# Can two notes be at the same frequency or different octaves, or vice versa?

I was reading something that mentioned playing the same octave of two notes on different instruments but having them at different frequencies. Is that possible?

• Sure, instruments can be tuned independently. en.wikipedia.org/wiki/Musical_temperament – dfhwze Jun 13 at 5:44
• Not in 12tet whith the same tuning i.e. A=44oHz. But the question as is, is difficult to understand. – Tim Jun 13 at 9:19
• It might a reference to transposing instruments. A simple case is the double bass. You might give the same music to a cello and a double bass but the bass would actually play an octave lower than the cello. More complex is something like the clarinet which will play A or Bb when given a written C. See en.wikipedia.org/wiki/Transposing_instrument. – badjohn Jun 13 at 10:53
• I'd like to know who downvoted a good question. – Randy Zeitman Jun 13 at 18:21

I think this is a case where the terms 'note' versus 'tone' are important, and scientific pitch notation can help make things clear.

When the term 'note' is used we really should be talking about notation, something written on paper or its equivalent. A 'tone' is a more abstract idea, basically it's just a pitch, a frequency.

The tone `C4` is 261 Hz. If two instruments are producing that tone, they are the same frequency of 261 Hz. (I'm glossing over the issue of exact frequency, no two instruments will produce perfectly the exact same frequency.)

Notation of those two tone is another matter. Some instruments are transposing which means the actual tones produced by the instrument are higher or lower that what is notated.

For example, a B flat trumpet transposes down a whole step. When a trumpet player reads a `C4` in notation the actual tone produced is a `Bb3`.

...playing the same octave of two notes on different instruments

As notated it's basically `C4` or 261 Hz.

...but having them at different frequencies.

Played on a violin it's a `C4` at 261 hz.

Played on a B flat trumpet it's a `Bb3` at 233 Hz.

I was reading something that mentioned playing the same octave of two notes on different instruments but having them at different frequencies. Is that possible?

There are a couple of senses in which this statement could be true:

• As per Michael Curtis' answer, there are transposing instruments where the notated note is a number of semitones different to the sounded note. If by "notes" you mean notated notes, it's true that the same notated note on different instruments would sound at a different pitch on instruments that transpose differently.
• The instruments might simply be tuned to a different temperament or pitch reference, or intoned differently for other reasons (such as the stretched tuning often found on a piano). This could cause a sounded "A5" to have a different pitch on two instruments.

A couple of slightly more esoteric points:

• It's very hard for some instruments to produce a 100% stable pitch
• On any instrument that has an overtone sequence that doesn't follow the ideal harmonic series, it may not be possible to pin down what the frequency of the note actually is, because the waveform will not repeat in shape. (If the instrument had a strong fundamental, we might take its frequency as "the note's frequency", but not all instruments produce a strong fundamental on all notes).