Music The interval of a double octave. [Stainer, John; Barrett, W.A.; A Dictionary of Musical Terms; Novello, Ewer and Co., London, pre-1900]
Ramsay
Speaking of acute harmonics Pole says - "The first six are the only ones usually considered to be of any practical importance, and it is rarely possible to distinguish more than 10 or 12."
Mercenne (French, 1636) says - "Every string produces 5 or more sounds at the same instant, the strongest of which is called the natural sound of the string, and alone is accustomed to be taken notice of; for the others are so feeble that they are only perceptible to delicate ears . . . not only the octave and fifteenth, but also the twelfth and major seventeenth are always heard; and over and above these I have perceived the twenty-third and ninth partial tones in the dying away of the natural sound."[Scientific Basis and Build of Music, page 59]
G# as it occurs in the scales of A, E, and B major, and A? as it occurs in the scales of F and B? minor, are only distant the apotome minor, and are well represented by one key of the piano. It is only G# as it occurs in the scale of F six sharps major, and A? as it occurs in the scale of E six flats minor, that is not represented on the piano. These two extreme notes F# and E? minor are at the distance of fifteenth fifths and a minor third from each other. This supplies notes for 13 major and 13 minor mathematical scales; but as this is not required for our musical world of twelve scales, so these far-distant G# and A? are not required. The piano is only responsible for the amount of tempering which twelve fifths require, and that is never more than one comma and the apotome minor. [Scientific Basis and Build of Music, page 80]
See Also