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Excellent challenge, Ron. I am drooling, but not holding my breath. Hopefully I won't have to hold my nose.

Ron,

I appreciate very much your positive intentions. I'm travelling, this is why I'm taking some time to reply.

..."list the tuning targets for a common piano model"...

Could you explain what you mean?

..."we can discuss the partials to list as well as the model of piano that we all have available."...

May I ask you to articulate your idea, and we could think of all the necessary comparesons.

..."Then we can look at how that compares to other methods of calcualting a tuning as well as standard aural approches and see the results..."...

Could you go deeper on this, by saying what you mean with "methods of calculating a tuning" and "standard aural approaches"? These of yours may be the starting points indeed.

Regards, a.c.

.

Hi Alfredo

While the math is important and interesting to some, I'm interested in the final product (tuning).

To measure a tuning, for example, in the US, we have the registered piano technician's exam. From A0 - B3, each note is measured at the 4th partial level against a machine to list an offset from a pitch standard. Likewise, from C4 -B4 the 2nd partial is measured. From C5 -C8, the 1st partial is measured. Any partial could be chosen, these are just the standards here.

So we could all compare tunings on a similar piano, we would agree on a piano. Steinway B, Yamaha P22 etc.. - doesn't matter, as long as we use the same model. Each individual piano may have it's own unique signature tuning, but those of the same model usually will end up with similar stretches if the same tuning approach is used.

For those of us using multiple machines over the years, we are accustomed to choosing alternate stretches. RCT has built in octave tuning styles from 1-9. These use the inharmonicity data collected during the measuring phase to calculate the width of the octaves in different regions of the piano. Further input through the custom equalizer function allows for more control from the technician. Tunelab and Verituner also have custom settings to force the machine to use a different method to calculate a tuning - usually choosing a different partial match, a blend of partial matches as well as any additional or lessening of stretch. I haven't used the SAT much, but understand that the double octave beat control also allows for technician input to create a different tuning style.

Standard aural approaches refers again to the registered piano technician's exam which is a standardized tuning approach for testing purposes.

Even without full tuning data, just 1 or two notes per octaves allows the visualization of stretch parameters. We might find out that your approach produces the same overall tuning stretch as RCT with OTS7, for example. (just a random example.)

Ron Koval
chicagoland

Ron, do you know what the default stretch for the A3-A4 octave on the RCT would be? How about the Verituner? Is it a 4:2 octave + 1 cent, the way the SAT FAC program works? Adding 1 cent to a 4:2 octave usually accomplishes the compromise between a 4:2 and 6:3 octave. Enquiring minds want to know, lol.

Hi Bill

Default for the Average style in the Verituner A3-A4 octave is a 4:2 octave, .32 beats/sec wide of pure. I think I have the RCT info at work...

Ron Koval
chicagoland

I am unsure those softwares know how to build a temperament with anything else than 12 or 13 notes , for what I know. I asked when wanting to have a pure fifth tuning)

May be Tunelab ( could you confirm Mr Scott please ?)

Seem to me that there is always a "temperament approach" (if not none of the HT could be used)
Even Verituner which is based on a multi partial analysis and weighting have a different process to compute the temperament than to expand the tuning in the piano.

Making a temperament and use octaves partial match to reproduce it within the scale is the logical all EDT may strive for, it seem evident that they try to act as most tuners do.

Asking them to use a partial relation to compute the temperament is not possible (pure 5Th, pure 12Th, semi pure 12th-15th, etc)


Comparing tunings on similar pianos may be possible without much trouble, assuming the same music samples is played on the pianos and they are in the same room.

Voicing and sound ability of the pianos have not much to do in that, from a musical point of view ( I believe).

So, we may only have to agree on the use of one precise ETD and one precise piano make and model. Correct?

I should tune as I normally do, measure the frequencies and list the offset from our ETD's pitch standard. Would this be correct?

Kamin, you write:..."I am unsure those softwares know how to build a temperament with anything else than 12 or 13 notes , for what I know. I asked when wanting to have a pure fifth tuning)

May be Tunelab ( could you confirm Mr Scott please ?)"...

I wonder too.

Regards, a.c.

.

Ron,

This is the first I have heard that a 4:2 octave sounds anything but "pure". Granted, .32 beats per second is a very slow beat but any 4:2 octave I ever tuned (by direct interval) sounded "pure" to me.

This does, however bring a little light to some of the math that Tooner has done. A 4:2 octave is, after all, wider than a 2:1. As I always thought of them, the 4:2 octave was just on the "edge" of creating an audible beat while a 2:1 is solidly "pure". .32 beats per second can still qualify (I suppose) as being on the edge since you would only hear a very slow beat that occurs over 3 full seconds. That would be difficult to perceive but I find it hard to believe that it could even be that much.

The instructions I give in the ET via Marpurg sequence tell the tuner to approach the octave from the wide side, narrowing the octave just to the point where the beat apparently stops. That approach will generally test out aurally for a 4:2 octave.

The opposite approach, to widen a narrow octave just until the beat apparently stops will usually test out aurally as a 2:1 octave.

Yes, a specific piano, but almost any of the electronic tuning devices should be able to measure the notes.

Something like
Yamaha c6

A2 110hz 4th partial -1 cent
A3 220 hz 2nd partial -.59 cent
A4 440 hz 1st partial 0.0
A5 880 hz 1st partial +2.85 cents
A6 1760hz 1st partial +13.9 cents

Cents will be easier for us to work with... I'm not sure I can translate Hz... Maybe Jeff can?

Ron Koval
chicagoland
A

I looked up the RCT values and they are the same for OTS 4 and for the RPT exam emulation mode. 4:2 +.32 beats/sec (OTS values from 1-9) It seems they both target a place somewhere between a 4:2 and a 6:3 octave for an average tuning approach. I'm not sure what the default tuning is for Tunelab.

Ron Koval
chicagoland

approximatively the same size in the "Pleyel" temperament based on a ladder of 3 thirds , F3-F4, then the progression follows the same kind of stretch to the treble until it is definitively too large.

Bill & Ron:

Here are some calculations from a Charles Walter Console in a simulator with A3 having an iH of 0.24 and A4 having an iH of 0.67:

A3 = -0.72 cents
2:1 = 0 bps
4:2 = -0.45 bps
6:3 = -1.8 bps

A3 = -1.6 cents
2:1 = +0.22 bps
4:2 = 0 bps
6:3 = -1.22 bps

A3 = -3.07 cents
2:1 = +0.6
4:2 = +0.75
6:3 = 0 bps

A3 = -2.48 cents
2:1 = +0.45 bps
4:2 = +0.45 bps
6:3 = -0.45 bps

Notice how when the 4:2 and 6:3 are equal beating, the 2:1 is also equal beating! This is always the case and I suspect that is why the compromise is so popular. I also suspect that this may be the origin of Virgil Smith’s “Natural Beat”. Not that all octaves should be tuned this way, but here is an about ½ bps wide 2:1 octave and is a guide or standard that can be used for all 2:1 octaves to be tuned to. It is really just speculation on my part, and I do not tune pianos that are large enough that I would try to tune this way.

I agree with what Bill said about coming from below tends to tune more of a 2:1 octave and tuning from above more of a 4:2 octave. I no longer trust myself to tune octaves where I do not have to. Instead I use 4ths and 5ths on plain strings below about C6, and then check octaves and 12ths etc.

Hope this helps. If you give me other sample iH values I can easily provide additional beat rates and cent deviations, or other values you may be interested in as well.

Tunelab average tuning.

A0 -5.83
A1 -2.83
A2 -1.94
A3 -1.06
A4 0.00
A5 2.96
A6 9.18
A7 24.37
C8 30.96

Before tossing numbers around - can we find a specific model of piano that we can all use for testing?

Easy for me:

Baldwin SF10, 243
Kawai RX-A
Steinway B, L, M, D
Yamaha CFIII, G7, C6, U1, P22

Harder, but possible
Yamaha C3, G1
Couple of Kawai grands - have to check the model - I know one is a GS-40 and another is a KG-2C...
Petrof 7' - I can get the model number

Ron Koval
chicagoland

Sure, how about Yamaha U1? I have that in the simulator.

I'll post the same numbers for a U1 in a little while if that is agreeable, or are there other numbers you'd like?

tunelab steinway D

A0 -2.50
A1 -0.81
A2 -0.37
A3 -0.16
A4 0.00
A5 2.13
A6 8.12
A7 25.30
C8 33.25

All:

Here is what I get with a Yamaha U1. iH is 0.2 for A3 and 0.57 for A4:

A3 = -0.61 cents
2:1 = 0 bps
4:2 = -0.34 bps
6:3 = -1.38 bps

A3 = -1.28 cents
2:1 = +0.17 bps
4:2 = 0 bps
6:3 = -0.87 bps

A3 = -2.42 cents
2:1 = +0.46
4:2 = +0.58
6:3 = 0 bps

A3 = -1.96 cents, or 0.68 cents wide of 4:2
2:1 = +0.35 bps
4:2 = +0.35 bps
6:3 = -0.35 bps

And 1 cent wide of 4:2

A3 = -2.28 cents
2:1 = +0.43 bps
4:2 = +0.51 bps
6:3 = -0.11 bps

And as a spill over from another Topic, here is the result from tuning F3-C4 P5 at -0.5 bps and C4-F4 P4 at 1.0 bps.

F4 = -0.43 cents, 0.39 iH
C4 = -0.86 cents, 0.26 iH
F3 = -1.47 cents, 0.13 iH

F3-F4 4:2 = +0.08 bps, or 0.2 cents wide of 4:2, and 0.23 cents from a 4:2/6:3 compromise.

And F3-C4 P5 6:4 partial match = -1.31 bps.

Hello.

Ron, you say:

..."can we find a specific model of piano that we can all use for testing? Easy for me:

Baldwin SF10, 243
Kawai RX-A
Steinway B, L, M, D
Yamaha CFIII, G7, C6, U1, P22..."


I share your proposal. I shall try to reduce the choise, so that we will eventually choose (look for and work on) one precise model. We'd better check the factory and the serial number too (for equal strings age/scaling?), yes? Any reasonable preference?

Kawai RX
Steinway B, D
Yamaha CFIII, C6, U1

Regards, a.c.

.

Ron,

Cents are easy translated to hz, the formula is:

f' = f * 2^(cents/1200)

so:

110 hz - 1 cent = 110*2^(-1/1200) = 109.94 hz
220 hz - 0.59 cents = 220*2^(-0.59/1200) = 219.93 hz
880 hz + 2.85 cents = 880*2^(2.85/1200) = 881.45 hz
1760hz + 13.9 cents = 1760*2^(13.9/1200) = 1,774.19 hz

Ron, you write:

..."There is nothing difficult about acknowledging modern ET's - except that in all the pages written, there hasn't been anything new at the tuning level about these new approaches. Simply an ET with a different width to the octave. While this may be new "across the pond", technicians over here have been experimenting with this since the early 1980's or before."...

While waiting for the favorite piano's choise, I'll try to explain what is new - at the tuning level - about Modern ET models.

Modern ET models establish new geometrical progressions rules and new tuning references: Cordier's model fixes pure-5ths, Stopper's model's fixes pure 12ths, Chas describes only beating intervals in the sound set, i.e. all intervals contribute to a beating whole.

You write:..."there hasn't been anything new at the tuning level about these new approaches"...

I do not think this is correct. You can well understand that a model and/or a Theory can change the approach to tuning and the relative targets. This could be the case for all the different and yet actual "true ET" tunings, actual true ETs (sometime Reverse Well) that have got no rules for 5ths and octaves and 12ths and 15ths, true ET that I can only call quasi-12th root of two ET (or what?), and yet today Modern ETs are able to rule also those "mysterious" intervals.

You write:..."While this may be new "across the pond", technicians over here have been experimenting with this since the early 1980's or before."...

You see Ron, here we are not talking about experiments, but truly new and finished and approved Modern ET Theory and models. I cannot really say when experimenting started "across the pond", but I can tell you about what my experimenting gained: it gained Chas ET Theory, in fact a Modern, approved and practicable ET model that can renew our tuning referencies once for all.

Modern ETs do not put an end to experimentations nor they limit the freedom in choosing other kind of temperaments. Modern ETs simply represent 12th root of two ET's evolution, i.e. the evolution of the first algebraic geometrical progression.

Regards, a.c.

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