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I would recommend Scala (free software) for that. It comes with just about every tuning
anyone has ever thought of, and you just type the offsets from ET to define a new temperament. It allows you to plot sizes of any interval you want in any format
you can imagine. It also allows you to tune MIDI files (good for quick checks).
http://www.huygens-fokker.org/scala/

Kees

I've played around with Scala some. I'm just wanting to create simple line drawings that put the widths of the M3's, M5's etc of the major temperaments, particularly the various meantones and wells, side by side. Which means that I just need to sit down and look at the charts and do it...

In Scala: Analyse-->Tone circle. Set generator to 7 (fifths). Then hit "Temperament Radar" button and you can see M3's m3's and P5's plotted in a circle of fifths.

Kees

Hello Kees,

I'm glad to learn that you are a musician, a theorist and a tuner practicer.

You say:...”if in a V-I cadence in C, GB is wider than CE, the cadence is enhanced as we now also hear the resolution of a poor third into a better third.”...

This may result from the approach to consonance and dissonance in those times, and from having to interpret and manage the “wolf”. Also, I would think that the degree of desirable enhancement can only be subjective.

...”Interestingly the neutral harmonic progressions of ET are also present in meantone, where we have a restricted symmetry group over a limited set of keys.”...

Saying “neutral harmonic progressions of ET...”, you may refer to equal size semitones, accessibility to all keys and overall harmony. Say that “neutral” was then the goal, unfortunately 12th root of two ET did not get it. In fact that model stretches 5ths and 3rds in favor of pure octaves. The 2:1 ratio determines a module restricted to 12 tones, so the temperament is not expandable beyond the octave (Research report, section 4.3).

In 12th root of two ET, thirds are theoretically the same size, though in stretched octaves practical tuning, beat-wise, they are not (I'm not sure this was a point).

You say:...”During the MT period there was no real harmony, so one could argue one of the reasons the well-temperaments became popular is that they also enhanced harmonic contrast.”...

Yes, It may also be argued that once we started seeking harmony we needed to contrast the wolf, so well-temperaments where enhanced. May harmony and shareability have called for ET (and ET's evolution)?

Patrick stated: “...putting energy into harmonic movement - simply cannot be done using a symmetrical tuning.”...

I wondered then about “energy” and “harmonic movement”, how they were related, and whether Patrick referred “symmetrical tuning” to theory or tuning practice, Patrick himself may say.

In Chas theory “energy”, “harmonic movement”, and “symmetry” are referred to beats and to their dynamic proportions and synchronism.

Chas is not a 12-tone nor a 19-tone set, as it is not related to zero-beating, pure intervals (Research report, section 3.4 ).

You ask:...”Does your CHAS theory have anything to say about major thirds?”...

What to say? With a classical approach, Chas 3rds on paper may result wider, but it goes in favor of minor 10ths. Actually in Chas all intervals (and tensions) are maximally related by the multiple, combined action of all partials. In fact, partial 3's delta acts on 4ths and 5ths, partial 4's delta acts on 3rds and 6ths. The octave then is a sub-module and the set symmetries can be defined purely in terms of beats and beat-coherence (Research report, section 3.5).

Regards, a.c.

CHAS Tuning MP3 - Amatorial recording on a Steinway S (5’ 1”, 155 cm)
http://www.box.net/shared/od0d7506cv

CHAS THEORY - RESEARCH REPORT BY G.R.I.M. (Department of Mathematics, University of Palermo, Italy):
http://math.unipa.it/~grim/Quaderno19_Capurso_09_engl.pdf

Gracias! I spent about two hours trying to map out a meantone last night. Entering the data took about two minutes. Trying to line up text boxes indicating the distance between the M3's while fitting them all in a single line took up the rest of the time. You may have saved me from much pain and suffering.

I assume music is subjective, perhaps you believe there is a divine music and tuning independent of mankind? A respectable point of view, held through the ages by tuning theorists, but not very common nowadays.


No I mean that a V-I sounds the same in F major and C major in meantone as well as in ET. In MT the semitones are very different. Listen to a chromatic scale in 1/4' MT, e.g. Sweelinck's chromatic fantasia. This tuning has strong melodic effects too.

Yet as long a you avoid the wolf all keys sounds the same in MT.

Thanks for the other clarifications.

Kees

Hello Kees,

To me saying: I would think that the degree of desirable enhancement can only be subjective.

You reply...”I assume music is subjective, perhaps you believe there is a divine music and tuning independent of mankind?”...

Well, in guessing my believes you may say “divine” meaning a precise category. In that case I do not think there is a divine music, nor a divine tuning. You can indeed say music be subjective, like this all world might be, but then I need to make some distinctions.

In this world there are some phenomenons that we can regularly observe. From their regularity we try to gain a Rule, from their loyal reproducibility we try to achieve a shareable Law.

I think of music mostly as production of sound and rhythm.

Sounds and resonance phenomenons are related by fairly precise proportions, which are manifest in nature, and therefore not strictly subjective.

A vibrating string is observable in quite objectives terms, and so is resonance. From objective observations we could see that in a vibrating string all partial sounds are ordered in a well known, precise sequence, the harmonic series.

From the harmonic series we may have learned the harmonic mean, one kind of average.

Then, I tend to think that my/your/our (musical) ear can well be related to/calibrated on fairly precise sound proportions. More than “divine”, I would then think in terms of “natural” harmony or “matter's harmony”, referring to those proportions which are independent of mankind and yet to a certain extent shareable, since they may already reside in most of us. Has it ever happened that you could agree with someone else on a poor, flat or sharp pitch? It has happened to me.

Rhythm as a notion, is even more objective than pitch and both are translatable into frequencies.

My research went for an order, both from sounds and rhythm, namely the beat rate (or beat-frequency, period, coherence time), two vibrating strings can steadily reproduce, what may then be said an “intrinsic” order.

Off course, words like objective and intrinsic are strictly related to investigation tools and subjective urges, first of all the urge to share some feelings and meanings.

Back to temperament and the enhancement of a V-I cadence, thinking to the dozens of artistic, compromise-type WT available, I prefer Chas*, simply because through my tuning I can enjoy all pitches and all keys, I can feel light (partial sounds), energy (resonance) and harmony (in tune) without having to be combed against poor and better intervals.

(*) The “s” variable of Chas algorithm (Research report, section 3.3) opens to any sort of subjective preference - on this you may find the kite analogy, in this thread. Thinking “dynamic” has helped me not to take a prejudiced position and overtake the objective Vs subjective antinomy. As a theorist, you may appreciate that.

Regards, a.c.

CHAS Tuning MP3 - Amatorial recording on a Steinway S (5’ 1”, 155 cm)
http://www.box.net/shared/od0d7506cv

CHAS THEORY - RESEARCH REPORT BY G.R.I.M. (Department of Mathematics, University of Palermo, Italy):
http://math.unipa.it/~grim/Quaderno19_Capurso_09_engl.pdf
.

The kite analogy was posted here in June 04, 2009 - 05:30 PM

If you are logged in:

http://www.pianoworld.com/forum/ubbthreads.php/topics/1194874/9.html

If you are logged out:

https://www.pianoworld.com/forum/ubb...CULAR%20HARMONIC%20SYSTEM%20-%20CHA.html

Regards, a.c.
.

Thanks Alfredo for that elaboration. I am encouraged to bring up yet another matter.

Does CHAS have anything to do with difference tones? As you probably know
apart from the series of partials, when two notes sound together the difference
of their fundamentals is also produced. A common trick used in pipe organs; you can get
a 32' pipe from two 16' pipes tuned a just 5th apart.

Now in conventional ET the difference tone of a M3 is about 80cent off, quite gross.
Also when sounding e.g. a just C6-E6-G6 the 3 difference tones are C4 (twice) and C5
but in ET you get C4-82cent, C4+67cent, and C5-6cent which is a disgusting mess.

Kees

Hello,

...”Does CHAS have anything to do with difference tones?”...

I have not calculated Chas difference tones.

Resonance enhancement may result from the relation between fundamental frequencies, partial frequencies and beats periods.

Chas manages to relate and proportion scale frequencies and beats periods with one (scale incremental) ratio. It is my opinion that this double-ring* relation opens to synergy and may determine a self-exciting system.

...”As you probably know apart from the series of partials, when two notes sound together the difference of their fundamentals is also produced. A common trick used in pipe organs; you can get a 32' pipe from two 16' pipes tuned a just 5th apart.”...

Are you familiar with pipe organs?

...”Now in conventional ET the difference tone of a M3 is about 80cent off, quite gross.
Also when sounding e.g. a just C6-E6-G6 the 3 difference tones are C4 (twice) and C5 but in ET you get C4-82cent, C4+67cent, and C5-6cent which is a disgusting mess.”...

Yes. That looks pretty bad. Are those figures theoretical or real? I haven't had a chance to measure Chas-ET real frequencies, so I'm not able to release any figure in cents. Sorry.

(*) Maybe I should say double-spiral.

Regards, a.c.

CHAS Tuning MP3 - Amatorial recording on a Steinway S (5’ 1”, 155 cm)
http://www.box.net/shared/od0d7506cv

CHAS THEORY - RESEARCH REPORT BY G.R.I.M. (Department of Mathematics, University of Palermo, Italy):
http://math.unipa.it/~grim/Quaderno19_Capurso_09_engl.pdf
.

Ok, no problem. But let's keep one thing clear - you can't refer to your expertise per se. I might not be as an experienced tuner or mathematician as you are, but I do know the theory as well as most professional tuners here. Besides from that, my hands-on experience includes regularly tuning the instruments at the conservatory (about 40 pianos), as well as most concert work in this town. I do NOT need you to fill any expertise gap, except considering your own findings related to your method (CHAS).

This doesn't mean that I wouldn't have a lot to learn from you about tuning and the theory behind it, but please don't think that I'm unable to comprehend.
If you have a problem with that, say so, and I'll stop the questioning and answering.


Yes, I admit this is vague. Let me clarify it: I'm talking about the extension of the midrange, which is based on equal-beating 12ths/15ths by Bill, and in CHAS. That's where the thinking coincides.


Musically, asthetically pleasing to the listener and performer, while music is played on it.


[…]

Yes, DoelKees, this is exactly what I mean.
EBVT (and other UT's) actually mimics some of the intonation that goes on in any combo of instruments of non-fixed pitch (including voices). I personally like that, because it sounds human.


No, I'm not relating it, far from it. I say that a symmetrical tuning by itself gives no special energy into the differnet harmonic progressions, where as the human-intonation mimicing EBVT III does. Any cadence will sound the same in ET, not in EBVT III. this I like, because it affects the rhythmic and dynamic interpretation of the piano player.


Yes, I wrote that line the day before. And then I talk about how my students described the tunings in my studio (EBVT III). What is it that you want me to make up my mind about?

PS the tunings on the other grands are my ET.



C'mon Alfredo, neither is this a claim of mystery or magics, it's just an informative line that I personally happen to think is interesting, but if you want to twist and turn it, fine.

Suggesting that I should tell my students that its a fairly close approximation of a modern ET theory, I have to be really blunt and ask if there is something you don't understand when
you repeatedly say things along these lines?

------

Meanwhile here's a couple of really plain questions, that you shouldn't have any trouble answering. I think I'm not the only one who wonders about this, so please be as clear as you can:

1) ET can be tuned with wider and narrower temperament octaves, and with different stretches, but there is one thing that remains the same: ascending cromatic M3's and M6's have a progressive beatrate. They do not have that at all in EBVT III. how could the EBVT III ever develop into being a modern ET, when it goes against the very nature of ET itself?

2) From reading your instructions for CHAS, and reading other peoples comments on the initial octave size in CHAS, I think (and correct me if I'm wrong) it ends up right between a 4:2 and 6:3. This octave is extended in a way that leaves only one constant: the equal-beating 12/15ths that as something of a read thread in a CHAS tuning.

3) Now, If Bill sets up ET, he recommends the initial octave to be between 4:2 and 6:3.
Then he extends the midrange utilizing equal-beating 12ths/15ths.

Shouldn't Bills ET method give a high-quality CHAS?

If so, why do it the hard way - from theory to practice? I think you yourself wrote about that earlier, that CHAS stems out of your tuning development, not vice versa.

I do not put scientific research down, quite contrary - I think it is needed. But if the end result is similar to another way of setting the temperament (your own method), but they both end up in a CHAS tuning, is there a practical difference?

If my thinking sounds reasonable, and If a good pitch raise is done before the fine tuning:

4) could CHAS be tuned using bills very smart and down-to-earth tuning instructions? Could CHAS even be described as "an temperament octave size between 4:2 and 6:3, and an extension of the temperament utilizing equal-beating 12ths/15ths?

If so, why not let us all know so we look at what we are doing already, and also relate to CHAS in a new light.

If you like to answer these questions of mine, please refrain from using word games instead of the facts and/or clearly stated personal opinions that are truly needed.

Hello.

Patrick, I've had to snip your post. Here is the first part.

You write...”Ok, no problem. But let's keep one thing clear - you can't refer to your expertise per se. I might not be as an experienced tuner or mathematician as you are, but I do know the theory as well as most professional tuners here.”...

My referring to “expertise” – in a forum - is inherent to what I can read and understand about my interlocutor.

When I say “gap” I'm not referring to specific “knowledge per se”, but to an outcome: how could one eventually elaborate knowledge together with enduring practice, in time.

So, I mean what one has eventually made out of his/her knowledge, how could one improve his/her practice on force of knowledge, and vice versa, how could one expand and shape knowledge (not necessarily theoretical nor mathematical) through long time practice. 

...”Besides from that, my hands-on experience includes regularly tuning the instruments at the conservatory (about 40 pianos), as well as most concert work in this town. I do NOT need you to fill any expertise gap, except considering your own findings related to your method (CHAS).”...

You may understand that I do not mean expertise as in “per se n-number” of pianos one may have tuned either, but as an essence, say a fund of field experience and elaborations, the fund that one may have been able to eventually collect out of consistent, if not exclusive, dedication and personal targets.

And let's make one more think clear: Chas is a Temperamental Theory. You surely know the difference between a method and a theory. 

...”This doesn't mean that I wouldn't have a lot to learn from you about tuning and the theory behind it, but please don't think that I'm unable to comprehend.
If you have a problem with that, say so, and I'll stop the questioning and answering.”...

What I'm saying doesn't mean that you are not able to learn and/or to comprehend, nor that I have problems with your questioning. As I said, I'd rather avoid discussing about tuning “while mixing different levels of expertise”, as it may be confusing to compare a “root” extract with some route experiences. 

...”Yes, I admit this is vague. Let me clarify it: I'm talking about the extension of the midrange, which is based on equal-beating 12ths/15ths by Bill, and in CHAS. That's where the thinking coincides.”...

In these terms, only your thinking and mine may partially coincide. Last June Bill wrote, more than one time, that 12ths and 15ths invert their progressions in the high register (?). Should not you ask Bill? 

..”Musically, asthetically pleasing to the listener and performer, while music is played on it.”...

Then we share that meaning. 

...”Yes, DoelKees, this is exactly what I mean.
EBVT (and other UT's) actually mimics some of the intonation that goes on in any combo of instruments of non-fixed pitch (including voices).”...

You may be talking about the “in tune approximations” of non fixed-pitch instruments (and voices), but the value of a “mimic”, in this case, cannot be ascertain, neither in absolute nor in relative terms. Then, I understand your statement as a mere conjecture. 

...“I personally like that, because it sounds human.”...

Do you say human meaning “in accordance” with those variable approximations? I would not take any approximation as a model, nor can I trust/share fixed/invariable “human” approximations. When I think of “human” I think about (hopefully) “variety” and “diversity”. Then, what sounds human for you...

...“I say that a symmetrical tuning by itself gives no special energy into the differnet harmonic progressions,”...

You may be expecting special energy from harmonic dissonances and consonances fixed alternations, I expect ever growing special energy from euphonicity and resonant synergies. I refer energy to resonance and partials outcome, and to synergy and beats-synchronization. 

...“where as the human-intonation mimicing EBVT III does.”...

To me, much of this sounds like an acrobatic attempt to give meanings to WT's and EBVT, but if the latter sounds OK it is simply because it "mimics" modern ET's. EBVT cents deviations are so small that we need (?) too many words to appreciate that gimmick. In my experience, the nature of the piano itself + the environment are enough for mimicking those “in tune” approximations you may refer to. 

...“Any cadence will sound the same in ET,... ”...

Now that you go from the theoretical idea of cadenza (from latin cadere = to fall) to temperaments, you ought to specify which ET you are referring to. Is it your own ET variant you are talking about? Or an ETD 12th root of two stretched variation? Is it a modern ET? Aural tuning?

About Chas ET, for what I can say, cadences result being safe and reliable as an Olympic swimming pool can be for divers, comfortable and adequate like hi-tech climbing boots and centered like the pistons of a racing car, in one word I'd say fair. 

...“not in EBVT III. this I like, because it affects the rhythmic and dynamic interpretation of the piano player.”...

That, I would not like for your same reasons. I prepare the piano so that the player's rhythmic and dynamic interpretation, what he/she may have spent hours onto, may not be affected. In my experience, a part from euphonicity and resonance, any other possible effect should be agreed on, and customized so that the player, if anything, can move within his/her own individual sizes. And in my opinion, when it comes to general and shareable preferences, only nature can be taken as a reference.

That said, we may keep a third think clear: the reason why I'm here is not to belittle other colleagues efforts, I'm here for adding my efforts and for sharing a new ET model.

The second part is following.

Regards, a.c.
.  

No, the quoted statement is true for all ET, so it is not necessary to specify which one.

Kees

(italics mine)

No, Alfredo, this is not true. We need only to listen to the music to appreciate EBVT. The amount of words is something that you notice, i don't think anyone else in this thread is really into that. You can twist and turn every word of my posts (And I personally think you get a great kick out of dissecting paragraphs... ) but that doesn't change the fact that the temperaments are serving the musical and artistic output. This doesn't mean that you can't dive into the semantics, but who really cares in the end?

Originally Posted By: alfredo capurso

...“Any cadence will sound the same in ET,... ”...

Now that you go from the theoretical idea of cadenza (from latin cadere = to fall) to temperaments, you ought to specify which ET you are referring to.

Hello Kees, you say:..."No, the quoted statement is true for all ET, so it is not necessary to specify which one."...

It may be true in theory although depending on the ET and on the key, the interval tensions produced by beats would slightly variate. Then, the cadence justness may sound the same.

I would also like to know how many ET's you have experienced. Is what you lament true for all ET tunings you have actually heard? What you refer to theory can be referred to practice?

a.c.

Well, I never kept track, but I would estimate around 50000.
May I ask you how many un-ET's you have experienced?

Kees

Patrick,

you write:...No, Alfredo, this is not true. We need only to listen to the music to appreciate EBVT."

The "many words" is referred to the arguments for supporting a WT, not the tuning itself, which is valid.

..."The amount of words is something that you notice, i don't think anyone else in this thread is really into that."...

Please, if you like talk about yourself, I do not need a spokesman.

..."You can twist and turn every word of my posts (And I personally think you get a great kick out of dissecting paragraphs... )"...

Tell me everything you personally think but please note, I'm not interested in twist games, and what you quoted is only my position. No false, no true.

a.c.

CHAS Tuning MP3 - Amatorial recording on a Steinway S (5’ 1”, 155 cm)
http://www.box.net/shared/od0d7506cv

CHAS THEORY - RESEARCH REPORT BY G.R.I.M. (Department of Mathematics, University of Palermo, Italy):
http://math.unipa.it/~grim/Quaderno19_Capurso_09_engl.pdf
.

..."May I ask you how many un-ET's you have experienced?"...

Experienced? Few. Found and tuned to Chas ET? Many.

Is what you lament (cadence) true for all ET tunings you have actually heard?

What you refer to theory can be referred to practice?

a.c.

What do you mean "found"? How on earth can you tune an unequal temperament to Chas ET?

Yes. And for all ET's that I haven't heard.

Sorry, I don't understand the question. If you mean can you hear the different size thirds in an unequal temperament in the cadences the answer is "yes". (Unless the difference is too small to be noticeable of course.)

I don't want to be patronizing, but I really think you should educate yourself about temperaments if you make grandiose claims about having invented the ultimate temperament.

Kees

Alfredo:

I hope you know how much I love the sound of CHas and the many recordings that have been posted by you, Kamin, and Patrick. I feel as though I must say something here, however:

The word "gimmick" is very insulting in English--it means a cheap trick or deception. (The term doesn't mean "a device," or "a method of questionable value.") Any temperament could be called deceptive, in the broad sense of the word, which may be what you mean, since each temperament by definition involves a tempering of some intervals, but "gimmick" in English, is very strong. EBVT is a well temperament, originally a development from meantone, isn't it, with an attempt to avoid the wolf while at the same time being more precise in definition, and more regular, than an ordinaire? Well temperaments predate ET. If the desire to give the impression of consonant intervals while not creating actual consonance equates to deception, isn't ET really the largest gimmick?