Talk:All-interval tetrachord

message: The F in the [0,1,4,6] tetrachord in the image should be an E. 
Starvinsky (talk) 14:13, 4 August 2011 (UTC)
replies: text: Fixed, apparently. Hyacinth (talk) 17:45, 22 February 2012 (UTC)

text: Fixed. Hyacinth (talk) 17:45, 22 February 2012 (UTC)
thread_title: Mistake in Image

message: 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)
replies: text: See WP:UCN. Hyacinth (talk) 01:48, 3 May 2012 (UTC)
thread_title: Consistency in Nomenclature

message: 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)
thread_title:  Proper uses of braces, brackets, etc. 

message: 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)
thread_title:  There are 4 all-interval tetrachords - not 2. 

message: 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)
thread_title:  inversion and number of AITs