Talk:All-interval tetrachord

Mistake in Image
The F in the [0,1,4,6] tetrachord in the image should be an E. Starvinsky (talk) 14:13, 4 August 2011 (UTC)


 * Fixed, apparently. Hyacinth (talk) 17:45, 22 February 2012 (UTC)

The second musical example, showing the intervals in each tetrachord, is very confusing. Many notes and accidentals are wrong in the intervals extracted from the first tetrachord. Also, wouldn't it be clearer if the extracted intervals were in some rational order, like increasing size? — Preceding unsigned comment added by 146.96.130.201 (talk) 16:31, 22 February 2012 (UTC)

In particular: In the second interval, both A and B should be flatted; in the third, there is no G# in the original tetrachord; in the fourth and fifth, there is no B natural in the original tetrachord; in the sixth, there is no A natural in the original tetrachord.

I'm also not aware of Webern or Schoenberg using this tetrachord much explicitly. There might be a few of them here or there in their music, but I'm pretty sure it's not a significant feature of either's music (as it certainly is in Carter; I don't know about Perle). I don't think either Webern or Schoenberg even knew of the special properties of this tetrachord. The literature on Webern and Schoenberg that I know certainly doesn't mention this. Mind providing citations?

Finally, the second "External Link" is dead. It's also questionable: Carter's Night Fantasies is usually cited as the quintessential example of registrally deployed all-interval twelve-tone series, quite a different phenomenon than all-interval tetrachords. There might be all-interval tetrachords within it, though - it'd be nice to have the link fixed so we can see!146.96.130.201 (talk) 16:45, 22 February 2012 (UTC)


 * Fixed. Hyacinth (talk) 17:45, 22 February 2012 (UTC)

Consistency in Nomenclature
The page for Tetrachord indicates that traditionally the term refers to four tones spanning the interval of a perfect fourth. The all-interval tetrachord spans an augmented fourth, making it a "tetrad" as per the wikipedia article definitions. It is true that the tetrachord article mentions in passing that some music theorists use the term interchangeably with tetrad, but it is little more than a footnote and does nothing to justify linking to this article (which, if you go there after reading the 'tetrachord' article, jumps out as being more than a little incorrect). 67.163.161.226 (talk) 01:04, 3 May 2012 (UTC)


 * See WP:UCN. Hyacinth (talk) 01:48, 3 May 2012 (UTC)

Proper uses of braces, brackets, etc.
This article (unlike some articles on related topics) is currently using [] both for sets and interval class vectors. [] is certainly correct for vectors, but sets should be denoted with {}. Does anyone object to correcting this mistake? 65.79.1.34 (talk) 16:59, 13 May 2013 (UTC)

There are 4 all-interval tetrachords - not 2.
The statement "There are only two possible all-interval tetrachords." is not true. Both these tetrachords can be inverted (the chords turned upside-down, or mirror-reversed) and still keep the same essential properties, just in reverse fashion.

The two given are C Db E F# and C Db Eb G.

The inversions would (for example) be C D E# F# and C E F# G. These also contain all 6 interval classes.

I'm not expert in pitch class theory, so I hesitate to change it myself; but what I've just said seems unquestionably true. Might it be the case that inversions of tetrachords or other entities are usually not counted in set class theory? But, even if so, perhaps this should be mentioned in the article, in this context. M.J.E. (talk) 11:29, 11 January 2014 (UTC)

inversions
C D E# F# and C E F# G are not inversions from other tetrachords. first, because you can't inverse tetrachords and change the set second, [0,2,5,6] and [0,4,6,7] you can write as [0,1,7,9] and [0,1,6,t] too so you get C C#/Db G A and C C#/Db F# Bb and that are not inversions from C Db E F# and C Db Eb G. Or what do you mean?

inversion and number of AITs
The confusion here is that there are two meanings of the word "inversion" - the traditional music theory one and the set theory one. If by "inversion" we mean permuting the order of the pitch classes in the tetrachord (the traditional meaning of chord inversion), then [0,1,4,6] and [0,1,7,9] are not inversions of one another. But if we use the set theory notion of inversion - what M.J.E. referred to above as "the chords turned upside down," or reflecting each interval about the tonic - then [0,1,4,6] and [0,1,7,9] are inversions of each other.

The article is correct in stating that there are only two AITs when expressed in prime form, since prime form represents two inversionally related sets equivalently. The article then goes on to mention the inverted sets of each of those AITs. I for one would be in favor of amending the article to explicitly state that there are four AITs when expressed in normal form. From a purely aesthetic musical perspective, the AITs sound quite distinct from their inversionally related counterparts and I think that's important. Not sure the atonal theory world agrees with me. Shrug.

Threerealtrees (talk) 16:51, 21 March 2019 (UTC)