Temperament, by Stuart Isacoff

Last week I read, for the first time, Temperament: How Music Became a Battleground for the Great Minds of Western Civilization, originally published in 2001. It was written by Stuart Isacoff, a “pianist, composer and writer, the founding editor of the magazine Piano Today,” and Lecturer at Purchase College, which is part of the State University of New York system. I found it to be fascinating, penetrating, and a very enjoyable read.

I was also pleased to discover that, indirectly, it presents a very strong argument in favor of Thumtronics’ musical innovations.

Superficially, Temperament could be read as a paean to 12-edo (Equal Division of the Octave, called simply “equal temperament” in the book). For example, Isacoff writes that:

• 12-edo is “the final solution” (p. 6).
• “if music depended on harmony for its expressiveness, then [12-edo] was crucial, because it offered any keyboard instrument a unique ability to facilitate harmonic movement” (p. 209).
• “equal temperament [is] a system that casually discards the simplest, purest musical ratios…for the sake of pleasing the ears” (p. 175).
• “no keyboard can execute all these different scales in meantone tuning without falling prey to the ‘wolves’” (p. 215).
• 12-edo’s adoption was “inevitable” (p. 224).
• “the temperament wars, after centuries of struggle, had essentially reached an end…[12-edo] settled in as the philosophical ideal” (p. 227).

However, the book frequent mentions an often-proposed alternative solution: extended keyboards and tunings, i.e., those with more than 12 notes per octave.

• “Instrument makers proposed the creation of keyboards with extra keys, so performers would have more than the usual number of choices for finding a note with the proper proportion. It was a cumbersome solution” (p. 18).
• “As late as 1768, the Foundling Hospital in London [installed an organ] capable of playing more than 12 pitches in an octave. Nevertheless, these complicated musical inventions found little acceptance” (p. 19).
• “one solution to [the problem of wolf intervals in meantone] was to offer extra keys, giving the performer a choice of playing either la-flat or sol-sharp…The idea would gain new adherents over time…but it was cumbersome, and ultimately unsatisfactory” (p. 104).
• “Nicola Vicentino…constructed an entirely new instrument, the archicembalo, with six rows of keys, to allow different versions of each scale member to be played (commas and all)” (p. 127).
• “Fabio Colonna’s sambuca, based on a division of the octave into thirty-one parts” (p. 131).
• “Mersenne, for example, urged the adoption of an instrument with nineteen keys” (p. 181).
• “Constantijn Huygens…used logarithms to calculate the division of the octave into thirty-one equal parts…Models of [his] keyboards, designed to fit over ordinary harpsichords, were, he reported, actually constructed in Paris” (p. 185).
• “Newton’s method boiled down to the cumbersome method of offering performers a greater-than-usual choice of notes to play” (p. 196).

Isacoff consistently uses the same word to explain the failure of extended keyboards: cumbersome, defined by the Merriam Webster Online Dictionary as meaning “unwieldy because of heaviness and bulk." The Thummer is one-thirtieth the size and one tenth the weight of an electronic keyboard, and vastly smaller & lighter than an acoustic piano.

Clearly, Isacoff considers the “cumbersome-ness” of any given keyboard design to be a significant factor in its acceptance or rejection.

Perhaps the Thummer's relative non-cumbersome-ness can be seen as a significant advantage.

Another word that Isacoff uses to describe extended keyboards is complicated, defined as “difficult to analyze, understand, or explain.” An alternative definition of cumbersome provided by Wiktionary, also smacks of complexity: “not easily managed or handled; awkward.” Does Isacoff prefer the simple and easy to the complicated and difficult? Apparently, he does.

• Isacoff quotes d’Alembert as praising Rameau for being “the first to have simplified the practice of [music] and made it easier,” implying that being simpler and easier – i.e., less complicated – are positive qualities (p. 223).
• Isacoff praises the innovations of Guido d’Arezzo – solfege and the staff, specifically – saying “The impulse to explore greater musical horizons demanded advances in technology…Portraying music visually made its structure easier to grasp and to vary; it enabled choirboys to learn in a few days what had taken weeks, and gave singers and composers newfound freedom to experiment. Musicians could more easily pose the question, ‘what if…?’” (p. 50)

The latter quote above is particularly important, as it elucidates a subtle point that is often lost: that by making things simpler, you can also make them more powerful. To quote Wikipedia, "A solution may be considered elegant if it uses a non-obvious method to produce a solution which is highly effective and simple. An elegant solution may solve multiple problems at once, especially problems not thought to be inter-related."

The Thummer’s isomorphic keyboard is said to be much simpler and easier than the piano keyboard, especially when also using the ThumMusic System to display and control musical information. (One might think of its solfege-based ThumLine staff as reuniting Guido d’Arezzo’s sundered innovations.) The Thummer’s ability to facilitate the exploration of “greater musical horizons” is discussed below.

Perhaps the Thummer's being less complicated can be seen as a significant advantage.

Throughout Temperament, Isacoff praises those instruments and tunings which enhance expressiveness and versatility:

• “Temperaments…unfettered the engine of musical progress” (p. 8)
• “Each of Leonardo [da Vinci]’s musical inventions seemed to break new ground in extending an instrument’s expressive possibilities” (p. 89)
• “The stretching of musical boundaries [in the late 1500’s] fueled a demand for more versatility from the keyboard instruments themselves” (p. 162)
• “For many musicians, the invention of the piano was a wish come true. Composer and keyboardist Francois Couperin had pleaded in print for the creation of just such an instrument in 1711. He would be ‘forever grateful,’ wrote Couperin, to anyone who could render the monotonous harpsichord capable of expression” (p. 210)

Independent experts claim (here, and here) that the Thummer, with its thumb-operated joysticks and internal motion sensors, has more expressive potential than any other instrument. As to versatility, the Thummer’s keyboard can be used to play the music of many different cultures and eras (which require tunings other than 12-edo), all with the same fingering. As to “unfettering,” the Thummer encourages musical progress through such novel effects as Dynamic Tonality.

Perhaps the Thummer's being more expressive, more versatile, and more enabling of musical progress can be seen as a significant advantage.

Isacoff also hints at the intimate relationship between tuning and timbre that is fundamental to Dynamic Tonality:

• “Unless the strings used to create the harmony are made of the same ‘material, length, thickness, and goodness,’ they simply won’t be in tune with each other…(the gut strings used in lutes, for example, will produce equal-tempered thirds that are more pleasant sounding than the ones produced on strings made of steel)” (p. 143).
• “Indeed, [the piano’s] timbre, like the lute’s, made the modified intervals of equal-tempered tuning easy to take” (p. 214).

During the time covered by the book Temperament, the only possible approach to the problem of consonance (described in the book as concordance) was tempering one’s tuning; it was not possible to temper the timbres of acoustic instruments. However, as Isacoff says (p. 39), “In our sophisticated, scientific age of black holes and anti-matter, dealing with such entities is child’s play.” Using electronic music synthesis, both tuning and timbre can be tempered together, opening the entire dynamic sweep of the syntonic temperament’s tuning continuum to exploration without sacrificing consonance.

This approach to solving the problems raised in Temperament is – as far as my collaborators, myself, and our papers’ peer-reviewers know – entirely novel. This use of “tempered timbres” slices through the Gordian Knot of temperament at an entirely new angle. Its result is not just one arguably-optimal approximation of Just Intonation – 12-edo – but rather a broad, continuous sweep of tunings, each maximally-aligned with its related timbres’ partials. Indeed, our approach embraces not only the syntonic temperament, but every rank-2 temperament, including the schismatic, Magic, Hanson, Porcupine, etc.

This newfound flexibility of tuning and timbre – “Dynamic Tonality” – is simply impossible to replicate on the piano-style keyboard, because a two-dimensional note-layout is required to capture the structure of a two-dimensional (rank-2) temperament, and the piano's keyboard is one-dimensional.

Perhaps the Thummer and Dynamic Tonality will be seen as offereing a more flexible solution to the problem of temperament.

There’s one last thread running through Temperament that’s relevant to Thumtronics’ innovations: Isacoff’s frequent praise for those creative musicians, scientists, and theorists who went against established orthodoxy in proposing new ways of balancing the needs of beauty and utility. However, this praise is offered more in tone than in text, so I can’t provide specific quotes.

It is unclear whether Isacoff's praise is for rational & experiential iconoclasm in general, or only for that which supports an anti-Pythagorean & pro-12-edo agenda. Thumtronics' innovations are certainly anti-Pythagorean (in that they modify the Sacred Harmonic Series itself – gasp, horror, heresy!), but they are hardly pro-12-edo. Nonetheless, they are built atop a firm scientific foundation, with mathematical proofs published in peer-reviewed scientific journals and with a demonstration synth that can be experienced by anyone.

In conclusion: Stuart Isacoff’s excellent book, Temperament, praises those innovations in the history of musical tuning, instrument design, and notation that enhanced simplicity, versatility, freedom, expressiveness, and progress, while being less cumbersome. I submit that the Thummer delivers all of these same benefits, and would welcome Dr. Isacoff's comments on it.

Tempered Calendars

A one-dimensional count of days, such as the Julian Day Number, has no inherent periodicity. Divide it up into 7-day weeks, however, and you get a calendar which is seven days wide and infinitely tall (usually clipped to display a single month’s days).

The periodicity of astronomical phenomena such as the rotation of the Earth around the Sun and the rotation of the Moon around the Earth are used as the basis of many calendar systems, such as the Buddhist, Chinese, Gregorian, Hebrew, Islamic, Korean, Mayan, or Persian. However, these astronomical phenomena can’t be captured perfectly in any calendar system because they are mutually indivisible. For example, it takes 365.2424 days (i.e., 365 days, 5 hours, 49 minutes and 12 seconds) for the Earth to orbit the Sun, and 29.530589 days (29 d 12 h 44 min 2.9 s) for the Moon to orbit the Earth – numbers which are not mutually divisible.

Each calendar system is a set of rules which defines the relationships among its various periodic intervals. Because the intervals are mutually indivisible, the rules of any given calendar system must favor one intervals over another. Therefore, these calendar systems can be viewed as temperaments. They compromise some intervals to capture the purity of others.

For example, the Islamic calendar compromises the purity of the solar interval in order to have an absolutely pure lunar interval, with months that precisely match the rising and setting of the Moon, but with years that drift relative to the Earth’s orbit around the Sun. On the other hand, the Gregorian calendar has a pure solar interval, but its months start and end with no relationship whatsoever to the rising and setting of the Moon. Other calendars temper their intervals differently, but they’re all temperaments, one way or another.

No such tempering would be necessary if the Earth orbited the Sun in exactly 336 days, and the Moon orbited the Earth in exactly 28 days. Then, every year would have 12 months of 4 weeks of 7 days. The new moon would rise on the first of each month; solstices and equinoxes would fall on the same dates (and days of the week) every year.

Unfortunately, we can’t temper the planets to conform to our calendrical needs. ;-)

Mapping Periodicity

I’m collecting examples of regular two-dimensional mappings of linear, periodic data. If you know of any good examples, please let me know.

Here are the best examples I know about.

The earth is a three-dimensional object, but maps are two-dimensional. They have to discard an entire dimension in order to present the curved surface of the Earth in a conveniently-flat manner, and there are lots of projections than organize this discarding in a systematic manner.

But what if you want to go the other way ‘round? What if you have low-dimension data, and you want to display it at a higher dimensionality?

Chemistry provides a famous example. Each of its elements has an atomic number, corresponding to the number of protons in its nucleus. Atomic numbers form a one-dimensional continuum from 1 (Hydrogen) to at least 118 (Ununoctium). The continuum of atomic numbers has no inherent periodicity, but the physical properties of the atom impose a periodic structure on this otherwise-undifferentiated continuum of atomic numbers, as seen in the Periodic Table of the Elements.

Another example is the calendar. One can think of time as a one-dimensional count of days, such as the Julian Day Number, which has no inherent periodicity. Divide it up into 7-day weeks, however, and you get a calendar which is seven days wide and infinitely tall (usually clipped to display a single month’s days).

Music provides the third example (and the point of this article). The human ear has a hearing range that runs from about 20 Hz up to about 20,000 Hz. This one-dimensional range of frequencies has no inherent periodicity, but if two tones from a harmonic source are sounded together within that range, the coincidence of their harmonics makes some inter-frequency ratios sound more consonant than others, giving rise to the musical intervals recognized as octaves, perfect fifths, and so on. Using only the octave and tempered perfect fifth to generate all other tonal intervals, one can map linear frequency into a periodic set of intervallic relationships, as seen in isomorphic keyboards.

If linear data contains periodicity, then that periodicity can supply the information needed to provide an extra dimension.

This seems to me to be rather magical: An entire dimension of data conjured up out of thin air!

If you know of any other examples, please let me know! :-)

Thummer Plays the Blues

What is the blues scale?.

In Africa and the Blues, Gerhard Kubik describes the blues scale as arising from two overlapping harmonic series, one starting a perfect fourth higher than the other. He shows this using a diagram showing only the 5th through 9th partials (harmonics) of each note's harmonic series, which I have modified as shown below (at right).

In the figure at right, the lower-pitched harmonic series is Do (outer ring, with harmonics as black-filled circles), the upper-pitched one is Fa (inner ring, harmonics as unfilled circles). Partials 5 through 9 are shown for each. There's very good alignment between Do's 8th partial and Fa's 6th partial (and of course the octaves thereof), and also between Do's 6th partial and Fa's 9th partial. These well-aligned pairs are a perfect fifth apart.

An alternative way to visualize two overlapping harmonic series is shown below.
In the figure at left, the harmonics of Do are in black while those of Fa, offset a perfect fourth higher, are in grey. At 700 cents above Do's fundamental, Do's 3rd, 6th, 12th, & 24th harmonics align with the 9th & 18th partials of Fa -- hence aligning the Do6 and Fa9 partials as in the circular figure above. Likewise, Do's 1st, 2nd, 4th, 8th, & 16th partials (far left, at 0 cents) align well with Fa's 3rd, 6th, 12, & 24th partials (far right, just past 1199 cents) -- hence aligning the Do8 and Fa6 partials as in the circular figure above.

At the top of the figure above and left, scale degrees are shown. The 3rd and 6th scale degrees are underlined, with each underline joining two stacks of harmonics. The third degree joins Do9 and Fa7 (and their octaves), while the sixth degree joins Do7 and Fa5 (and their octaves). According to Kubik (if I understand his section of his book correctly), these not-quite-aligned Do9/Fa7 and Do7/Fa5 pairs enable the tunings of these scale degrees to be flexible within a fairly wide range.

Another point raised by Kubik is that the 7-edo scale -- also known as the "equiheptatonic" scale, dividing the octave into 7 intervals of equal width -- is common in some parts of Africa. A "third" in 7-edo tuning is 343 cents wide, which is right in the middle of the range of the 3rd scale degree in the above-left figure, providing yet another source of instability in this range.

Does the Thummer suit the blues?

Played in today's standard Western 12-edo tuning (i.e., an “equal division of the octave” into 12 pieces), the Thummer should be at least as blues-capable as the piano or guitar. Its expressive controls (thumb-operated joysticks & electronic motion sensors) allow the user to play the blue notes "between" the notes of 12-edo as a guitarist can do by bending strings, and which a pianist simulates by "crushing" adjacent keys.

However, the Thummer's real potential as a blues instrument arises from the tuning invariance of its isomorphic keyboard, which gives it the same fingering in any tuning of the syntonic temperament, which includes both 12-edo and 31-edo (i.e., an “equal division of the octave” into 31 pieces, in which the tempered perfect fifth is 696.8 cents wide -- only 3.2 cents narrower than 12-edo's tempered perfect fifth).

The use of septimal (7-limit) ratios for the blue notes is explored by W.A. Mathieu in his excellent book Harmonic Experience (Chapters 17 & 33).

In 12-edo tuning, the augmented second (A2) has the same width as the minor third (m3) -- 300 cents -- so they are often treated as if they were "the same" interval.

However, in any other tuning, including 31-edo tuning, the A2 and m3 have different widths, each signifying a different just interval, as does the M3.

• 31-edo's A2, at 271.0 cents, is only four cents narrower than the just septimal minor third (7/6 = 266.9).
• 31-edo's m3, at 309.7 cents, is only 5.9 cents narrower than the just minor third (6/5 = 315.6).
• 31-edo's M3, at 387.1 cents, is less than one cent wider than the just major third (6/5 = 386.3 cents).

This harmonically-relevant distinction between the A2, m3, and M3 gives musicians a choice of three different notes to play across the range of blue 3rds. They can use the A2 to signifiy the 7/6 ratio, the m3 to signify the 6/5 ratio, or the M3 to signify the 5/4 ratio. All of these notes provide a better match with the harmonic series when using 31-edo than when using 12-edo.

Perhaps even more importantly, 31-edo distinguishes the augmented sixth (A6) from the minor seventh (m7).

• 31-edo's A6, at 967.7 cents, is only 1.1 cents narrower than the septimal minor seventh (7/4 = 968.8), making it well-suited for the harmonic seventh, also known as the "babershop seventh," chord.
• 31-edo's m7, at 1006.5 cents, falls almost exactly between just intonation's Pythagorean minor seventh (16/9 = 996.1) and diatonic minor seventh (9/5 = 1017.6), making it well-suited for use in a dominant seventh chord.

Hence, musicians can use the A6 to signifiy the 7/4 ratio, or the m7 to signify the 16/9 and/or the 9/5 ratio. Either way, musicians get a better match with the harmonic series when using 31-edo than when using 12-edo. (Well, actually, 12-edo's m7, at 1000 cents, is a better match with the Pythagorean m7, but it's a worse match with the diatonic m7 and is completely useless as a septimal m7.)

According to this reference, the tonic, subdominant, and dominant chords (I7, IV7, and V7) should be played as harmonic seventh chords (i.e., with an A6) except for the V7 at the turnaround, which should be played as a dominant seventh chord.

If I understand this correctly -- which I very well may not -- then in C, using the tuning described above, the I7, IV7, and V7 blues chords would be played in 31-edo as:

• I7: C-E-G-A#
• IV7: F-A-C-D#
• V7: G-B-D-F (turnaround) or G-B-D-E# (otherwise)

31-edo supports free modulation as well as 12-et does, with a caveat or two. For example, you can't play Coltrane's Giant Steps in 31-edo, becuase Giant Steps' chord progression relies on the fact that 12-edo's way-too-wide 400-cent major third tempers out the diesis , so that a chord progression through three M3's will return to the same pitch class. 31-edo's major thirds are almost perfectly just at 387.1 cents, so progressing through three of them will bring you to a point that's 38.7 cents short of the starting pitch class. Oops! In 31-edo, Giant Steps is a giant stumble, because it relies utterly on the unique structure of 12-edo -- whereas most blues relies on a structure that mixes 7-limit intervals with 5-limit intervals, at which 31-edo excels.

So, how does the Thummer compare to other blues instruments?

• On the piano keyboard, making a distinction between the A6 and m7, or the A2 and m3, is impossible. Both intervals share the same key. Pianists can fake it by crushing adjacent keys, but that's clearly a kludge, which does nothing to distinguish among the relevant harmonic ratios.


• On the guitar, it's possible to play perfectly intoned notes -- through string bending -- but difficult. In this YouTube video lesson from Berklee, the instructor states (2:09 in) that "String bends are kinda tricky. They take a little getting used to...like YEARS, actually, to develop a good sound."


• On the Thummer, you can learn to play perfectly-intoned blue notes in minutes. To paraphrase Bach, you just press the right button at the right time, and the instrument plays itself. In C, for example, if you want the A2, you play the D# button; if you want the m3, you play the Eb button; if you want the M3, you play the D button. You can use the portamento controller to slide smoothly from one precisely-tuned note to another, with no guesstimation involved. Or, you can play any of the notes above, and use pitch bending to slide 'em around at will.

31-edo is good for other musical styles, too. It is nearly identical to 1/4-comma meantone, which dominated the early centuries of Europe’s Common Practice Era, of which the use of augmented sixth chords was distinctive part.

31-edo may also be well-suited to klezmer and gypsy music, which use many augmented intervals.

If 31-edo is so cool, why hasn't it been more widely used? Apparently, because it was thought to require the use of an instrument with 31 keys per octave, for which there could be no mass-market in a 12-edo-dominated world.

This barrier may have been eliminated by the recent discovery of tuning invariance, combined with electronic transposition. Despite having only 19 buttons per octave, it appears to be true that all of the tonally-relevant 5-limit and 7-limit intervals of 31-edo fall on the Thummer's keyboard. (The above-mentioned neutral third does not, because it's an 11-limit interval.) Add to this the Thummer's expressive potential (controlled by its thumb-operated joysticks and internal motion sensors), and the Thummer could be a very credible blues instrument.

However, it's important to realize that 12-edo and 31-edo are just points along the syntonic temperament's tuning continuum, along which the Thummer can be retuned dynamically in real time. On the one hand, that means that a Thummer player can slide smoothly back and forth between 12-edo and 31-edo (or Pythagorean, or 7-edo, or whatever) in real time, choosing the tuning that best fits the current note or phrase. On the other hand, this real-time flexibility enables entirely new musical effects such as expressive polyphonic tuning bends, tuning progressions, and temperament modulations.

My collaborators and I have barely scratched the surface of the possibilities of tuning invariance -- our initial scientific paper was published just three months ago -- so we're not yet sure how big the creative opportunity really is.

Now, if y'all could please point out the errors I've undoubtedly made in this blog article, I'd appreciate it, and will update the article accordingly.

Thanks! :-)

Technology Evangelism

The goal of technology evangelism is the establishment of a new technology as a de facto standard within a given market. In markets dominated by network effects, the status quo tends to be locked in, making it impervious to alternative technologies that offer only minor advantages. However, these same network effects tend to favor new technologies that offer disruptive advantages, such as being simple, cheap, powerful, and unique.

The technology evangelist’s job is the creation of a critical mass of support for a new technology. Once critical mass is reached, the new technology becomes self-evangelizing, and the technology evangelist’s efforts can be invested in some other new technology.

In evangelism, speed is critical. The new technology must reach critical mass before the status quo’s backers can blunt its momentum – because change is always resisted. Once critical mass is reached, a new status quo will emerge, centered on the evangelist’s new technology.

The technology’s evangelist must:

• create materials that facilitate each potential adopter’s progress through the decision process,
• bring these materials to the attention of those potential adopters who have the most leverage (see below),
• organize a system of incentives to encourage early adopters to actively engage their leverage on behalf of the new technology, and
• drive a public relations campaign to publicize the early adopters’ support of the new technology, thereby
• maximizing the technology’s benefit from bandwagon effects and social proof.

Leverage is the ability to get other potential adopters to adopt whatever technology you adopt. The more people your technology adoption influences, and the more powerful your influence on each such person, the more leverage you have. Identification and exploitation of leverage is the key to efficient evangelism.

At each stage of the technology evangelism process, the technology evangelist's focus must always be on ensuring that the adopters of the new technology gain compelling benefits (a) directly, from adopting the new technology, and (b) indirectly, from getting others to adopt the new technology, too. "Ask not what your adopters can do for your technology; ask what your technology can do for your adopters." (Unless your technology is a whole lot better, don't even ask that.)

Instrument Selection

Every three years, NAMM hires Gallop to conduct a telephone survey of American households. I can't find the 2006 survey online, but the 2003 survey concluded that

1. 64% of instrumental music-makers started studying music when they were 5-11 years old; 18% starting 12-14; 7% 15-18; and 6% after 18.


2. 75% chose for themselves the instrument that they learned to play, with 15% making the decision jointly with parents and 10% having the choice of instrument made by the parent alone.


3. 30% took lessons at school, 26% took private lessons, and 22% taught themselves. The “taught themselves” percentage has risen over time (and may be rising much faster now due to the Internet). Boys teach themselves three times as often as girls do.

It is illuminating to make a chart of the ages at which music-makers started studying music (below).


The chart shows the percentage of instrumental music-makers who started learning music at each given age (in red) and the culumative total up to that age (in green).

The ages 5-11 are clearly critical. 69% of people who will ever learn to play an instrument have started learning by the end of their 11th year, and 87% by the end of their 14th year. Clearly, if I want to sell a lot of Thummers, I need to *eventually* meet the needs of very young students (although it may not be efficient to target them first).

NAMM’s surveys don’t ask what instrument is played, or why that particular instrument was chosen. There is little research into the factors which affect musical instrument choice among beginners, and that limited research tends to constrain the available options to band & orchestra instruments. A better understanding the factors affecting instrument-selection could suggest opportunities for improving the Thummer such that it would consistently win this selectrion process.

NAMM's survey data suggest that

• Ensuring that the Thummer meets the needs of beginners aged 5-11 is critical to its long-term success;


• We can emphasize self-teaching (online) initially, but will need to penetrate the private lesson and school-based lesson channels, also, to maximize Thummer sales;


• The ability of a given instrument to help a teenage boy “get chicks” is not sufficient, in itself, to maximize Thummer sales, as (i) it doesn’t help sell instruments to girls, and (ii) more than 80% of music-makers have already selected their instrument before their mid-teens, leaving at most 20% to be affected by this benefit.

People usually mention the "get chicks" factor with regard to the guitar -- but history suggests that jazz instrumentalists did pretty well in that regard, too, so there appears to be more to that benefit than just instrument choice.