Ear training to learn perfect pitch
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The mp3 files for the 88 piano note recordings used in this site were taken from https://github.com/fuhton/piano-mp3/tree/master. Here is the license for that repository:
Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
The recordings are intended to match a 12-tone equal temperament piano tuned to A4 = 440 Hz. That is how a physically ideal piano would be tuned, but in practice, the strings' dispersion relation causes higher harmonics to be slightly sharp. Most pianos actually use "stretched tuning" instead of equal temperament, so that they sound good despite having some inharmonicity. The very slight upwards slope of the nearly-horizontal lines in the graph below is the Railsback curve, which indicates that the piano uses stretched tuning.
The bottom line is the fundamental frequency, and the lines above that are the second harmonic (at +1200 cents = +1 octave), the third harmonic (+1902 cents), and the fourth harmonic (+2400 cents = +2 octaves). Note that for the lowest few notes of the keyboard, the first harmonic appears to be missing. Interestingly, our brains can use the higher harmonics to figure out what note it is anyway, meaning that a C1 (32.7 Hz) will still sound like a C1 without having any 32.7 Hz vibrations. For some of the higher notes, the higher harmonics appear to be weaker, but this is just because of an artifact in how I made the graph.
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