Not once in your numerous criticism and constant negativity have you made any intelligent comment upon the spreadsheet providing the mathematics of harmonic accordance to temperament and it's clear that you've been unable either to apply yourself academically to that or to make any constructive comment.
David,
This statement of yours puzzles me. In fact, I addressed your spreadsheet at some length, and I would describe what I wrote as constructive. I'll quote a full post below:
The major problem with something like that spreadsheet is that it is too simplistic. (BTW, one quick and easy way to make it far more apparent what there is to see in the spreadsheet would be to eliminate the 2nd, 4th and 8th partials: they are the same for all cases, so they add nothing to the graphic).
First, it doesn't take into account inharmonicity, by giving "harmonics" rather than "partials" (Obviously those vary depending on the scale of the instrument, but they represent the reality of the situation).
Second, it fails to note how intervals "line up," in terms of how the various partials of each interval coincide. It is that coincidence (or lack thereof) that creates the sound you hear when playing an interval.
Third, it fails to note how more complex relationships of intervals coincide and conflict. It isn't as simple as "the thirds and the fifths." Even if we limit ourselves to triads, various inversions and spreads of notes have distinctly different flavors, caused by varying coincidences and conflicts.
A closed position second inversion is a simple case in point (let's say G C E), where the major sixth from the bottom note (GE) and the major third from the second from the bottom note (CE) have beat rates that are quite close (in ET) and blend nicely to create a composite beat. However, they are at different partial levels. GE beats at B (3rd partial of E), while CE beats at E (4th partial of E). It is interesting to note that the B is forming a semitone with the 4th partial of C. This is a partial view of what is going on with one example of a close triad, and the complexity quickly multiplies even with the most simple minded actual music.
Fourth, and probably most important, is the sound of the instrument with the pedal down. The characteristic sound of the piano is inextricably tied to the sympathetic vibrations of all the strings when you depress the pedal in many different ways. That is completely ignored in any analysis of this sort, and is where a system like that developed in entropy-tuner
http://piano-tuner.org/entropy is far more indicative of the actual picture.
Bottom line, you have to be thinking of a far bigger picture to come up with anything meaningful in the realm of the subject line of this thread.
[And another full post]:
If you fixate on the 3/2 relationship of the 5th and the 5/4 relationship of the third, you are missing a tremendous amount of the total picture of the resonance of the piano. The total sound of the piano, the sound that is particularly characteristic to the piano as opposed to almost any other instrument, is the one you hear with the pedal depressed, dampers up. It is then that the sympathetic vibrations of all the other strings come into play.
Any analysis that only analyzes individual intervals and one or two of their partial coincidences is not really useful in predicting the effect of a tuning on the instrument's tone.
"Sweeter" and "less sweet" thirds occur in ET as much as in any UET. It simply depends where in the range you are playing the third. As for whether a third beating at 3 bps is actually perceived as "sweeter" than one beating a 15 bps, that is partly a matter of taste, partly a matter of context.
Until you get to the just third, with no beats, you are dealing with an interval that is "out of tune." But in another sense, a beating third (or other interval) is simply one with a built in vibrato, and a noticeable vibrato may be far more desirable than the clean but dull sound of the just interval.
Amazingly enough, there are multiple ways of looking at the issues surrounding tuning :-)
I think it is well to bear in mind this quote from Mattheson on the subject, to keep things in perspective: "One must take refuge in temperament when tuning claviers and harps. Many books make as much to do of this as if the welfare of the entire world depended on a single clavier."
Most musicians are far more interested in getting on with the business of playing music to be overly concerned with the finicky details of tuning we obsess about. Musicians (and listeners) for whom our level of detail is important or even noticeable is relatively small.
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Fred Sturm
University of New Mexico
fssturm@unm.eduhttp://fredsturm.nethttp://www.artoftuning.com"We either make ourselves happy or miserable. The amount of work is the same." - Carlos Casteneda
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Original Message:
Sent: 03-27-2019 10:11
From: David Pinnegar
Subject: Improving piano tone through tuning and temperament
Dear Fred
From beginning to end your manner and thrust has been bullying and dismissive and being wholly expressive of a genre of establishment that is fearful of change I have to thank you for according to type.
On
https://www.youtube.com/watch?v=oV0bkcSr_Kg you started a campaign of "debunking" and have not let up since. In the course of exchange of comments on that video it was apparent that you self contradicted and you diverted attention from anything relevant. For anyone not having heard that recording before, it was an experiment for the purpose of exploration, not more, and is not the tuning that I would normally adopt or advocate universally, so actually nothing to debunk there, and the instrument having both brass and steel strings is hideously susceptible to temperature change.
A central plank of your thrust is that Jorgensen was misguided and even dishonest in his alleged adjustment of data to that which he wanted to hear, and that a whole generation have been misled as a result by Jorgensen. I find your attack on Jorgensen wholly disreputable and objectionable in so far as I believe you only started defaming him after he died and was unable to defend himself. Your attack on anyone and everyone else who follows an unequal temperament path is faulty on the basis that all have followed from Jorgensen's alleged misguidance is a hubristic obsession with Jorgensen. Numerous of us have come to conclusions concerning temperament wholly independent of Jorgensen using our ears and researches of our own.
In my particular case I came to temperament issues as a result of the early volumes of the BIOS journal, thereafter the pink bible written by Padgham in the early 1980s, had not heard of Jorgensen at all, and then a revelation in my knowledge of temperament effects whilst listening to Rose Cholmondeley performing Chopin's 2nd Sonata, the hunch proving correct when I started exploration of alternative tuning.
In listening to my tunings, however anyone likes to interpret the mathematics or belittle my analysis and interpretation of the mathematics, the wide major thirds are audibly not much wider when critically compared to equal temperament major thirds, and especially when octaves are stretched to the extent of Perfect 5th ET.
The corpus of a dozen years of work in tuning, performance and documentation in recordings is there on the public record and I have pointed to 20th century recordings of repertoire where the use of the "colour tuning" does not at all detract from the performance.
Not once in your numerous criticism and constant negativity have you made any intelligent comment upon the spreadsheet providing the mathematics of harmonic accordance to temperament and it's clear that you've been unable either to apply yourself academically to that or to make any constructive comment.
As I write in listening to the Beethoven Tempest in Meantone, I hear a performance, not a tuning, but a performance that's grand, that's expressive, that's actually phenomenal by an extraordinary pianist of whom his friend Paul Badua Skoda would have been proud, with a bravery of rendition and experimental exploration that I believe to be admirable. The fact that not once through your now long history of derogatory comments have you ever given credit to some of the exceptional performers who have been exploring and exploiting the tuning research indicates a meanness of spirit common to those often of a jealous disposition indicating a submission to your feeling of no longer being top of their game.
For that reason I take your constant derogatory stance to the point of trolling as the greatest compliment.
Best wishes
David P
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David Pinnegar, B.Sc., A.R.C.S.
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+44 1342 850594
Original Message------
Yes, 1.0125 is different from 1.0000 in the second decimal place. And the syntonic comma is HUGE sonically. For the F3A3 third, it is the difference between zero and 10 beats per second.
Your values for third decimal place were about 1/2 of the value I cited, the equivalent of 1.006 to 1.000. And you claimed they were essentially unnoticeable - using the fact that it was "only the third decimal place" as evidence. The point is that your use of numbers was misleading.
As was my facetious use of numbers. The syntonic comma is relatively tiny in arithmetic terms, but it is the source of centuries of tuning angst, and literally countless schemes to overcome it and devise "the best possible solution." Frankly, looked at dispassionately, it is an amusing history of generation after generation rediscovering a mathematical problem that was identified millennia ago, and with the naivety of youth, embarking on yet another reinvention.
I quite understand what you are trying to do. Your sincerity seems genuine. You are writing to an audience consisting almost entirely of professionals, each of whom has vastly more practical experience tuning than you probably ever will. And you think that if only you can get everyone to listen to your wonderful Youtube videos, they will all be converted to your magical method of tuning that transforms pianos and music, and that will usher in a new world.
I think perhaps your contribution to tuning has been amply displayed, and needs no further discussion.
Regards,
Fred Sturm
"Travel is fatal to prejudice, bigotry, and narrow-mindedness." Twain