3 octaves? Why are they important?

    Registered Piano Technician
    Posted 07-27-2019 12:04
    Fred: 

    "The thing is that we don't tune fundamentals, other than the reference pitch (A4, C5, whatever). Particularly in the bass, we have no idea where the fundamental is. We are always tuning by matching partials, whether we think we are or not. In the high treble, we are often matching the fundamental of the note being tuned to a compromise of several partials of notes below."

    Yeah. Thanks!

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    Maggie Jusiel
    Athens, WV
    (304)952-8615
    mags@timandmaggie.net
    ------------------------------



  • 36.  RE: What are the 2:1, 4:2 and 6:3 octaves? Why are they important?

    Registered Piano Technician
    Posted 07-27-2019 13:53
    Following the Railsback lead, 

    I find it interesting that piano technicians by and large are so focused on their own perceptions of what they should do and why, and have little understanding of other perspectives (scientific, psychological, or artistic, for instance). We argue that we "know" what is the best tuning, but have we challenged our assumptions?






  • 37.  RE: What are the 2:1, 4:2 and 6:3 octaves? Why are they important?

    Posted 07-27-2019 14:05
    Fred wrote:
    "I find it interesting that piano technicians by and large are so focused on their own perceptions of what they should do and why, and have little understanding of other perspectives (scientific, psychological, or artistic, for instance). We argue that we "know" what is the best tuning, but have we challenged our assumptions?"

    Well, Fred, in the midst of many discussions, I have thought, and sometimes said "If it were necessary, in order for a piano to serve as a functional musical instrument, that it would have to be tuned to the degree of accuracy being argued, pianos and piano music would have never existed."


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    Ed Sutton
    ed440@me.com
    (980) 254-7413
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  • 38.  RE: What are the 2:1, 4:2 and 6:3 octaves? Why are they important?

    Registered Piano Technician
    Posted 07-27-2019 14:09
    Fred said: but have we challenged our assumptions?

    Richard replies: I wholeheartedly agree. Whether it's the algorithm on an ETD or the "algorithm" in our head, we try to impose our singular, tried and true vision on every piano. That single algorithm isn't effective on every piano, but it's a starting point and making adjustments from the general algorithm is what tuning, especially aural tuning is all about. The only input I've received over the years about what is "right" or "sounds good" is when I've helped with super tunings, or listened to tunings of concert tuners on concert instruments at the annual PTG convention. Years ago Virgil Smith came to Nebraska and demonstrated his tuning and that was interesting. Sometimes going back to a piano that I tuned the day before can teach me a lot, especially in regard to stability.

    Richard West







  • 39.  RE: What are the 2:1, 4:2 and 6:3 octaves? Why are they important?

    Posted 07-27-2019 12:01
    Larry - wouldn't be the point of perfect 12th tuning that the notes of the scale line up exactly with the 3rd partial of the lower string? By definition, how would it be possible even to tune perfect 12th systems without that coincidence?

    By your assertion the perfect 12th system could be tuned only mathematically with an ETD or have I misunderstood something? So one's for instance taking A at 220 and tuning E an octave up to 660 irrespective of the inharmonicity? Were I to be setting out to tune a perfect 12th system I'd be tuning that E to the sounding 3rd partial of the A whatever frequency the natural inharmonicity took it to. Or have I got the wrong end of the stick?

    Whilst I'm a die-hard and inflexible unequal temperament advocate, the concept of perfect 12th tuning is interesting and actually important to what I've been doing. In the temperament I use, fifths CF,FBb.BbEb.EbAb,AbC#,C#F# and BE are perfect. I hope that readers will find the anomaly I'm leading to interesting and apologise if not. The result, I promise is interesting.

    I set out the scale and go down to Tenor C. Below Tenor C I consider that the function is for harmonic support rather than scale relationships. So I start going down, B, Bb etc and have been tuning aurally to match the octave harmonics on tempered 5th notes to the relevant notes of the scale in the middle octave. Just for fun I keep the CTS5 tuner running to see how my aural tuning is matching with what the machine is indicating. Then one day I took a break at Tenor C and switched the tuner off. Switching it on reverts to A440 so one has to press the down button to go down to the note, or better, just down 10 to B so as to tune to the 2nd Partial. But then I was lazy and curious one day and pressed down three going from A to F#, which is the 3rd partial of the B below Tenor C. And going down note by note I found that the machine was agreeing quite reliably with my aural tuning. Tuning to the 3rd partial of course one's taking the inharmonicity into account.

    But this isn't equal temperament. So tuning the B for the 3rd partial to align with the F#, one's tuning the B to the 12th and not the tempered fifth that it should be. Going down, the A should be perfect with the E so no problem. The G then gets tuned a perfect 12th to the D, rather than a tempered relationship as it should be. With the subsequent tuning to tempered or untempered notes one might see that working out whether octaves are pure as some notes are tuned on perfect 12ths, and other perfect 5th relations are broken becomes rather complicated. But by tuning the perfect 12ths to the 3rd partial alignment to the scale notes rather than pure octaves gives interesting resonance and solidity to the sound. In effect I'm using a combination of both 4:2 and 6:3 systems but harmonically complicated by the 7 perfect 5th scale system.

    Can anyone describe a tangible difference to the sound of an instrument tuned 6:3 rather than 4:2?

    Best wishes

    David P



    --
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    David Pinnegar, B.Sc., A.R.C.S.
    - - - - - - - - - - - - - - - - - - - - - - - -
    +44 1342 850594





  • 40.  RE: What are the 2:1, 4:2 and 6:3 octaves? Why are they important?

    Registered Piano Technician
    Posted 07-28-2019 09:38
    "Can anyone describe a tangible difference to the sound of an instrument tuned 6:3 rather than 4:2?"

    David, isn't it the case that one tunes whatever partial pair is the most obvious and offensively beatimg in a given range of the piano? It's my understanding that, to a large extent, we tune the 6:3 partials in the bass of most smaller pianos because that's what we hear. If some other partial pair is louder and more obnoxious, such as a 10:5 or 12:6, then we'd tune that pair instead.
    We tune 2:1 in the upper treble because those are the most prominent partials, and not the 6:3. If the 6:3 were loudly beating in the high treble, we would typically tune that one, right? So the tangible difference is that if you tune a 4:2 in the bass of most pianos, you'll hear a beating 6:3.

    "Then when it comes to unisons, the fundamental is king"

    Ed, if the fundamental is "king," isn't it true that the 3rd partial of a unison is the "queen?" 


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    Scott Cole, RPT
    rvpianotuner.com
    Talent, OR
    (541-601-9033
    ------------------------------



  • 41.  RE: What are the 2:1, 4:2 and 6:3 octaves? Why are they important?

    Registered Piano Technician
    Posted 07-28-2019 11:01
    Scott,
    It is possible and indeed likely that many tuners tune as you describe: listen to the octave and try to quiet the most offensive beating. However, this would tend to be in conflict with other priorities, as, for instance, maintaining the ET parameter of evenly decreasing beat rates (M3, M10, M17, possibly double octave m7), and also maintaining a coherent pattern of partial coincidence (for instance, beatless 3:1 or 6:2 12ths, beatless 6:1 19ths, beatless double or triple octaves, or a compromise between those ideals).

    One of the problems with tuning the bass is the incoherent sound, especially in smaller instruments. It is a good idea to have something consistent and rational to grab hold of. Otherwise, you end up moving pitch up and down experimentally, never finding a place that actually sounds good, and leaving it somewhere or other in frustration.

    Most tuners and most ETDs will do something quite close to 6:3 octaves in the bass, and this more often than not results in 6:1 19ths, interestingly enough (one of the first things I discovered in using an SAT - it was something I generally aimed at, and it was happening pretty consistently).

    Many tuners do tune 2:1 or thereabouts in the high treble. Not I. I favor wider intervals, like 19ths and triple octaves. This puts my octaves quite wide of 2:1. Since I have been tuning this way successfully for going on 40 years, I deduce that whether or not it is preferred by my customers, it is not offensive :-) It is probably the area of the piano that has the greatest variance among tuners. 

    For me, a major aim in tuning is coherence of sound, which is achieved by having partial structure support in both directions: high notes supported by the partials of lower notes, and low notes having their partials supported by higher notes. This leads to more sustain, and a more singing tone. Individual octaves and how they sound are fairly low on my priority list, especially as I move out from the mid range.
    Regards,
    Fred Sturm
    University of New Mexico
    fssturm@unm.edu
    http://fredsturm.net
    www.artoftuning.com
    "Education is not preparation for life; education is life itself." John Dewey






  • 42.  RE: What are the 2:1, 4:2 and 6:3 octaves? Why are they important?

    Posted 07-28-2019 11:26
    Scott- thanks so much. That puts into words something that otherwise one merely wonders about and possibly does naturally but finds it difficult to describe. Without such clear statement of standard practice that option between 4:2 6:3 and 10:5 gives rather a dilemma or trilemma.

    I've noticed that most pre 1870 instruments I've come across have prominent 3rd partials and no 5th partial and later pianos in the larger sizes at least bring the 5th partial to the fore. Before the 1880s I haven't met an instrument with 5th partial sound in most of the bass. Has anyone else noticed this?

    A consequence of this is that tuning 6:3 brings the instrument more in the pre-1870s tonality and then using systems involving perfect 5ths or perfect 12ths will get the instrument to resonate strongly.

    It's for this reason that actually I debate whether I like the sound of the 1859 Hallé concert Broadwood but that instrument is really interesting as it can take a stronger unequal temperament and to the extent I find equal temperament less objectionable than on modern instruments 
    and it's this experience that causes me to dispute the alleged universality of the adoption of equal temperament before the 1870s. The reason for this is that equal temperament in the instruments after this date had a really important function, to provide beating between the 5th partial and the notes of the scale, and the even progression of that beating gave to the reliable glistening and shimmering of sound and an even tone colour in every key. And even then I wonder if real exact equal temperament was wholly universal as evidenced possibly by https://www.youtube.com/watch?v=OBOdhthgsxs which people have said seems to evoke a spirit of 1930s recordings. The piano there is tuned to Prof Jonathan Bellman's Chopin temperament giving a very warm sound.

    Best wishes and many thanks.

    David P
    --
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    David Pinnegar, B.Sc., A.R.C.S.
    - - - - - - - - - - - - - - - - - - - - - - - -
    +44 1342 850594





  • 43.  RE: What are the 2:1, 4:2 and 6:3 octaves? Why are they important?

    Registered Piano Technician
    Posted 07-27-2019 11:28
    Steven Rosenthal:

    "The Tao of piano tuning."

    Haha! 😜😁😉😜

    ------------------------------
    Maggie Jusiel
    Athens, WV
    (304)952-8615
    mags@timandmaggie.net
    ------------------------------



  • 44.  RE: What are the 2:1, 4:2 and 6:3 octaves? Why are they important?

    Registered Piano Technician
    Posted 07-27-2019 21:04
    The definition of an "In-Tune" state for a piano is derived by ear. The human aural mechanism is coupled to the brain and the brain is looking for musically intelligible context. Thus an adequate understanding of what makes for adequate intervalic consonance across the compass must be developed to allow one to judge an In-Tune state. I am not sure the entropy model can capture this fully without knowing how the ear/brain interface judges intonation.

    Piano Technicians have developed a remarkable skill to derive the In-Tune state of any particular piano scale by using feedback loops of beat rate comparisons between intervals. It has been shown it is not necessary to use each and every beat rate comparison to derive each In-Tune state.

    As has been mentioned earlier, very little of the intervallic intonation relationships involve the fundamental until you are tuning in the top octave or so of the compass. The trend of partial matches across the compass involves higher and multiple pairs of coincident partials in the lower portions of the compass and lower and fewer coincidental partials as you ascend the compass. So discussions about 1-2, 2-4, 6-3 etc. octave matches are just one point on a complex series of partial intersections.

    Then when it comes to unisons, the fundamental is king. In fact one can hear the fundamental develop as the unison strings come into full coupling in the bass and tenor regions. An added, (wonderful) complication is how certain types of string scales allow for the ear to perceive difference tones that "create" a fundamental that is nowhere to be found by the spectrum analyzer. Having perfectly phased unisons also adds to the development of the fundamental. That is why out of phase unisons always sound a little out of tune even when they are as perfectly tuned as possible.

    Thus proper musical aural discretionary skills must be developed in the context of comparing intervalic beat rates to each other across the compass to be able to grasp how to derive an In-Tune state.

    It is far more difficult to write out all the material than it is to simply listen and learn the patterns from teachers and then apply them to any particular piano one is tuning. Once one knows enough, the whole thing falls into place.


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    Edward McMorrow
    Edmonds WA
    425-299-3431
    ------------------------------



  • 45.  RE: What are the 2:1, 4:2 and 6:3 octaves? Why are they important?

    Posted 07-29-2019 08:34
    As an aside, there are others as well, Pure 12th stretch (3:1), Pure 19th (6:1), Pure 22nd (8:1) and more. My favorite in the bass (especially spinets) is what I call the 1:sub octave where I use the subtone or undertone of let's say a C1C2 octave.

    Let's say C1 is 98Hz and C2 is 200Hz (just for this example). 200-98=102 (102Hz being the undertone, subtone, resultant tone, virtual tone, natural beat, or whichever you want to call it). Since 102Hz and 98Hz beat against each other at 4bps you will be able to hear and even feel that 4bps disturbing the air in the room you are in.

    I strive for the undertone in the 1:sub octave to be calm (along with the numerous other stretches [8:4, 6:3, 3:1, 6:1 8:1]).

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