In the mid-to-late 1800s, Herman Helmholtz was building spectrographs of musical sounds by listening to them through a bunch of resonators of varying sizes that acted as band-pass filters, and recording how loud each harmonic sounded.
His writings are still relevant today.
https://www.amazon.com/Sensations-Tone-Dover-Books-Music/dp/...
I've heard that the Sethares book (which is much more recent) is really good too, but I don't have a copy of that one.
https://www.amazon.com/Tuning-Timbre-Spectrum-William-Sethar...
"Helmholtz concluded that the spectral description of a sound had the most straitforward correlation with its timbre.... For instance the qualitative description of 'brilliant' or 'bright' characterizes spectra that have a great deal of energy at high frequencies [e.g. brass instruments] ... A spectrum with little energy in the even-numbered harmonics characterizes the particular timbre that is produced by the clarinet in its low register...." (2nd Ed. Section 2.6)
Understanding that each instrument produces a spectrum of harmonics peculiar to it ... and that those harmonics have relatively different pitches and amplitudes and evolutions ... that vary with how the instrument is played ... is key to quantifying its timbre.
(At first, not an easy thing to grasp let alone quantify. But Partch made a lot of progress!)
https://commons.wikimedia.org/wiki/File:Timbre_analyser-CNAM...
In most genres you have a palette of timbres to work with for each instrument based on the genre conventions. You can push at the edges or add things in, but have to balance audience expectations carefully as you do it. So for example the way an electric bass sounds in contemporary metal is just not normally going to "fit" into a chicago blues band, even though both are heavily dependent on the sound of electric bass.
Different genres have different relationships to this constraint, for example western classical has a huge palette available in an orchestra but is relatively averse to using instrumentation outside of that collection. Except in percussion, where there is a lot more flexibility! Jazz has a fairly small & rigid set of acceptable timbres for its core instruments, but is fairly tolerant of experimenting with new instrumentation.
So then the two genre-timbre relationships I find most interesting are electronic and pop. Pop is, more than any other genre I think, curious about how timbre effects emotional response in music. An album by the same artist could have a huge range of different sounds for recognizable instruments, using the tension between them for different effects.
And then large swaths electronic music are built largely around active change of timbre over time through a piece. Something you see used conservatively and carefully in most genres becomes almost the central practice.
IDK it's hard to articulate and I'm not trying to set a reductionist framework about how music sounds or anything. Just a line of musical thought I've been exposed to and found valuable.
And that's why I love folk-ish metal so much.
Why shouldn't we have a lead/harmony violin on top of a metal rhythm section? https://www.youtube.com/watch?v=F17sxgZdXZw
Or a hurdy gurdy? https://www.youtube.com/watch?v=LT7HqIP55tI
Or a pipa, which was btw very hilarious in poland: https://www.youtube.com/watch?v=MwpKZtPBIEQ
I'm honestly thinking of dropping some money to get myself an A-tuned drone flute[0]. Drone flutes sound really cool, and the drone would be tuned to just about the highest two notes on the guitar... and if you work with it a bit, drums/bass/rhythm guitars helping with rhythms, chords and harmony could really push that somewhere really interesting.
Was brilliant, a lot of groups focusing on the use of ML to characterise the "unexplainable" in sound synthesis.
We ended up submitting a tool for interacting directly with Ableton using LLM agents after becoming disenchanted with text2audio models, wrote about it here - https://montyanderson.net/writing/synthesis
I have been out of it so long muff wiggler is now mod wiggler. Come on, that is absurd. Muff Wiggler was the best name ever.
There's a neat documentary floating around which includes some scenes where he explains how he increased his understanding of waveforms in the frequency domain by physcially modeling them in the time domain.
Different harmonics have different ADSR curves (Attack, Decay, Sustain, Release).
Above all, one cannot overstress the importance of the attack transient. There are famous experiments in psychoacoustics that show that, when deprived of their attack transient, the sounds of two different instruments may become hard to tell apart.
Personal anecdote: as a classic guitarist, it took me three years of experimentation to find the right way to cut my fingernails in order to have a better sound. The Electronic Engineer in me says that those were three years spent to look for how to improve 0.1 seconds of noise at the start of each of my notes.
Roland used this fact to produce surprisingly realistic sounds at low cost. When memory was too expensive to sample the whole note, you could get excellent results from sampling just the transient and using traditional subtractive synthesis for the rest:
A neat trick is playing guitar through a volume pedal. You mute the sound, pluck a string and then swell in the volume pedal. The rest of the ASDR envelope can be created with other effects like delays.
Classical composers had a set of fixed timbres to play with, each instrument having their own. With synthesizers everything is possible.
Generating that sound in a live performance that is partially or fully improvised is a harder problem.
The evolution of solutions to either problem depends on which instrument you're interested in, and is based partially on Means, Motive, and Opportunity. There's a reason to synthesize a piano or Hammond organ, which is that they're hard to transport and maintain. Less motive for synthesizing a violin.
Vocal timbre is a big identifier of different rap subgenres and artists, seems like. Certainly seems like much of the vocal delivery on a track explores fluctuation of the timbre, even when the pitch is constant or has little dynamics.
It's interesting to think how the timbral effects of a regional accent would interact with the beat construction/development. Is the trap hi-hat a result of the Southern drawl?
I would go so far as to say understanding and selection of timbre is 50% of the work of a synth player.
Violin and the bow are both made of wood and a rainy damp day can easily sound different than dry summer's day.
You can get good carbon fiber bows and they are much less weather sensitive.
You can also get carbon fiber violins but I haven't heard one that sounds as good as one made from wood.
> The utility of the piano for composing was its neutral and uniform tone color: in theory (although not in reality) the tone quality of the bass is the same as the treble. In any case, the change in tone color over the whole range of the piano is, or should be, gradual and continuous (there are breaks, of course, when the notes go from one string in the bass to two and then to three in the treble). The monochrome piano might be used therefore just for its arrangements of pitches, and the quality of the sound could-absurdly in many cases-be considered secondary.
> What made it possible for composers to refuse to acknowledge the difference on the piano between treble and bass and leave whatever problems arose to be solved by the performer was the fact that the change in tone color over the span of the keyboard is not like the leap from a bassoon to a flute but continuous and very gradual when the instrument is properly voiced. These imperceptible gradations are the result of a deliberate policy of a unified sonority on the part of musicians and instrument makers. All attempts over the history of piano construction to incorporate anything analogous to the picturesque changes of registration in the organ and the harpsichord had little success, were not exploited by composers, and were finally abandoned. Radical contrasts of tone color were traded for the possibility of making a gradual crescendo or diminuendo. This was a decision that took place at the same time as the preeminence accorded to the string quartet over all other forms of chamber music; that, too, emphasized the importance of a unified tone color. Chamber music with wind instruments, while the occasion for several masterpieces, became the exception, an exotic form. That is why the use of colorful sonorities in the orchestra has so often been considered somewhat vulgar, as if calling attention to the sound were paradoxically to detract from the music. The prestige given to pure string sonority is part of the asceticism of nineteenth-century high culture. Contrasts of tone color were given a significantly lower place in the hierarchy of musical elements. This is one reason that only the piano repertory rivals the string quartet as the most respectable medium for private and semiprivate music-making from Haydn to Brahms.
"I think the tone becomes perceptible by virtue of tone color [timbre], of which one dimension is pitch. ... Pitch is nothing else but tone color measured in one direction. Now, if it is possible to create patterns out of tone colors that are differentiated according to pitch, patterns we call 'melodies', progressions, whose coherence evokes an effect analogous to thought processes, then it must also be possible to make such progressions out of the tone colors of the other dimension, out of that which we call simply 'tone color', progressions whose relations with one another work with a kind of logic entirely equivalent to that logic which satisfies us in the melody of pitches. That has the appearance of a futuristic fantasy and is probably just that. But it is one which, I firmly believe, will be realized.
...
Tone-color melodies! How acute the senses that would be able to perceive them! How high the development of spirit that could find pleasure in such subtle things!"
-- Arnold Schoenberg, Theory of Harmony, 1911, toward the end of chapter 22.
Personally, I anticipate that if humanlike AGI is achieved, then it will understand the illusion of music. Not merely because music understanding is an attribute of humanlike, but because there must be something intrinsic in the process of human cognition that causes the illusion of music occur. Music understanding could be viewed as an essential waypoint on the path to AGI.
Despite the different sensory systems (sound, or visual) and the difference in actual data (I don't know how many photons or audio waves entering your brain), we can abstract them down and understand/relate them with a simple pattern.
When I get mentally crystallized, I hear music as proof-of-work in the vein of Bitcoin hashes.
Maybe a reason for calling music an illusion is to try to point out that it's all in our heads. Sure, the physical instruments are over there, but they are just some atoms and molecules rattling about creating vibrations that, like everything ultimately, share the meaninglessness of the physical universe of just more material stuff (ignoring the quantum and the unknown). In which case though life seems also to look more like an illusion. Ah but the meaningless vibrations enter our ears and are processed and become music, so like color there is none but in our heads, thus illusion? But these notions also fall apart. The redness of apples isn't all in our heads; it requires a certain relationship to light frequencies that we see as redness. It's not an illusion it's just what red looks like through a living human body. If not through our senses and brain, and then mind, where should we experience it?
Music is only ever meaningless if it is unheard, as apples can only not be red when they are unseen (or are Granny Smiths).
So music is only meaningless if there is nobody -- no body -- to listen. And maybe that's where all of this leads. Your AGI needs to be embodied and alive.
Skeuomorphic design, to me, largely feels lazy and unattractive; rather than designing for the new, maybe unfamiliar, medium you're working in, you attempt some facsimile which inevitably cannot live up to the original, either out of lack of ambition, or lack of faith in your audience to understand or appreciate without the anchor of a common metaphor. It lacks idiomaticity - there are particular details, quirks, associated with different mediums that lend themselves to different sorts of designs, and a skeuomorphic design language ignores these. (The same is true of musical instruments. A piece written for the lute, say, played on piano, would feel very different than a piece written for piano, played on piano; what is easy, or possible, on one instrument, is not necessarily as sonorous on another.)
To me, the use of synthesizers to emulate acoustic instruments, where the express intent of the composer/producer/whatever is to evoke the sound of that acoustic original (read: where the creator would prefer the sound of the real instrument), is, at its most generous, telling of a lack of creativity and at worst laziness. (If what you want is expressly the sound of a synthetic imitation for the purposes of your art, none of this applies.) It is a lack of creativity in the case where the creator simply does not have access to "real" instruments they'd rather use, and it's laziness where you have access and ability but opt for something you yourself deem inferior.
Of course, this all presupposes that there is something lost when say, a synthesizer plays a violin patch in an earnest effort by the creator to emulate a violin - where a real violin is actually what's desired. I think this isn't controversial to say, but of course it's a spectrum; I have much less of a problem in cases where the delta is smaller; e.g., simple legato harmonies from a string section can be emulated more convincingly (by orders of magnitude) than some virtuosic cadenza by a solo instrumentalist.
I've met winemakers who think of planting in terms of multigenerational experiments with highly intentional controls for different aspects of soil and micro-climate that may vary on a scale of a single meter, who work to find and train their successors because they will not see the results of some of these experiments in their lifetimes; winemakers who absolutely understand that blending is not just a linear combination of the characteristics of blended wines, but a truly complicated system where certain flavors may heighten others; winemakers who rely on centuries of experience in how funguses and other microorganisms can be used in safe and flavor-enhancing ways.
Winemaking is engineering, just as musical instrument design is (both physical and digital), and just as building a startup is. The presence of human subjectivity as an evaluating oracle in a complex system does not imply that its creators work without intention or without rigorous systems-level thinking.
Anyone who's played Outer Wilds should disagree with this.[0]
To say we can't describe timbre is a bit misleading, because there are concrete mathematical ways to analyze sounds; they exist in a three-dimensional space of frequency, amplitude and time. But that's helpful in the same way that describing programming languages as collections of 1s and 0s is.
What's lacking for describing timbre, I suppose, are the steps between "this sound is a sum of a particular arrangement of sine waves" and "this sound is a piano". There are common terms such as ADSR or "brightness" and "warmth" but those don't tell the full story.
The question is, how valuable is that intermediate step when you could just say "this is a piano, this is a banjo"?
That’s what stops music from being math.
I'm scandalized. /s