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Say I recorded an audio of C major: do re mi fa so la si do.

Now imagine I used some software to change the pitch higher (I think Audacity has a feature like this). I was wondering: if I change the pitch of this to be higher, is that like cycling through each key? (C major, C♯ major, D major, E♭ major, etc).

(I'm sure it's micro-tonal but I mean eventually you get to each key right?)

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    @NeilMeyer Yes, there is. The notes are D# E#, F##, G#, A#,B#, C##. It's unlikely that music would be written in this key as it's an enharmonic equivalent of Eb, which is much more readable, but there is such a key. – AJFaraday Apr 18 '18 at 10:26
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    Also known as F𝄪 and C𝄪. – NH. Apr 18 '18 at 15:21
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    This question is so semantic, I'm really hesitant to assume I understand what you're trying to ask. Why are you even asking this question? – Tab Alleman Apr 18 '18 at 17:25
  • @AJFaraday I've had to play in G# as a trumpet player before. I was sight-transposing off of music written in F# (for a C instrument), and its far easier to think the transition from F#->G# than F#->Ab . – fyrepenguin Apr 18 '18 at 21:54
  • @fyrepenguin that genuinely sounds very difficult. Then again, I understand it’s a skill brass players need to get good at. – AJFaraday Apr 18 '18 at 21:56
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Yes; if you move each pitch by the right interval, you can move from C major to C♯ major, then D major, etc.

But there is one main caveat to this: assuming you move each pitch by the same interval, this only works in an equal-tempered tuning system (see edit below). Within equal temperament, each half step is precisely 100 cents and each whole step is precisely 200 cents. With those equal and equivalent intervals between each pitch of the initial C-major scale, moving every pitch up 100 cents moves the entire scale up a half step to C♯.

But if you were using another tuning system, you would not have a series of 100 and 200 cents between the pitches of the C-major scale. If you were to move each pitch of, say, a meantone-tempered C-major scale up 100 cents, you would have a mean-tone tempered C♯ major scale that is suddenly in a different meantone system than the original scale.

Doing so would basically destroy the whole point of a meantone-tempered scale. So not only does the action you describe only work in an equal-tempered environment, the very concept is really best fit for an equal-tempered environment.

Edit: I was unclear with the end of my fourth paragraph. The subsequent scale would still be in a meantone temperament, but it would be a different C♯ scale than if you took the C♯ scale within the meantone environment where you took the original C-major scale. As @topo morto succinctly put it, these would be "pitches that weren't in the temperament being originally played, but the notes will still be pitched the same relative to each other." This was my intent.

Furthermore, I didn't realize programs could do work within different tempered systems. As such, this works in all temperaments as long as your program supports it. That's good to know!

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    @foreyez Because a key isn't just a pitch :-) Note that I say we have to move "each pitch"; a key is a collection of pitches and the relationships among them. – Richard Apr 18 '18 at 5:37
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    +1 from me too, but I'm not sure why you say "this only works in an equal-tempered tuning system"; That would make sense if the OP was proposing moving each note up or down a certain number of semitones (where, as you say, there might be differences in the cent sizes of some of those semitones), but if he's just proposing pitching up the whole thing, then assuming the pitch-shift algorithm works ok, it doesn't seem that there's any potential for the result to end up in a different temperament to the original. – topo Reinstate Monica Apr 18 '18 at 7:52
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    Or, to be even more unclear - the result might end up playing pitches that weren't in the temperament being originally played, but the notes will still be pitched the same relative to each other. – topo Reinstate Monica Apr 18 '18 at 8:02
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    I agree with topo-what does temperament have to do with electronically changing pitch levels? This doesn't really answer the question, imho. – Scott Wallace Apr 18 '18 at 8:54
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    Small error: There's 1200 cents to an octave. In equal temperament, each half step is precisely 100 cents and each whole step is precisely 200 cents. (Not 50 and 100.) – JiK Apr 18 '18 at 10:14
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Like Richard, I'm going to say yes, but with a slightly different caveat - it will work as long as your re-pitching algorithm works well! You'll generally be fine if you simply resample the audio such that the 'speed' change is what causes the pitch shift (the only cleverness needed there is some filtering to avoid aliasing), but if you use any pitch-shift algorithm that as able to work independently of audio speed, that's more complicated and will introduce distortions that may alter the perceived pitch of some of your notes. Such algorithms are typically very good these days, but it is something to watch out for.

  • thanks for pointing that out, I also wondered what equal temperament has to do with this, when you're just changing a .wav file – foreyez Apr 18 '18 at 13:12
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    @foreyez Richard is right to say that temperament is relevant (see my more recent comment on his answer) - but temperament problems aren't going to cause issues to be apparent in the pitched up recording itself; you might see problems though if you then play that against something else in your target key, but differently-tempered. Use of equal temperament will make these considerations go away. – topo Reinstate Monica Apr 18 '18 at 13:37
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I will assume that you are only considering equal temperament so that the frequency ratio between of any semitone interval is the same.

The answer depends on your point of view. Suppose that you were able to play a certain piece on a keyboard but only in the key of C. Your friend could play it on the guitar but only in the key of E. Played normally, these would not sound good together. However, if you recorded one, moved its pitch as you suggest, and played the other instrument against the recording then it may sound good. Some electronic keyboards can do this in real time. You play as if in C but the keyboard outputs a set interval higher or lower. You would think that you are playing in C but a listener would hear it as if you were playing in E.

I used to have that problem with my piano. It was relatively in tune but slightly flat. So, I could not practise together with a recording. I had considered processing some recordings so that they were equally flat. I no longer need to as I have just had the piano restored to standard pitch.

Another example is historically informed performances. These might not be at the modern standard of A4 = 440Hz. A historical performance in C might sound as if it were in Bb and maybe even A to modern ears. It is a matter of opinion which key it is in.

Finally, you could consider a capo on a guitar which has a similar effect. If you put a capo on the first fret then you could play as if you were in E but give the effect of playing in F.

  • I don't think the temperament itself has much bearing on the matter. The 'historically informed' didn't seem to matter even in the 60s, and there are quite a few tracks from those days that were 'in the cracks'. but probably software now could put them into concert pitch. I got very good at re-tuning my guitar in the 60s to play along with tracks on the radio - I mean like half a semitone. – Tim Apr 18 '18 at 12:53
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    @Tim I recall once playing my (clarinet) part along with a full orchestral recording and discovering rather to my shock that the 2nd movement was pitched differently from the 1st movement on the LP! – Carl Witthoft Apr 18 '18 at 13:11
  • @Tim HIP is another reason that you might want to play with pitch. For example, I have a HIP performance of Mozart's Clarinet Concerto. I could not play along with that using my modern clarinet. Another challenge would be that I only have a Bb clarinet. – badjohn Apr 18 '18 at 13:40
  • I mentioned that my piano used to be flat. This was no issue when playing with a guitar or violin but it was with the clarinet. It was impossible to play with my Irish tin whistle. – badjohn Apr 18 '18 at 13:49
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    @badjohn my suspicion is that they spent more than one day on "takes" and selected the best of each movement (this was pre-digital days). It's not unthinkable that they might have adjusted the playback speed to avoid running out of vinyl. – Carl Witthoft Apr 18 '18 at 15:14
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Old music module players like SoundTracker, on legacy computers where memory was low, and where you had 4 channels to play with, the trick of using the same chord played at different replay sample rates was widely used specially for:

  • piano chords (in techno tunes)
  • string chords

With 1 sample (looped for strings) recorded in, say F (Fa/La/Do), you could play with slower sample rate or higher rate to cover all major chords, and using only 1 channel out of 4.

Natural piano/string play would use reversed chords to stay in the same range (ex: to play A# you'd play Fa/Sib/Re not Sib/Re/Fa), whereas in that case the chord notes are is always in the same order. So those chords sound very "techno".

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