As the oft quoted Thelonious Sphere Monk once remarked, "All musicians are subconsciously mathematicians!"
It's no secret that in the known universe, the relationship between music and numbers is intrinsically woven.
In order to make sense of it all - pitches, intervals, chords, scales (modes) and cadences - have all been organized by number into groups, sets, etc. For example, Major Scale steps 1-3-5 might represent a Major triad in traditional harmony, whereas in Set Class Theory, 037 might be designated as a Major or minor triad; while 013, 026 & 027 all represent non-triadic 3-note "pitch collections".
Rhythms are grouped into repeating cycles - 4/4, 6/8, 7/4, etc. in various ways, across many different cultures.
It's no secret that in the known universe, the relationship between music and numbers is intrinsically woven.
In order to make sense of it all - pitches, intervals, chords, scales (modes) and cadences - have all been organized by number into groups, sets, etc. For example, Major Scale steps 1-3-5 might represent a Major triad in traditional harmony, whereas in Set Class Theory, 037 might be designated as a Major or minor triad; while 013, 026 & 027 all represent non-triadic 3-note "pitch collections".
Rhythms are grouped into repeating cycles - 4/4, 6/8, 7/4, etc. in various ways, across many different cultures.
Acoustically speaking, everything from vibrations per second - which measures pitch (A 440, for example) - to decibels (+/-db) - which measures loudness - is expressed as a number. The Harmonic Overtone Series itself is expressed as a series of ratios (3:2, 4:3, etc).
The "magic number" we'll be dealing with here is "5" - representing the Pentatonic Scale, which technically speaking, is any scale containing 5 notes. The most common Pentatonic - played and heard - is the one derived from the Major Scale.
Removing its 4th and 7th degrees - which is the only tritone relationship inherent in any Major Scale (e.g. C-D-E-F-G-A-B) - leaves us with C-D-E-G-A, or C Major Pentatonic (scale steps 1-2-3-5-6 of the Major Scale).
The descending Pentatonic sequence shown below utilizes the skip-step-up, step-down concept. The twist here is that the time signature and feel is in 12/8. This allows for 4 groups of 3 notes per measure - each group having the same shape.
Each successive 3-note grouping begins on the next descending Pentatonic Scale step.
The number below each note represents its position in the Major Pentatonic Scale. Just as a Major key has a relative minor key, the same holds true for Pentatonics. In this case, as shown, C Maj and A minor are relative Maj / min Pentatonics.
The number scheme for what is referred to as a minor Pentatonic is 1-b3-4-5-b7 (A-C-D-E-G). As you can see, it contains the same exact set of note names as its relative Major.
To convert the scale step numbers from Major to minor - add 2; from minor to Major - subtract 2 ("8" is always the octave, and is shown here as "1").
The "magic number" we'll be dealing with here is "5" - representing the Pentatonic Scale, which technically speaking, is any scale containing 5 notes. The most common Pentatonic - played and heard - is the one derived from the Major Scale.
Removing its 4th and 7th degrees - which is the only tritone relationship inherent in any Major Scale (e.g. C-D-E-F-G-A-B) - leaves us with C-D-E-G-A, or C Major Pentatonic (scale steps 1-2-3-5-6 of the Major Scale).
The descending Pentatonic sequence shown below utilizes the skip-step-up, step-down concept. The twist here is that the time signature and feel is in 12/8. This allows for 4 groups of 3 notes per measure - each group having the same shape.
Each successive 3-note grouping begins on the next descending Pentatonic Scale step.
The number below each note represents its position in the Major Pentatonic Scale. Just as a Major key has a relative minor key, the same holds true for Pentatonics. In this case, as shown, C Maj and A minor are relative Maj / min Pentatonics.
The number scheme for what is referred to as a minor Pentatonic is 1-b3-4-5-b7 (A-C-D-E-G). As you can see, it contains the same exact set of note names as its relative Major.
To convert the scale step numbers from Major to minor - add 2; from minor to Major - subtract 2 ("8" is always the octave, and is shown here as "1").
Rhythmically, this 12/8 sequence can be felt as if it were in 4/4, with four groups of eighth note triplets. The push and pull of the 3-against-4 pulse is almost always inherent in African derived rhythms - from sacred Afro-Cuban Bata drumming, to Blues, R&B and Jazz - and is the essential ingredient in what is commonly referred to as "swing".
In the above sequence, accents can be placed just about anywhere.
In the above sequence, accents can be placed just about anywhere.
Listen
(Audio example is without measure repeats)
(Audio example is without measure repeats)
The downloadable PDF presents this sequence in 12 keys.
The bass line in the audio example ascends diiatonically along C Mixolydian (C-D-E-F-G-A-Bb).
Along with the inversions of C 6/9 and A min 11 formed naturally in C Pentatonic, the two non-diatonic bass notes (F & Bb) create F Maj9 #11 13 and Bb Maj7b5 9 13 chord structures respectively. These chords are quite "inside sounding", but give the C Pentatonic some added color.
But really... how important is "playin' the numbers"?...
Not as important as "Playn' the Music"!... i.e., actually making it live and breath!
But numbers - being intertwined with music on so many levels - can be an aid and a guidepost when properly understood and appreciated.
B. Stern
The bass line in the audio example ascends diiatonically along C Mixolydian (C-D-E-F-G-A-Bb).
Along with the inversions of C 6/9 and A min 11 formed naturally in C Pentatonic, the two non-diatonic bass notes (F & Bb) create F Maj9 #11 13 and Bb Maj7b5 9 13 chord structures respectively. These chords are quite "inside sounding", but give the C Pentatonic some added color.
But really... how important is "playin' the numbers"?...
Not as important as "Playn' the Music"!... i.e., actually making it live and breath!
But numbers - being intertwined with music on so many levels - can be an aid and a guidepost when properly understood and appreciated.
B. Stern
For an even more in-depth look, the following Shortbooks™ are recommended
and available for immediate download.
and available for immediate download.
RSS Feed
