Talk:Regular diatonic tuning

Typo: "A chain of three fifths generates a minor third (A, D, G, C)"

"A chain of three fifths generates a minor third (A, D, G, C)" This is a chain of three fourths, isn't it? 79.79.171.35 (talk) 13:07, 3 January 2017 (UTC)

Yes you are right, thanks for the correction, fixed now. Robert Walker (talk) 14:59, 3 January 2017 (UTC)

Well, as a matter of fact, it does not really matter. We are talking here of pitch-classes, not actual pitches. I terms of pitch-classes, say, A-D is a fourth or a fifth; in terms of actual pitches, it is an ascending fourth or a descending fifth. But three ascending fourths produce a minor tenth (= octave + third), not a third, and three descending ones produce a major thirteenth (=octave + major sixth). Tricky, isn't it? Hucbald.SaintAmand (talk) 15:54, 3 January 2017 (UTC)

Good point. Just added " - in all those examples the result is reduced to the octave" Robert Walker (talk) 20:36, 3 January 2017 (UTC)

Assumption of ascending pitches, rather than pitch-classes, inferred from context:

"A chain of four equal sized fifths (E.g C, G, D, A, E) generates a major third consisting of two whole tones

A chain of three fourths generates a minor third (A, D, G, C)"

79.79.170.213 (talk) 13:24, 7 January 2017 (UTC)

== Plamondon's edit ==

Gentlepersons,

I apologize for not paying more (any!) attention to this article over the last few years. I trust that the edits that I made today answer the many excellent and cogent questions that y'all raised in the discussion above. I apologize for having the initial article be so unclear.

When we were first writing this content, it seemed haughty to insert it into any existing Wikipedia article, so we wrote it to be stand-alone (and made minor additions to other articles to refer to it). I am honored that you considered its content to be worthy of inclusion into Wikipedia's article on regular diatonic tunings.

I am no longer researching this topic. However, I encourage you to contact the lead researchers on this work, Dr. Bill Sethares (U. Wisconsin) and Dr. Andrew Milne (Western Sydney University), regarding any questions you might have.

Respectfully,

Jim Plamondon

P.S.: The key point is that the regular diatonic tunings aren't a set, they're a continuum, on which an infinite number of points fall. The tuning range of this continuum is narrow if one's timbre is harmonic (and one wants consonance, which, of course, one does). To widen the tuning range (all the way to the endpoints, which are culturally-important non-Western tunings), one need only align the current timbre's partials with the current tuning's notes (within the chosen temperament, which defines the mapping of notes to partials & vice versa). Do that, and you can have consonance along the temperament's entire tuning range. Or, you can choose to intentionally mis-align a note's partials, thereby introducing dissonance "on demand." Or, whatever: lots of new effects. JimPlamondon (talk) 13:16, 28 March 2017 (UTC)

Rightio. I don't understand though, why have you removed the text connecting it to regular diatonic tunings and linear temperaments? That also is a continuum. The syntonic temperament seems to equate to:

• Regular diatonic tuning which have the tone and semitone of arbitrary size, including either of them zero, but always with the T T S T T T S pattern
• Plus timbre mapping to make the more extreme regular diatonic tunings sound consonant.

The definition using fifths and octaves is equivalent to that.

Am I missing anything there? If that's the case, then the term "Regular diatonic tuning" is in much more common use than "Syntonic temperament" so it would seem to make sense to explain "Syntonic temperament" by reference to "Regular diatonic tunings" as this article did before your edit. The rest is probably fine as is, I can check the details to make sure but I think your section needs an introductory paragraph or sentence explaining the connection to Regular diatonic tuning.

This is also why I removed mentions of syntonic temperament elsewhere and replaced them with "Regular diatonic tuning" as the more common word. I can understand why you called it a syntonic temperament because the idea through timbral remapping is to make it sound like a tuning with the syntonic comma eliminated. But it is not a term in common use and it can be confusing at times because the term is intended for tunings that are meant for use with timbral remapping, but often when theorists and composers use various temperaments they are meant to be used "as is" without timbral remapping. So it is potentially confusing to classify them as "syntonic temperaments". Hope you understand why we did this. That's also why I did a new version of your diagram labeled as "Regular Diatonic Tunings" because it was being used throughout Wikipedia to illustrate articles that had nothing to do with timbral remapping.

I write this as someone who is myself interested in timbral remapping :). Robert Walker (talk) 13:55, 28 March 2017 (UTC)

Jim Plamondon writes: I apologize for deleting the text connecting the two definitions. That was inadvertent.

The definition of the syntonic temperament does not mention timbre, intentionally. The main value is that it facilitates a focus on the continuity of the string, rather than on the discrete beads. (By analogy, in physics, shifting focus from particle to field.) When focusing on the string, maintenance of consonance across the entire string is facilitated by mapping partials to notes...but this is a consequence of the change in focus, not a requirement of the definition of the syntonic temperament.

When introducing a new concept, as we were doing, one is always faced with a challenge: what word should be used to describe the concept? Use a neologism, or redefine an existing word? We decided that the strict definition of "temperament" as "a tuning system" (as opposed to a specific tuning) fit our intended usage quite well, especially since (in our usage) a temperament is defined by a comma sequence, hence tying everything together rather elegantly. Inevitably, this use of "temperament" is unfamiliar. So would be the definition of a neologism. It's a trade-off.JimPlamondon (talk) 06:37, 30 March 2017 (UTC)

Oh, okay, then I'll re-introduce the text connecting the two. A short paragraph at the head of your section should be sufficient I think. I think your distinction between a continuum and "beads" is more of a matter of emphasis. Tuning theorists always have thought of it as a continuum. They may talk about particular points like quarter comma or sixth comma, but always thought of linear temperaments as a continuum, as shown most strikingly by examples such as tuning using the golden ratio itself and the many phi tunings - those are not diatonic tunings of course, but there's also the linear tuning that achieves a golden ratio between the semitone and the tone in "golden meantone" [1] and PI based Lucy Tuning. Perhaps it may help the article to mention examples like those somewhere in case the reader comes away with the impression that it is a discrete set of tunings rather than a continuum. I agree it is important to make clear that it is a continuum. Anyway Wikipedia goes by notability and established usage and so far your term "syntonic temperament" hasn't been taken up by the tuning community at large and the only cites I found were in the context of timbre remapping. While "Regular Diatonic Tuning" has much wider usage. The guideline is to go by the current situation rather than to try to predict the future (I'm not sure where, can look it up but it's somewhere in the guidelines).

And the thing is that normally syntonic comma tunings are thought of as occupying a particular range, in particular although you can use fractional and negative syntonic comma to express any tuning you like in the range of the regular diatonic tunings, it is very unusual to use this approach to describe schismatic temperaments or tunings with the fifth tuned slightly wide of pure. So, unless it becomes standard usage, which it hasn't yet, it's going to confuse the reader to refer to schismatic temperaments, for instance, as a special case of syntonic temperament even though mathematically they can. After all, mathematically syntonic temperaments and indeed all the tunings in the entire regular diatonic tuning could all be treated as special cases of schismatic temperaments too.

Hope that all makes sense. I'll add in that extra paragraph and look over what you've written and see if I have any more questions. Are you okay with what I just said? Robert Walker (talk) 09:02, 30 March 2017 (UTC)

Jim Plamondon writes: I appreciate your continued attention to this matter.  :-)

I have a question: What metric did you use to determine that the term of art, "regular diatonic tuning," has a "much wider usage" than the term "syntonic temperament"? I wonder, because my preferred metric -- a Google search for the phrase in question -- returns 1,280 hits for "syntonic temperament" but only 695 for for "regular diatonic tuning". I am demonstrably not an experienced editor of Wikipedia articles, so I am eager to learn what the preferred metrics are, and their application to this example.

I agree wholeheartedly that one would not "use a fractional syntonic comma to describe schismatic temperaments or tunings," but I suspect that my reasons for not doing so are completely different from your reasons for not doing so. Both of these temperaments are generated by the tempered P5, so I would describe each specific tuning, uniquely, in terms of (a) its temperament (including its comma sequence), and (b) the width [in cents] of the tempered P5 (since that's the generator, the value of which changes smoothly across the temperament's valid tuning range).The first three sections of the following paper, referenced in the article above, explain this: http://sethares.engr.wisc.edu/paperspdf/tuningcontinua.pdf That article also discusses the "valid tuning range" of any temperament as we define it. This may clarify the issue of overlapping ranges among temperaments.

However, I am by far the junior author of these papers. Please allow me to bring my esteemed co-author, Dr. Andrew Milne, into this conversation. I suspect that his continuing attention to this matter, over the last decade (while my attention was elsewhere), will enable him to explain it far better than I.JimPlamondon (talk) 10:25, 30 March 2017 (UTC)

I will briefly just say a few things -- I haven't and time to read this full thread or review the articles changes. The term "syntonic temperament" -- to describe a range of diatonic tunings from 685.714 cents to 720 cents fifths -- has been used in Milne, A. J., Sethares, W. A., and Plamondon, J. (2007). Isomorphic controllers and Dynamic Tuning: Invariant fingering over a tuning continuum. Computer Music Journal, 31(4):15–32, and in Milne, A. J., Sethares, W. A., and Plamondon, J. (2008). Tuning continua and keyboard layouts. Journal of Mathematics and Music, 2(1):1–19. So above comments that this term is found only ina blog are incorrect. The 685-720 cent tuning range corresponds to what we denoted the 5-limit valid tuning range (VTR) in the second of those two papers. This is the tuning range over which all 5-limit consonances are correctly ordered by size (i.e., the tempered 3/2 is larger than the tempered 4/3 is larger than the tempered 5/4 is larger than the tempered 6/5). We specifically used the designation "syntonic" rather than meantone because the latter is usually used to refer to tunings from about 19-TET to 12-TET, while the syntonic temperament or continuum was specified as existing over the broader 685-720 cent 5-limit VTR. Perhaps also worth noting that this page shows the VTR for "meantone" as being 685-720 -- http://xenharmonic.wikispaces.com/Meantone+family. Having said that, the syntonic section Jim recently added needs a bit of tidying and some corrections (e.g., Wicki-Hayden is not "the best" layout for the syntonic continuum, but it is one of a few sensible choices). I'm off camping now for a few days... I'll aim to do some edits early next week. .../// Andy Milne ///... — Preceding unsigned comment added by 122.106.107.68 (talk) 11:57, 30 March 2017 (UTC)

Jim and Andrew, the problem with google searches is that it can include anything including blog posts, many copies of wikipedia itself (there are many mirrors or wikipedia that are updated only infrequently), and so on. Wikipedia is supposed to be based on reliable sources. What counts as a reliable source depends on the topic matter. Also they might not even be about music. Many of the hits for "syntonic temperament" are about the term's use in psychology, I don't know what it means but it's not about music. E.g. "Normally this patient was of syntonic temperament, extroverted, "happy-go- lucky," with manifold interests and activities and a warm relationship to her husband and other members of her family".

Anyway, I think it's clear we are all talking about the same range of tunings here. So, it's not really a question about how to define them - except as a question about exposition. The question is what to call them. The article seems to give only one source for the phrase "Regular Diatonic Tuning", this thesis [2]. I thought I had more than that but this is written a fair while back, I don't know if I had more sources and forgot to include them, I can look to see if I can find more, or ask friends if they know of more.

You give several sources but they are all by the same authors, so I don't think that's enough to establish that the term "syntonic temperament" has a wider usage than in your papers. Anecdotally microtonal friends, including composers, had no idea what "syntonic temperament" means and found the wikipedia articles confusing when they used this term. But of course that is not a basis on which to decide what word to use here.

I'll answer inline...

Yes, but they are proper peer reviewed journal articles!

The problem is that it is often a bit hard to find good or numerous sources for microtonal tuning theory as there is much less by way of scholarly articles than you'd expect from a topic that is under such active development - many composers for instance don't write scholarly papers.

I've just given you two examples.

We are not supposed to use Wikipedia to impose a new terminology on a field if it has not been widely accepted yet. And I don't think we can say that you have yet established "syntonic temperament" as the terminology for this range of tunings. But unless we find more sources, perhaps it is fair to say that "Regular diatonic tuning" hasn't been established in reliable sources either.

Indeed. But we have to call it something.

If neither has been established, and given that we have to use some word to describe it, then the range "Regular diatonic tuning" or "Syntonic temperament" whatever we call it, is much wider than for meantone surely, as you wouldn't use negative amounts of comma to construct a meantone scale with the fifth wider than pure.

So, then, using the term "syntonic temperament" to describe a tuning with a negative amount of the comma seems particularly confusing, and would make exposition difficult, as you'd have to keep explaining these points. Also "regular diatonic tuning" is a phrase that pretty much describes what it is, a tuning that has a regular pattern of tones and semitones as for the diatonic tuning. It also seems especially confusing if it means you have to say that a shizmatic temperament is a syntonic temperament, or indeed any tuning that is not constructed using the syntonic comma, but some other comma. Because it is most natural to describe the tuning using its own native comma, and why should they all also be defined with reference to the syntonic comma?

It shouldn't be confusing. The comma defines the mapping from JI to the tuning system. The VTR defines the tuning range over which the tempered consonances are correctly ordered by size (as detailed in Milne, A. J., Sethares, W. A., and Plamondon, J. (2008). Tuning continua and keyboard layouts. Journal of Mathematics and Music, 2(1):1–19 and reiterated here http://xenharmonic.wikispaces.com/Tuning+Ranges+of+Regular+Temperaments).

Of course if the term was in general usage to describe such tunings we'd have to use it, however confusing the exposition might be at times. But I don't think there is enough evidence to establish that.

And especially, the way it is used at the moment seems to be tied to timbral remapping, and that it requires us to call a tuning with a negative amount of the syntonic comma a "syntonic temperament" - all that makes sense in the context of timbral remapping, but, do you not think that it is potentially confusing outside of that context? Why would you want to use the amount of the syntonic comma to characterize a shizmatic tuning or one with the fifth wider than pure if you are not involved in timbral remapping? Anyway those are a few first thoughts. It's tricky, mainly because there is often so little published scholarly research on even the most basic of microtonal topics. Yet surely it is notable. Robert Walker (talk) 19:57, 30 March 2017 (UTC)

Temperaments are mappings from JI to lower rank tunings (which can be defined by a comma or list of commas). They do not have clear or precise boundaries over which they can be said to have perceptual validity -- probably dependent on person and context. The valid tuning range and the "nice" tuning range are at least two principled boundaries. The notion that a given tuning can be interpreted as being an exemplar of more than one temperament should not be a problem -- the VTRs of different temperaments overlap. After all, in an equal temperament, one can smoothly "modulate" between different temperaments by changing which intervals and scales are used. The original definitions of Syntonic temperament and VTR etc in the journal papers made no mention (as far as I recall) of timbral remapping, I don't know why that is even in the article. ...\\Andy Milne\\...

Andy, well the current version is substantially rewritten by Jim. But the original is here [3] and it is based on this article: [4]

The abstract for this paper says

"This paper describes Dynamic Tonality, a system of realtime alterations to tuning and timbre that extends the framework of tonality to include new structural resources such as polyphonic tuning bends, tuning progressions, and temperament modulations. These new resources could prepare art music for the 21st Century"

This paper is what I was going on when I described it as being intimately connected with timbre remapping. It's true that there is no fixed boundary beyond which you stop using the syntonic comma to describe a tuning, but in one direction,there is a reasonably sharp boundary. It's my understanding that it would be rare to use it to describe a temperament with its tempered fifth sharper than the twelve equal fifth. A sharper fifth than that, flatter than 3/2 would be described using the schisma, as a Schismatic temperament. Calling a schismatic temperament a "syntonic temperament" seems particularly confusing for those used to it as being treated as a separate kind of temperament from meantones. And then tunings with the fifth shaper than 3/2 would not be referred to as schismatic or syntonic temperaments because they require negative amounts of the comma. Though it makes mathematical sense to use negative amounts of a comma, it just doesn't seem to be normal practice. I can't think of an instance of someone referring to a tuning using a negative fraction of a comma. Can you? Outside your own papers that is? It would just make the expositions here so complex, to have to explain that a schismatic temperament is also a syntonic temperament, and to introduce this historically novel idea of tempering by negative multiples of a comma, at least, as far as I know, it has no historical precedence. And I don't know of anyone outside of your papers that has used this idea of a syntonic temperament in this way.

Jim Plamondon writes: You appear to be confusing a temperament's valid tuning range with the temperament itself. Please allow me to quote from Milne 2007 (the most-often downloaded paper in the history of the Computer Music Journal, last time I checked):

A regular temperament... can be characterized by the small JI intervals called commas that are tempered to unison (Smith 2006). This means that a regular temperament is characterized by its temperament mapping, not its tuning, so any given temperament has a range of suitable tunings.

So, the fact that the valid tuning range of the syntonic temperament happens to include the valid tuning range of the schismatic temperament does not mean that we are, to use your words, "Calling a schismatic temperament a 'syntonic temperament'." We are not. The difference between temperaments is their comma sequence, not their tuning range. The fact that the syntonic temperament's tuning range includes the schismatic's temperament's tuning range is irrelevant (except that they both include P5=700, at which the syntonic temperament's major third is enharmonic with the schismatic temperament's diminished fourth, which makes that tuning a "pivot tuning" for temperament modulation between the syntonic and schismatic temperaments). The comma sequence can be used to inform the mapping of partials to notes of a tuning. The syntonic temperament, as per its comma sequence, maps the 2/1 partial to the octave, the 3/2 partial to the tempered perfect fifth, and the 5/4 partial to the major third, such that one would play a C-Ionian triad as C-E-G. The schismatic temperament, by contrast, maps the 5/4 partial to the diminished fourth, so that one would play the C-Ionian triad as C-F♭-G. Look at the Wicki–Hayden note layout. Do you see the G♭ button? The F♭ button would be just to the left of that, if the note-layout contained just two more notes per octave. (You can't assume that the D♯ and F♭ are enharmonic; that is only true for one particular point on the schismatic temperament's tuning continuum.) The Wicki-Hayden note-layout is very good for the syntonic temperament because it tightly groups the syntonic temperament's primary consonances; not so good for the schismatic temperament.--JimPlamondon (talk) 08:49, 29 April 2020 (UTC)

I can understand that you want to emphasize the continuous nature of these temperaments, especially with a background in timbre remapping. But I don't think, when it comes to a phrase to be used throughout wikipedia to talk about all tempered diatonic scales, that calling them all syntonic temperaments is the way to go, any more than calling them all schismatic temperaments. While calling them all Regular diatonic tunings is a way to both recognize the continuum that goes all the way from five equal to seven equal (not inclusive) while recognizing meantones, and schizmatic temperaments, as part of that continuum. Of course while referring to your own work then it makes sense to use your own term for these tunings. So my solution was to introduce the section describing your work with an explanation.

You can see how I did it in the introduction to the section here: [5] Robert Walker (talk) 00:29, 31 March 2017 (UTC)

I suspect many of these issues can be resolved with a suitable careful rewrite, which I may attempt next week if I have time. I personally am not particularly bothered by the name of the page. The purpose of my last two responses was to correct some previous assertions that have cropped up in this discussion page. Just to quickly add that there is, arguably, a natural correspondence between the syntonic temperament and the 7 to 5 range because tempering out the syntonic comma is the only temperament (as defined by the commas it tempers out) that has precisely this VTR. And if this page is actually about diatonic (maximally even 5 large, 2 small) then syntonic temperament, schismatic temperament etc, are just overlapping ranges within this continuum. But, it's not at all clear what this page is even about, or how it relates to other pages. — Preceding unsigned comment added by 122.106.107.68 (talk) 02:54, 31 March 2017 (UTC)

Oh, just re-read what you said about "Valid Tuning Range", I get what you are saying there. Though the valid tuning range is a different thing from the range over which the syntonic comma is customarily used to define tunings. As after all it requires use of negative amounts of the comma apart from anything else. As for the scope of this page I lead out with a definition that the reader would find easy to understand which also makes it easy to understand why it is called a "regular diatonic tuning":

"any musical scale consisting of "tones" (T) and "semitones" (S) arranged in any rotation of the sequence TTSTTTS which adds up to the octave with all the T's being the same size and all the S's the being the same size, with the 'S's being smaller than the 'T's."

That's a well defined continuum of tunings, and I'm not sure therefore how one can be unsure what it is about? I then go on to give the more technical definition from the thesis in which "Regular Diatonic Tuning" is defined, as

"Regular" here is understood in the sense of a mapping from Pythagorean diatonic such that all the interval relationships are preserved".

They could be defined in many other ways too. But it's the same continuum of tunings, no matter how you define them. Just different definitions which mark out the same entities. I'm trained as a mathematician, so it might be that I am coming to this from a slightly different perspective, so that things that seem identical to me look different to others? For me the continuum of tunings is what this page is about, and how you define them doesn't really matter so long as you mark out the same tunings, and it just seemed that in an article addressed to the ordinary non mathematical reader, it's best to start off with the simplest easiest to understand definition. And of all the definitions, the TTS TTTS definition seemed by far the easiest to both state and to understand. That's the motivation for doing it that way. Robert Walker (talk) 03:56, 31 March 2017 (UTC)

Proposal to restore Syntonic temperament as a stand-alone article

Gentlepersons,

Let me again thank you all for your learned attention to the matter of the "syntonic temperament." Again, let me emphasize that the lead authors of the seminal papers -- Prof. William Sethares and Dr. Andrew Milne -- both know infinitely more than I do about both music and mathematics. I am a mere marketing slime, who happened to read about the Wicki-Hayden keyboard and realized that its having "the same fingering in all keys" HAD TO BE the result of some correspondence between the geometric pattern of the notes and the deep structure of music. Reading Sethares' book "Tuning, Timbre, Spectrum, Scale" introduced me to the notion that consonance arose solely from the alignment of a tuning's notes with a timbre's partials. Everything else arose from those two observations, with nearly all of the heavy lifting having been done by Milne and Sethares (et al.) while I kibbitzed. So, whenever either of them corrects me, they are right, and I am wrong.

That said, please allow me to propose that Wikipedia's stand-alone article on the syntonic temperament should be restored, with only a brief summary of it included in Wikipedia's article on Regular diatonic tunings.

Here's why: The inclusion of the syntonic temperament in the "regular diatonic tunings" article is problematic, because it assumes that all tunings of the syntonic temperament are regular and diatonic, when, in fact, both of these assumptions are false.

First, "diatonic:" The valid tuning range of the syntonic temperament includes an endpoint at which the minor second has a width of zero (5-tet) and another endpoint at which it has a width equal to the major second (7-tet), neither of which are diatonic.

Second, "regular:" Consider the discussion of "Related Just Intonations" on the pages numbered as 79-80 in Spectral tools for Dynamic Tonality and audio morphing, which describes the Tone Diamond used in Dynamic Tonality synthesizers. Moving the control-point within the Tone Diamond systematically shifts the tuning away from regularity. To quote a paragraph on the page labeled as 80:

When the Tone Diamond’s control point is anywhere along the central horizontal line (the “Max. Regularity” line), the tuning is a one- or two-dimensional tuning such as 12-TET or quarter-comma meantone, as shown on the main tuning slider. When the control point is moved upward or downward the tuning moves towards a related just intonation. The tunings that are intermediate between perfect regularity and JI are like the circulating temperaments of Kirnberger and Vallotti in that every key has a (slightly) different tuning. And all of these tunings have the same fingering when played on a 2D lattice controller.

The syntonic temperament is therefore not, strictly speaking, a regular tuning, nor a family of regular tunings, nor even a regular tuning system. It embraces closely-related irregular tunings, too.

In summary: because the syntonic temperament embraces tunings that are not regular and not diatonic, having Wikipedia's only discussion of the syntonic temperament be subsumed into Wikipedia's article on "Regular diatonic tunings" is illogical and inappropriate. It attempts to squeeze a hypercubic discussion into a cubic hole.

That's why I initially put my description of the Syntonic temperament into its own Wikipedia article, and then added references from other articles to it (and vice versa), rather than attempting to shoehorn it into any existing article. This "where to put this discussion?" problem is just one small piece of evidence that the ideas embodied Dynamic Tonality, and hence in Musica Facta (the research project into Dynamic Tonality), the syntonic temperament, and Guido 2.0 (the aspect of Musica Facta focused on music education) may be incommensurable with those of music-making's current paradigm.

I apologize for not presenting these arguments when the idea first arose of merging the discussion of the syntonic temperament article into some other pre-existing article.

I hereby propose reverting the article on the Syntonic temperament to being stand-alone, and adding a brief summary of it, with a reference to the full article, in the Regular diatonic tunings article.

Respectfully,

Jim Plamondon --JimPlamondon (talk) 06:44, 26 April 2020 (UTC)

Relationship between tuning, timbre, etc.

Gentlepersons,

Thank you again for your continued attention to this matter.  :-)

In the Talk above, people have repeatedly questioned the relationship between the syntonic temperament and timbre. Temperament, they say, has nothing to do with timbre; the linking of the two, which runs throughout Sethares, Milne, Plamondon, Prechtl, Tiedje, et al., they see as aberrant.

I think I now understand where y'all are coming from. I suspect that the microtonal community has assumed the use of Just Intonation and Harmonic Timbres for so long that they have forgotten that they are even making an assumption. They often write about ratios of small whole numbers, as Pythagoras did, as if the ratios themselves were the source of tonal meaning -- when it has been abundantly clear since Joseph Sauveur, or, for the doubtful, since Helmholtz, and inescapably since Plomp & Levelt that these intervals arise from the specific pattern of vibrations defined by the Harmonic Series, not from some magic of numerology.

Alternatively put: Sethares, Milne, Plamondon, et al. are explicitly relating tempered pseudo-Just tunings and tempered pseudo-Harmonic timbres, whereas microtonalists and previous music theoreticians have implicitly related [un-]tempered Just tunings and untempered Harmonic timbres.

Examples of the above implicit assumptions in the Talk section of this article:

• Hucbald: "The possibility of negative temperament (fifths wider than pure) is a bit farfetched." Why are pure intervals being assumed? Because (I suspect) harmonic timbres are being assumed.
• Walker: "But the chart shown includes tunings with the fifth wider than the pure fifth. So it's hard to be sure what it is about." Why are tunings wider than the pure (i.e., Just) fifth confusing? Because (I suspect) harmonic timbres are assumed.
• Walker: "Hucbald, Okay, I see what you are saying, that any regular diatonic scale is a meantone in that more general sense that the tempered major third is equally divided into two equal tones. However, though that is logical, it doesn't correspond to established usage. As an example, 17 equal, with a fifth of 705.884 cents, so tempered by (705.884-701.955) or 3.929 cents wider than just, is -1/5.47 meantone but I don't think anyone calls it that, and it would also be almost exactly -2 schisma but again that doesn't sound right either." Walker is confusing tuning (that is, a specific width of the P5) with temperament-as-defined-by-a-comma-sequence (which determines the association between notes in a tuning and partials in a timbre). This "doesn't correspond to established usage" iff one ignores the many peer-reviewed publications of Sethares, Milne, Plamondon, Prechtl, Tiedje, et al., over the last 15 years. Please let me elaborate. It is true that, at P5=705.884, an untempered Just diminished fourth aligns excellently with the 5th partial of an untempered Harmonic timbre, and the association of the diminished fourth with the 5th partial is exactly what you'd get from a comma sequence (1/2, 5/4, schisma) -- that is, from theschismatic temperament-as-defined-by-a-comma-sequence. However, P5=705.884 is just a tuning -- that is, a specific width of the generator -- which could be within the valid tuning range of any of a large number of temperaments, each defined by a different comma sequence. I suspect that Walker's implicit assumptions are leading him to make a very specific and systematic error, as described above.

• Hucbald: "I utterly fail to see in what sense something called 'timbre' could 'conform to the harmonic series'." This is an utterly pure example of an assumption that is so implicit that it is not even recognized as an assumption. Hucbald should, perhaps, read Sethares' "Tuning, Timbre, Spectrum, Scale," published in 1998, and now in its second edition. The content of this book makes the relationship between the terms in its title crystal clear. That the content of the Syntonic temperament article does not clarify the reader's implicit -- and, in this case, mistaken -- assumptions, is a problem for which I suggest a solution below.
• Walker: " Anyway he [Gene Ward Smith] developed various tools that let composers see interconnections between tuning systems and to devise new tuning systems and to see individual tunings as part of larger patterns that they hadn't been able to see before. This has been a vibrant synthesis of maths and music. Much of it developed in just the last ten years. I'm a mathematician by training myself but it's one of the things about maths that it is very common that you don't understand the maths developed even by people who are working in very closely related areas. It is just the nature of it because of the way it works with such abstract ideas. But that doesn't prevent it from being valuable." We agree with this assessment of Gene Ward Smith's work, and indeed our definition of temperament-as-defined-by-a-comma-sequence is his invention. We would welcome y'all's affording the same courtesy to our our mathematics, documented in peer-reviewed journals such as the Computer Music Journal and the Journal of Music and Mathematics, which clearly (well, using mathematics, so it's only clear to those who speak the lingo) makes and proves, using mathematical tools, the validity and usefulness of our approach.
• Hucbald: "We would easily agree, I trust, about what a temperament is: in addition to make use of tempered intervals, it is also meant for instruments of fixed tones, producing a limited number of tones." I do not, in fact, agree with this definition, and for very good reasons, as documented in our published papers. The fact that y'all are arguing about the meanings of these terms among yourselves, shows that there is ample ambiguity in them, into which we can offer definitions that are both narrower and more general, as we have done in our publications and in the original Syntonic temperament article. It is entirely possible that we have failed to be sufficiently clear in those papers, or that we failed to translate that clarity to our original stand-alone Wikipedia article. However, as Oliver Cromwell famously said, "I beseech you, in the bowels of Christ, think it possible that you may be mistaken." Particularly, I beseech you to take note of (what I suspect is) the microtonal community's -- and nearly all previous Western music theorists' -- assumption that Just Intonation tunings would be used almost exclusively with timbres that followed the Harmonic Series, and the impact of that assumption on your attempts to shoehorn any discussion of the Syntonic Temperament into a space that doesn't have enough dimensions to contain it.

Sethares, Milne, Plamondon, Prechtl, Tiedje, et al. have offered something that is truly novel, and y'all seem to be working very hard to deprecate its novelty and force it into the lower-dimensional framework of what has historically been done. Our work COMBINES:

• The use of a temperament-as-defined-by-a-comma-sequence to define the mappings between the notes of a pseudo-Just tuning and a pseudo-Harmonic timbre (Example: In the syntonic temperament, the 5th partial is mapped to the major third; in the schismatic temperament, it is mapped to the diminished fourth);
• Dynamic tuning within the valid tuning range of a pseudo-Just temperament-as-defined-by-a-comma-sequence, including tunings that are regular and irregular, equal and unequal, major-aligned and minor-aligned, which is in itself a significant advance in the state of the art;
• Dynamic changes to timbre to align said timbre's pseudo-Harmonic partials with any said tuning of the notes of said temperament, and to systematically emphasize and/or de-emphasize sets of prime partials, and to systematically mis-align said partials away from said note, all of which are novel real-time musical effects;
• Two-dimensional note-layouts (notably the Wick-Hayden note-layout) which enables consistent fingering within the valid tuning range of a rank-2 temperament-as-defined-by-a-comma-sequence, thus enabling a musician to perform novel musical effects such as those listed above, and also polpyphonic tuning bends resulting from the narrowing or widening of the generator in real time, which in turn enables novel tonal effects such as temperament modulations (for example, from syntonic to schismatic using P5-700 as a pivot tuning, because at P5=700, the diminished fourth and major third are enharmonic, enabling the temperament to be switched from the syntonic temperament's mapping of the 5th partial to the major third, to the schismatic temperament's mapping of the 5th partial to the diminished fourth, without a jarring change in timbre);
• A means of changing the width of the generator, within the current temperament's valid tuning range, in real time.

All of these innovations have been documented in the peer-reviewed literature -- and some non-peer-reviewed technical reports -- for over a decade. Our Computer Music Journal article was still, the last time I checked, the most-often downloaded article in its history. Our "sight reading music theory" article has been downloaded from ResearchGate over 3500 times. To claim that these innovations, or the ideas that they document, or the terms that they use, are not "established," begs the question of what definition of "established" you are using.

When combined, our system's components enable a systematic expansion of the frontiers of tonality and novel tonal effects. However, each component by itself is of little particular interest. How useful is an automotive transmission without an engine? A computer without electricity? A browser without the Internet? So, our explanation of each component explicitly refers to the other components.

Y'all, I suspect, are not making such explicit connections among your uses of "temperament," "timbre," etc., because youimplicitly assume:

• That the goal of a tuning is to maximize the alignment of its notes' fundamentals with the ratios of Just Intonation;
• That such tunings will be used with timbres that conform to the Harmonic Series; and
• That these tunings and timbres will be played on the piano keyboard and/or instruments dedicated to a particular fixed tuning.

In summary, we are explicitly stating relationships that you are assuming implicitly.

The solution is to update all of the other articles on microtonality and music theory to make their implicit assumptions explicit.

Y'all are resisting this. Your resistance is manifesting itself in an attempt to shoehorn our innovations into a box defined by your lower-dimensional implicit assumptions, in which the interconnections and synergies must be stripped away to fit in those lower-dimension boxes. This looks to me to be a clear-cut case of the Semmelweis Reflex. That reflex is a natural human and institutional reaction to novel ideas, so I don't blame y'all in any way for exhibiting it. I have every confidence that I am displaying similar human reflexes and cognitive biases.  :-)

I am happy to see that the discussion surrounding the original Syntonic temperament article led to the creation of the Regular diatonic tunings article, which is a boon to Wikipedia.

As a first step towards resolving the "problem of assumptions" described above (and the fact that the Syntonic temperament includes non-regular and non-diatonic tunings), I will de-merge the Syntonic temperament article out of the Regular diatonic tunings article sometime in early June 2020.

In the meantime, I will add to the article on Dynamic Tonality a section that discusses (a) the implicitly-assumed relationships described above, and (b) the explicitly-defined relationships made by Dynamic Tonality. I can them update the discussion of the Syntonic Temperament to refer to this section in the Dynamic Tonality article. I can then add a reference to this same "implicit assumptions" section to all other articles on traditional music theory. This will clarify the distinction between Dynamic Tonality and everything that came before.

That should resolve all of the issues raised in this Talk page, and improve Wikipedia's discussion of music theory considerably.

I look forward to your comments on this suggestion.

Respectfully, --JimPlamondon (talk) 04:49, 2 May 2020 (UTC)

Either remove article or remove everything related to Syntonic Temperament and Dynamic tonality

Maybe about 80% of this article seems to correspond to a fringe theory by user JimPlamondon. This is against wikipedia's philosophy, as you can see here. In the fringe theories page. This has nothing to do with whether I agree or disagree with this theory, it is an objective fact that this is not broadly supported and as such should be deleted. Wikipedia is not a place for promoting your own theories, it should reflect what is broadly acceped in a field, there are many other websites that can be used to promote or support this research.

In a nutshell, as my reference states: To maintain a neutral point of view, an idea that is not broadly supported by scholarship in its field must not be given undue weight. I don't think this deserves extra discussion, and JimPlamondon's own comments on the matter make this very clear. I will procede to delete everything associated with Dynamic Tonality IgnacioPickering (talk) 23:52, 17 July 2021 (UTC)

Ignacio, et al.: Wikipedia states that "fringe theories in science depart significantly from mainstream science and have little or no scientific support." The content that you deleted is, by that definition, not a fringe theory, in that it is well-supported by numerous publications in the peer-reviewed scientific literature. Indeed, the content that you deleted contains more references (7) that the content that you did not delete (4).

This leads to the second criteria for identifying fringe theories: Parity of sources. Four of the seven sources cited in the content you deleted are to respected peer-reviewed publications, such as the Computer Music Journal (H-Index: 41), the Journal of Mathematics and Music (H-Index: 14), and the Proceedings of the College Music Society. Only three of the seven sources are not similarly peer-reviewed. By comparison, of the four sources cited in the non-deleted content, the first refers to a master's thesis; the second to a non-peer-reviewed book; the third to a non-peer-reviewed review of said book; the fourth to a non-peer-reviewed wiki post. None but the first of these four sources can credibly be claimed to be peer-reviewed. The other three can reasonably be categorized as "self-published texts," which Wikipedia's description of fringe theories cites as a sign of fringe theories. In short: The deleted content is demonstrably less fringy than the non-deleted content.

Please note also that publications on the syntonic temperament and Dynamic Tonality are cited frequently, according Google Scholar:

Deleted contents' papers' citations

Paper	Citations
Spectral tools for dynamic tonality and audio morphing	52
Isomorphic controllers and dynamic tuning: Invariant fingering over a tuning continuum	51
Tuning continua and keyboard layouts	39
Dynamic tonality: Extending the framework of tonality into the 21st century	7

This is an impressive level of citation for papers in the humanities (such as music theory), in which 65% of papers are never cited. These citations prove the "broad acceptance" of the content that you deleted.

I would go a step further, and point out that many of the papers supporting the syntonic temperament and Dynamic Tonality include mathematical proofs of their claims. Such proofs are the gold standard for claims made about models of phenomena in the natural world, such as musical tunings. The citations supporting the non-deleted content contain no such mathematical proofs. Therefore, the theory of the non-deleted content is less strongly supported by its citations than is the content that you deleted.

Finally, as Wikipedia's discussion of fringe theories states, "One important barometer for determining the notability and level of acceptance of fringe ideas related to science, history or other academic pursuits is the presence or absence of peer-reviewed research on the subject." As shown above, the content that you deleted meets this standard much better than the content that you did not delete.

Therefore, the deleted content should have been retained, and the non-deleted content should have been deleted as a fringe theory.

However, Ignacio, I am not unreasonable. I will not press for the deletion of the obviously-fringy theory represented by the content that you did not delete. I will only insist that you follow Wikipedia's rules fairly, and therefore not delete the material on the syntonic temperament and Dynamic Tonality. --JimPlamondon (talk) 03:27, 18 July 2021 (UTC)

Incorrect description of syntonic comma

The article claims: "The small difference in pitch between [a chromatic and diatonic semitone] is called a comma, usually prefixed by the name of the tuning system that generates it, such as a syntonic comma (21.5 ¢)..."

This is clearly incorrect. While the Pythagorean comma does work out such a difference, as seen on the corresponding page, the syntonic comma is not the difference between the chromatic (25:24) and diatonic (16:15) semitones of just intonation, equivalently the minor second and augmented unison - that yields 128:125, i.e. the (enharmonic) diesis.

The syntonic comma (81:80) - the one referred to when one speaks of "fractional-comma meantone" - is a ratio between the major tone (9:8) and minor tone (10:9) of just intonation - which is not a regular diatonic tuning, as it uses two different tones. Equivalently, it's the difference between a just-intonation ditone and major third.

216.209.47.135 (talk) 07:57, 31 January 2024 (UTC)