Do musical instruments pitched at different frequencies play different notes when compared to each other?

Question

I'm trying to get a better understanding how the pitch affects the note. Say if person A has a flute that is pitched to 440Hz and person B has a flute pitched to 335Hz, and they both decide to play the note C on their flutes. Would they be playing the same note? Would the C that was played relative to 335Hz be also a C note in 440Hz? Or does the pitch only make the note a high or low note? Like for example, when I play the C note in the lower and higher octave they both still are a C note one just higher than the other.

Edit

I'm sorry about the question being unclear, I'm very new to music theory. When I had this question in mind I thought of relative methods for naming musical tones. I thought that the letters (A to G) were relative too, however I now read in my book that the letter method is absolute, meaning that for example A always refers to a specific frequency.

Answer 1

I don't understand what you mean by 'pitched at'. Most instruments will use A=440Hz as a reference point, and that's how each and every orchestral instrument gets to be in tune with the rest.

A flute is a concert pitch instrument, thus will play a C or whatever and it'll sound like a concert C.

You may be confused by transposing instruments, like trumpet, which essentially will play notes a tone below what they call the notes. When the player sees a C, they will blow, and a Bb will come out. If an alto sax player sees a written C, it comes out as Eb. Odd, but true!

The scenario you state is incorrect, as 440Hz equates to an A, but in any case, playing one note at 440 and another at 335, how on earth could they sound the same - they're completely different pitches, producing completely different notes. The only way any two instruments are going to play the same sounding pitch is when they each play the same note at the same cycles/sec - Hz.

So, in summary - pitch = that a selected note is high or low - higher number = higher pitch. One would not have a flute tuned or 'pitched' to 335Hz. Basically, I think you've confused some terminology.

EDIT: second example (after your comment) - a flute tuned to 440Hz WILL NOT play the same sounding notes (pitches) as one tuned even to 432Hz. That's the whole point in using only one reference or datum point. And yes, everything will be relative to that datum point. How could it be otherwise?

EXTRA EDIT- That 335Hz note isn't far off half an octave from that (concert) A. Close to E/F. So that's the note it'd sound when 'playing an A (335). Now, does it make any sense...

Answer 2

I think that your attempt at "understanding how the pitch affects the note" needs an answer with a deeper root than has been given. This is slightly mathematical, but rather necessary.

First, let's establish common simplified terminology:

• A frequency is a physical characteristic of the sound and it is absolute (does not depend on the instrument, tuning system etc.). Example: 100Hz.
• A pitch is the designation (name) given to a frequency. This is just a helpful convention and there is no physical measurement for a pitch. Example: C₀.
• A note is a combination of a pitch and a duration. In Western musical notation, it is the basic representation of an instruction to produce sound. When written on a staff, it has to be combined with a clef for it to have a well-defined pitch. Example: 1/4 (quarter) D₀.

Your question is about frequencies and pitches. There are 2 parts which are needed to address this relation.

1. Tuning System

In order to determine how the relate to each other, we need to introduce something called a tuning system. A tuning system is a (bidirectional) mapping between the relation of frequencies and pitches. That is, it tells you when changing a frequency how the pitch changes.

Following are a couple of examples. I will use roman numerals (instead of A, B, ..., G) to symbolize pitches so to avoid a confusion which will be addressed in the 2nd part.

Note that because of octave equivalence, it is standard for tuning systems to establish that when multiplying/dividing the frequency by 2, the change pitch goes up/down an octave.

Pythagorean tuning: When multiplying/diving the frequency by 3/2, the pitch goes up/down a fifth. Example:

  I    V    IX
  1   3/2   9/4 ...

When combined with the "blanket rule" of octaves, we can find the full frequency relation to pitch relation: by dividing the frequency ratio of IX by 2 we get the frequency for II (9/8). We can continue to multiply by 3/2 and then divide by 2ⁿ (this is called folding) to find the rest of the relations. Here is a major scale:

 I   II     III    IV     V     VI      VII    VIII |  IX     X
 1   9/8   81/64   4/3   3/2   27/16   243/128   2  | 9/4   81/32 ...

(For example, X is a fifth from VI and an octave from III.)

Equal temperament 12: When multiplying/diving the frequency by ¹²√2 (2^1/12), the pitch goes up/down a minor second (same as saying: divide the octave into 12 equal parts). Here is a major scale:

 I    II      III     IV       V       VI     VII    VIII |   IX       X
 1   2​2⁄12   2​4⁄12   2​5⁄12   2​7⁄12   2​9⁄12   2​11⁄12   2​   | 2​14⁄12   2​16⁄12 ...

Equal temperament n will divide an octave into n equal parts with a frequency multiplication factor of 2^1/n.

This should be (probably more than) enough to understand what a tuning system is.

2. Concert Pitch

Up to now we didn't mention pitch names, we just showed how a pitch changes with the change in frequency. In order to have a 1-to-1 mapping from frequencies to pitches, and not only from their relations, we need to establish a base point.¹ This is an arbitrary choice - it is not a part of the tuning system (and is not given by some mathematical restriction).

The historical arbitrary decision was to map a pitch named A₄ to various frequencies (though some tunings use C₄ instead).

^{1Only if it helps, you can think about the linear function y=a*x+b: a is the tuning system and b is the base note.}

Frequency-Pitch mapping

With the choice of a base point, we can have a full mapping of frequencies to pitches. For Pythagorean tuning with A₄=440Hz, A₄ minor scale is (approx. Hz):

A4   B4   C5   D5   E5   F5   G5   A5
440  495  521  587  660  695  782  880

For ET12 with A₄=440Hz, A₄ minor scale is:

A4   B4   C5   D5   E5   F5   G5   A5
440  494  523  587  659  699  784  880

(Not too bad for a practical ET tuning!)

Answering Questions

Here are your revised questions:

If flute A is pitched to A₄=440Hz and flute B is pitched to A₄=335Hz, and they both play the note C₅, would they be playing the same pitch?

On each flute they would be playing the same pitch.

For example, in ET12, flute B will sound C₅=335*2^3/12=398Hz, and flute A will sound C₅=440*2^3/12=523Hz. They are both C₅ on each of the flutes (same fingering, same place of note on the staff...).

Would the C₅ on flute A be also a C₅ on flute B?

No, they would not be the same pitch relative to each other.

For example, in ET12, C₅ on flute B sounds like something between a G₄ and a G#₄ on flute A, about a fifth difference. This situation is reminiscent of that of transposing instruments, where playing a pitch sounds a different one (when they both use the same concert pitch). For example, Bb and Eb saxophones and clarinets - playing a C on a Bb instruments is like playing a G on an Eb instruments. However, in our case, the frequency difference is the result of different concert pitch tunings and not of transposition. (Thanks to guidot for pointing this out.)

Note that in another tuning system, C₅ on flute B could match a different note than G-G#₄, so the "effective transposition" amount varies by tuning systems. Thus, you can't ask "what would a pitch on flute A/B would sound like on flute B/A?" by giving only the concert pitch (though ET12 is assumed today).

Does the pitch only make the note a high or low note?

The pitch is the "height" of the note.

For example, when I play a C note in the lower and higher octave, are they both still a C note, one just higher than the other?

No, the confusion is purely due to a naming convention for pitches.

When dealing with octaves, it's useful to adopt a pitch notation (like Scientific or Helmholtz). A C above the discussed C₅ is a C₆, and the one below is a C₄. They are different pitches (because they are mapped by different frequencies on the same instrument²), they just use the same letter in this pitch notation to signify that they are octaves. In my tuning systems examples above, I used roman numerals where the octave does not reuse the symbol, so there is no confusion there and the answer is obvious.

^{2Different pitches can be mapped by the same frequency on different instruments. On a bass clarinet, a C₅ will sound (have the same frequency) like a C₄ on a regular clarinet.}

Answer 3

In earlier times the concert pitch was different. In the 18th century across Europe a concert pitch shift corresponding to two semitones in either direction was possible (this shrank to one semitone in the 19th century) and ensembles with baroque repertoire and authentic period instruments today still have a preference of 415 Hz - especially recorders don't allow much modification.

So it does not help, that a 415 Hz and a 440 Hz instrument are playing their respective a - they will sound out of tune.

Answer 4

Okay, scenario:

• Two flutes
  • One tuned to an A at 440Hz
  • One tuned to an A at 435Hz
• Both flautists play a C

Question:

Are they both playing a C?

Pretty much. They're both playing the same note in the sense that they're both undertaking exactly the same actions with their hands and mouths, to play a C.

Are they playing the same note?

The audible frequency coming from each flute will be different, you'll be able to hear the difference. If they both play at the same time, you'll hear the note 'wobbling' at a frequency which is the difference between the two pitches. This is known as a beat frequency. If they were apart by 2 hz, you'd hear the sound wobbling 2 times a second. This is particularly noticeable when there's only two 'voices' playing the same note (but not in tune with each other), and when it's a particularly pure tone, such as a flute. When there are 3 or more voices, it tends to get lost and just sound a little bit thicker.

Is a C played an octave higher still a C?

Yes, each time you double the frequency it's heard as the same note, at a higher pitch.

Take the 440Hz for A, for example. 220Hz is an octave lower, still an A. 880Hz is an octave higher, still an A.

Answer 5

I think that you are simply misunderstanding something. A mere name cannot affect the frequency. Consider this analogy:

I have a brother named John. But I also have a cousin named John. Are my brother and cousin the same person? No. They would have different personalities, different beliefs, different bad jokes, etc. Are they both John? Yes.

A is simply a name given to a frequency. If any group of people decides to give A as a name for 440Hz, then it is A. If another group decides to give A as a name for 335Hz then it is also A. Are they both the same frequency? No. They would sound different, feel different, etc. Are they both A? Yes.

The group of people deciding to give names to pitches is an oversimplification of people creating a tuning system. For more of that, see the answer of user1803551

Answer 6

Being pedantic, 440 Hz is an A, not a C. In the case that you have given, the two flutes would sound out of tune with each other. One would be playing 335 Hz and one at 440 Hz. I admit that I misread the question, and thought that you hadwritten 435 and 440 Hz. 335 Hz would be something like an F, but still the two flutes would not be playing the same absolute note.

This is what happens with transposing instruments (the flute is normally not considered to be a transposing instrument): playing C in a Bb saxophone will actually sound Bb.