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Details about this videoNotice how the beats of the two rhythms nearly coincide when they reach successive Fibonacci numbers 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, ...So for instance when you get to 21 beats for the blue ball and 34 for the red ball the clicks are close together, and even closer for 34 and 55, etc. Although the musical interval is as inharmonic as you can possibly get - in a way, "as out of tune" as you can possibly go, you may be surprised to find that it is a pleasant interval to listen to. Part of the reason for that may be that it is so far away from any pure ratio interval that you don't get the beating you get for notes that are just slightly "out of tune" from a pure ratio. With out of tune intervals you often get a shrill "wah wah wah" type effect - but very fast like 10 times a second or more - and often at many pitches simultaneously at different speeds, which is partly why they may sound painful to the ear. This doesn't happen in the same way with the golden ratio interval. To find this metronome, download Bounce Metronome Pro, and select the Harmonic Fractional Metronome from the drop list. You get a free 30 day Test drive - with all the features completely unlocked. Get your free trial here. Screen Shot (doesn't play notes)skip - skip back As with the Basic Metronome, you can accent or unaccent beats with RIGHT CLICK, skip beats with LEFT CLICK, adjust beat volumes with MIDDLE CLICK or SHIFT + LEFT CLICK. For details see the page about the Basic metronome. You can also play your rhythm with a gradually changing tempo, or add a lilt to the bar timings. For more about this see the page about the Pro metronome.
What it sounds likeHere is what it sounds like: Harmonic Metronome golden ratio / 4 The golden ratio rhythm is in a sense the most polyrhythmic possible rhythm, and the golden ratio pitch interval is the most inharmonic possible pitch interval. So if you asked two musicians to play as far out of tune with each other as possible, and also to play steady rhythms as far out of time with each other as possible, then in a certain well defined sense, this is what they should play. It is so far out of tune and out of time that it sounds really good! Like a meeting of two completely different realms :-).
More about the golden ratio rhythmAlthough the golden ratio rhythm is as inharmonic as you can get, i.e. as far as you can get from a harmonic series based interval - it is a pleasant musical interval actually on most instruments. Some inharmonic pitch intervals are very pleasant sounding. The intervals that are most often hardest on the ear are ones close to a very pure interval such as a fifth, octave or fourth, but obviously not hitting it, such as the detuned "wolf fifths" (though this is timbre dependent). So anyway, the golden ratio rhythm preset for this metronome gives the most polyrhythmic possible rhythm combined with the most inharmonic possible interval. For an introduction to the golden ratio rhythm see the Fractional Rhythms Metronome.
Combining more rhythms like thisYou can also combine more rhythms in the same way, each part as far out of time and out of tune (i.e. out of tune in the harmonic sense) with the previous part as possible:
Here is what it sounds like: Harmonic Metronome golden ratio with g squared and g cubed / 4 Of course you can also make rhythms at other musical intervals such as PI / 4 etc.
More audio clips and informationFor more about this with more audio clips, see Fractional Beats per measure
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