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Tap on your leg at 60 bpm.
Tap your other finger at 90 bpm.
Congratulations. You just played a chord. It's a flat B and a flat F#
which when played together make a fifth (3:2)
In fact 3:2 and 3:4 produce recognizable rhythmic patterns.
They are also musical intervals.
So compose tonal
music with them and their multiples.
Also, convert the hz measure of the key to bpm, and make that the
tempo.
Rhythm is tone, tone is rhythm
Tempo is key, key is tempo
Prime_20Melodies
See also my annotations here [spidermother, May 13 2013]
Willie Ruff, Harmony of the World
http://www.willieruff.com/kepler.html
[pocmloc, May 18 2013]
[link]
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I've done this. I even tried speeding up recordings of tappings until I could hear pitches and intervals. You can hear beats at low frequencies, and pitches at high frequencies, but in the transition region you can't really hear either. |
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I also set a software synth to play a pulse 8 or so octaves lower (either alone or with the higher frequency) to create exactly this effect. You get some awesomely rhythms, whose complexity directly relates to the harmonic complexity of the (just intonation) chord played. |
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I didn't use the hz-bpm relationship, as the factor of 60 seemed too arbitrary; hence the power of two (octave) relationship. |
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One thing that arises naturally from this is note lengths that are inversely proportional to frequency - so that, for instance, an ascending scale gets faster. The result is that there is an underlying, very slow Grand Tempo which is the lowest common factor of all the individual tempos created by the pitch space one is working in. |
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Spidermother,
That's funny. I proved this the same way you did
(descending into the lower octaves using a saw wave.) |
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And I have noticed that disappointingly, any old percussive
sound cannot just be sped up. Nonetheless. |
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If you play a simple 60 90 cross rhythm, it might still be
possible that it is perceived on some level as "in tune" with
the same chord played in a normal register, like say, 7680
and 7680*(2/3) bpm, aka 128hz and 192hz. |
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I only used Hz and bpm to communicate the point to the
DAW majority. |
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I suppose what is happening is not that strong just intervals
have no "beat", as in piano tuning parlance, but rather the
beat is so simple or short it's not even perceived. Whereas
you can hear the cycles of the longer cross rhythms (like
whatever a second works out to) because they are so long
that you can perceive their cycles even when played at
very high speeds. |
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//there is an underlying, very slow Grand Tempo which is
the lowest common factor of all the individual tempos
created by the pitch space one is working in.// |
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Like the fundamental frequency of harmonic tonality. |
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One concept of mine was for an entire composition's duration, and the duration of every note within it, to be an integer multiple of the least common multiple of the periods of all the frequencies used within the composition. The result is that all notes, and the composition as a whole, contain an exact number of periods of all the pitches, and all their harmonics. Thus the main aspects of sound - pitch, rhythm, and phase - are at all times in integer relationships. It seemed like the ultimate realisation of the just intonation concept. |
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//I suppose what is happening is not that strong just intervals have no "beat", as in piano tuning parlance, but rather the beat is so simple or short it's not even perceived.// |
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Yes! The beat frequency of the fundamentals of 80 Hz and 120 Hz is 40 Hz, which is not discernible as a beat; but 80 Hz and 90 (9/8, a just major second) gives 10 Hz, which is. |
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[Edit] I've used 'beat' in two different contexts; it might be better to use the terms 'difference frequency' for the general case, 'difference tone' for the case where the difference frequency is perceived as a pitch, and 'beat' for the case where the difference frequency is heard as pulsations. |
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//And I have noticed that disappointingly, any old percussive sound cannot just be sped up.// |
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If you trim off the beginning of your percussive sample, so the attack is sharp, you get much better results. |
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I like this. And especially the awesome suggestion of the Grand Tempo. The idea that maybe this Grand Tempo is unifying among frequencies in more respects than simple music or rhythm has a little hint of madness. It would make a good story if the application or real world effects of this realization were comparably vast. |
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[+] interesting, and somewhat related to my half-attempts to introduce pitch-bend to a Hammond/Leslie by varying the AC frequency of the tone-generator and voltage of the spinny motors. |
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[bungston] Just to be clear, what [fishboner] and I have done is to deliberately create mathematical relationships between rhythm frequency and pitch frequency, just for the hell of it. It tuns out to be rather cool, because the frequency ratios that produce pleasing harmonies also produce pleasing rhythms. And in some cases, it is possible to tie the two together, in the sense that a perceivable pulsing is generated by combinations of frequencies that are themselves in the recognisable-pitch range; and altering the frequency of any of the pitches, or of the beat, increases rhythmic and/or pitch dissonance. Thus pitch and rhythm are able to be in tune with each other. Which is also cool. The Grand Tempo simply arises naturally from all the other frequencies. None of the underlying concepts are original (although I've never heard of anyone else exploring them in this particular way). |
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Search for 'A 413' for lashings of the precise madness you describe. |
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Obviously, from a Fourier perspective, it's rather keen if all frequencies present are harmonics of the entire piece. Put that way, my extended concept can be thought of as ... (new posting coming). |
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Hmmm. It never occurred to me to bring the duration if
the piece into this. And I have not run any of this through
my memories of wave physics. So many possibilities. |
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Your idea helps me with one on my earlier ideas posted
here. It was to choose an "arbitrarily low" fundamental so
as to access the more numerous natural harmonics where
they fall way way up in the series, only at an audible pitch. |
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With your composition duration as period of the
fundamental frequency, the fundamental does not have to
neccesarily be arbitrary. |
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I've been composing in harmonic series, and developing
models to do so. I was not aware until today that removing
the octaves in the series makes the prime number set
(right?) |
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What i love about the harmonic series is that there is a
fundamental frequency, and some big
jumps at he beginning, but that once you get up higher into
the series you have infinite tones between octaves, ALL OF
WHICH are sympathetic, and theoretically, if any two are
played simultaneously, they "point to" the fundamental.
Obviously the effect is weaker the higher you get in
practice because in engineering concerns. |
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What scares me about JI is it appears ro deviate from this
natural harmonic model. You can
take relationships from higher up in the series,
and transpose them down closer to the fundamental. I am
suspicious of this practice. Like when I tune my keyboard
to the harmonic series' first few octaves, there are a lot of
empty keys. That's the way it has to be if you want the
fundamental on the board. I feel like JI gives into the
temptation to take those numerous intervals from the top
octave on the keyboard, say, and transpose them down a
few octaves so they can be used to fill in the blanks. Isn't
this unnatural? I mean, I guess you might say that once you
do that you are simply suggesting an even lower
fundamental, so it's still natural maybe, I don't know. My
instincts tell me its wrong. |
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On another note..
Somewhere on the Csound web page there is a link to a
source forge page of a program called "rationale" by a very
thorough and dedicated fellow named Chuck Hubbard. I
think his web page is badmuthahubbard.com. It is a
sequencer for composing in JI. I highly recommend it. I
have been composing with
that lately. It's in beta, but it works well. More later... |
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You mean, transposing down by octaves to fill in the blanks? I agree, that is unnatural. I've also composed using the raw harmonic series. It's a great way to break the habit (as mentioned by Chuck Hubbard) of thinking about intervals as additive. When using a keyboard, and using the raw harmonic series, I tend to assign consecutive keys to consecutive members of the series, so there are no gaps. The keyboard then has linear frequency, rather than linear pitch. |
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I hadn't come across 'rationale', so thanks. SCALA, ZynAddSubFX, and SuperCollider are amongst my favourites. |
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I also have played with making the sample rate a harmonic of the Grand Fundamental - just because ;-) |
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OK which one of you is Eno? |
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[spider] I was hoping to find a synth (software or other)
where each key could be tuned by Hz rather than cents.
Have you seen anything that does that? |
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Also, Chuck told me he's planning to make rationale
compatible with scala. I just wish I could manually type in
ratios as well as drag them around. |
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In distinction to your harmonic keyboard tuning (which I
have also tried) is something I posted here about. That is
the unfortunately named "harmonically pure equal
temperament". I chose a fundamental, and then climbed
way up and picked all the nearest neighbors to the ET
values. I then converted to cents, and tuned each key of
my synth (this was before i kney about scala) |
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I was informed by other half bakers that "inharmonicity" of
the piano string would make it impossible to do this on a
real piano. Basically, harmonics are produced by
oscillating strings, and in a piano, they string them so tight
that they don't vibrate enough relative to the thickness of
the string. As a result, pianos produce odd harmonics, and
this is part of what goes into tuning them. The main reason
pianos are designed this way is for loudness, which is
wonderful. but i want to hear a harmonic piano!! A quick
and dirty way around this would be to detune the piano.
The idea being that floppier strings produce better
harmonics. |
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Other than that, I have been limiting rationale to the
harmonic series and composing from there. I don't know
why I like single fundamental, strict harmonic series music.
I don't know why I feel like it is "more natural". I guess i
just want to fully appreciate the tones im using. I mean,
human vocals have a fundamental frequency, but we can
sing between the harmonics in the lower registers.
Elephants can't, and I don't know about birds. But I love
that human vocalists and players of fretted instruments
know a chord is tuned properly because their ear indicates
the point of stability. Whereas with ET, the piano decides
what is in tune for you, and it never fully satisfies your ear. |
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<link> Willie Ruff's Kepler recording includes pulses for the lowest "tones" (for the outer planets) - the "notes" of Neptune and Mercury being too wide apart to hear as pitches. |
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