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Hello Alfredo,

Are there 12 offsets for etd's that we can try for CHAS? thanks, GP

Hi GP,

Nice question, straightforward and not wordy. There is one precise reason why I'm not making an effort in that direction, related to the fact that I would not be 100% sure about how those offsets would work in general. ETD's are not standardized (yet) and 12 offsets (probably) are not enough for Chas. The best solution (for my serenity) would be a "take" of all the offsets for one precise ETD, relative to one precise piano, directly from my tuning. Thinking how keen you are... I wish I could have answered yes.

Thank you for your consideration.

Regards, a.c.
.

Grandpianoman, CHAS is an ET-type tuning so it does not have specific offsets for an EDT that you would find in an UT tuning, such as EBVT. All 12 notes will offset in theory by zero. However, since the tuning is stretched slightly beyond normal 2-root-1/12 then the offsets will fan out progressively by about 0.1 cent or so for each semitone depending on the piano and the amount of stretch required.

To put this in another way, a normal ET tuning with an aggressive stretch starting though the mid-treble range will result in something like a CHAS tuning from my understanding. Something like a SAT tuning with a decent DOB added perhaps.

Not exactly Chris, the nearest approximation would be to obtain an even beating between 12th and 15th all along the scale.

But to get to the Chas tuning the piano have to be tuned a little large on the center string. Anyway that method works perfectly well (using pure 12 th on center string for instance, it will temper in the Chas final product when unisoned)

Since GP asked for offsets I put my reply into an ETD perspective.

Alfredo, Chris, Kamin, thanks for the explanations.

My next question....do 12 offsets only work with UT's?

Alfredo, will you be here for the PTG Convention?

GP, the twelve offsets are relevant only to UTs. For ET the non-iH offsets would be all zero!

Not quite. CHAS specifies equal beating octave+fifth and double octave, without imposing 2:1 octaves, leading to a stretch even without inharmonicity. There is a large discussion on this in the context of tuning some electronic piano (in which Alfredo participated) here.

You can thus compute the offsets on an imaginary zero inharmonicity piano and get:

! CHaS.scl
!
CHaS s=1
12
!
100.038318440222
200.076636880444
300.114955320666
400.153273760888
500.19159220111
600.229910641332
700.268229081554
800.306547521776
900.344865961998
1000.38318440222
1100.42150284244

As you can see the offsets are much smaller than the offsets generated by inharmonicity, so largely irrelevant for real piano tuning.

Kees

Hmmm... Perhaps "largely irrelevant" or "relevant" is to be related to approximations?

Hi GP,

I even wonder if 12 offsets, on paper, would work with UT models. I do not know... perhaps in practice?

In fact, the 2:1 theoretical ratio, every 12 steps, would "double" differences-from-pure-ratio values. Then, if I understand correctly (...not sure at all), in order to expand the tuning beyond 12 UT's values, ETD's adopt an "iH model" (empirically re-shaped (?)) that (in practice) enables to correct and "regularize" the overall tuning curve, also compensating the 2:1 "doubling" effect?

I'm sure Robert Scott would be able to tell us more, as Robert has good knowledge of how ETD's can work, perhaps how different degrees of approximation can make a difference amongst ETD's?

On top of that, I'll have to rectify (in the near future) the ideas concerning the Chas target and principle... As Isaac mentioned, equal beating 12ths/5ths is (in practice) one close approximation that we can consider, when setting the premises.

Regards, a.c.
.

The iH model is just using the iH recorded with the notes of the piano, then use a decision on which interval may be beating more than the other.

The model is the problem of ETD , from what I understand, unless an iterative computation can be used that take in account maximum possibilities and choose which is nearer the wanted preferences.

That is how Dirk's tuner is working and I find it providing a very progressive tuning , less "model imprint" than I haver seen previously.
Those choice does not use an octave as model but the whole piano, more or less, so in the end it sticks more to consonance (or lessening of partials beating) than the others ETD have used.

If we use the partial match to compute a tuning, as it can be done with Verituner, the problem would be to weight the 2 prominent beats from the 5ths the 12 th, the 3ds etc..

Because what we hear in the end induce all the partials, some more than others but I believe it can be simplified only up to some point.

It works quite well in theory and in practice.

You do not understand, because you don't know what a cent is apparently.

Kees

Cent.

Kees

I like how the replies get shorter and shorter here.

Probably the most effective route.

I sure would like to understand what mathematical basis Alfredo was going for here in his work. I can't understand the math in the paper because it's not correct/sufficient to explain what he qualitatively describes.

I do believe Alfredo understands something about tuning that most machine tuners do not understand. Only the best aural tuners have talked about tuning this way. There is something between machine tuning (the strict science of offset numbers) and aural tuning.. and it is a big gap for those who can hear: The difference between considering the entire partial bandwidth, instead of a point and considering all partials, instead of one at a time.

I see Alfredo going for this in his own way. There seems to be a point at which all partial expansions can be balanced to a point of best fit. Sometimes I would call this similar to Haye Hinrichsen's reduction of entropy.. but this does not describe what happens all of the time.

So aside from your confusing logic, a word of support Alfredo, for your non-reductionist ideas about tuning.

Now if you could just answer questions honestly and openly...

I don't think such posts are acceptable. Since it was not directed at me I'll just tell you to go wash your mouth with soap, rather than ask the moderator to ground you for a while.

Kees

Hi Grandpianoman,

Here is a short paper (below) that may explain exhaustively the meaning of my replies (above - let me know).

Look for: Fred Lieberman, WORKING WITH CENTS: A SURVEY.

Best wishes,

Alfredo

- . - . - . -

Kees, you may devote yourself to study and/or, if possible, post your comments in the …Comments thread.
.

I tried on Tunelab using those offsets on 12 tones, to see if when going up the scale by ear with similar progression, I obtained an even beating of 12 th and double octave.

It seem to work to some point, but I was not really sure.

Anyway when I use an ETD I tune "by ear" in the "marshmallow zone" of the ETD display.

BTW I have used an ETD with a display in Hz, makes you really aware of the pitch instability of the piano tones, in fact the cts display seem to show only apart of the tone, I mean you are more or less obliged to wait for the tone to be quiet to use the display.
(or there is an algorithm that helps to smoothen the display so it is easier to read).

I used that Dirk's software and the display is very fast, so I had to choose a moment in tone and to tune at that moment.

I was very surprised by the accuracy (progression of all intervals) in the end, when compared with that display.
To be complete I may say I tuned a vertical piano and Dirk's noticed to me that a few notes have really unstable and uneven partials (which explain the jumps in the beat curves of some intervals.

That is presented as a tool for pianists and amateurs, but frankly the result is straightforward with a very nice tuning. (and the price is not very high)

Someday other styles of tuning will be inserted based on even beatings or any pure interval wanted.



That software use an algorithm that sound logical, doing the same thing as the aural tuner that look for the nicest tone in the intervals he tunes. (simply as he can check for more intervals than an aural tuner the progressiveness is less skewed (with a favor for 5ths and octaves , seem to me, but no problems with octaves beating at the 2:1 level, which is what most tuners are doing)

I kindly thank you for permitting me to do this.

Kees

CHAS (chaz, n.; chaz*zed, to chazz, v.):

1. (n) A specific kind of equal temperament stretch tuning that aligns equal beating lower note 12ths and 15ths along a curve (as distinguished from Bill Bremmer's method of equal beating upper note 12ths and 15ths), while regarding all other intervals as well; not to the exclusion of the former.

2. (n) The theory that purportedly explains this more specifically, or any related theory that goes by this name.

3. (v) Any theory which uses the same tactics as CHAS and presents lengthy evidence to confuse the reader into a spindle of illogical fury, in order to eclipse the absence of any explanation whatsoever.

Syn.: Any equal temperament tuning methods that are already in wide use by the best aural tuners today, to put greater stretch into modern piano tuning to maximize harmonic alignment.

Any discussions relating to these subjects that confuse all of the above.



I'm confused. Are you? After all this work, talking about CHAS and trying to understand what it is, I confess, I still do not.

Is it supposed to be like a Jackson Pollock?.. I will 'get it' after staring for several hours in an alcohol-induced haze? But everyone 'gets it' in their own way?

Torsional plane? Helix structures? The golden ratio inscribed in the tuning? Nevermind that the number referenced is the sqrt {5}, not the actual golden ratio, which is [1 + sqrt {5} / 2].

Kamin, what 12 CHAS offsets are you referring to?

I dont recall exactly but I suppose I used the 12 first offsets as stated above : + 0.038 + 0.076 + 0.114 etc..

As it is (was ?) supposed to be linear, I thought I would get to a Chas temperament when making the 2 first octaves like that.