TEMPO & PITCH - RHYTHM & HARMONY
The idea of an assumed relationship between Bpm (Beats Per Minute) and Cps (Cycles Per Second, a once-common English name for the unit of frequency now known as the hertz) is - in my opinion - a valid one.
Both Bpm and Cps are a: "particular number of occurrences + repeating event + time unit" (you could call this "periodicity").
Some composers / producers do actually use a tempo that 'synchronizes' with the tonality of the composition, this idea isn't something "new". Temperament does have an effect as well ...
TEMPO & PITCH: BPM & CPS (HZ)
In the case of Bpm the time unit is minutes, in the case of Cps the time unit is seconds.
From Cps to Bpm we need to multiply the number of cycles by 60.
From Bpm to Cps we need to devide the number of beats by 60.
EXAMPLE CPS TO BPM:
The tone C4=256Hz has 256 Cycles Per Second. In order to find a matching tempo (Bpm) we have to multiply 256 by 60 (turning second into minutes). 256 Cps · 60 = 15360 Cpm. Naturally 15360 Bpm would be too fast to use for any musical piece, so we have to halve the tempo until we get a usable tempo.
15360 /2/2/2/2/2/2/2 = 120 Cpm or Bpm
15360 /2/2/2/2/2/2/2/2 = 60 Cpm or Bpm
What if you find 60 Bpm or 120 Bpm too slow or fast for your composition?
Well, perhaps it would be worth exploring other tone frequencies of importance in your composition, for example the 3rd or 5th. Depending on the tonality (Major or minor) and Temperament used you create the following tempi with the 3rd and 5th, based in this example on Concert Pitch C4=256Hz:
|Scale Degree||CPS (Hz)||BPM||rounded-up|
|Equal Tempered minor Third||304.4370214406993||142,7048538 or 71,3524269||143 or 71|
|Just Intonation minor Third||307,2||144 or 72||144 or 72|
|Equal Tempered Major Third||322.5397887730913||151,190525987 or 75,595262994||151 or 76|
|Just Intonation Major Third||320||150 or 75||150 or 75|
Naturally you could select any tones you feel is important in your composition. If your melody has one tone that is used more often then any other, then you could experiment with adjusting the tempo to that tone as well.
EXAMPLE BPM TO CPS:
If we like to use 130 bpm as tempo for a piece of (dance) music, what tone frequency would be "in sync"?. In order to find this tone, we have to divide 130 by 60 (turning 130 beats per minute into beats per second).
130 Bpm / 60 = 2,1666666667 Bps.
This tone of 2,1666666667 Cps (Hz) is too low to use as reference pitch (concert pitch) so we have to double it untill we reach a frequency between C4 and C5.
2,1666666667 ·2·2·2·2·2·2·2 = 277,333333338Hz
The tone in this example is actually pretty much the C♯4 or D♭4 (277.183Hz) when A4=440Hz and Equal Temperament is used.
If you would like to use the Bpm to Cps method, do keep in mind that you might have to use a different Concert Pitch then the standard 440Hz. This is important to know, because not all instruments are capable of changing pitch.
RHYTHM, TEMPO & PITCH
If you take a basic "4 on the floor" kick drum pattern and speed it up, a tone will appear. The higher the tempo, the higher the pitch. Adam Neely shows this in his youtube video (on the left).
In the article so far we only looked at converting a single tone to tempo (Cps to Bpm).
Melody (and harmony) - generally only looked at from the point of pitch and ratio - does have a rhythmic aspect as well. Rhythm, melody and harmony are kind of the same thing, just on a different scale.
THE POLYRHYTHMIC ASPECTS OF HARMONY
Harmony can be seen as complex interlocking polyrhythm.
When you play two different rhythmic patterns, for example 5 equally spaced rhythmic elements in one measure together with 4 equally spaced rhythmic elements and speed it up, a Just Major Third appears.
This way you can actually create complete chords (see video above).
You might wonder why I specifically mention Equal Temperament and Just Intonation? Well, there is a good reason for that.
The difference between 12-TET and Just Intonation is more then just pitch. As mentioned in other articles on Roel's World, with 12-Tone Equal Temperament all intervals are slightly "off pitch" in comparison with the harmonic series (except for the octave of course). I will not go into detail about ratios and temperament in this article, but it is important to "address" this.
DIFFERENCE E.T. AND J.I.
In the video on the left Adam Neely let us hear the difference between a Just and an Equal Tempered Major triad. With the Just triad the "beats" of the tones align. The 12-TET chord though does not align perfectly, creating a phaser-like effect.
In the example given by Adam Neely of the Major Thirds, the ratio of the Equal Tempered Major Thirds is 24/12, while that of the Just Intonated Major Third is 5:4. and the ratio of the Equal Tempered Minor Thirds is 23/12, while that of the Just Intonated Minor Third is 6:5.
The blue tracks are (from top down) the Tonic, 3rd and 5th of the Equal Tempered Major chord, the green tracks those of the Just Intonated Major chord.
All waves of the tones of the Just Intonated chord (green tracks) align (get in sync) at particular moments (where the white line is drawn). This is though not the case with the waves of the tones of the Equal Tempered chord. The 3rd end too early and the 5th a tiny bit too late relatively to the Tonic. They never get completely "in sync" with one another.
Generally speaking: the more "synchronized" all "elements" within the music are, the more "harmonious" and "natural" it sounds to the listener.
If you like to create music that is rhythmically, harmonically and melodically in "sync" with one another, then you might like to consider using Just Intonation, rather then Equal Temperament.
With other words: calculate a tempo to "match" the tonality of the composition AND make sure that the harmony and melody themselves synchronize with the rhythm and tempo of the piece as well.
If you like to covert Cps to Bpm yourself, then try the online Cps to Bpm converter at www.convertworld.com