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Building a Temperament

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  • 1.  Building a Temperament

    Registered Piano Technician
    Posted 05-25-2017 22:14
    Hello all,

    I am trying to improve my aural skills, and thought it might be helpful to build my own temperament sequence. How would I go about doing that? Thanks

    ------------------------------
    Benjamin Sanchez
    Professional Piano Services
    (805)315-8050
    www.professional-piano-services.com
    BenPianoPro@comcast.net
    ------------------------------


  • 2.  RE: Building a Temperament

    Posted 05-26-2017 04:34
    Hello Benjamin - If you haven't got this book I suggest you get it: Arthur Reblitz 'Piano Servicing, Tuning, & Rebuilding. from The Vestal Press, NY. 13850 USA. Having acquired it, open it at p.38 (How are Pitches Organized in the Musical Scale?)  and study it. Or get a copy or Mario Igrec's book 'Pianos Inside Out' (2013) Published by In Tune Press, LLC., PO Box 2653 Manderville, LA 70470-2653. USA Even better - create a Document in Excel which shows ALL the frequencies both Fundamental and up to 6th. Harmonic (Partial) then look at the numbers and compare them to see why you hear beats when two notes are played together. Hint: from your new Frequency Table, compare, say, the 6th Harmonic of C3 with the 4th. Harmonic of G3. Having understood this principle things begin to get exciting . . . . .   What you are hearing here is the result of applying the Formula of the '12th. root of 2' (1.059463094) to each subsequent semi-tone to build up a Table of Frequencies. 
    Hope this helps!     Michael    UK





  • 3.  RE: Building a Temperament

    Registered Piano Technician
    Posted 05-26-2017 10:05
    Benjamin,

    1) What is your present experience?
    2) How would you characterize your strengths and weaknesses surely?

    Pwg

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



  • 4.  RE: Building a Temperament

    Registered Piano Technician
    Posted 05-26-2017 19:13
    Peter,
    Experience: ETD user, specifically SAT. In business for the last year, one year training prior, strictly by ear during that time, so I know the basics of aural tuning, and am trying to learn the fine points now.

    Really the only strengths I can positively identify are: I can hear the roll in a fifth well, and can tell when two beat rates are equal.

    Im trying to build a temperament around these strengths, but am not sure exactly how to go about doing that. Any ideas?

    ------------------------------
    Benjamin Sanchez
    Professional Piano Services
    (805)315-8050
    www.professional-piano-services.com
    BenPianoPro@comcast.net
    ------------------------------



  • 5.  RE: Building a Temperament

    Member
    Posted 05-26-2017 20:31

    On Pitch: The Integration and Equation of Aural and Electronic Tuning Techniques (Paperback)
    ​ by Rick Baldassin​



    | || ||| || ||| || ||| || ||| || ||| || ||| || |||
    jason's cell 425 830 1561

    On Fri, May 26, 2017 at 4:12 PM, Benjamin Sanchez via Piano Technicians Guild






  • 6.  RE: Building a Temperament

    Registered Piano Technician
    Posted 05-26-2017 21:25

    Hi, Benjamin

    Any number of different temperament sequences can work, but it makes sense to find a good one and stick with it.

    The one Ted Sambell taught us in school has served me very well through almost 40 years. It was only much later at a convention that I found out it is called "both ends from the middle". Essentially it is four first inversion triads, going up by semitones.

    Set A3 from the fork, using the F below it. (F beating to the A4 fork, compared with F beating to the A in the piano.) Then when the A is right, set the F to a guessed (remembered) beat rate.

    Then I do the one new thing I've added to the original system: I tune F4 from F3, then I add C#4. This gives a series of major thirds stacked on each other: F-A, A-C#, Db-F. The beat rates of these progress roughly four to five. (i.e., each is 20% faster than the one before.)  Different pianos will require slightly different speeds, but the thing is to make the increase uniform. Setting up these major thirds assures that the guessed at F-A beat rate will work right. The F-A can be altered a little if needed to get a uniform progression.

    So, once the bracketed thirds are done, you've already got four notes right. Moving on to the first inversion triads:

    You already have F and A ... next you add D4, a just slightly wide fourth. You test F-A, and then F-D. The F-D should be just slightly faster than the F-A.

    First triad finished: you next set Bb (A#, really) from F, slightly wide. You set F# next, so that the beat rate is just a tad faster than the F-A. You add the D#, so the F#-D# is just slightly faster than the F#-A#, just like in the first triad.

    To start the third triad, you set the B from the F#, just slightly wide, like the F-Bb was. Continuing, you set the G from the B, so that the beat rates F-A, then F#-A#, then G-B slowly progress faster. You add the E, just like you added the D# -- the sixth from G to E is slightly faster than the third from G to B.

    For the fourth and last triad, you set the C natural from the G, a slightly wide fourth like the others. Then you set the Ab from the C, so that the beat is just slightly faster than the G-B. You can run thirds from the bottom: F-A, F#-A#, G-B, Ab-C, and they should all fit in nicely, and the A-C# which would be next in line should already be right. You don't need to set F4 to complete the last triad (Ab-C-F), because you've already tuned it. You just see if it fits in right. Then you check from Ab (G#) to C#, having already set the C#, and see if the fourth is slightly wide, like the others.

    At this point, being done, I run major 3rds (which progress) perfect fifths and perfect fourths (are they uniform, 4ths slightly less quiet than fifths?), and major sixths (which progress) to see if they all are happy. The fifths should be only slightly narrow, and the fourths, wide, of course, just a bit faster than the fifths. You can listen carefully to the perfect fifths to see if any do not sound just like the others. If anything doesn't seem to fit, you tinker with it.

    There are other tests you can use as you go, but this is the gist.

    It is probably a lot easier to see how this works by watching someone doing it ... and of course the process gets a lot faster and easier with practice.

    Just fill yourself with confidence beforehand, and approach it as a voyage of discovery, and you'll do fine. Instead of fretting about official beat rate numbers (how do I find out how fast 8 beats is from a stopwatch??), try dividing the F to F octave into the progressing major thirds, and that will tell you the approximate rate to remember for F-A. The fourths and fifths one judges more as a curl in the tone, fourths a little less happy than the fifths, and little spinets require a little bit different size and brashness than concert grands. Each piano will tell you what it needs and can do.

    Ah, you said you've already spent a year aural tuning, and you want the fine points ... okay.

    First, at the risk of starting a fracas, study aural tuning by tuning aurally, and don't check your work with an ETD. You want as much contact with the sounds and the interval sizes as you can get. A sense of what makes a musical octave stretch develops over time by listening to music, and making music. Hopefully you already have it, and just need to polish it by use. Twenty two years of playing cello, and two music degrees in applied cello (useless degrees except for this!) and five years of orchestra work did help, but there are many other perfectly satisfactory roads to hearing how wide an octave wants to be.

    Work on non-ETD ways of responding to intervals --- is this a sweet octave? What is the texture of these unisons? (I like creamy or buttery.) What are the vowel sounds of unisons? You want open vowels -- ahhs, or ohhhs, not curling eeeyews. As you stretch the initial F to F octave, listen for how the fifths clear up. If they are beatless, the octave will beat audibly, and the upper register will sound harsh. Some jazz people might like this, but generally, one wants clean octaves, fifths, and fourths, in that order. Notice that small changes in third or sixth rates will not be audible in the music, since they are all pretty fast already -- but the character of fifths and fourths and octaves will be extremely critical to the musical effect of the tuning. If you pull the octave out the right amount so that the fifths are a little calmer, and then you tune right to the top checking fourths and fifths below each note to be sure they are acceptable, you will end up with a crystal clear tuning. Test open chords -- C-G-C, C-F-C, etc. They should be -- beautiful, all over the piano.

    Unisons should be warm and very quiet, and of course very stable. Different styles of unisons will yield very different musical results. They do have an emotional component, which you will hear if you listen for it. If you get a reasonably good temperament, good octave stretch, and excellent clarity in the fourths and fifths, and then listen to a good pianist playing, you will hear what just seems like good architecture. One could imagine a cathedral, and how all the weight is conveyed down through the structure.

    One other fine point, just from my own observations: in the middle register, if you play harmonic intervals (like an octave playing both notes at once) and then melodic intervals (the two notes one after another) both will sound in tune. But as you get into the upper register, if the harmonic interval sounds in tune and beatless, the melodic interval will sound like the upper note is flat. Imagine a pianist playing a kind of cadenza, and after noodling around in the middle register, he or she reaches out a couple of octaves and -- bing -- plays a high note. More often than one would like, that note sounds flat. If the octave stretch is minimal (which works well for some music) that upper note sounds VERY flat. And the contrary situation can also happen -- imagine a stretched octave yielding extremely pleasing jumps to high notes. If someone plays a lot of octaves or especially double octaves up in the very high register, the results sound terrible. What sounds good as a melodic octave sounds harsh and bitter as a harmonic octave. So, partly, it helps to know what music is going to be played, but for general use, I think of tempering between harmonic and melodic intonation. As you work up there, try a little of each. Play some octaves simultaneously and then play them one note after another. You'll hear the difference. You want them both to be pretty acceptable, since they can't both be really good.

    Regards,
    Susan



    ------------------------------
    Susan Kline
    Philomath, Oregon
    ------------------------------



  • 7.  RE: Building a Temperament

    Registered Piano Technician
    Posted 05-27-2017 00:59
    Thank you Susan. I will be reading your posts over the next few days as I experiment with that temperament. I have heard of this one before, but only remembered the "up a sixth, down a third down a third." Now I will try the whole thing.

    As as far as why I'm trying to build my own temperament, I was using the European A-A, A4, A3, E4, B3, F#4, etc. It just wasn't working for me due to not having any checks until the end.

    Thanks again,

    ------------------------------
    Benjamin Sanchez
    Professional Piano Services
    (805)315-8050
    www.professional-piano-services.com
    BenPianoPro@comcast.net
    ------------------------------



  • 8.  RE: Building a Temperament

    Registered Piano Technician
    Posted 05-27-2017 22:30
    Good luck with it, Benjamin.

    The stacked major 3rds right at the beginning help give you feedback. Using thirds and sixths (faster beating intervals) in the body of the temperament helps give you lots of tests, and more detailed data than just relying on fourths and fifths.

    Email me if you hit any obstacles. This temperament and me go way back.

    ------------------------------
    Susan Kline
    Philomath, Oregon
    ------------------------------



  • 9.  RE: Building a Temperament

    Registered Piano Technician
    Posted 05-28-2017 16:50
      |   view attached
    Benjamin,
    I hope you find a tuning sequence that works for you. I've run into a lot of them, some heavy on thirds, some heavy on fourths and fifths. I think we're all looking for the perfect sequence. I don't think it exists.  But you've given me incentive to think about your quest. I've attached some ideas that may or may not be helpful. I was just happy to try to organize thoughts that have been percolating and that I've been wanting to put down on paper. I'll be interested to see if my random thoughts strike a chord with you and the more experienced tuners on this list.
    Richard West


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

    Attachment(s)

    pdf
    Basic tuning concepts .pdf   47 KB 1 version


  • 10.  RE: Building a Temperament

    Registered Piano Technician
    Posted 05-28-2017 17:29
    Richard wrote:

    "William Braid-White's book Piano Tuning and Allied Arts is a good basic start, if you don't mind dated language. Some more recent texts also are good but have problems with the language/description of the tuning process; they tend to make tuning more complicated to understand than is necessary, IMHO."

    Braid-White's book was the first text that I used when learning to tune and, for a long time, the only text. Many other tuning books have come out since then. Much more recently, we have Daniel Levitan's "The Craft of Piano Tuning," which is what I recommend first and foremost to my tuning students these days. Dan has done a superb job of describing what we listen for and the mechanics of how we affect precise and lasting changes in pitch. Exceedingly well-written.

    Alan


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



  • 11.  RE: Building a Temperament

    Posted 07-13-2017 18:57
    I'm reading through this thread (because I need to do this), and found
    "Modern Piano Tuning and Allied Arts" online:
    https://archive.org/details/modernpianotunin00whit




  • 12.  RE: Building a Temperament

    Registered Piano Technician
    Posted 07-13-2017 19:38
    Thanks Benjamin, I was looking for that!

    There's the final part of this thread posted in the Fine Aural Tuning community, just so you know, but of course feel free to add to this part.

    Sincerely,

    ------------------------------
    Benjamin Sanchez
    Professional Piano Services
    (805)315-8050
    www.professional-piano-services.com
    BenPianoPro@comcast.net
    ------------------------------



  • 13.  RE: Building a Temperament

    Registered Piano Technician
    Posted 05-26-2017 23:33
    Benjamin,
    Enjoy hearing what you hear, and don't get too caught up in the intellectual puzzles.
    The aural tuners I most admire are very patient with the piano, and never seem in a hurry to work out the tuning...it takes time to hear what the piano is doing.
    The fourths have a lot to tell you.

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



  • 14.  RE: Building a Temperament

    Posted 05-27-2017 02:23
    And another thing to bear in mind . . the piano is probably the most difficult instrument to tune. Reason? The string tones decay so fast! You don't get a chance, at the beginning of your tuning career, to change the pitch of a string before . . . it's gone! There's a way to help here and that is by developing your perception of beats between two intervals. Listen to a pipe organ being tuned. The notes just hang on there until fingers are removed from the keys. It's quite possible you can get the flavour of an interval on an electronic organ. Go to that Frequency Chart you have created using the information I gave yesterday - and inspect the harmonics of two notes which, when played together, produce a not too fast beat. Look at the harmonic frequencies of each note and try to determine why this is. This way you can cultivate your ear to perceiving those very quiet harmonics which beat together. I can't think of a better way to train the ear than this. I started off as an Organ Builder's Apprentice some 60+ years ago in the Voicing Dept. I was the one who sat at the keyboard waiting for the Tuner to say "Next!" He would 'lay the bearings' as it was called, by ear.     Michael    UK





  • 15.  RE: Building a Temperament

    Registered Piano Technician
    Posted 05-26-2017 21:46
    There must be dozens of temperament sequences out there. Um... Why are you trying to create a new one?

    Any, and every, temperament sequence will get you to about the same place. Close. And that's all it's supposed to do. The trick in selecting a temperament sequence is to try many and settle on one that works for you. Is it easy to remember? Does it make logical sense to you?

    There's no such thing as a one pass temperament sequence. The skill comes in refining that temperament so you can then spread it out over the rest of the piano. ANY temperament sequence that you identify with will get you to that refinement point. The hard part is finding the right one. (Wink-wink: Creating your own is even harder.)

    The one that works for me is called "Every Which Way" and was developed by Kent Swafford, RPT. Don't know why Kent has allowed it to become hard to find. None of the links in the following page work any more. Even the ones back to his own site. Pity. It's brilliant!

    https://www.scribd.com/doc/2424528/Every-Which-Way-Temperament-Swafford

    When I started learning to tune, the biggest obstacle for me was finding a temperament sequence that I could identify with. Kent's sequence was my answer. I passed my tuning exam with it. I still use it when I stupidly walk out of the house without my ETD. It's easy to remember. It's absolutely logical. For me, it was, and remains, the answer.

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



  • 16.  RE: Building a Temperament

    Posted 05-27-2017 02:19
      |   view attached
    Hi, Geoff, Benjamin,

    Hoping that the system does not totally mangle (or make otherwise
    unavailable) these two attachments:

    - Kent's excellent paper on Temperament; and,
    - Wm. Braid White's classic: "Modern Piano Tuning and Allied Arts".

    I'm not sure how I got a copy of Kent's work, but here is a PDF of same.
    I've checked the links; and, while most of them seem to still work,
    apparently Kent's site is no longer running...very much too bad, he has
    published some really wonderful articles over the years.

    Scribd is a membership based site. There's more there than one can
    easily read in a single lifetime; but, it's great fun to poke around on.

    While I've played with various ETDs off and on for decades, I'm still a
    dinosaur, and prefer Wm. Braid White's instructions in Chapters 4 and 5
    of the attached PDF of his Modern Piano Tuning and Allied Arts. I come
    by the prejudice naturally as I worked with one of Braid White's
    students for a number of years.

    Another good source for learning more is the document published as
    Steinway's World-Wide Technical Reference Guide, the section entitled:
    Tuning and Voicing. I say a good start because, in the 2007 version
    that I have, it includes stuff from both Hamburg and NY in ways which do
    not (to my eye) always clearly differentiate between the differences in
    production; and, the nuances between the two instruments. Further, I've
    run into a number of otherwise very competent technicians who have
    inadvertently become confused when trying to learn from it. (Yes, my
    Hofsammer Mk7 flame suit is on and fully zipped.)

    I hope that this is of some help.

    Kind regards.

    Horace


    On 5/26/2017 6:45 PM, Geoff Sykes via Piano Technicians Guild wrote:
    > Please do not forward this message due to Auto Login.
    >
    > There must be dozens of temperament sequences out there. Um... Why are you trying to create a new one?
    >
    > Any, and every, temperament sequence will get you to about the same place. Close. And that's all it's supposed to do. The trick in selecting a temperament sequence is to try many and settle on one that works for you. Is it easy to remember? Does it make logical sense to you?
    >
    > There's no such thing as a one pass temperament sequence. The skill comes in refining that temperament so you can then spread it out over the rest of the piano. ANY temperament sequence that you identify with will get you to that refinement point. The hard part is finding the right one. (Wink-wink: Creating your own is even harder.)
    >
    > The one that works for me is called "Every Which Way" and was developed by Kent Swafford, RPT. Don't know why Kent has allowed it to become hard to find. None of the links in the following page work any more. Even the ones back to his own site. Pity. It's brilliant!
    >
    > https://www.scribd.com/doc/2424528/Every-Which-Way-Temperament-Swafford
    >
    > When I started learning to tune, the biggest obstacle for me was finding a temperament sequence that I could identify with. Kent's sequence was my answer. I passed my tuning exam with it. I still use it when I stupidly walk out of the house without my ETD. It's easy to remember. It's absolutely logical. For me, it was, and remains, the answer.
    >
    > ------------------------------
    > Geoff Sykes, RPT
    > Los Angeles CA
    > ------------------------------
    > -------------------------------------------
    > Original Message:
    > Sent: 05-25-2017 22:14
    > From: Benjamin Sanchez
    > Subject: Building a Temperament
    >
    > Hello all,
    >
    > I am trying to improve my aural skills, and thought it might be helpful to build my own temperament sequence. How would I go about doing that? Thanks
    >
    > ------------------------------
    > Benjamin Sanchez
    > Professional Piano Services
    > (805)315-8050
    > www.professional-piano-services.com
    > BenPianoPro@comcast.net
    > ------------------------------
    >
    >
    >
    >
    >
    >
    >
    > Reply to Sender : http://my.ptg.org/eGroups/PostReply/?GroupId=43&SenderKey=25d111e5-69df-4509-b862-b712660e51a6&MID=675573&MDATE=756%253c45%253a47%253b&UserKey=3feecf45-4a69-4cff-bbb2-fd6c7eaf0569&sKey=KeyRemoved
    >
    > Reply to Discussion : http://my.ptg.org/eGroups/PostReply/?GroupId=43&MID=675573&MDATE=756%253c45%253a47%253b&UserKey=3feecf45-4a69-4cff-bbb2-fd6c7eaf0569&sKey=KeyRemoved
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    >


    Attachment(s)



  • 17.  RE: Building a Temperament

    Registered Piano Technician
    Posted 05-27-2017 08:45
    Benjamin,

    Susan's dissertation is outstanding. The sequence she described is also essentially what I do regularly. Here though, is a little tidbit recently picked up from the PTG journal:

    7 beats per second happens to be the same speed as the Bee Fees song "Stayin' Alive".  Very handy reference to have. My memory wants to "play" it faster than it was originally (when I youtubed it I found it a little slower than I thought). So...I consciously slow it down slightly less than my memory serves, and it's perfect! (Turns out that they determined the meter of the song to closely match the average human heartbeat).

    Also, it turns out that, if you get that F3-A3 third exactly where the piano wants it, everything else will work out correctly.

    Practice makes almost perfect!

    Pwg

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



  • 18.  RE: Building a Temperament

    Registered Piano Technician
    Posted 05-27-2017 09:06
    For 7bps, I use "From Chicago to New York". It works well for me.

    Paul

    ------------------------------
    Paul T. Williams RPT
    Director of Piano Services
    School of Music
    813 Assembly St
    University of South Carolina
    Columbia, SC 29208
    pwilliams@mozart.sc.edu
    ------------------------------



  • 19.  RE: Building a Temperament

    Registered Piano Technician
    Posted 05-27-2017 09:19
    Michigan Mississippi

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



  • 20.  RE: Building a Temperament

    Registered Piano Technician
    Posted 05-27-2017 09:56
    Benjamin,

    As a follow up:

    As mentioned, learn to hear the 4th...beautiful and useful.

    Since not every piano WANTS 7 bps, Jack Stebbins wrote an article within the last 3 years (somebody find it for me please) on a procedure to identify the exact speed that is needed for the F3A3 3rd on ANY specific piano.

    This procedure is unbelievably MASTERFUL and accurate! I am astounded with how well it works. And it came from one of his NBSS students no less!

    Another benefit to the "down a 3rd, up a 4th, down a 3rd, up a 4th" method is that, once you get it, it is FAST!  Yes, 2-3 minutes to set a great temperament...not bad. Sure beats taking samples, calculating, etc., etc........

    Pwg


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



  • 21.  RE: Building a Temperament

    Registered Piano Technician
    Posted 05-27-2017 12:32
    The article can be found in the December 2014 PT Journal - Page 14.

    Setting a Stack of Major Thirds Using the Stebbins/Sumrell Procedure.

    Paul.

    ------------------------------
    Paul Brown, RPT
    Vice President
    Piano Technicians Guild
    Vancouver, BC Canada
    Email: paulbrn@telus.net
    ------------------------------



  • 22.  RE: Building a Temperament

    Registered Piano Technician
    Posted 05-27-2017 13:36
    A related question for the aural experts (this may help the original poster as well):

    We know that the ration of contiguous thirds is 4:5. However, I'd like to know if there is a similarly dependable ratio when using the 4ths test
    (M3/M6) or the 5ths test (m3/M3).

    For example, in the 4ths test we use a major third below the lower note of the 4th, and that should beat slower than that same test note beating against the upper note of the 4th for a major 6. So I know it's slower, and I know it should be noticeably slower, but how much slower?

    Similarly, a minor 3rd up from the lower note of a 5th should beat faster than the same pitch a major third below the top of the 5th.

    Is there a theoretical ratio that should apply like that of the contiguous thirds? Should the ratio of the fast/slow tests be the same for a 4th as for a 5th?

    I don't think there's anything in Baldassin or Levitan about this.

    ------------------------------
    Scott Cole
    Talent OR
    541-601-9033
    ------------------------------



  • 23.  RE: Building a Temperament

    Registered Piano Technician
    Posted 05-27-2017 22:41
    Scott, there is one little tidbit which only became apparent to me after quite a long time. It was there all along, but I didn't notice it for awhile.

    Thirds and sixths progress .... but if you put a good aural tuning on a decent piano and check, the fourths and fifths do not progress.
    A4 to D5 is not twice the rate of A3 to D4. It probably has something to do with the octave stretch. This might affect the ratios you are looking for.

    ------------------------------
    Susan Kline
    Philomath, Oregon
    ------------------------------



  • 24.  RE: Building a Temperament

    Posted 05-28-2017 05:11
    Dr. Cole,

    There is a misunderstanding of the history and chronology of tuning pianos in their development as keyboard instruments in general that would confuse any PhD attempting to understanding this in a structured way that scholars are familiar with in assembling knowledge about a concrete subject like literature or music.

    Rick Baldassin is behind the times. He appeared with a tuning system that for the most part applies to the modern grand piano and its cast iron string frame, which means he is 150 years too late. There is plenty to disagree with him about, nevertheless. He never actually proposes an octave temperament in On Pitch that I found and did not omit to. He provided computer programmers a sampling method for designing software for tuning pianos by making reference to natural harmonics, which certainly fascinated him more than other string players typically are as a double bass player. Yet he is presented as ahead of the times when somebody should have made the content he made clear over a century ago. I do not know how the strobe tuners like Peterson work, but having followed technicians using them, guess that that strobe tuners are somehow designed to reflect the fundamental sound of the string from termination to termination, i.e., bridge to agraffe, which is much closer to the numbers that Heinrich Hertz arrived at when calculating that a semitone has 100 cents. This system will not work on a modern grand piano with a string frame, due to the potential for tension the frame creates, sympathetic as the ear can be to the fundamental. The further we move away from the fundamental sound of the string due to not only added stiffness in the string that the tension causes, but also the likelihood because of augmenting sound by increasing tension and expanding scale that we will play lightly, exciting the string in addition to tension to vibrate in fractions of the fundamental, i.e., a second, a third, a forth, a fifth, a sixth, a seventh, of string length, and so on, the more we will move toward the harmonic series in an instrument with the range of the piano. Harpsichord tuners claim the opposite of stringed keyboards, i.e., that we are moving toward the fundamental sound of the string when tuning. The dynamic range of the piano also has everything to do with how a string vibrates, a subject on which Baldassin is entirely silent.

    You claim,

    We know that the ration of contiguous thirds is 4:5. However, I'd like to know if there is a similarly dependable ratio when using the 4ths test
    (M3/M6) or the 5ths test (m3/M3). 

    I assume this to be in reference to the major third in creating a one octave temperament. A major third is not required to have a contiguous third. You can have contiguous minor thirds in an octave, which musicians would call a diminished chord. You are correct about the ratio, but the nomenclature is backwards from what Baldassin used. No matter, I've seen computer programs for analysis of what Baldassin called the tonal spectrum use zero for the fundamental, so every number would be one less. It appears in what you go on to inquire about, that

    in the 4ths test we use a major third below the lower note of the 4th, and that should beat slower than that same test note beating against the upper note of the 4th for a major 6. So I know it's slower, and I know it should be noticeably slower, but how much slower?

    Similarly, a minor 3rd up from the lower note of a 5th should beat faster than the same pitch a major third below the top of the 5th.

    Is there a theoretical ratio that should apply like that of the contiguous thirds? Should the ratio of the fast/slow tests be the same for a 4th as for a 5th?

    you are dissatisfied with a method for expanding and contracting intervals that never seemed precise to me as it should be either, but has prevailed in tuning theory to this day. It is difficult to find fault in a theory of tuning based on octaves if we understand piano tuning as a business, theory designed to implement a system for computer programming that can only make one consideration at a time, if it satisfies clients, but it can be done, particularly if we understand we must make more than one consideration at a time, like pianists do when playing more than one note at a time. This goes beyond tuning and is a voicing problem as well. Baldassin made reference to ratios of thirds and sixths for the purpose of assimilating his system for computer programming by sampling the vibration of a piano string with what most aural tuners do for the most part, make fifths and fourths sound good enough, and make the vibrations per second of thirds increase as you ascend the piano. However, his theory for sampling piano strings did something different entirely and does not make reference to thirds at all, outside of what a third check would reveal in the expansion of an octave. Baldassin seemed as unconcerned about precision with fourths and fifths as many aural tuners, but that never aligned with his general theory for me in understanding the role of natural harmonics in tuning perfect intervals. It is a contradiction in argument and theory. It remains to be seen whether it follows in revealing such partial sequence in thirds that by programming a device based on partial sequence of octaves that are part of the same system of harmonics in a piano string, that the difference is negligible when using software programmed this way, between the partials of a 3rd and an octave, more so, the partials of other perfect intervals in equal temperament. It is important to keep in mind when determining how to execute a one octave temperament to tune the rest of the piano to that an octave has only one octave, and that it follows, that thirds, fourths, fifths, and sixths therefore, are more important than the octave in that there are more of them in an octave temperament. Baldassin did not try to see in microcosm, and in general neither do ETD users. Yet admittedly, his work was overdue.

    More to your question, though I am not sure I have the latest edition of On Pitch, 1994, on the fourth, Baldassin only recognized the 4:3 partial, which applies to the test you mentioned. There is also the 8:6 partial of the fourth, a check for which is the minor 6th and minor 3rd above the fourth, and the 12:9 partial of the fourth, check for which is the major 6th and major 3rd above the fourth.

    On the fifth, there is a check below the fifth for the 3:2 partial, a M6 and M10. What you proffered is the 6:4 check. Then there is a 9:6 check also flanked by the fifth, M3 above the root, and a m3 below the fifth. There is also a 12:8 fifth check, a m6 and a m10 above the fifth. Baldassin only goes far as 3:2 and 6:4 with the fifth.

    This is by no means an exhaustive lists of checks for fourths and fifths, but do provide some guidance in determining just how much to "Expand" a fourth and "Contract" a fifth, terms I find entirely unsatisfying, as that "Contracting" a fifth frequently means nothing different than tuning an octave narrow of 1200 cents, or 2:1. A lot of that is just for tuning hillbilly and cowboy instruments like the guitar. You'd be lucky if it had 12 strings total. Baldassin definitely has helped a few "tuners" get past their first rodeo, I will admit. Or their first ETD.

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    Benjamin Sloane
    Cincinnati OH
    513-257-8480
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  • 25.  RE: Building a Temperament

    Registered Piano Technician
    Posted 05-27-2017 15:54
    The theme song for Final Jeopardy works well for me.

    A disco music producer once explained to me that the heartbeat rate relates quite closely to the frequency at which the mass of an average human body can comfortably bounce up and down in synchronous rhythm with gravity. In other words, to dance at the natural fundamental 1st partial frequency of your bouncing body requires a lot less energy when the tempo of the music is in unison with your body's natural 1st partial bounce frequency. That frequency just happens to be very close to a normal heartbeat. Slower and faster tempo's require more energy for the dancer to maintain.

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    Geoff Sykes, RPT
    Los Angeles CA
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  • 26.  RE: Building a Temperament

    Registered Piano Technician
    Posted 05-27-2017 20:06
    Hello Benjamin,

    I commend you for wanting to improve your aural tuning skills. I've been an aural tuner for 45 plus years and I still believe it's important for me to work on my aural tuning skills. Every time I tune a piano I view it as a learning experience. 

    I absolutely believe it would be helpful to build your own temperament sequence. I would start by encouraging you to think about 'Nature's' scale; the harmonic series. For example, take the first four notes of the harmonic series; four notes, but only two letter names. If for instance you began with the note C2, the first four notes are; C2, C3, G3, and C4. C2, C3 and C4 are all the same note, just in a different register. Therefore, the first and strongest harmonic interval of 'nature's' scale is the fifth. The next interval is the fourth (in our example that would be G3/C4). And notice that, in 'nature's scale', an octave is defined by an adjacent fifth and fourth. So, having a predetermined 'stretch' number in mind for an octave may not be the best musical decision.  

    So in developing your own temperament sequence, think about the prominence the fifth might receive. If you think about fifths in a musical way, the 'circle of fifths' might just come to mind. If you looked at an illustration of this 'circle of fifths', you'll notice the relationship between fifths and thirds. Then you might think about the size of 'circle of fifths'. The bigger the circle, the more stretch in the octave and the wider the fifths. The wider the fifths, the faster the thirds. 

    So, having a temperament sequence that you make your own is a big deal. But understanding interval relationships is even a bigger deal. It allows you to develop your own sequence and quickly adapt to whatever circumstances the piano you're tuning presents. I would suggest that you even think beyond a temperament sequence and develop a 'tuning stradegy' for the whole piano. And remember, 'it's all about the music". As has been stated; 'tuning is as much a question for the arts and humanities as it is for science.

    I appreciate your desire to improve your aural tuning skills and wanting to develop your own sequence. It sets a wonderful example for our profession. 

    Best,
    Rick

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    Rick Butler
    Bowie MD
    240 396 7480
    RichardRichardRichardRichardRichard
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  • 27.  RE: Building a Temperament

    Registered Piano Technician
    Posted 05-27-2017 22:51
    I never used mnemonic one-potato-two-potato kinds of tricks to remember the F-A rate. I just remember the rate. If I were to guess it wrong the stacked thirds dividing F3-F4 wouldn't work well -- besides, some pianos don't want quite the same rate as others.

    I like simplicity. I don't like fiddling around working out coincident partials, either. Sure, the data is there, and the machines make it easy to access -- but is it useful? If partials coincide or don't coincide, I'll hear it in the whole sound. Each piano has a different profile as to which partials sound more prominent -- I'll hear that in the whole sound, too, without having to make allowances for it. Virgil Smith took this much further than I have. The one seminar I got to hear him do, he had curls in all the unisons, but he got a very musical result -- and a differently musical result than conventional tuners. Too bad I heard that only once, and didn't get to play and listen to the piano after he was done.

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    Susan Kline
    Philomath, Oregon
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  • 28.  RE: Building a Temperament