Talk:Holdrian comma

message: Most theorists discuss intervals and tetrachord species at great length, often presenting them through various frettings on [a kind of lute]. In the 8th and 9th centures, according to Ibn al-Munajjim, its fretting was:
open string  	g(0)     	c'       	f'         	bb
first finger 	a (204)  	d' (702) 	g' (1200=0)	c (498)
second finger	bb' (294)	eb' (792)	ab' (90)   	db (588)
third finger 	         	e' (906) 	a' (204)   	d (702)
fourth finger	c' (498) 	f' (996) 	bb' (294)  	eb (792)
             	         	         	           	e (906)
The notes f'-e formed a normative series from which eight diatonic modes were derived, the second and third finger notes being mutually exclusive....
During the 9th and 10th centuries Persian influence again made itself felt....The most far-reaching innovation was the introduction ... of a neutral third. By the 11th century the notes found within the tetrachord (i.e. on any one string of the [lute]) were g ab a x a bb b x b c' (x is halfway between b and [natural]).... In the 13th century these were integrated into the Pythagorean system by Safi al-Din, being placed one comma below the diatonic intervals so that the tetrachord becomes in theory g(0) ab (90) a-c (180) a (204) bb (294) b-c (384) b (408) c' (498).
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:The word "comma" in the last sentence is unqualified, and the "-c" notes are about 24 cents below the major thirds, which is at least in the ballpark of what we're talking about here. But this stuff about the 53 perfect fifths is just bogus. —Wahoofive (talk) 16:03, 15 September 2005 (UTC)
replies: text: On second thought, surely he means a Pythagorean comma. —Wahoofive (talk) 16:06, 15 September 2005 (UTC)
thread_title: Excerpts from Harvard Dictionary of Music entry on "Arab music"

message: :"Three of the most important and related theoretical concepts [in early theoretical treatises dating back to the 4th century BC] are the establishment and calculation of the 12 fundamental pitches, the idea of scales and that of modes....The earliest account of the intervallic relationships of the 12 pitches is documented in Lu-shih ch'un-ch'iu (3rd century BC); the method of their calculation is the simple application of the Pythagorean (cycle of 5ths) method...."
:"For centures theorists tried to solve the [problem of the Pythagorean comma] by devising a system of notes which could rotate their functions identically; various methods were attempted. In the 1st century BC Ching Fang tried calculating up the the 60th note, while Ch'ien Yueh-chih (5th century) went as far as the 360th note....The complex series of notes which resulted was not carried out in any known musical practice, nor did it have any influence on later theoretical developments...."
:"The first attempt at creating an equal-tempered scale was made by Ho Ch'eng-t'ien (5th century), who lowered the frequency of each of the tones of the Pythagorean series by a simple factor so that the 13th note was exactly twice the frequency of [the fundamental]...Chu Tsai-yu (16th century) finally created an equal-tempered scale of 12 notes by successively dividing the fundamental number by the 12th root of 2."
And? Hyacinth 07:11, 17 September 2005 (UTC)
replies: text: And this contradicts Touma's assertion that Ching-Fang's research had anything to do with the "Arabian comma"; rather, he was trying to temper the scale to avoid the Pythagorean comma. Between that and the meaningless fraction (not to mention the bad arithmetic shown above), I'd say Touma's credibility is shot. —Wahoofive (talk) 16:24, 17 September 2005 (UTC)
thread_title:  Excerpts from the New Grove article on China 

message: I think this article should be deleted, and I intend to list it on AfD unless someone can give a good reason why it should stay. The article appears to be based on a single passage in a book, and this passage is deeply confused, mentioning three different intervals and talking about them as though they were the same thing. Two of these intervals are relevant to the 53-tone system (in this list of intervals they are referred to as the 53-tone comma and Mercator's comma). The third interval appears to have no relevance to anything, as others have already pointed out. --Zundark 11:16, 19 November 2005 (UTC)
replies: text: I second that, unless someone can get some better sources and figure out what interval this actually is. —Keenan Pepper 16:29, 19 November 2005 (UTC)
replies: text: OK. nobody has objected, so I've added it to AfD: Wikipedia:Articles_for_deletion/Arabian_comma. --Zundark 11:34, 22 November 2005 (UTC)
thread_title:  Deletion 

message: I have the third, expanded edition of Touma's book in the original German (1989, but still seems to be the current edition). He mentions the "Arabian comma" on page 49, putting it in scare quotes (the Pythagorean and syntonic commas don't have these). It's 53root2. A term like "Holdrian" is neither on this page nor in the index; this is the only difference between the book and the wikipedia article.
He goes on to describe the Mercator comma, attributed by him to Ching Fang. Although this is a real komma, he still calls it "Arabian comma" in the same scare quotes.
On page 50, he gives the maqamat Rast and Navahand in terms of steps of an unspecified comma. They do add up to 53 for the whole octave. As in the article, this is qualified: all diatonic steps except c-d are medium seconds; no mention of the flattened notes. I always took this to mean that theory and practice don't have much to do with each other, but it would be nice the know for sure.
Meanwhile, I have asked for Touma's address at the publishing house.
— 84.160.147.123 (klaus) 10:44, 7 December 2005
:The comment on the structure of Nihavent - citing Touma - does not make any sense, i.e. "has medium seconds between d–e♭, e–f, g–a♭, a♭–b♭, and b♭–c', a medium second being somewhere in between 8 and 9 commas". Is this what the reference is saying? kupirijo (talk) 17:53, 21 December 2019 (UTC)
thread_title:  What Touma says 

message: I have added an audio example to the article. Hyacinth (talk) 08:14, 9 August 2008 (UTC)
thread_title: Requested audio

message: There is something wrong in the section describing the Arabian comma in this article. I never noticed it before, but now I am completely puzzled – all the more so that I cannot verify Toma's book just now.
The article says that the makam rast has the following set of Holdrian commas: 9 8* 5* 9 9 8 5 for the scale c d e f g a b c'. No explanation is given for the sign * (there should be one!), which probably corresponds to the statement that follows, that "in common Arabic and Turkish practice, the third note e in rast is lower than in this theory, almost exactly halfway between western major and minor thirds, i.e. closer to 6,5 commas above d and 6,5 below f". That is to say that 8* and 5* would stand for twice 6,5 "in common Arabic and Turkish practice". What is unclear for me (apart for the lack of explanation of the *) is to what other common practice the scale with 8 and 5 would correspond. Is there a common makam practice outside the Arabic and Turkish ones? 
Makam nihavend is then described as "similar to the Western minor scale", 9 4 9 9 4 9 9, c d e f g a b c'. Up to there, no problem. But the text continues saying that nihavend "has medium seconds between d–e♭, e–f, g–a♭, a♭–b♭, and b♭–c', a medium second being somewhere in between 8 and 9 commas." But 9 commas is a major second, and a minor second is 4 or 5 commas; a medium second should then be 6,5 or 7 commas, not "between 8 and 9". One may suppose that the mention of "medium seconds between d–e♭, e–f" really means "between  d–e♭, e♭–f": the case would then be identical with that of rast in "common Arabic and Turkish practice". 
Further, g in all these descriptions is 31 commas above c, and therefore there remains 22 commas between g and c', for a total of 53 commas in the octave. If however there are medium seconds of 6,5 commas between g–a♭, a♭–b♭, and b♭–c', they make a total of only 19,5 commas: there are 2,5 commas missing, probably indicating that one of the seconds should be major (9 commas) instead of medium.
Either nivahend is "similar to the Western minor scale", or it has medium seconds. And if it has medium seconds, these must come in pairs, dividing a minor third of 13 commas in two equal parts. In its present state, the section is unclear and while I can see the error, I have no idea of how to correct it. — Hucbald.SaintAmand (talk) 20:43, 25 October 2017 (UTC)
thread_title:  Arabian comma?