Talk:Pyknon

Some remarks concerning edits of October, 24, 2012

• Ptolemy defined two different "shades" of the chromatic genus <...> (edited by Jerome Kohl)

Ptolemy never talked about 'shades'. This is a specifically Aristoxenian concept. For Ptolemy they are all 'genera'. Please correct this. Olorulus (talk) 06:12, 25 October 2012 (UTC)

• not just hypate to mese, but also parhypate to trite, lichanos to paranete, etc. (editorial remark by Jerome Kohl)

'Tetrachordon' in the Antiquity is not just any sequence of 4 consequent scale steps, this is modern (school) understanding. The Greeks understood 'tetrachord' only as a segment of Full System (wrongly transmitted as Perfect; there was not any word about 'perfection' by Greeks) limited by unmovable 'chordai' (these were originally called 'hestotes'). On the next phase (after defining genera melorum) 'harmonike' talked about 'eide (or 'schemata'), but these were specifically 'schemata', no more called 'tetrachorda' Olorulus (talk) 06:12, 25 October 2012 (UTC)

• In the chromatic genus, the largest incomposite interval is a minor third,.. (edited by Jerome Kohl)

I think, this was not a good idea to 'retro-extrapolate' modern (school) terminology of intervals on a terminology of intervals used by Greeks. 'Minor third' implies counting from the tenor pitch (tertia <implied vox>) which got start in contrapuntal textbooks in ca. 13th century. Greeks instead considered intervals as 'capacities'. Replacement of 'trihemitonion' (by Romans 'triemitonium incompositum') through 'minor third' is therefore wrong. Such replacement can be justified only by didactic simplification, but if so, this should clearly marked by an editor (you) the authentic understanding and the way 'we use to name such and such... as...'. Please think it over and restore whenever possible original terminology (see my edition of the text). Olorulus (talk) 06:19, 25 October 2012 (UTC)

• There is a larger number of variations in the tuning of the chromatic than in the enharmonic. (edited by Jerome Kohl)

This is somewhat imprecise statement. In any classification of genera by any Greek musician there was one and only one enharmonic genus (simply by default that it contains the smallest possible intervals), while chromatic and diatonic genera could be 'beliebig viel' (Aristoxenus writes that principially 'shades' are 'unlimited' in number). However, in the Pythagorean branch (authenticaly transmitted by Boethius) there were traditionally just one intervallic pattern for each genus, therefore this became 'widely disseminated' throughout whole 'scholar' world and commonly recognized division (up to present courses of music). Olorulus (talk) 06:37, 25 October 2012 (UTC)

• The makeup of the pyknon serves to identify the genus of a tetrachord (edited by Jerome Kohl)

It seems to me that this statement is a bit misleading. 'Genos' and 'eidos' ('schema') are terms (in the limits of the discussed subject, of course; not generally!). Therefore, I'm pretty sure, they should be handled by an editor with care. I can't remember any Antiquity text (both Greek and Roman) which talked about 'genus' of 'tetrachord'. If you know such, please correct me. Olorulus (talk) 06:54, 25 October 2012 (UTC)

• A tetrachord is bounded by the interval of a perfect fourth, the outer notes of which remain fixed in all genera and therefore are called "standing notes". The positions of the inner notes vary from one genus to another, for which reason they are called "moving notes"...
• In Greek theory, a tetrachord consists of four notes. The outer, bounding notes are fixed at the interval of a perfect fourth and for this reason are called "standing" notes; the two inner notes are "movable"... (edited by Jerome Kohl)

I guess, you overlooked duplication. Also, it seems better to write 'Antiquity' because Roman (up to Boethius) and Greek authors were perfectly unanimous in that matter. Olorulus (talk) 09:00, 25 October 2012 (UTC)

Thanks for your thoughtful comments. A few of your objections are actually directed at cited sources (e.g., it is Chalmers who says there is a larger number of variations in the chromatic than the enharmonic), but the ones involving possible misrepresentation I shall have to examine one by one. On the issue of using "modern" terms such as "minor third", I think we must take into consideration our readers, few of whom will appreciate the difference between (for example) "ditone" and "major third", and mot will be perplexed by the term "ditone". (By the way, what is the correct Ancient Greek term for this interval, when it is not necessarily a Pythagorean ditone, but neither is it necessarily a 5:4?)—Jerome Kohl (talk) 18:59, 25 October 2012 (UTC)

OK. I've now gone back over your points and checked the sources. Let me speak to them each separately:

• Ptolemy defined two different "shades" of the chromatic genus <...> (edited by Jerome Kohl)

Ptolemy never talked about 'shades'. …

Yes, you are right, of course. I have corrected this.

• not just hypate to mese, but also parhypate to trite, lichanos to paranete, etc. (editorial remark by Jerome Kohl)

'Tetrachordon' in the Antiquity is not just any sequence of 4 consequent scale steps, this is modern (school) understanding.

Yes, of course this is true, but this was only an editorial comment. My point is that the diagram following the statement (based on Chalmers, I think) shows two tetrachords, not just the one from hypate to mese, but also the parallel tetrachord above it, from paramese to nete. The fact that modern discussions sometimes regard any four consecutive notes of the scale as a "tetrachord", distorting the ancient sources who always refer such note sets back to "the" (referential) tetrachord merely adds to the reader's confusion. The main point is that they are going to see two parallel tetrachords in that diagram, and wonder why the text refers only to one.

You wrote (editorial comment) "not just hypate to mese, but also parhypate to trite, lichanos to paranete, etc." This assumption was wrong and it is clearly explained by the modern (school) elementary music theory (so do all my Russian colleagues :) ). I am afraid, more confusion arises with your addition of a word 'any', because any reader would now routinely extrapolate (modern) understanding just in a way you did it in your editorial comment. So please consider adding a remark, something like 'any tetrachord (that is 4-step scale progression bounded by unmovable notes, 'hestotes'). Sorry for the style (don't forget, I am not a native speaker). Hopefully you got my point now, anyway. Olorulus (talk) 06:36, 26 October 2012 (UTC)

While you didn't raise objections, I added a footnote. The point is to prevent a reader from (routine) understanding of a 'tetrachord' as 'any 4-step scale' which (in the context of the article) would be misleading. This understanding is persistent, as I observe it in my everyday teaching experience and in lots of scholar articles. If you still consider a note superfluous, please let me know.

I believe that any essential material belongs in the main text; shunting it into a footnote implies that it is dispensable, and should be removed. I will see what I can do to incorporate this in the text, without disrupting the flow unnecessarily. Your point is well-taken, however.—Jerome Kohl (talk) 22:25, 27 October 2012 (UTC)

Olorulus (talk) 08:15, 27 October 2012 (UTC)

• In the chromatic genus, the largest incomposite interval is a minor third,.. (edited by Jerome Kohl)

I think, this was not a good idea to 'retro-extrapolate' modern (school) terminology of intervals on a terminology of intervals used by Greeks. …

Perhaps but, as I said previously, we are trying to communicate information to a general readership here. Introducing the correct Greek or Latin terms is of course perfectly valid, but we are going to have to tell the readers what they mean, in terms that they can understand. Insisting that they master Ancient Greek before starting to read this article is counterproductive. (Although it is completely beside the point here, I don't think your explanation of the derivation of the term "minor third" is valid, by the way.)

Compare these two constructs which you composed:

• In the enharmonic genus, the large incomposite interval was originally a ditone (the major third of Pythagorean tuning),
• In the chromatic genus, the largest incomposite interval is a minor third,

Do you see the difference? So, the 'authenticity' of terminology can be rendered with (relative) ease, so this is not a problem of readers' compehension, it is just an editorial issue. As I already said, Greek treated intervals as capacities (dia tessaron), while medieval writers counted from the "root" (quarta <vox>). Sorry, this is a trivial issue, I will not go here in details. Olorulus (talk) 06:27, 26 October 2012 (UTC)

Of course I see the difference. The problem is that I do not know what the technically "correct" term might be for the English "minor third", which is the only term used by Mathiesen and M. L. West (for example) to describe this interval. In medieval Latin theory treatises, semiditonus is often used, but that is obviously not a word from ancient Greek theory. You have suggested trihemitonion, but I do not know this word, nor can I find a source for it. Perhaps you can help me here.

I added some examples of English translations of the discussed incomposite interval (called now 'minor third') of Nicomachus, Cleonides, Boethius. If you need more citations, please let me know. Olorulus (talk) 09:17, 27 October 2012 (UTC)

One citation would have sufficed. Two of these (Barker and Strunk) are on my bookshelf, where I can easily check them. (Others, alas, are not available even at my university library—Winnington-Ingram 1936, for example, which I would have to obtain through interlibrary borrowing.) Since Strunk is translating Cleonides, we should probably also reference the newer edition by Jon Solomon (1980), which provides not only an English translation but also a critical edition of the Greek text. I see that you are unfamiliar with the formatting used in parenthetical referencing, which is easily fixed. Thanks for supplying all this information.—Jerome Kohl (talk) 22:25, 27 October 2012 (UTC)

Solomon's translation of Cleonides is wacky in some relations and, so to say, 'unmusical' (as well as his Ptolemy's translation, btw, is worse than Barker's) though here is not a place to prove this (obvious) fact. And (maybe due to this) it has never been published. Strunk's is quite reliable (and reveals 'musical' understanding of a scholar) even being earlier by date. Olorulus (talk) 06:24, 28 October 2012 (UTC)

Nevertheless, we are talking about multiple translators' rendering of a single word and, if we are going to list five or six others, it will do no harm to drop one more name into the pot. BTW, is Solomon's critical edition of the Greek text also "wacky" (I am not equipped to judge it)? There are earlier editions, of course, but none (I think) that treat all of the variant sources together.—Jerome Kohl (talk) 07:13, 28 October 2012 (UTC)

• There is a larger number of variations in the tuning of the chromatic than in the enharmonic. (edited by Jerome Kohl)

This is somewhat imprecise statement. …

Yes, of course it is, but we need to exercise some judgment here between providing a fully accurate but mind-numbingly boring explanation, and something that the general reader can grasp easily. I have read far too many complaints on other music-theory articles (dealing with much less technical and arcane subjects than this one) that they are "incomprehensible", except to people who already know the subject well.

Again, this was just an editorial remark. What I mean, latently it implies that there were several 'enarmona', but 'chromata' were more. This is not true. So, as to me, it must be simply stated more directly like (again, I'm not a native speaker, you'll do it definitely with raffinement) 'in any classification of genera there was only one enharmonic division while division of chromatic and diatonic genera was one (as in the Pythagorean tradition fixed by Boethius) or more (as in Aristoxenian tradition and Ptolemy)', that's it. Olorulus (talk) 07:06, 26 October 2012 (UTC)

Depending on how you view things, there were several enarmona. If you read any one theorist, of course, what you say is correct, but if you read multiple theorists, you will find several variations of the enharmonic tuning. This is already clear in the article: the classic form of the genus has a Pythagorean ditone (81:64) at the top and a pyknon of a minor Pythagorean semitone (256:243), but Eratosthenes replaced the Pythagorean ditone with a smaller ditone of 19:15 and a correspondingly larger pyknon divided as 40:39 and 39:38, while Archytas and Didymus divided the pyknon as 28:27 and 36:35, and 32:31 and 31:30, respectively. We can probably make this distinction clearer than it presently is.

• The makeup of the pyknon serves to identify the genus of a tetrachord (edited by Jerome Kohl)

It seems to me that this statement is a bit misleading. 'Genos' and 'eidos' ('schema') are terms (in the limits of the discussed subject, of course; not generally!). Therefore, I'm pretty sure, they should be handled by an editor with care. I can't remember any Antiquity text (both Greek and Roman) which talked about 'genus' of 'tetrachord'. If you know such, please correct me. Olorulus (talk) 06:54, 25 October 2012 (UTC)

I'm not sure I follow you here, but I have to confess that I am not capable of reading the original Greek texts, so I am dependent on modern authors' interpretations. If "genus" does not apply to tetrachords, then to what does the word apply? To take just one modern authority as an example, Barbera, in "Arithmetic and Geometric Divisions of the Tetrachord", says "Archytas divides the tetrachord into three genera" (p. 296), "here are [Aristoxenus'] divisions of the tetrachord into three genera" (p. 297), "These six genera and shades are derived from infinitely many possible divisions of the tetrachord" (p. 299), "Ptolemy divides the tetrachord into one enharmonic and two chromatic genera" (p. 304). The Wikipedia articles on the three genera all refer them to tetrachords (not trichords, pentachords, hexachords, octave species, or anything else). Are these all incorrect, then, and if so, do we need to go into those articles and add the contradicting evidence?

Just don't use 'genus of tetrachord', this is misleading (and non authentic). I would rewrite this phrase with care, something like 'divisions of a tetrachord'. Genus is a term (in the limits of this article!), it's not worth using a word genus in a common sense. Olorulus (talk) 06:49, 26 October 2012 (UTC)

That might be good advice, if it were not for the fact that most of the best sources in English (Mathiesen, for example, both in Apollo's Lyre and in his New Grove article) speak precisely of, for example, "the three genera of the tetrachord", and "Aristoxenus recognized three basic genera of tetrachords". These may be "non authentic", but their provenance is impeccable.

Mathiesen is a great authority. No ifs and buts. Olorulus (talk) 10:26, 27 October 2012 (UTC)

Regarding the duplicated definition of standing and movable tones, I am obliged to you for pointing this out. Indeed it was an oversight: one drawn from M. L. West, the other from John Chalmers. I have corrected this.—Jerome Kohl (talk) 21:36, 25 October 2012 (UTC)

Mathiesen's Apollo's Lyre

According to the copyright in my exemplar and date shown in worldcat.org Mathiesen's fundamental book is dated 1999, not 2000. I think, the Google short info is wrong, therefore I corrected all references to the book in the Pyknon article. Olorulus (talk) 06:57, 28 October 2012 (UTC)

Absolutely right. You will notice, however, that the GoogleBooks link gives the year 2000, which is where I got the erroneous year. (That will teach me not to trust GoogleBooks, ever!).—Jerome Kohl (talk) 07:13, 28 October 2012 (UTC)