Talk:Scientific pitch notation

Is 440Hz A4 or A3

Unfortunately, there is no universally-accepted standard associating a particular octave number with a specific frequency range. Is that true? ISTM that it completely defeats the purpose of the notation if so! Andrewa 16:10, 11 March 2006 (UTC)

See http://www.dolmetsch.com/musictheory1.htm for one definition that sets middle C as C4 and 440Hz as A4. That's the only usage I have previously encountered. But, according to the current article, Japanese midi specs may (interesting word) use C3 to mean middle C.

I feel a little like I have just heard a rumour that a friend has been executed. What right has anyone to redefine the notation in this way? What possible use could it have? Surely it just reflects a mistake on the part of the writers of these specs? But perhaps the situation is not as grave as the rumour.

Assuming it is true, it would mean that those following the Japanese midi convention were an octave out with everyone else. But would it mean that this then becomes an alternative scientific pitch notation in English? I'm skeptical. ISTM that, at worst, we now have two notations:

Scientific pitch notation (otherwise unqualified, in English) still means middle C is C4, 440 Hz is A4.

The midi specification uses C3 to mean middle C, A3 to mean 440 Hz. I originally was going to say Japanese midi specification but I'd like to avoid that phrasing if at all possible, and if the Japanese specs use this convention then my initial reaction is that the English specs should too.

* Reply to the above paragraph: According to  and several other easily found secondary sources, General Midi sets A4 to note 69. The MIDI specification uses note numbers, not SPN, so the question here is not whether A3 or A4 should be 440, but whether MIDI note 69 is A3 or A4 or A5 (since A4=440 is fixed in SPN). Some non-GM-compliant systems do indeed shift A4 by an octave (to note 57 or 81). mirabilos (talk) 22:35, 8 May 2018 (UTC)

Actually, just dreaming a little, if we do have the situation that scientific pitch notation in English puts A4=440Hz and the midi spec in Japanese puts A3=440Hz, then that would be one of the toughest translation decisions I've ever considered! In the fullness of time, one will hopefully change, with all that entails. (Not an inviting prospect.) But failing that, one will be abandoned and forgotten except by musical historians and the like. But which? And meantime, in the vernacular confusion seems inevitable. So what should the English midi specs say? Hmmmm.

Either way, I'd qualify it in the English specs. Specifications need to be specific.

I'm going to research this a little more before updating the article. Comments very welcome. Andrewa 16:51, 11 March 2006 (UTC)

From http://scientific-pitch-notation.brainsip.com/ :

Scientific Pitch Notation in music is a method of naming the notes of the standard western chromatic scale by appending a number identifying each octave, so that each note is unambiguously defined according to its fundamental frequency.

Example: A4 is the A above middle C, and has a fundamental frequency of 440.00 Hz.

Now, that article cites http://www.dolmetsch.com/musictheory1.htm#uspitch (as does the current Wikipedia article) so it's not an independent source. But I'm interested in the word unambiguously. I feel like saying Hear! Hear!.

But I recognise I need to take a step back here. I'm very tempted to advocate keeping scientific notation as it always was. I'm guessing by the current article that there are those who want to give the midi convention equal time.

Neither is acceptable in Wikipedia of course. We don't decide, we just describe. So the question is simply, what does scientific pitch notation mean? Not what it should mean, simply what it does mean. Hmmmm again. Andrewa 17:14, 11 March 2006 (UTC)

Note also Middle C: In Western music, the expression "middle C" refers to the note "C" or "Do" located between the staves of the grand staff, quoted as C4 in note-octave notation (also known as scientific pitch notation).

I'm hardening a little. Andrewa 17:19, 11 March 2006 (UTC)

I guess it's obvious, but this Google search might be useful. Andrewa 17:26, 11 March 2006 (UTC)

The claim that there is ambiguity was introduced by an anon with no other contributions. Might it even be a test or prank? But it's surprising that it has survived so many edits, including rephrasing of the claim itself. Hmmmm.

Curiouser and curiouser, the current article at Musical Instrument Digital Interface does not mention this alleged quirk of the MIDI specification, in fact it does not mention scientific pitch notation at all, either by name of by using note names such as C4. Rather, it describes notes as being expressed as a 7-bit unsigned integer 0-127, from C,,,, ... designated as MIDI note 0 to g''''' ... designated as MIDI note 127, so there they are using Helmholtz notation not scientific pitch notation. Still more hmmmm. Andrewa 11:05, 18 March 2006 (UTC)

Oh, and scientific pitch notation does not assume equal temperament. The table that is part of the article does assume this, and the article on piano key frequencies does too. But, if for example you choose to tune an organ to mean tone tuning, middle C is still C4, and the A above it is still A4. It may not be A440 however (depending on exactly how you've chosen to implement your mean tones). Equal temperament is generally assumed by users of scientific pitch notation, but the notation itself doesn't assume it. Andrewa 11:13, 18 March 2006 (UTC)

Action

Time to be bold. Removed text:

Unfortunately, there is no universally-accepted standard associating a particular octave number with a specific frequency range. For instance, Japanese MIDI specs and American MIDI specs may specify dissimilar ordinals for middle C (C3 vs. C4). In addition, this notation system assumes 12 tone equal temperament and does not specify that A above middle C must conform to ISO 16 frequency standard (440.00 Hz). In typical American usage, however, the ISO standard is taken for granted, and middle C is labeled "C4."

As explained above, I think these claims are quite simply false.

Also removed

For this reason, the notation C4b would be slightly more consistent, though significantly less legible.

as would be suggests to me that this is an original proposal. Assuming that it is, then it has no place in a Wikipedia article. Andrewa 11:05, 18 March 2006 (UTC)

References

Not to throw a wrench into the works, but ...

I've definitely read books in which "C5" was used to refer to middle C. Don't have any on hand at the moment, though I associate this with earlier English writing.

I've read books that said that the earth has existed for less than 10,000 years. But I don't propose to update the brontosaurus article based on these books.

Personally I consider "C4" to be the modern name for "middle C" and think there's a reasonable consensus around this terminology. However, some sort of warning might not be inappropriate: "Although most writers use C4 to refer to middle C, one occasionally finds variant systems in which middle C is referred to as C5 or C3." Tymoczko 04:26, 20 March 2006 (UTC)

No, if the article mentions them at all (and I think it probably should) it should state clearly that these are different systems of notation. They are not scientific pitch notation.

Update: a little Googling shows that there are definitely a lot of different conventions about octave numbers among software manufacturers--C3, C4, and C5 can each be used for middle C. Tymoczko 04:31, 20 March 2006 (UTC)

Agree there are lots of different usages. Whether any of these should be called conventions is less clear. They only become conventions when they have some wider following than one software manufacturer, or even a group of software manufacturers who use a compatible notation for whatever reason.

If any of them do have this following, then each of these should each have their own article, describing not just what they call middle C but the whole system. There are many ways in which it could depart from this one, and I expect some of them do.

Thanks for the comments. I don't think they throw a wrench in the works at all. Andrewa 10:16, 10 April 2006 (UTC)

I've expanded the introduction a little, both to mention these variant systems and to put the rather pedantic point made there about Cb into some sort of perspective. Andrewa 15:41, 13 April 2006 (UTC)

Aha!

I think the ambiguity to which you refer may be due to using the terms scientific pitch notation and note-octave notation as synonyms, as the article itself did until a few minutes ago. What seems to be the case is that there are several systems of note-octave notation (probably owing to errors by the writers who proposed them, but that's another story) but only one of these is scientific pitch notation.

That's not to say that some writers may not claim to use scientific pitch notation, but get it wrong. We're all human, and like myths of extreme plutonium toxicity, once something is in the press then however ridiculous it is it will stay in the press. See Snopes. Andrewa 16:41, 17 April 2006 (UTC)

==Other notation c' c'' In Netherlands I learned a different way of numbering the octaves, see Dutch wikipedia

• C0-B0: C₂-B₂ (Sub-contra octave)
• C1-B1: C₁-B₁ (Contra octave)
• C2-B2: C-B (Great octave)
• C3-B3: c-b (Small octave)
• (C4-B4 in this article): c'--b' (one-primed octave)
• every higher octave gets an additional prime: c'', c''' etc. (two-primed, etc.)

I know that the naming of notes in different languages is a horrible mess, but does the above convention have a name in English? —Preceding unsigned comment added by hankwang (talk • contribs)

OK, it was actually described under note, it's the "conventional octave naming system"... Han-Kwang 20:18, 12 June 2006 (UTC)

The system mentioned above is used not only in Netherlands but in a considerable part of Europe for instance in Germany, Scandinavia and eastern Europe. To make things even worse, a contra C at a pitch of about 32 Hz is sometimes noted 1C. This is the same tone as C1. One octave above we find C (great) or C2, then c (small) or C3. When we come to next c "the middle c" at about 256 Hz it is sometimes noted c1 in parts of Europe and C4 in english. The risk of confusion is obvious here so it is necessary to know which system is used. The english system is probably based on human ear where C0 at 16 Hz is barely audible. The central european system corresponds to the organ where the C (great) at 64 Hz or C2 is the lowest tone of the 8' stop. The 4' will start at C3 while the 32' actually goes down to C0 or 16 Hz.Phstrom 14:39, 15 June 2007 (UTC)

This is the Helmholtz system: also described here which should have it's own article, and be separated from here. Perhaps both articles could be developed together in a standard way as both are in common usage. –MDCollins (talk) 11:55, 11 July 2007 (UTC)

Helmholtz pitch notation now created. Any views welcome. –MDCollins (talk) 00:37, 3 August 2007 (UTC)

If it's a problem, all b/# should be replaced by flat/sharp.

(Comment moved from Han-Kwang's talkpage)

I'd like that, too, but it doesn't show up in IE. — Omegatron 20:59, 27 August 2006 (UTC)

I'm not sure how to read this. Do you mean that ♭ (flat symbol, "b", & coding) and "♭" (flat symbol, direct UTF) and "♯" (sharp symbol, UTF) are all invisible in IE? In that case, all occurences should be replaced by the words "flat" or "sharp". I don't think a lowercase b is a suitable replacement for a flat symbol. Han-Kwang 21:05, 27 August 2006 (UTC)

Huh. They used to be. But now that I try them they all show up fine (IE6). I don't know what determines whether they show up or not, then. If they are going to show up as a rectangle on the vast majority of readers' screens though, they are even less suitable than # and b. Otherwise I would prefer using the proper symbols. There is also the {{unicode}} template to consider, which supposedly fixes some such problems in IE. See Template_talk:Unicode#Discussion, [1], Talk:Accidental_(music)#Viewing_Problems — Omegatron 22:07, 27 August 2006 (UTC)

One could consider $\flat$ and $\sharp$ (LaTeX math mode) to render them as images. Han-Kwang 22:22, 27 August 2006 (UTC)

The accidentals aren’t showing up on my computer either. They appear as squares. I think that using ‘#’ as a symbol for sharp and ‘b’ for a flat is a lot better than seeing blank boxes. Either that or all of the accidental symbols need to be replaced with their respective terms (a.k.a flat, sharp, and natural, respectively). 15:32 11 April, 2007 Tophatpianist

Did you consider ♭ and ♯ (use Template:Music?) Lanthanum-138 (talk) 04:14, 27 March 2011 (UTC)

sources?

I've tagged the definition with citation needed, being an agnostic with regard to 'Scientific' claims. Especially since note-octave notation has been merged here, we need to re-include the caveats of the first version of the article.

Anyone consulting this article (it links from {[Magic flute]] should be made aware that any writer serious about being precisely understood will define his/her system near the beginning of the book. It would be interesting to collect examples and see what regional/ national paterns might exist. Harvard gives both CCC, CC, C, c, c1, c2 and C2, C1, C, c, c1, c2 along with their prefered C1, C, c, c'. (btw, this 'English' system appears to have been introduced by Ellis' translation of Helmholtz; he notes that previous english writers used lines abouve and below letters). I first encountered something like the system being described in the article in a British book I've since forgotten, but it started from an 88 note keyboard A1, B1, C1, D1.; this is what my (Californian) piano tech. uses. For what it's worth, Sibelius software uses A0, B0 C1. Sparafucil 23:30, 15 July 2007 (UTC)

JASA reference

I came across this Wikipedia article, and I thought I might include the reference to the Acoustical Society of America, because this article had been tagged as requiring sources. The article was in fact a discussion of an informal convention used by someone else, but it defines C0 as 'a reference frequency of 16.35 cycles/sec., a frequency which is in the neighborhood of that producing the lowest pitch audible to the average ear'. At the time of me writing this, there is a public abstract of the report that I found here. I also added some clarification to the section about variant methods. I must confess I've not edited much on Wikipedia, so if I've got my formatting or maybe my etiquette wrong, do fix it or drop me a line :)Geraint 10:00, 5 September 2007 (UTC)

C4 and A4

If Middle C is C4, how can A4 be above it??? Last time I checked, "a" came BEFORE "c" in the alphabet. Lower than C4 should be B4, and then A4, a third BELOW C4/Middle C. Not a sixth above mid-c as the article's "example" says. Can somebody clear this up for me PLEEEEZ? SingingZombie (talk) 02:00, 28 December 2009 (UTC)

Musically, octaves follow the C major scale, for example C4-D4-E4-F4-G4-A4-B4-C5, corresponding to "do-re-mi-fa-so-la-ti-do" popularized some 50 years ago in The Sound of Music. The chart at http://www.dolmetsch.com/musictheory1.htm#MIDI illustrates this nicely. --Glenn L (talk) 02:57, 28 December 2009 (UTC)

I read the article looking for an answer to the question "on which note does the transition occur", and couldn't find it - C is implied but not stated outright. I'll add this. 79.75.24.63 (talk) 09:03, 10 June 2010 (UTC)

Superscript or subscript?

Subtle point but has it been standardized as putting the octave number as a superscript or subscript? In other words, is middle C written as C⁴ or C₄? Justin Tokke (talk) 14:25, 3 May 2010 (UTC)

I don't know about standardization but, in music theory articles at least, I find the subscript used far more often, not least because the superscript can too easily be confused with the mathematical "power of" operator, which may occasionally occur.—Jerome Kohl (talk) 23:22, 3 May 2010 (UTC)

12TET

It would be convenient if the article would state that the frequencies and the calculation thereof are based on the 12TET tuning-system and not the just intonation. —Preceding unsigned comment added by 217.19.26.21 (talk) 20:18, 18 October 2010 (UTC)

 Done. --DavidCary (talk) 16:03, 13 July 2016 (UTC)

Scientific pitch

Binksternet, is there a distinction to be drawn between scientific pitch and scientific pitch notation?. If there is, your "history" section would seem to be about the former, and could do with merging with the section on "scientific pitch" that I wrote. If not, perhaps the article ought to be renamed Scientific pitch since it is no longer entirely about the notation. SpinningSpark 16:22, 12 March 2013 (UTC)

Dang! Looks like we need a real article about scientific pitch. Binksternet (talk) 17:10, 12 March 2013 (UTC)

To put it more plainly, the thing I don't understand is whether scientific pitch notation was originally the notation of scientific pitch or whether it was always applied to any pitch such as the modern use with concert pitch. SpinningSpark 17:51, 12 March 2013 (UTC)

I've added links to Lyndon LaRouche and the Schiller Institute to this article's small section on "scientific pitch." I'm not sure which came first, but the LaRouche promotion of "Verdi pitch" seems to have gained steam in the late 20th century, say around 1988. I suppose it's notable enough for its own article, if someone wants to write it, but for now the section in the Schiller Institute article is plenty. It might be interesting to find reliable sourcing for the story that LaRouche and his followers tried to have legislation passed in Italy which would have made tuning forks illegal and subject to confiscation, if they weren't at A432 to within a small tolerance, with fines mulcted from the owners of such pernicious contraband.

I've left "Scientific pitch" redirecting here, per the Principle of least astonishment, with a hatnote for those looking for philosophical pitch. __Just plain Bill (talk) 18:58, 12 March 2013 (UTC)

Commented out scientific pitch except for references

The article on Scientific pitch notation has become mistakenly mixed up with Verdi tuning, also called Scientific pitch. However the two are not related: although writers describing Scientific pitch notation often use A440 to give particular examples, Scientific pitch notation and Helmholtz notation are both just ways to describe octaves relative to whatever is designated as C₀ in any system. Please help by avoiding re-introduction of the mix-up. 76.178.152.143 (talk) 15:40, 21 April 2013 (UTC)

I removed the material and used it start the new article scientific pitch. Binksternet (talk) 17:03, 21 April 2013 (UTC)

Two schools or one?

First I question the usefulness of section C♭ and B♯ problems: what person in their right mind would choose to designate what everyone else calls B and C using C♭ and B♯? (The only tiny exception could conceivably be the designation of the frequencies of the strings of the double-action concert harp as their basic tuning is in the key of C♭, see e.g. here).

Second there's no reference given. Then how do I know this statement made in that section: "The convention is that the letter name is first combined with the Arabic numeral to determine a specific pitch, which is then altered by applying accidentals" is accurate and reliable?

Third I fail to see the sense of "The matter may be clarified by viewing "♭" and "♯" as denoting lowering or raising by a variable amount". What can this have to do with scientific pitch designation which deals with exact frequencies not "variable amounts"?

Fourth I have a question, out of curiosity, as to the combination of accidental and octave designation. Apparently (judging from what this article does, although no specific authority was brought to bear) it is universally first accidental then octave designation: F♯₅ not F₅♯ (a notational practice which incidentally seems to be in contradiction with the view that "the letter name is first combined with the Arabic numeral to determine a specific pitch, which is then altered by applying accidentals"). But I'm curious if there were ever theological debates around this question. Were there ever in the history of scientific pitch notation two schools the F♯₅ school and the F₅♯ school?

Contact Basemetal here 09:01, 21 February 2014 (UTC)

As regards the usefulness of the C♭/B♯ section, I can see where some confusion might arise in this area. As currently written this section may actually be adding to that confusion by, I believe, over-thinking the problem. Certainly there are key signatures and harmonic situations in which C♭ or B♯ are used, and if one wished (for whatever reason) to discuss such situations using Scientific Pitch Notation -- in printed text, perhaps --, the question might well need resolution.

Really, though, the answer is simple:

• in SPN the octave breaks occur between B and C, and are tied to the alphabetic character used to describe the pitch. Thus:
• "B3" and all of it's possible variants (B♭♭, B♭, B, B♯, Bх) would properly be designated as being in octave "3".
• "C4" and all of its possible variants would properly be designated as being in octave "4".

Past that, one just has to know the axioms of the system, two of which are

• B♯(n) = C(n+1) , and
• C♭(n) = B(n-1), for any octave, "n".

As to your theological question, all I can say is that I've been using SPN, both scientifically and musically, for 40 years, and I have never (until now) seen the accidental placed following the number. It's always been F♯4, and never F4♯.

YMMV :)

I have to agree that the present B#/C♭ section is more confusing than helpful. The paragraph discussing equal temperment, meantone etc. really has nothing whatsoever to do with octave designations in Scientific Pitch Notation, and muddies a simple system with a bunch of unnecessary numbers.

I propose eliminating that paragraph and replacing it with your two "axioms" .

74.95.43.249 (talk) 23:21, 21 January 2016 (UTC)

Since no one seems to have had any objections to the original "axiomatic" proposal in well over a year, I have made the changes indicated.

74.95.43.249 (talk) 21:52, 11 February 2016 (UTC)

Grand staff

The opening illustration showing the octaves of C would be better if the notes were shown on a grand staff. That would be conventional.CountMacula (talk) 22:34, 8 February 2015 (UTC)

Agreed, but I don't find an example of that in the commons. Do you have one to upload?

74.95.43.249 (talk) 23:23, 21 January 2016 (UTC)

Why so many frequencies?

Since the article makes it clear that this a system of notation, and independent of actual pitch standards and frequencies, I am wondering why there needs to be a big table of specific frequencies near the end of the article? Seems like that table would be more relevant in an article on "twelve tone equal temperment", than in an article on notation.

Also, it is unclear what the parenthetical +/- numbers are supposed to be telling us.

I suggest that this table could be replaced with something simpler and more relevant to the rest of the content. For example:

Scientific pitch notation	Helmholtz pitch notation	Helmholtz subprime notation	Octave name	Frequency @ A=440Hz standard	Frequency @ C=256Hz standard	Common name
C-1	CCCC	C,,,	Subsubcontra	8.176	8
C0	CCC	C,,	Subcontra	16.352	16
C1	CC	C,	Contra	32.703	32	Lowest C on piano
C2	C	C	Great	65.406	64	Low C
E2	E	E	Great	82.407	81	Guitar low E string
C3	c	c	Small	130.813	128	Tenor C
G3	g	g	Small	195.997	192	Violin G string
C4	c′	c'	One-lined	261.626	256	Middle C
A4	a′	a'	One-lined	440.000	432	pitch reference (IPN)
C5	c′′	c''	Two-lined	523.251	512	Treble C
C6	c′′′	c'''	Three-lined	1046.502	1024	High C
C7	c′′′′	c''''	Four-lined	2093.005	2048	Double High C
C8	c′′′′′	c'''''	Five-lined	4186.009	4096	Eighth octave C, Highest C on piano
C9	c′′′′′′	c''''''	Six-lined	8372.018	8192
C10	c′′′′′′′	c'''''''	Seven-lined	16,744.036	16,384

74.95.43.249 (talk) 23:25, 11 February 2016 (UTC)

Sources for these pitch notation names?

I'm not able to find much use of these terms, especially the title term "scientific pitch notation", predating this WP article (only the ext link added in 2004). The referenced 1939 JASA abstract does not use this term. Where did this come from, and are any of these terms used in music literature? Dicklyon (talk) 17:58, 25 July 2019 (UTC)

Remove octave 10?

I added octave 10 to the frequencies chart some time ago, since some of those frequencies can be heard by at least a minority of people. But practically speaking, those frequencies would rarely, if ever, be used in any kind of music. It may be better to remove them to improve formatting and reduce clutter. Thoughts? Jtrevor99 (talk) 21:51, 9 January 2023 (UTC)

I don't think removing that column from the table would contribute much to the decluttering of the article, although users of mobile devices might have a different opinion. The usually cited hearing range for humans is 20 to 20,000 Hz, so if anything, column "−1" could be removed. But on balance, I don't think removing these columns would be a net gain. -- Michael Bednarek (talk) 02:53, 10 January 2023 (UTC)

Thanks. If the MIDI notes didn't extend through octave -1, I'd agree. Jtrevor99 (talk) 03:47, 10 January 2023 (UTC)