Talk:Pitch class

message: I've substantially reworked this material as well as the pitch-class space entry.  My goal is to bring some of the music-theoretical entries in line with current thinking by professionals in the field.  I hope people won't be offended.
The major changes are 1. emphasizing that chroma is an attribute of pitches; 2. mentioning that pitch classes result from identifying octave-related pitches, and 3. explaining that pitch class space is a quotient space.  I emphasize the continuous perspective, since not all music confines itself to a discrete lattice.
:Thanks for bringing some sense into this article. I will copy edit sometime. Please don't forget to sign your comments. PizzaMargherita 22:07, 19 February 2006 (UTC)
thread_title:  Reworking the entries 

message: Can someone give a cite for the alleged influence of logical positivism on the choice of the name pitch class? Without a cite it should probably be removed. Gene Ward Smith 02:16, 21 April 2006 (UTC)
replies: text: The origin of the term "pitch class" with Babbitt is well-known.  The term first appears in print in Babbitt's "Twelve Tone Invariants as Compositional Determinants."  The influence of positivism on Babbitt is clearly stated in Babbitt's "Words About Music," where he refers to Schoenberg, Schenker, and Carnap as his "Viennese Triangle."  The logical positivist analysis of properties as extensions (sets) is well-known, and can be found in any history of positivism. Tymoczko 16:15, 21 April 2006 (UTC)

text: I disagree with this.  The idea of representing a physical *property* as a class is not at all intrinsic to mathematics, but is instead a characteristic of logical positivism considered as a philosophical movement.  (In general, mathematicians do not ask questions like: "how should we represent the concept 'whiteness' in a logically perfect language?")  There is a difference between "the class of all white things" and "whiteness" as a property.  For instance, you can count the members fo the class of all white things, whereas ordinary linguistic practices do not allow us to count the elements of "whiteness." Tymoczko 12:07, 9 July 2006 (UTC)
thread_title:  Logical positivism 

message: Does the note "b-double sharp" (or E##) actually exist? Wouldn't that only exist in C## keys or higher (i.e. with more sharps)? I would be shocked if I could find a composer using either (E## or B##) correctly. Sorry to nitpick Diddydoobop 10:57, 13 November 2007 (UTC)
thread_title:  Just a minor note 

message: Why, where, how, and what needs additional citations in this article? Hyacinth (talk) 07:37, 20 March 2010 (UTC)
replies: text: Tag removed. Hyacinth (talk) 16:52, 16 September 2010 (UTC)
thread_title: Additional citations

message: Seems like this highly related topics, or topic and subtopic, would be more clear all in one article. Hyacinth (talk) 07:35, 20 March 2010 (UTC)
replies: text: Concur. 100%. I had no idea the article "Integer notation" existed. It clearly declares itself at the beginning to be a method of notation strictly for application to musical pitch classes, and it is small enough to be absorbed easily into this one.—Jerome Kohl (talk) 19:50, 20 March 2010 (UTC)
replies: text: Quick merge done. Hyacinth (talk) 04:09, 29 March 2010 (UTC)
thread_title: Merge: [[Integer notation]]

message: The current table is shown on the left, a two column version in the center, and a three column version on the right.
Pitch class
Pitchclass	Tonal counterparts
0         	C (also B, D)
1         	C, D (also B)
2         	D (also C, E)
3         	D, E (also F)
4         	E (also D, F)
5         	F (also E, G)
6         	F, G (also E)
7         	G (also F, A)
8         	G, A
9         	A (also G, B)
10, t or A	A, B (also C)
11, e or B	B (also A, C)
Pitch class
Pitchclass	Tonal counterparts	Tonal counterparts
0         	C                 	also B, D
1         	C, D              	also B
2         	D                 	also C, E
3         	D, E              	also F
4         	E                 	also D, F
5         	F                 	also E, G
6         	F, G              	also E
7         	G                 	also F, A
8         	G, A              	
9         	A                 	also G, B
10, t or A	A, B              	also C
11, e or B	B                 	also A, C
Pitch class
Pitchclass	Tonal counterparts	Tonal counterparts	Tonal counterparts
0         	B                 	C                 	D
1         	B                 	C                 	D
2         	C                 	D                 	E
3         	E                 	D                 	F
4         	D                 	E                 	F
5         	E                 	F                 	G
6         	E                 	F                 	G
7         	F                 	G                 	A
8         	                  	G                 	A
9         	G                 	A                 	B
10, t or A	B                 	A                 	C
11, e or B	A                 	B                 	C
Which is superior? Hyacinth (talk) 04:09, 29 March 2010 (UTC)
thread_title: "Other ways" table

message: I propose the following paragraph or something to the likes of it be added into the Integer notation section, mainly because it's fucking hard to figure it out! 93.103.93.103 (talk) 11:18, 15 January 2012 (UTC)
replies: text: How does an  explanation that relies on a programming language that only a tiny fraction of readers can possibly understand help with a difficult-to-understand explanation? I would say the problem must have to do with the wording, which evidently needs revision for clarity. Alternatively, an ordinary mathematical formulation would have a better chance of reaching more readers.—Jerome Kohl (talk) 22:23, 15 January 2012 (UTC)
replies: text: Mathematical formulation, I agree! Then again, round, log and mod (either prefix or infix) are functions in math too, so it doesn't really make much difference to the initiated. I'm not an editor nor I strive to be one (so I won't do it:-), but I'd really like to see it included in the article as I think it might help someone. Thanks. 93.103.93.103 (talk) 16:59, 16 January 2012 (UTC)
replies: text: It seems to me that the first step is to scrutinize the description, in order to see whether there may be ways of clarifying the English. Once that is done, a mathematical formula could be added. I am neither a mathematician nor a programmer (though I do have some background in both areas—never heard of Python, though), so I am not really qualified to do this, but I will look at the English.—Jerome Kohl (talk) 20:31, 16 January 2012 (UTC)
replies: text: Well, having examined the offending passage, I can see two problematic things: first, it succeeds in making a very simple concept sound complicated and, second, it does so in part through the use of just the sort of mathematical explanations being called for here! Because I already know what is being described I can follow the convoluted explanations, but I doubt whether any beginner could do so. I think what is really needed is a simple explanation in plain English, with the more complicated mathematical formulas given only afterward (if at all). I'll see what I can come up with.—Jerome Kohl (talk) 23:31, 16 January 2012 (UTC)
replies: text: Lol, I too understand the 'Integer notation' section quite well, and having in common only the mathematical background, it didn't help me not one bit devise the formula above. That's what I think is missing, but you're free to rewrite the section as you please (though I though simpler explanations are preferred on simple.wikipedia.org). Anyway, thanks. Regards. 93.103.93.103 (talk) 15:57, 20 January 2012 (UTC)
thread_title: Integer notation

message: Ideally you would arpeggiate all of the unison octaves, then sound them together. The same should be done with the single octave example. Thanks in anticipation. Arrond wolf (talk) 09:11, 12 February 2012
:Why? Hyacinth (talk) 00:51, 13 February 2012 (UTC)
replies: text: Thanks. It took over two years, but arpeggio added. Hyacinth (talk) 17:18, 31 May 2014 (UTC)
thread_title: [[:File:Pitch class on C.png]]

message: The section about integer notation speaks about one pitch class higher than another. Allthough one can imagine how pitch classes may be ordered, the article doesn't mention such. 82.75.155.228 (talk) 23:49, 18 December 2014 (UTC)
replies: text: Maybe it depends on what they have been smoking? That is quite a funny error, but one that is heard all the time. It is difficult sometimes even for experienced theorists to remember that there is no up or down in pitch-class space, which just goes around in circles. In context it seems fairly plain what is meant: the successively higher integers represent what could be heard as chromatically ascending notes, if they were all converted to pitches within a suitable octave. That is very clumsily phrased, though. I shall have to think how it might better be put, without making the tacit gear-shift from virtual pc-space into the mundane pitch space of reality. Thanks for pointing this out.—Jerome Kohl (talk) 01:02, 19 December 2014 (UTC)
replies: text: I have taken a stab at fixing this. See what you think.—Jerome Kohl (talk) 01:28, 19 December 2014 (UTC)
thread_title:  Order 

message: User:Xayahrainie43 believes that English solfeggio uses the syllable "Ti" for the minor seventh scale degree, and "Si" for the major seventh. The solfeggio I learned (in the US) uses "Ti" for the major seventh degree and "Te" for the minor seventh, with "Si" as the sharped fifth degree. No reliable source is being cited for either belief (it does seem a case of "Sky is blue" to me), so let us discuss this here.—Jerome Kohl (talk) 19:36, 15 October 2018 (UTC)
thread_title:  "Ti" vs "Si" 

message: The equation for integer notation has a typo. It should be:
:p = 9 + 12\log_2 \frac{f}{440\text{ Hz}}.
That way, concert A @440 Hz gives p = 9, i.e., A4 is 9 semitones above C4 (because \log_2 (1)=0). ScriboErgoSum (talk) 08:08, 27 December 2021 (UTC)
thread_title:  Integer notation: equation typo