| By middle | C | tune | F | fifth below. | Temper | sharp. |
| By | F | " | B♭ (A♯) | fourth above. | " | " |
| " | C | " | G | fourth below. | " | flat |
| " | G | " | D | fifth above. | " | " |
| " | D | " | A | fourth below. | " | " |
| " | A | " | E | fifth above. | " | " |
| " | E | " | B | fourth below. | " | " |
| " | B | " | F♯ | fourth below. | " | " |
| " | F♯ | " | C♯ | fifth above. | " | " |
| " | C♯ | " | G♯ | fourth below. | " | " |
| " | G♯ | " | D♯ | fifth above. | " | " |
| Then try | D♯ | with | A♯ | previously tuned for "wolves." | ||
We think a little study and trial of this system will produce the conviction that it is a very difficult and precarious one, and that it has every disadvantage but one, namely, that it uses the smallest possible number of tones, which is really of little value, and does not compensate for the difficulty encountered and the uncertainty of the results.
Another system which has many advantages over the above, is one which employs fifths only and covers a compass of an octave and a half. This system is similar to ours in that it employs fifths in the same succession as far as G♯, the most of them, however, being an octave higher. From this G♯ there is a break in the succession, and the tuner goes back to middle C from which he started and tunes by fifths downward until he reaches the G♯ at which he left off. This system employs the tones from F below middle C to C, octave above. Below is the succession, starting upon 3C, whose pitch is determined as usual.
SYSTEM B.
| By | 3C | tune | 2C | octave below. |
| " | 2C | " | 2G | fifth above. |
| " | 2G | " | 1G | octave below. |
| " | 1G | " | 2D | fifth above. |
| " | 2D | " | 2A | fifth above. |
| " | 2A | " | 1A | octave below. |
| " | 1A | " | 2E | fifth above. |
| " | 2E | " | 2B | fifth above. |
| " | 2B | " | 1B | octave below. |
| " | 1B | " | 2F♯ | fifth above. |
| " | 2F♯ | " | 1F♯ | octave below. |
| " | 1F♯ | " | 2C♯ | fifth above. |
| " | 2C♯ | " | 2G♯ | fifth above. |
| " | 2G♯ | " | 1G♯ | octave below. |
| By | 2C | tune | 1F | fifth below. Temper sharp. |
| " | 1F | " | 2F | octave above. |
| " | 2F | " | 1B♭ | fifth below. Temper sharp. |
| " | 1B♭ | " | 2B♭ | octave above. |
| " | 2B♭ | " | 2E♭ | fifth below. Temper sharp. |
| Now by | 2E♭ | try | 1A♭ (G♯) | fifth below for the "wolf." |
| Note that this last trial brings you back to the last tone tuned before the break. | ||||
This system is used by a great number of very successful tuners, and it has but one appreciable disadvantage, which is that involved in changing from fifths upward to fifths downward. This difficulty is easily overcome, if it were all there is to encounter; but in practice, we find that after tuning the intervals in the above succession down to the last step in the first series, middle C will often have changed pitch somewhat, and the last five tones with their octaves tuned from it will not be in true harmony with the intervals tuned in the first series. For this reason it is better to go on through, as in our system, tuning by fifths upward, and if there is any change of pitch in the first tones tuned, they may be more easily corrected by going over them in the same way as at the start; also, the amount of difficulty in locating discrepancies is greatly lessened.
SYSTEM C.
The following system is one that is followed by many good tuners of the present day and has many advantages. To use this system successfully, however, one must be familiar with the number of beats necessary in each interval used.