DAVIS BLANCHARD MUSICAL CENTS

All the chimes Davis Blanchard currently produces are tuned to Just Intonation (a system of tuning using perfect harmonic intervals of simple whole number ratios). Rather than simple scales within only one octave, Davis Blanchard composes over a range of more than an octave and a half for more interesting melodies. The lower 3 notes produce the chordal triad (a simple 3 note chord basic in all Western music), usually major (1 3 5 or an inversion) or minor (1 3b 5 or an inversion), but sometimes a suspended chord (1 4 5 or an inversion) or a diminished chord (1 3b 5b). The higher 5 notes produce a pentatonic (5 note scale, the black keys of a piano) melody in all but Dusk, Lullaby, and Ursa Major. Some of my tunings are variations of the ancient Greek and Chinese pentatonic scales. Chinese varies from the Greek in that all intervals are derived from 4 perfect ascending fifths (a perfect fifth is 702 cents compared to that of 700 cents well tempered) transposed to fit within one octave. The Greek is derived from 2 ascending and 2 descending perfect fifths transposed to fit within one octave. Upon inspection, they are exactly the same with modal transposition (the second note of the Chinese scale is 2 fifths above the fundamental and 2 fifths below the third.

Chinese: C > G > D > A > E; transposed: C D E G A (interval structure of black keys starting on F#).
Greek: C < G < D > A > E; transposed: D E G A C (symmetrical interval structure of black keys starting on G#).

Keeping the first note of each scale as the fundamental, the Just Intonation ratios of the intervals differ as follows:

Greek: 1/1, 9/8, 4/3, 3/2, 16/9, 2/1
Chinese: 1/1, 9/8, 6/5, 3/2, 5/3, 2/1

So what is a fifth? Currently it is the fifth note in our diatonic scale (7 notes) or fifth white key on a piano in all musical keys (imagine no black keys) but B (the Devil's key, because it has a tritone or flat fifth). It has the most consonant or harmonic relationship with the fundamental (first note of the scale) other than the octave (twice the frequency of the fundamental) and unison (note of the same frequency as the fundamental). If you take a single vibrating string such as one on a guitar, and fret it exactly in the middle, you will have an octave vibrating on either side at twice the frequency of the fundamental unfretted string. If you fret it exactly at a third of the length, you will have a frequency vibrating on one side twice that of the other side. Transpose these frequencies to fall between the fundamental and its octave, and you will hear what is known as the perfect harmonic fifth. Further simple divisions make up the remainder of the Just Harmonic intervals. The octave gets its name from being the eighth note in the ancient Greek diatonic scale (7 notes). Our chromatic scale (12 notes) results from maintaining the interval structure during key modulation of those 7 notes and their 7 corresponding keys. Modes (the ancient Greeks and the Gregorian monks used the same names, but the Greeks' scales were descending, so do not correspond with the Gregorian modes, an issue of some confusion) are a way of naming the scale depending on which starting position of the 7 notes is used (including only the white keys of the piano).

Ursa Major is derived from the 6 perfect harmonic intervals (of equal frequency differences) resulting from using 6 as the denominator: 6/6, 7/6, 8/6, 9/6, 10/6, 11/6, 12/6; or reduced: 1/1, 7/6, 4/3, 3/2, 5/3, 11/6, 2/1. Some of these tone intervals become microtonal and quartertonal, such as found in some Eastern ragas that use notes and harmonic intervals that Western music cannot emulate easily except with the voice and unfretted instruments. (Another 6 tone scale is the 'wholetone scale' derived from 6 equal intervals of 200 cents each, resulting in a tritone or flat fifth.)

The Blues is derived from the harmonic series: 1:2:3:4:5:6:7:8 resulting in the fundamental 1/1, the octave 2/1, 4/2, 4/1, 6/3, 8/4, 8/2, 8/1, perfect fifth 3/2, 3/1, 6/4, 6/2, 6/1, perfect fourth 4/3, 8/6, 8/3, perfect major third 5/4, 5/2, 5/1, perfect minor third 6/5 (added to the perfect major third= 5/4 x 6/5 = 30/20 = 3/2 = perfect fifth), and a flat seven 7/4, 7/2, 7/1, (narrower than the usual just intonation interval of 16/9) resulting from adding 7/6 to 3/2 = 7/6 x 3/2 = 21/12 = 7/4. The remaining 8/7 (reciprocal or inverse of 7/4) makes up the interval between 7/4 (flat 7) and 2/1 (octave), or same as interval between 7/1 and 8/1. Adding the intervals 8/7 and 7/4 = 8/7 x 7/4 = 56/28 = 2/1. (Note: the next harmonic 9/8 is the normal just intonation interval for the whole tone, and it is found between the fourth and the fifth, 3/2 divided by 4/3 = 3/2 x 3/4 = 9/8.)  For more information see Tunings .

So why use Just Intonation? Perfect harmonic intervals have simple and pure relationships with the fundamental tone, creating a more consonant and pleasing tone than with 'well tempered' music. 'Well tempered' was conceived as a compromise between scales of pure harmonic intervals and the convenience of instrument building for key modulation and 'playing well' with others. (It rounded off the interval values in favor of the fifth to 100 cents per halftone.) So became lost a certain quality in music over the last couple centuries. Listen to these chimes and decide for yourself: