When pitch shifting, Audacity is neither using, or not using 12-Tone Equal Temperament. “Pitch shifting” scales frequencies by a specified ratio. (“Frequency shifting” change frequencies by a specified amount).
Pitch shifting preserves the original temperament of musical intervals because musical intervals are based on ratios. Frequency shifting does not preserve the original temperament.
Example of pitch shifting:
Say that you have recording of two frequencies: 200 Hz and 400 Hz. We say that these frequencies are “one octave” apart because in Western music we define an octave as a frequency ratio of 2:1.
We now “pitch shift” by an arbitrary ration - say 1.4:1.
The frequencies become: 280 Hz and 560 Hz. (1.4 x 200 = 280 and 1.4 x 400 = 560)
Notice that the the higher frequency is still double the (new) lower frequency (2 x 28 = 560).
The “music interval” is retained after pitch shifting.
It is worth noting that in the real world, acoustic instruments are rarely tuned to exactly match Equal Temperament across their entire range. For example, see the “stretch” section about piano tuning in this Wikipedia article: Piano tuning - Wikipedia
It is also worth noting that a single note from an acoustic instrument is not a single frequency contains a near infinite number of different frequencies. The proportions of different frequencies determine the tone of a note, whereas the timbre is determined by both the tone and the way that the tone changes over time. Some of the frequencies within a single note are harmonically related, while some are not.
- Pitched instruments such as pianos, violins, guitars, clarinets, trumpets etc produce notes where most of the stronger (higher amplitude) frequencies are harmonically related.
- Non-pitched instruments such as snare drums, castanets, shakers etc produce sound where harmonically related frequencies are not prevalent.
- Some instruments, such as toms, wood blocks, gongs, heavily distorted guitar etc. lie somewhere between the two, such that some degree of harmonically related frequencies can be heard while a lot of harmonically unrelated frequencies are also present.
It is interesting to note that many instruments are deliberately tuned “slightly off” from the theoretical “in tune” frequencies. I’ve already mentioned piano tuning “stretch”, but also it is common to tune toms so that the upper and lower skins are slightly out of tune with each other. Cylindrical resonator instruments (wind, brass, organs etc.) produce dominant frequencies rooted on the natural harmonics of resonator, but may also have valves / slides / holes that are tuned for (approximately) equal temperament. Fretless string instruments are not tied to any temperament, but are usually tuned such that each string is approximately an equal temperament interval from its neighbour.
Example of Frequency shifting:
Starting again with 2 tones; 200 Hz and 400 Hz.
We now shift the frequencies by an arbitrary “amount”, say 40 Hz.
The frequencies become 240 and 440 Hz (200 + 40 = 240. 400 + 40 = 440).
Notice that the higher frequency is no longer double the lower frequency.
The musical interval is changed by frequency shifting.
Audacity’s “Change Pitch” is a “pitch shifter” (not a “frequency shifter”).
It is a mistake to think that a recording can be “re-tuned” to a different scale by either pitch shifting or frequency shifting. Musical pitch is far more complex and nuanced than simple frequency ratios. If you really want music that is tuned to a non-standard tuning, then tune the instruments as required before recording.
