Two octaves are used for the temperament:  an octave above, and an octave below middle C. Middle C can be told by its being, the C nearest the name of the piano on the name board.  In other words, it is the fifth C from the highest C, and the fourth from the lowest in the modern piano, which has seven and a third octaves.

The diagram illustrates the two octaves of the key-board, and shows how each key is designated in giving the system of temperament.

Pitch.—­The Piano Manufacturers’ Association has established what is known as “international pitch.”  Tuning-forks made to this pitch are marked “C-517.3,” meaning that our 3C vibrates 517.3 per second.  Concert pitch is nearly a half step higher than this.  Some manufacturers still tune their instruments to this higher pitch.

If it is desired to tune a piano to a certain pitch, say concert pitch, tune the C that is an octave above middle C by a concert pitch tuning-fork or pipe.  If, however, the piano is too much below that, it is not safe to bring it up to it at one tuning.  But, say it will permit tuning to concert pitch; after this C (3C) is well laid, tune middle C (2C) by it, then tune the C octave below middle C (1C) to middle C. Having 1C for a starting point, proceed by tuning a fifth up, then its octave, then a fifth, then an octave, always tuning the octave whichever way is necessary to keep within the two octaves.

The simplicity of this system can be readily seen; yet for the use of beginners, we give on the following page the whole succession of intervals as they are taken in setting the temperament.

DIAGRAM OF THE TWO OCTAVES USED IN “TEMPERAMENT,” AND OF THE SUCCESSION IN WHICH THEY ARE TUNED.

C[#] D[#] F[#] G[#] A[#] C[#] D[#] F[#] G[#] A[#] C D E F G A B C D E F G A B C
*
1C, 1D, 1E, etc. 2C, 2D, 2E, etc. 3C ------------------------------- --------------------------------

Middle C begins second octave; known by the asterisk (*) under it.

THE FISCHER SYSTEM OF SETTING TEMPERAMENT.

First, tune 3C by tuning pipe, or as directed.

By this, tune 2C, and by 2C tune 1C; then tune as follows: 

By  1C         tune 1G    fifth above,
"  1G          "   2G     octave above,
"  1G          "   2D    fifth above,
"  2D          "   1D     octave below,
By  1D         tune 1A    fifth above,
"   1A          "   2A     octave above,
"   1A          "   2E    fifth above,
"   2E          "   1E     octave below,
"   1E          "   1B    fifth above,
"   1B          "   2B     octave above,
"   1B          "   2F[#] fifth above,
"   2F[#]       "   1F[#]  octave below,
"   1F[#]       "   2C[#] fifth above,
"   2C[#]       "   1C[#]  octave below,
"   1C[#]       "   1G[#] fifth above,
"   1G[#]       "   2G[#]  octave above,
"   1G[#]       "   2D[#] fifth above,