ETD offsets for the Jencka temperament

For those who are interested, here are the offsets from Equal temperament for ‘programming’ ETDs with the Jencka temperament (alternative interpretation of the Bach graphic than the Lehman temperament). They come courtesy of Rafael Melo (‘Gadzar’ in PW).

A 0
A# 5.87
B 0
C 5.87
C# 3.91
D 1.96
D# 5.21
E -1.96
F 7.82
F# 1.96
G 3.91
G# 4.56

Notice that the F is almost 8 cents (almost 1/16th tone) sharper than an Equal F. Ron Koval says that if you don’t require A=440 exactly then the temperament can be ‘balanced’ by dropping all the offsets above by 3:

A -3
A# 2.87
B -3
C 2.87
C# 0.91
D -2.96
D# 2.21
E -4.96
F 4.82
F# -2.96
G 0.91
G# 1.56

This means that all notes are within 5 cents of Equal.

Rafael is somewhat skeptical of the Jencka interpretation, wondering if back in the 1700’s that anybody could have accurately tuned 1/18th of a Pythagorean Comma.


18 responses

  1. You don’t actually ever need to hear the 1/18th comma, you simply set c# so that c# to f# beats very slowly like c# to g#. The basis of the temperament is just 1/6th comma, and one of those 6ths is spread over f# to c# to g#. Nothing hard about it at all.

  2. Hi Digitus08,

    Got into your blog by chance when surfing to find out more about buying grand pianos. Unlike you, I don’t have a budget for a Sauter which I would love to give my kids. We did try a Sauter upright when Alvin was still with Galleria but was not able to comply with the strict rule of totally airconed room. And horrors! No heater.

    In the end we did settle for an upright grand Kawai XO-8 which have served us well. Second hand. The tone is rich and the action is good for an upright. A flaw is that the XO-8 does not have a sostenuto unlike the later K8. Was wondering why you settled for a Kawai over a Yamaha in your purchase?

    My eldest girl is doing Dip and teacher hinted for us to get a grand. My second child is doing Gd 5 this year so it might be good to look into a grand. An Omega or Delta is definitely way beyond the budget. My neighbours would not appreciate the roar as mine will have to sit in an open concept living room (thankfully airconed) in a part of Singapore that is wettest (ie near a nature reserve). It will have to have heaters, unfortunately.

    I am looking at a second hand grand Yamaha C2/C3 or even a Kawai RX. Any view on the merits and demerits of this range.


    PS: Hope your hand is healing well.

    • Hi ghyap,

      Thanks for visiting my blog and for writing.

      I selected the Kawai K-8 over the equivalent Yamaha YUS7 simply because I liked the K8’s tone and action better. The K-8’s having a sostenuto pedal did play a small part in the decision. It shouldn’t have at all as it turns out. Very few piano works in the piano repertoire require its use, and certainly not the pieces that student pianists play.

      Getting a grand would definitely be beneficial to your daughter. The grand’s action is fundamentally different from that of an upright piano, and affords a far greater degree of tonal control than your typical run-of-the-mill upright can give you.

      The feel of the action between an upright and a grand is also subtly different. But the difference is felt the most when the soft pedal (also known as the una corda pedal) is depressed. In the better uprights the reduction in volume is achieved by using a half-blow action, where the entire action is moved closer to the strings so that the throw distance of the hammers is reduced by approximately half. This changes the feel of the action. The sales rep will tell you that you can’t tell the difference but I assure you that the advanced pianist can.

      In a grand piano, depressing the soft pedal shifts the entire action (including the keys of course) fractionally to the right so that the hammers that strike 3 strings now strike 2 or 2.5 strings, and the hammers that strike 2 strings now strike 1 string. This does not change the feel of the action at all.

      There are other differences, such the grand piano allows you to play repeated notes very quickly. This is because the key needs to come up only about half-way before the action is reset and ready to the starting position. So you can play the note again as soon as the key rises to that half-way point. In an upright piano, the key has to return completely to its original position before the note can be played again. Some upright pianos boast a quick repetition action, but its just just a gimmick.

      Incidentally, I don’t know where you heard the term ‘upright grand’ from, but there is no such thing! 🙂 Piano sales reps like to make their tall models seem more impressive by referring to them as upright grands but it is just plain wrong. The only similarity between an upright piano and and grand piano are that the sounds are made by striking steel and copper-wound steel strings tensioned across a cast iron harp.

      As for which brand of second-hand to get, that is really a matter of personal taste. Personally I would go for a Kawai RX, again because I prefer the Kawai tone. The condition of the piano, particularly the action, pin block and strings are all important. Unfortunately there aren’t many second-hand dealers here in Singapore who will allow you to bring in your own piano technician to evaluate the instrument before buying. But you can try asking though. Better yet you can buy from a second-hand dealer that is also an expert piano restorer and technician.

      Having said all that, while a grand piano would be nice to have, it is not absolutely essential for the diploma. Many many students prepare on upright pianos and get great results for the diploma.

      Hope this helps!

  3. Digitus08,

    Thanks for taking the time to write an insightful piece. It definitely help to keep me focus on what is important in the buying process.

    Will let you know if I am successful in getting one.


    • You are very welcome!

      And thanks for asking about my hand. The wound has healed nicely. I can barely see where the incision was made! I also have full mobility and stretch.

      My guess is that your home is near the central catchment area. Regardless of that you might want to consider leaving your living room’s doors and windows closed and your aircon on. But not necessarily all the time. What I do is set my aircons to ‘dehumidify’ mode (looks like a drop of water). All aircons in dehumidify mode are programmed to dry the air to 60% RH as measured by the humidity sensors in the fancoil units. My fancoils units are near the ceiling and since my ceilings are quite high (3 meters) the return air is warmer and more damp than the air lower down. So the room RH usually ends up around 45-50%. That’s fine.

      When I retire upstairs for the evening or go out I close the piano and cover it with a proper lightweight cover. The RH in the piano slowly rises to 60-70%. When I come down or come home I turn on the aircon. Not ideal but better than exposing the piano to the outside air. Oh, when I moved to this property in August last year I replaced the two single-split aircons in my living room with the latest Mitsubishi models. They have a special low fanspeed ‘silent’ mode which is really quiet.

      Also, I set the aircons to ‘dehumidify’ mode because it always takes the indoor temperature to 2-3 degrees below outside temperature. You might think that living room will be stuffy. But it isn’t, because the low humidity makes it very comfortable.

    • Ah, I forgot to mention that Kawai uses a special plastic for parts of it’s action. Ignore disparaging remarks about how these plastic parts are cheap and inferior to an all-wood action. The plastic parts have lower mass than than the equivalent wooden parts, are more rigid, and are of course completely impervious to moisture.

      This is not to say that you can be less careful with air-conditioning. You still have to take care of the soundboard and the keys. Yes the keys. Prolonged exposure to high RH will cause the keys to swell and rub up against each other.

      • Digitus08,

        Took my kids out on “piano shopping the whole day after church. Went to see a 20 year old Kawai GE-1 which has the great Kawai sound. Owner, a piano tuner, said it came from the hotel lounge so there was some wear on casework and a small burnt mark on the first key. Strings looks it normal age and inside was a bit dusty. The felt looks in need of replacement. Asking for $8000.

        Then we checked out an antique Challen (old would probably be closer to describe it). My kids berated me for wasting time. It was to satisfy my curiosity. So there.

        After lunch, we saw a Yamaha G2E about 19 years old. This was so much better. The kids loved it and was having a great time on it. Unlike the bright Yamaha, this was much warmer. The inside of the piano is definitely better than the Kawai. The casework is in good condition. Only nagging feeling was the wear on the felt above the keys. It definitely needs replacing.

        The sales guy/owner of shop was telling me stories of another buyer being interested and I felt he was pressuring me to make an offer; which I did not. At $11,000 I felt it was a tad high. Any opinion on this?

        Then we drove to Millenia Walk to try new Kawais: GM, RXs and SKs as well. My kids fell in love with the SKII and RX2. They were even invited to try the Hasslers and Bluthner.

        Next was Yamaha at Plaza Singapura. Kids tried the whole range from GC to C7. My kids liked the C2 over the C3. C2 had a clearer tone than C3 though lost out on bass.

        The fallout from this little experiment was that my kids said, “Now our upright sounds pathetic”. They are in love with a grand. I must keep them away from Sauter otherwise we might have to sell the dog we don’t own. He, he…..

        Verdict: we are still mulling over this even at 1.03 in the morning. Well at least I am.
        Now I must get rid of the tunes my kids were playing the whole day testing those pianos.

  4. I re-read what I wrote about control of RH. I want to make it clear that I never open the doors and windows of my living room for prolonged periods. Even the doors to the adjoining kitchen and bathroom (which always have their windows open to the outside) are kept closed all the time.

    I forgot to mention that I also have Sharp air-cleaners running in every room and space in my home. They help keep the dust level under control (plus cat fur and cat dander). Equally importantly they also perform humidification. Yes, you got that right–humidification. You see, when the humification function is enabled these units will attempt to add moisture to the air as it passes through the air filters, until the incoming air has a RH of about 60%. So I use these to ameliorate the over-drying effects of the aircons.

    My piano just loves it!

    If you are looking at second-hand pianos please do yourself a favour and drop in to Emmanuel & Sons. You can reach the proprietor Mr Kwan on his mobile at 91000111. The fixed line might work–61000111–but also may not because he moved the location of his shop a few months ago, and I haven’t visited him at the new place yet. He deals mostly in second-hand pianos, and some truly magnificent old pianos pass through his hands from time to time. Mr Kwan is also a piano restorer, and a trained musician himself.

    But if you can swing the money for a new grand piano, then the SK-2 should be your first choice, followed by the RX-2. Obviously if you can get a larger instrument then do so.

    Heheh…there is no danger of your children getting near a good Sauter. The current dealer’s shop closed some time ago (it was at the Victoria Concert Hall) and he is having great difficulty finding a shop with a reasonable rent in the CBD area.

  5. Hi Digitus08,

    After reading your thread on PW about getting a lemon from Kawai on your first K8, this is what I fear most about buying new. With old, you get what you see like my Kawai XO8. I had only the serial number to go by to check on the age which was under 10yrs. The sound was great and I bought it five years ago.

    When I read the threads on PW on buying piano in Singapore, I felt I have been blessed with a good one as I did not even get a tech to look at it. The thought that the sound board number will not match the metal heart in some recon pianos was something new to me. I do hope mine match.

    So my journey to a grand resumes unless the price for new can drop drastically. Tan gu gu as some might say. Well the adventure continues unless I tire like you did and succumb to the gloss of new.:)

    • To the Kawai agent’s credit they did acknowledge that there was a problem with the action, and that they couldn’t solve it. They then replaced the K-8 with a unit of my choice. So that’s the advantage of getting a new piano.

      Yes sound boards can be replaced. But it is usually avoided unless it is severely cracked or has lost its crown.

      OK, so looks like a new quality grand is out of the question for you, budget-wise. Then I really suggest that you visit Mr Kwan and talk to him. He may already have something in his stock that you can have, or else he can let you know when something good comes in. There are one or two other companies that do piano restoration. They might be pretty good, but I am most comfortable with Mr Kwan. Your mileage may vary.

  6. Digitus08,

    On the upkeep of your Sauter baby, it blows my mind. I believe you are giving it more care than I did when my kids were in their baby stages. I would be unable to afford that kind of care to a second hand much more a new grand.

    I failed to mention that my living room has a 15-foot high ceiling and the open concept kitchen is adjacent to it. At best I keep my upright at the further and coolest/driest corner of living room and away from sunlight and courtyard. It has two heaters instead of one. Tuner put in one at first but he warned that I might need another as he feels the air is humid in the central catchment area (how perceptive of you to deduce this from the little info I gave). We did when we spotted two spots on the hammers in one of the tuning. So another was added above the keys.

    This is the other reason why I am inclined towards second hand. I know I won’t be able to give the kind of tender loving care you give to a new grand. Not so ‘sum tong’ when it ages in the long run.

    A Sauter is way to go though….sigh.

  7. Correction: I believe you are giving it more care of the piano than I did with my kids when they were in their baby stages. I would be unable to afford that kind of care to a second hand what more a new grand.:)

    • Many people are surprised at how robust pianos are. Pay a visit to Mr Kwan. Describe your home environment to him and ask him for advice on how to look after your piano. You might be surprised at what he says, especially after reading about the lengths I go to. Its just me. The Sauter was the fulfillment of a dream that I never thought would ever happen. It is therefore of special significance to me.

  8. Digitus08,

    Saw a C3 at Emmanuel. 11 years old, good condition. The one thing that bothers me is the Disklavier attached which adds to the cost. My kids do not need it and also it is an older model which makes it almost useless in the electronic market.

    Would the disklavier affect the acoustics of the piano? And would you buy one with?

    The piano is in tip top condition, hardly played but the sound does not wow me. Maybe I need to give it another go to see if that changes?


  9. The Disklavier optical sensors and electromechanical elements do not interfere with the action at all. Neither do they affect the tone of the piano. And yes I would buy one with it even if I never use the Disklavier.

    At the risk of offending Yamaha fans, I’d say that your not being excited by the sound is a pretty normal reaction to Yamaha grands. Having said that, I should also say that I have played a couple of good Yamaha grands over the years. They include C5 in the Yamaha showroom at Plaza Singapura an old but magnificent C7 in Mr Kwan’s workshop. There was also that wonderful CFIIIS at the Musikmesse in Frankfurt….

    If you are able to tell Mr Kwan what you don’t like about the tone of that C3 he might be able to tweak it a bit. By all means go and spend more time on the C3. Keep in mind that the acoustics in the shop aren’t the same as that in your living room. But don’t wait too long to make up your mind. Good instruments don’t stay in Mr Kwan’s shop very long!

  10. Digitus08,

    Could you enlighten me on the Kawai Millenium III vs the previous Quick Reaction ABS Styran? I believe you have tried the old and new.

    Is it a marketing gimmick that just wants me to pay more?

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