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Section: 14 | Musical Scales |
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The recommended form of citation is:
John R. Rumble, ed., CRC Handbook of Chemistry and Physics, 103rd Edition (Internet Version 2022), CRC Press/Taylor & Francis, Boca Raton, FL.
If a specific table is cited, use the format: "Physical Constants of Organic Compounds," in CRC Handbook of Chemistry and Physics, 103rd Edition (Internet Version 2022), John R. Rumble, ed., CRC Press/Taylor & Francis, Boca Raton, FL.

MUSICAL SCALES

The equal tempered scale is the most common musical scale used today in western music. This scale divides the octave into twelve equal steps (semitones). An octave is defined as the interval between a tone (noteor pitch) at one frequency and a tone at twice that frequency. For example A4 is defined at 440 Hz by international agreement and A5 therefore has a frequency twice that of A4, or 880 Hz. While the equal tempered scale is used by orchestras, bands, individuals, and composers today as the standard, earlier composers and musical groups used a different pitch standard for A. Consequently some familiar classical compositions are today performed at a pitch standard different from what the composer used. One distinct advantage of the equal tempered scale is that a musical piece can be transposed upor down in the scale without a change in musical intervals.

Table 1 defines the notes (tones) used in the equal tempered scale. It should be noted that A0 is the lowest note on the piano, C4 is refered to a middle C, and C8 is the top note onthe piano.

The just or scientific scale (Table 2) maintains exact interger ratios between tones. Thus the interval between C and G is a "just" fifth.While the just scale is mathematically appealing, it has had little practical use in music. In addition, the difference between the even tempered and just scales is important in the design of instruments, such as those made from brass, that use higher resonances as notes are played in harmonic sequence.

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TABLE 1. Equal Tempered Chromatic Scale A4 = 440 Hz



NoteFrequency in HzNoteFrequency in HzNoteFrequency in HzNoteFrequency in Hz
Continued on next page...
C016.352C265.406C4261.63C61046.50
C#017.324C#269.296C#4277.18C#61108.73
D018.354D273.416D4293.66D61174.66
D#019.445D#277.782D#4311.13D#61244.51
E020.602E282.407E4329.63E61318.51
F021.827F287.307F4349.23F61396.91
F#023.125F#292.499F#4369.99F#61479.98
G024.500G297.999G4392.00G61567.98
G#025.957G#2103.83G#4415.30G#61661.22
A027.500A2110.00A4440.00A61760.00
A#029.135A#2116.54A#4466.16A#61864.66
B030.868B2123.47B4493.88B61975.53
C132.703C3130.81C5523.25C72093.00
C#134.648C#3138.59C#5554.37C#72217.46
D136.708D3146.83D5587.33D72349.32
D#138.891D#3155.56D#5622.25D#72489.02
E141.203E3164.81E5659.26E72637.02
F143.654F3174.61F5698.46F72793.83
F#146.249F#3185.00F#5739.99F#72959.96


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