Piano World Home Page Forums Our Most Popular Forums Piano Tuner-Technicians Forum Tuning - Mathematical or Musical

If you answer "both", may a pox be upon you and your house (not really).

Rather than hijack threads already in progress on related issues, I'd like to know if you worry about mathematical esoterica as you tune, or are you listening for musical sound.

For me, theory doesn't enter my everyday work. I listen to the sound of the instrument and work with the tuning to make the instrument sound musically pleasant. That's it. Hardly a number or formula goes flitting through my head.

I would agree with that. At the end of the day, the end result requires that the instrument sounds pleasant to the ear.

I would agree too David. I tune by remote. A tuning on say, a Steinway may not sound the same on a Baldwin. On most Baldwin verticals in particular, there seems to be a lot more give and take than in many other brands to get the over all musical sound and tuning correct while on some other brands, it all just sort of falls into place. I don't think much while tuning. In fact, half of the time, I'm day dreaming, I'm so used to just doing it. When I check the final outcome, if I don't like a third for example, I may decided to compromise a fifth or fourth slightly to make the 3rd or maybe an octave sound just a wee bit better.

Just an example.

David:

Well, sometimes I think about the math a little, but really I try to balance three different types of tuning; harmonic, melodic and musical. To do so I do think about the theory, but without numbers.

Like a typical spinet with some wound strings in the temperament octave. I know that the lowest M3 in the unwound section will beat at the same speed or slower than the next M3 down which will have one wound and one unwound string. And how much slower is an indication of the jump in iH. Or while tuning octaves in the treble I will listen to the 12ths and 15ths (harmonic tuning) and decide if I want the octaves wider or not depending also on how the note sounds with its major chord being played in the temperament octave (melodic tuning). Then in the bass the quality of the strings will determine what I may try there (musical tuning).

So, I don’t think about math, as far as numbers (how would I?) but I do think about tuning theory and not just make things “sound nice.” It is a conscious decision on how it happens.

This brings up a question I've had--do tuners have characteristic tunings, so that their tunings are personally recognizable, or are they able to use different strategies for different results? I don't mean dealing with Balwin vs Steinway quirks, but rather whether if I said, for instance, that I want my piano to be a certain way (shimmery, smooth, whatever), IF we could agree on the terminology (I realize that communication is a huge problem here) could it be done by one person, or would I need to find the tuner who naturally did what I wanted? Or another way to put it, what level of awareness and intent do tuners bring to their tuning? I am suspecting that this related to how skilled they are?

I realize this is a loaded question with a lot of variables--I'm curious about what people will say about the subject. The reason I ask is because I'm able to do this with adjusting a violin, and people have definite preferences about the amount of texture they want in a violin sound, which in violins has a lot to do with something I'd call inharmonicity, and I have noticed the same type of variability in pianos, even in recordings by performers who'd you'd assume would have their piano tuned "right", whatever that means.

I don't think about math for the temperament or octaves but I see different images in my mind that are hard to describe. My minds way of accomplishing the task. When I'm listening to beats I am not thinking about the numbers but I am thinking about evenness and comparing speeds and so on.

I do think about physics and math while adjusting pitch. Over pulling or under pulling by what I consider to be the correct
amount for that piano at that time and how the piano is going to settle. After that it is all about the sound and the stability. If I calculated mathematically every little thing that I did during a tuning it would not be a fun experience for me at all.

On Monday, I tuned a Yamaha C7 immediately after tuning a Hamilton Console. The only number they had in common was A-440...

For me, as a novice tuner, while it is good to attempt to understand the math behind achieving equal beats or increasing beat rates up the piano's register, it is the relationship of the notes to one another, sympathetic vibrations, resonances, proper stretch, etc., based on the piano's ability to respond to a tuning.

Regardless, the best temperament in the world is useless without perfect unisons and proper pin-setting technique.

Also, to me, voicing and regulating is fundamental to how a string vibrates and how, ultimately, the piano sounds, rings, sings, how musical it is, etc. So I take that into account as an invaluable skill I need to develop to get an instrument to sound its best as I make my way through the tuning morass.

Glen

I was getting a BA and MA in mathematics while I was learning about piano tuning. At the same time, I was learning that not everything is well described by mathematics.

The way I understand mathematics is different from most people, I understand that it is more than just numbers, and that the thorniest problems come when you try to describe a problem mathematically and expect the physics to be as perfect as the math can be.

I have enough understanding of mathematics to know when people around here do not understand what they are talking about, and enough understanding of human nature to know that it is a waste of time to convince them that they do not know what they are talking about.

Inlanding,

what a nice post. As a novice, you sound very ready (maybe I should say set up?).

Two things: soon or later you'll see that tuning is not a "morass", only it takes time to select what you have to listen to, especially once you know what to go for and how (in aural tuning).

You say:..."it is the relationship...based on the piano's ability to respond to a tuning."...

There, if I were you I'd concentrate on my/your ability...any piano can find its best, it depends on you.

David Jenson,

..."I'd like to know if you worry about mathematical esoterica"...

If you had to pay for a bill, I'm sure you would not call that "esoterica"... In my case, I wanted to translate my tuning evidencies and I had to go back to my math studies, no choise.

..."theory doesn't enter my everyday work"...

In my opinion that depends on your attitude. I do not think theory or maths as necessary for good tuning.

One question though: how is it that you can have a warm bath? Maybe this is esoterica too. What do you think is behind your chance to "listen to the sound of the instrument"?

Byronje3, you write:..."I see different images in my mind that are hard to describe. My minds way of accomplishing the task. When I'm listening to beats I am not thinking about the numbers but I am thinking about evenness and comparing speeds and so on."...

That's nice, that happens to me too.

a.c.

.

I tune by machine and ear together for the majority of my daily tuning work. Lately I've been enjoying tuning the bass aurally only. I've settled on a series of checks and a routine that has become almost musical. After I have the temperament and octaves and unisons completed from about F3 up. I establish a rhythm going down into the bass checking with a tenth followed by the octave followed by the fifth with the bottom note and finally its unison and then repeat going down chromatically. I switch to seventeenths as I approach A2 usually. Occasionally I need to do a 6:3 test. I know this is basic stuff but I've just discovered that it can be almost musical when a certain rhythm is established along with the order of checks chosen. I've never thought of tuning as a musical experience before.

The reason I mention it is because the topic of the thread is musical vs mathematical tuning.

I don't count beats much anymore while tuning. Maybe once in a while I guess during a concert tuning I catch myself. I remember watching my dad moving his mouth in a "waaa waaa waaa" fashion matching so many beats per second. I catch myself doing that without thinking too and have to watch myself when customers are around. They probably think I'm talking to myself! Which I would NEVER DO!

Of course it is possible to have a warm bath and not know the inner workings of a hot water heater. To have to analyze every pipe in the walls of the house, the molecular structure of the water itself, what ratio of hot and cold water I'm mixing into the tub.......that would be esoterica and it would drive anyone nuts.

I appreciate this thread and your comments to the most, particularly Inlanding, seem to have exactly the good state of mind to involve in piano prep. (musician's service)

When it comes to my way of tuning, it have changed more than once,I dont think too much of the maths behind it, in fact , as I am lazy I rely on my hearing (when i used the Verituner I was relying on it, with slight corrections from me but the global resonance was generally very quiet with the tuning "out of the box", at 1/3 bps on 2:4 temperament)

Today I mostly concentrate on having a piano well regulated and hammers/strings in condition so sensations are good to begin with. yesterday I had to tune a vertical piano I never have seen before, it have been, tuned 4 months ago and did not need a PR. I took 1.5 hour and a screw driver, some 80 grit, a wooden block, and I made basic work to have a pleasant tone to tune, I needle a little before the tuning too. The visit took 2.5 hours.

I corrected the temperament that had slept a little, tuned the basses with thirds and octaves as references, the medium and top region with octave, doubles an thirds, pedal engaged.
3 notes had to be corrected in the end.

But I rely on my hearing (so called "absolute pitch...") and my tactile sensations only.

And I don't worry if one interval is a tad faster or whatever small uneveness as long as no major/minor chord is bad sounding

More interesting is to have a nice coloured tone and a pleasing touch.

On the other hand I appreciate the logical and theory, and I like to have a clear figure of what is going on (for action setup and repair, voicing, strings replacement, and eventually tuning).
I like to the most the very pure resonance of the well naturally "stretched" tunings, but will not prefer it to a good harmonic behavior.
I have listened to numerous records and concerts, and we know how to tune pianos, if not, anyway we are used to a way that satisfy my ears and the one of the musicians enough, practicable, easy to miss but not so difficult to provide in the end.

Yes when tuning became musical you tune better , I believe The only problem is the one of the size of our hands, hence good use of tonal pedal can be useful, and why I compare eventually the center of the keyboard with the extremes with pedal engaged, minor/major chord in the mediums show you well where to tune the treble or bass. (Verituner get absolutely crazy when you do so, BTW thats the main problems with EDT, you cant use checks and the EDT at the same time so you are obliged to rely on the EDT more than you wish !)

The same apply with the way you play the notes, no need to hammer those poor keys; only move the strings segment in a pleasing way suffice. You always can check it pedal engaged in the end, or apply a good hard but very short karate note for security, even that one can be somehow "musical" !

I find that it helps because it gives some "distance to your hearing" (may be misleading too, we need the 2 hearing most probably, but with time, the analytic one is a reflex)

When a tuner tunes the temperament octave, does he/she tune it according to a mathematically equal temperament (taking into account the necessary stretch), or do IH considerations and lining up the partials affect the placement of each note within the octave, such that the octave itself ends up being a compromise???

If the latter, then those who tune the temperament octave making each note mathematically equadistant from every other note in the octave are making a mistake??

I was feeling very confident in my first day as a novice. Many years of compliments about my musicality...ten years of tuning my guitar...then tuning a piano would have been a walk. That afternoon I happened to get my lesson.

I tuned 12 notes but no way I could get the sound I wanted. I knew nothing about theory, actually another novice had told me there and then...pure octaves, wide 4ths, narrow 5ths, progressive 3ds. I could not care less about theory in that awkward situation, I was wanting to get the piano sound right, I wanted to get out of a nightmare.

Later I calmed down, then I could understand that beats were stronger than my ear, that beats could hurt or satisfy my musical ear, that maybe the all question was to be played on a rate/rhythmic ground. Only recently I got to know that the word "rhythm" comes from ρυθμό, "number" derives from Αριθμός.
ρυθμό, Αριθμός, slightly different words, very close phonetics.

a.c.

.

Yea, I found that amusing myself. I think something is getting lost in translation so-to-speak. You filled in the gaps in the thread of logic and came to the obvious conclusion. Over-thinking things makes one nuts!

Just stick your finger in the water to see if the temperature is to your liking!

Theory helps you get your bearings as a beginning tuner and helps to make some sense of the process. In my experience at least, you eventually have to stop crunching the numbers and start listening to what you are doing. That's when you really start getting into the artistry of tuning.

A mathematically equidistant temp. octave is a mistake if it sounds wrong. (and yes, I know the theory)

Why does everything have to come down to being mathematical anyway with tuning? We count beats, memorize how many beats are in a fifth, fourth, memorize what a good sounding third or 10th is and go from there. In the years of old, I used my 2nd hand watch as a counter for accuracy. Now, I no longer need that vice. I just know, it's either right, or it's wrong and if it's wrong, it is either the piano, or something I did wrong or something that changed in the temperament which happens to everyone sometimes. That's when we go through it, double check it, fix it and move on listening.

If you have done some studying you should have seen a diagram of a Railsback curve. It shows the cents deviation from theoretical ET that a piano is tuned at. If in any part of a piano each note is “mathematically equidistant” then that part of the Railsback curve would be a straight line and yes that would be a mistake and aural checks should be able to point out the mistakes.

The goal when tuning an aural temperament is to have all intervals (or at least the 3rds and 6ths) have progressive beatrates. Of course an aural tuner can have no idea what frequency ratio one note is from another and does not need to to set the temperament. The effects of iH will cause the tuner to tune frequencies that will not be “mathematical equidistant” because the partial matches are used, not frequencies.

As far as setting the octave width, it seems that many choose the same partial matches to define the octave regardless of the piano. I prefer to listen to the fourths and fifths within the octave to determine the octave width. Then the beatrate of fourths and especially the fifths can be used as a reference for tuning the rest of the temperament.