Doubling perceived pitch of a 2-kHz tone requires about a 15-kHz frequency jump

Evidence

It turns out that when subjects are asked to double the pitch they double the frequency, on average, for frequencies below about 500–1000 Hz (Fastl and Zwicker, 2007). Above this frequency limit, subjects adjust the frequency to increase in considerably larger steps than the pitch (see Figure 10.5). It can be seen that when doubling the pitch of a 2-kHz tone, subjects have adjusted the frequency to about 15 kHz. — Ville Pulkki, Matti Karjalainen, Communication Acoustics- An…, 1092