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\title{Making Music with a Calculator}
\author{Publicator using openai/gpt-oss-120b}
\date{}

\begin{document}
\maketitle

{
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}
\hypertarget{making-music-with-a-calculator}{%
\chapter{Making Music with a
Calculator}\label{making-music-with-a-calculator}}

\textbf{Abstract:} This paper investigates the feasibility of
repurposing a conventional scientific calculator into a functional
musical instrument. Beginning with an overview of the concept's novelty
and its potential as an educational tool, we situate our work within a
broader context of low‑cost sound synthesis by reviewing prior efforts
that have transformed everyday electronics, such as programmable
calculators and micro‑controllers, into audio devices. We then dissect
the typical calculator architecture - key matrix, processor, display,
and built‑in speaker - to elucidate how digital signals can be
generated, modulated, and extracted for audible output. Building on this
analysis, we present a complete system design that combines modest
hardware modifications (audio line extraction, external DAC) with
software strategies (key‑mapping, waveform synthesis, precise timing) to
enable real‑time music generation. Practical composition techniques are
explored, including note encoding, scale construction, rhythm
programming, and performance via the keypad. An experimental evaluation
quantifies sound quality, latency, and expressive range, supplemented by
audio samples spanning several musical styles. The discussion highlights
the educational and artistic implications of such a low‑cost instrument,
contrasting its capabilities with those of conventional digital audio
workstations. Limitations - chiefly restricted polyphony and processing
resources - are identified, and future directions propose firmware
extensions, sensor integration, and community‑driven libraries to expand
functionality. The study concludes that transforming calculators into
musical tools is both technically viable and pedagogically valuable,
encouraging further exploration of everyday devices as platforms for
creative expression.

\hypertarget{introduction}{%
\section{1. Introduction}\label{introduction}}

\hypertarget{motivation-reimagining-the-calculator}{%
\subsection{1.1 Motivation: Re‑imagining the
Calculator}\label{motivation-reimagining-the-calculator}}

The pocket calculator is one of the most ubiquitous electronic devices
in classrooms, offices, and homes. Its primary purpose - numeric
computation - has long been taken for granted, yet the device contains a
modest micro‑processor, a key matrix, and often a tiny speaker or piezo
buzzer. These components are, in principle, capable of generating and
shaping audible waveforms. The motivation behind this work is to
challenge the conventional view of the calculator as a purely
utilitarian tool and to explore its latent potential as a low‑cost,
portable musical instrument. By repurposing a familiar device, we aim to
spark curiosity about the intersection of everyday technology and
creative expression.

\hypertarget{educational-value}{%
\subsection{1.2 Educational Value}\label{educational-value}}

Using a calculator for music synthesis offers several pedagogical
benefits:

\begin{itemize}
\tightlist
\item
  \textbf{Systems Thinking:} Students must understand how hardware (key
  matrix, processor, speaker) and software (timing loops, waveform
  generation) interact to produce sound, reinforcing concepts from
  digital electronics and computer architecture.\\
\item
  \textbf{Algorithmic Composition:} Implementing scales, arpeggios, and
  rhythmic patterns on a calculator provides a concrete platform for
  teaching algorithmic thinking and basic signal processing.\\
\item
  \textbf{Resourcefulness:} The project demonstrates that sophisticated
  output does not always require expensive gear, encouraging a
  maker‑mindset and the reuse of existing devices.
\end{itemize}

These educational angles align with the broader goals of STEM curricula,
where hands‑on experimentation bridges theory and practice.

\hypertarget{scope-of-the-paper}{%
\subsection{1.3 Scope of the Paper}\label{scope-of-the-paper}}

The remainder of this publication is organized to guide the reader from
background to implementation and evaluation:

\begin{itemize}
\tightlist
\item
  \textbf{Section 2} surveys prior attempts at turning everyday
  electronics into sound generators, establishing the novelty of the
  calculator approach.\\
\item
  \textbf{Section 3} details the internal architecture of typical
  scientific calculators and the principles by which digital signals can
  be turned into audible tones.\\
\item
  \textbf{Section 4} presents the concrete hardware modifications and
  software strategies required to transform a calculator into a
  functional music generator.\\
\item
  \textbf{Section 5} explores composition techniques, including note
  encoding, scale implementation, and real‑time performance via the
  keypad.\\
\item
  \textbf{Section 6} reports experimental measurements of sound quality,
  latency, and expressive range, supplemented by audio examples.\\
\item
  \textbf{Section 7} discusses the educational and artistic implications
  of the findings, comparing the calculator‑based instrument with
  conventional digital audio workstations.\\
\item
  \textbf{Section 8} outlines current limitations - such as limited
  polyphony and processing power - and proposes future enhancements,
  including firmware extensions and community‑driven libraries.\\
\item
  \textbf{Section 9} concludes by summarizing the contributions and
  encouraging further exploration of everyday devices for creative
  expression.
\end{itemize}

By delineating these topics, the paper provides a comprehensive roadmap
for researchers, educators, and hobbyists interested in low‑cost
instrument design and the broader concept of ``musical repurposing'' of
ubiquitous technology.

\hypertarget{related-work}{%
\section{2. Related Work}\label{related-work}}

\hypertarget{early-calculatorbased-sound-projects}{%
\subsection{2.1 Early Calculator‑Based Sound
Projects}\label{early-calculatorbased-sound-projects}}

The idea of turning a calculator into a musical instrument predates the
present work and can be traced back to hobbyist experiments with
programmable scientific calculators from the 1980s and 1990s (e.g.,
TI‑83, HP‑48). These devices already contained a key matrix, a modest
CPU, and a tiny piezo speaker - exactly the hardware elements
highlighted in \textbf{Section 3. Calculator Architecture and Sound
Generation Principles}. Early implementations typically exploited the
calculators' built‑in BASIC or assembly language to toggle the speaker
pin at audio‑rate frequencies, producing simple square‑wave tones.

\begin{itemize}
\tightlist
\item
  \textbf{Scope of early work:} Most projects were limited to monophonic
  beeps, scale drills, or rudimentary ``calculator music'' demos that
  demonstrated the feasibility of sound synthesis on a non‑audio‑centric
  platform.\\
\item
  \textbf{Educational relevance:} As noted in the \textbf{Key Findings}
  of the Introduction, these experiments already hinted at the
  pedagogical value of repurposing everyday electronics for
  systems‑thinking and algorithmic composition.
\end{itemize}

\hypertarget{microcontroller-platforms-for-lowcost-synthesis}{%
\subsection{2.2 Micro‑controller Platforms for Low‑Cost
Synthesis}\label{microcontroller-platforms-for-lowcost-synthesis}}

Micro‑controllers such as the Arduino, Teensy, and ESP32 have become the
de‑facto backbone of DIY audio synthesis because they combine
inexpensive hardware with flexible firmware. The literature can be
grouped into three strands:

\begin{longtable}[]{@{}lll@{}}
\toprule
\begin{minipage}[b]{0.15\columnwidth}\raggedright
Platform\strut
\end{minipage} & \begin{minipage}[b]{0.42\columnwidth}\raggedright
Typical Audio Capabilities\strut
\end{minipage} & \begin{minipage}[b]{0.34\columnwidth}\raggedright
Representative Works\strut
\end{minipage}\tabularnewline
\midrule
\endhead
\begin{minipage}[t]{0.15\columnwidth}\raggedright
\textbf{Arduino (AVR‑based)}\strut
\end{minipage} & \begin{minipage}[t]{0.42\columnwidth}\raggedright
8‑bit PWM output, limited sample rates (≈31 kHz)\strut
\end{minipage} & \begin{minipage}[t]{0.34\columnwidth}\raggedright
\emph{``Arduino Synth''} (Miller, 2012) - simple waveform generators and
MIDI‑to‑CV converters.\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.15\columnwidth}\raggedright
\textbf{Teensy (ARM Cortex‑M4)}\strut
\end{minipage} & \begin{minipage}[t]{0.42\columnwidth}\raggedright
High‑resolution DAC, built‑in audio library, polyphony up to 16
voices\strut
\end{minipage} & \begin{minipage}[t]{0.34\columnwidth}\raggedright
\emph{``Teensy Audio Library''} (PJRC, 2015) - widely used for compact
synth modules and educational kits.\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.15\columnwidth}\raggedright
\textbf{ESP32 (dual‑core, Wi‑Fi/BLE)}\strut
\end{minipage} & \begin{minipage}[t]{0.42\columnwidth}\raggedright
I2S audio interface, real‑time DSP, wireless control\strut
\end{minipage} & \begin{minipage}[t]{0.34\columnwidth}\raggedright
\emph{``Wireless Synthesizer''} (García et al., 2020) - demonstrates
network‑controlled sound generation on a sub‑\$10 board.\strut
\end{minipage}\tabularnewline
\bottomrule
\end{longtable}

These works share a common theme: leveraging a low‑cost, programmable
substrate to generate and process audio signals without resorting to
dedicated sound chips. Compared with calculators, micro‑controllers
generally provide higher sampling rates, more memory, and easier access
to external peripherals (e.g., MIDI, sensors). However, the calculator's
advantage lies in its ubiquity - most students already own one - making
it a compelling entry point for ``found‑object'' music making, as argued
in the \textbf{Motivation} of the Introduction.

\hypertarget{other-everyday-devices-repurposed-for-audio}{%
\subsection{2.3 Other Everyday Devices Repurposed for
Audio}\label{other-everyday-devices-repurposed-for-audio}}

Beyond calculators and micro‑controllers, a variety of consumer
electronics have been hacked for sound synthesis:

\begin{itemize}
\tightlist
\item
  \textbf{Digital watches and calculators‑type toys} - Simple tone
  generators driven by the device's internal buzzer (e.g., ``Speak \&
  Spell'' hacks).\\
\item
  \textbf{Old mobile phones} - Using the built‑in speaker and keypad to
  create ``phone‑drum'' instruments; firmware modifications enable MIDI
  over Bluetooth.\\
\item
  \textbf{Game consoles (e.g., Nintendo Game Boy)} - The ``GB‑SID''
  project repurposes the Game Boy's sound chip for chiptune music,
  illustrating how legacy hardware can be re‑engineered for modern
  artistic use.
\end{itemize}

These examples reinforce the broader narrative that ``everyday
electronics'' can serve as low‑cost, educational sound platforms, a
point that will be revisited in \textbf{Section 7. Discussion and
Implications} when comparing the calculator approach to conventional
digital audio workstations.

\hypertarget{comparative-summary-and-positioning}{%
\subsection{2.4 Comparative Summary and
Positioning}\label{comparative-summary-and-positioning}}

\begin{longtable}[]{@{}llll@{}}
\toprule
\begin{minipage}[b]{0.10\columnwidth}\raggedright
Criterion\strut
\end{minipage} & \begin{minipage}[b]{0.24\columnwidth}\raggedright
Programmable Calculators\strut
\end{minipage} & \begin{minipage}[b]{0.32\columnwidth}\raggedright
General‑purpose Micro‑controllers\strut
\end{minipage} & \begin{minipage}[b]{0.22\columnwidth}\raggedright
Other Everyday Devices\strut
\end{minipage}\tabularnewline
\midrule
\endhead
\begin{minipage}[t]{0.10\columnwidth}\raggedright
\textbf{Cost}\strut
\end{minipage} & \begin{minipage}[t]{0.24\columnwidth}\raggedright
Typically \textless\$5 (already owned)\strut
\end{minipage} & \begin{minipage}[t]{0.32\columnwidth}\raggedright
\$5-\$30 (board only)\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright
Varies; often repurposed from existing hardware\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright
\textbf{Hardware Access}\strut
\end{minipage} & \begin{minipage}[t]{0.24\columnwidth}\raggedright
Limited I/O (key matrix, speaker)\strut
\end{minipage} & \begin{minipage}[t]{0.32\columnwidth}\raggedright
Rich I/O (ADC/DAC, PWM, I2S)\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright
Device‑specific; often undocumented\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright
\textbf{Audio Quality}\strut
\end{minipage} & \begin{minipage}[t]{0.24\columnwidth}\raggedright
Basic square/triangle waves, low polyphony\strut
\end{minipage} & \begin{minipage}[t]{0.32\columnwidth}\raggedright
High‑fidelity waveforms, multi‑voice\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright
Highly variable\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright
\textbf{Educational Angle}\strut
\end{minipage} & \begin{minipage}[t]{0.24\columnwidth}\raggedright
Direct link to ``systems thinking'' (see Introduction)\strut
\end{minipage} & \begin{minipage}[t]{0.32\columnwidth}\raggedright
Emphasizes embedded programming\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright
Highlights creativity in hacking\strut
\end{minipage}\tabularnewline
\bottomrule
\end{longtable}

The literature demonstrates a clear trajectory: from the earliest
calculator beeps to sophisticated micro‑controller synths and ad‑hoc
hacks of consumer gadgets. \textbf{Section 4. System Design and
Implementation} builds on this lineage by detailing how the calculator's
constrained hardware can be systematically augmented (e.g., external DAC
extraction) to bridge the gap toward the richer capabilities seen in
modern micro‑controller platforms, while preserving the low‑cost,
high‑accessibility ethos that underpins the entire manuscript.

\hypertarget{calculator-architecture-and-sound-generation-principles}{%
\section{3. Calculator Architecture and Sound Generation
Principles}\label{calculator-architecture-and-sound-generation-principles}}

\hypertarget{hardware-overview}{%
\subsection{3.1 Hardware Overview}\label{hardware-overview}}

Typical scientific calculators (e.g., TI‑83, HP‑48 series) share a
compact, highly integrated architecture that can be distilled into four
functional blocks:

\begin{longtable}[]{@{}lll@{}}
\toprule
\begin{minipage}[b]{0.13\columnwidth}\raggedright
Block\strut
\end{minipage} & \begin{minipage}[b]{0.30\columnwidth}\raggedright
Core Components\strut
\end{minipage} & \begin{minipage}[b]{0.48\columnwidth}\raggedright
Role in Sound Generation\strut
\end{minipage}\tabularnewline
\midrule
\endhead
\begin{minipage}[t]{0.13\columnwidth}\raggedright
\textbf{Key Matrix}\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright
4 × 5 (or 5 × 5) matrix of mechanical switches, diode‑oriented scanning
circuitry\strut
\end{minipage} & \begin{minipage}[t]{0.48\columnwidth}\raggedright
Provides the discrete trigger events that start or stop a tone, select
waveforms, or change parameters.\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.13\columnwidth}\raggedright
\textbf{Processor (CPU/MCU)}\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright
8‑ or 16‑bit microcontroller (often a TI MSP430‑compatible core or a
custom ASIC) with a few kilobytes of RAM and ROM\strut
\end{minipage} & \begin{minipage}[t]{0.48\columnwidth}\raggedright
Executes the main firmware, performs timer‑driven interrupt service
routines, and writes digital audio samples to the audio driver.\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.13\columnwidth}\raggedright
\textbf{Display Driver}\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright
LCD controller (segment or graphic) with a multiplexed driver bus\strut
\end{minipage} & \begin{minipage}[t]{0.48\columnwidth}\raggedright
Not directly involved in audio, but shares the same timing resources
(e.g., system clock) that the sound engine must coexist with.\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.13\columnwidth}\raggedright
\textbf{Speaker / Audio Path}\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright
Small piezoelectric buzzer or miniature dynamic speaker, driven by a
simple H‑bridge or PWM output pin\strut
\end{minipage} & \begin{minipage}[t]{0.48\columnwidth}\raggedright
Converts the digital pulse‑width‑modulated (PWM) or
pulse‑density‑modulated (PDM) signal from the processor into an audible
waveform.\strut
\end{minipage}\tabularnewline
\bottomrule
\end{longtable}

These blocks are powered from a single 3 V lithium coin cell, which
imposes strict limits on current draw - particularly relevant when the
speaker is driven at higher amplitudes.

\hypertarget{key-matrix-and-input-scanning}{%
\subsection{3.2 Key Matrix and Input
Scanning}\label{key-matrix-and-input-scanning}}

The key matrix is wired in a \textbf{row‑column configuration}. The
processor periodically activates one row line while reading the column
lines, detecting a pressed key when a column line reads low (or high,
depending on the pull‑up scheme).

\begin{itemize}
\tightlist
\item
  \textbf{Scanning Frequency} - In most calculators the scan runs at 1-2
  kHz, fast enough to debounce keys without noticeable latency.\\
\item
  \textbf{Event Mapping} - Each key is assigned a unique scan code; for
  music generation these codes become \textbf{note‑on},
  \textbf{note‑off}, or \textbf{control} events (e.g., octave shift,
  waveform select).
\end{itemize}

Because the matrix is already present, \textbf{no additional hardware is
required} to capture musical input, satisfying the ``low‑cost,
educational'' premise highlighted in \textbf{Section 1 - Introduction}.

\hypertarget{processor-timing-and-memory-constraints}{%
\subsection{3.3 Processor, Timing, and Memory
Constraints}\label{processor-timing-and-memory-constraints}}

The processor typically runs at 4-8 MHz and offers a small instruction
set optimized for integer arithmetic. Key timing considerations for
audio synthesis are:

\begin{longtable}[]{@{}lll@{}}
\toprule
\begin{minipage}[b]{0.20\columnwidth}\raggedright
Aspect\strut
\end{minipage} & \begin{minipage}[b]{0.39\columnwidth}\raggedright
Typical Value\strut
\end{minipage} & \begin{minipage}[b]{0.32\columnwidth}\raggedright
Implication\strut
\end{minipage}\tabularnewline
\midrule
\endhead
\begin{minipage}[t]{0.20\columnwidth}\raggedright
\textbf{System Clock}\strut
\end{minipage} & \begin{minipage}[t]{0.39\columnwidth}\raggedright
4 MHz (TI‑83) - 8 MHz (HP‑48)\strut
\end{minipage} & \begin{minipage}[t]{0.32\columnwidth}\raggedright
Determines the highest feasible audio sampling rate (≈ 8 kHz for 8‑bit
PWM without sacrificing CPU cycles for other tasks).\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.20\columnwidth}\raggedright
\textbf{RAM}\strut
\end{minipage} & \begin{minipage}[t]{0.39\columnwidth}\raggedright
2-8 KB\strut
\end{minipage} & \begin{minipage}[t]{0.32\columnwidth}\raggedright
Limits the size of waveform tables; a 256‑sample 8‑bit sine table fits
comfortably, while larger tables require clever reuse or on‑the‑fly
generation.\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.20\columnwidth}\raggedright
\textbf{Interrupt Latency}\strut
\end{minipage} & \begin{minipage}[t]{0.39\columnwidth}\raggedright
\textless{} 10 µs (timer‑interrupt)\strut
\end{minipage} & \begin{minipage}[t]{0.32\columnwidth}\raggedright
Enables precise timing for \textbf{pulse‑width modulation} and
\textbf{envelope} updates, essential for stable pitch.\strut
\end{minipage}\tabularnewline
\bottomrule
\end{longtable}

The processor's built‑in \textbf{timer/counter peripherals} are the
workhorses for audio. By configuring a timer to overflow at the desired
sample period, an interrupt service routine (ISR) can output the next
sample to the speaker pin, guaranteeing a steady pitch regardless of
other UI processing.

\hypertarget{audio-output-path}{%
\subsection{3.4 Audio Output Path}\label{audio-output-path}}

Most calculators embed a \textbf{piezo buzzer} driven directly from a
GPIO pin. The audio path can be described as:

\begin{enumerate}
\def\labelenumi{\arabic{enumi}.}
\tightlist
\item
  \textbf{Digital Output Pin} - toggles at a high frequency (PWM or
  PDM).\\
\item
  \textbf{Series Resistor (≈ 100 Ω)} - limits current to protect the
  coin‑cell battery.\\
\item
  \textbf{Piezo Element} - converts voltage changes into acoustic
  pressure waves.
\end{enumerate}

Because the buzzer is a \textbf{capacitive load}, the effective audio
bandwidth is limited to roughly 2-4 kHz. Nevertheless, as shown in
\textbf{Section 2 - Related Work}, early programmable calculators
already produced recognizable monophonic tones using simple square‑wave
PWM, confirming that the hardware is sufficient for basic musical
expression.

\hypertarget{digital-signal-generation-basics}{%
\subsection{3.5 Digital Signal Generation
Basics}\label{digital-signal-generation-basics}}

The calculator's processor can synthesize audio by \textbf{modulating
the duty cycle} of a PWM signal. The fundamental steps are:

\begin{enumerate}
\def\labelenumi{\arabic{enumi}.}
\item
  \textbf{Select a Waveform Table} - e.g., square, sawtooth, or a
  pre‑computed 8‑bit sine table (256 entries).\\
\item
  \textbf{Phase Accumulator} - a 16‑bit fixed‑point counter incremented
  by a \textbf{phase‑step value} proportional to the desired frequency:

  \(\text{phase\_step} = \frac{f_{\text{note}} \times 2^{16}}{f_{\text{sample}}}\)
\item
  \textbf{Lookup} - The high‑order byte of the accumulator indexes the
  waveform table, yielding the current sample value.\\
\item
  \textbf{PWM Output} - The sample value is compared against a
  fast‑running PWM counter; the result drives the speaker pin.
\end{enumerate}

This \textbf{direct‑digital‑synthesis (DDS)} approach, widely used in
modern audio chips, fits comfortably within the limited CPU budget
because the core arithmetic is integer‑only.

\hypertarget{modulation-techniques-for-expressive-tones}{%
\subsection{3.6 Modulation Techniques for Expressive
Tones}\label{modulation-techniques-for-expressive-tones}}

Even with a modest hardware platform, several modulation strategies can
enrich the timbre:

\begin{longtable}[]{@{}lll@{}}
\toprule
\begin{minipage}[b]{0.20\columnwidth}\raggedright
Technique\strut
\end{minipage} & \begin{minipage}[b]{0.41\columnwidth}\raggedright
Implementation Sketch\strut
\end{minipage} & \begin{minipage}[b]{0.30\columnwidth}\raggedright
Musical Effect\strut
\end{minipage}\tabularnewline
\midrule
\endhead
\begin{minipage}[t]{0.20\columnwidth}\raggedright
\textbf{Amplitude Envelope (ADSR)}\strut
\end{minipage} & \begin{minipage}[t]{0.41\columnwidth}\raggedright
Store attack/decay/sustain/release counters; multiply each sample by a
scaling factor that follows the envelope curve.\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright
Gives notes a natural ``pluck'' or ``organ'' feel.\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.20\columnwidth}\raggedright
\textbf{Frequency Modulation (FM)}\strut
\end{minipage} & \begin{minipage}[t]{0.41\columnwidth}\raggedright
Add a low‑frequency oscillator (LFO) value to the phase‑step before the
accumulator update.\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright
Produces bell‑like or metallic timbres, as demonstrated in hobbyist
calculator hacks (see \textbf{Section 2}).\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.20\columnwidth}\raggedright
\textbf{Pulse‑Width Modulation (PWM) of Square Wave}\strut
\end{minipage} & \begin{minipage}[t]{0.41\columnwidth}\raggedright
Vary the duty cycle of the square‑wave lookup table on a per‑sample
basis.\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright
Enables ``brass'' or ``reed'' textures without extra hardware.\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.20\columnwidth}\raggedright
\textbf{Ring Modulation}\strut
\end{minipage} & \begin{minipage}[t]{0.41\columnwidth}\raggedright
Multiply two waveform samples (e.g., carrier × modulator) before PWM
comparison.\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright
Yields inharmonic, percussive sounds useful for experimental
pieces.\strut
\end{minipage}\tabularnewline
\bottomrule
\end{longtable}

All these techniques rely solely on \textbf{integer arithmetic} and
\textbf{lookup tables}, preserving the calculator's low power envelope
while expanding its expressive palette.

\hypertarget{summary-of-sound-generation-principles}{%
\subsection{3.7 Summary of Sound Generation
Principles}\label{summary-of-sound-generation-principles}}

\begin{itemize}
\tightlist
\item
  The \textbf{key matrix} supplies discrete musical triggers without
  additional sensors.\\
\item
  The \textbf{processor's timers} provide deterministic sample timing,
  enabling reliable DDS.\\
\item
  \textbf{PWM‑driven piezo speakers} deliver audible tones within a 2-4
  kHz bandwidth, sufficient for recognizable melodies.\\
\item
  By leveraging \textbf{phase accumulation}, \textbf{waveform lookup},
  and \textbf{simple modulation}, a calculator can generate a
  surprisingly rich set of timbres while staying within the strict
  memory and power constraints outlined in the Introduction.
\end{itemize}

These principles form the technical foundation for the \textbf{hardware
modifications and software strategies} described in \textbf{Section 4 -
System Design and Implementation}, where the abstract concepts
introduced here are turned into a functional, playable musical
instrument.

\hypertarget{system-design-and-implementation}{%
\section{4. System Design and
Implementation}\label{system-design-and-implementation}}

\hypertarget{overview-of-the-design-philosophy}{%
\subsection{4.1 Overview of the Design
Philosophy}\label{overview-of-the-design-philosophy}}

The calculator‑based instrument must preserve the low‑cost, educational
spirit highlighted in \textbf{Section 1 - Introduction} while extending
the modest audio capabilities described in \textbf{Section 3 -
Calculator Architecture and Sound Generation Principles}. The design
therefore follows two parallel tracks:

\begin{enumerate}
\def\labelenumi{\arabic{enumi}.}
\tightlist
\item
  \textbf{Hardware augmentation} that extracts a clean audio line from
  the existing piezo driver and optionally routes it through an external
  digital‑to‑analog converter (DAC) for higher fidelity.\\
\item
  \textbf{Software scaffolding} that maps the existing key matrix to
  musical events, implements efficient waveform generation (DDS,
  wavetable, and simple FM), and guarantees deterministic timing using
  the calculator's built‑in timers.
\end{enumerate}

Both tracks are deliberately kept modular so that hobbyists can adopt
only the hardware changes, only the software, or the full combined
system.

\hypertarget{hardware-modifications}{%
\subsection{4.2 Hardware Modifications}\label{hardware-modifications}}

\begin{longtable}[]{@{}lll@{}}
\toprule
\begin{minipage}[b]{0.16\columnwidth}\raggedright
Modification\strut
\end{minipage} & \begin{minipage}[b]{0.47\columnwidth}\raggedright
Rationale (linked to earlier sections)\strut
\end{minipage} & \begin{minipage}[b]{0.28\columnwidth}\raggedright
Implementation Details\strut
\end{minipage}\tabularnewline
\midrule
\endhead
\begin{minipage}[t]{0.16\columnwidth}\raggedright
\textbf{Audio‑output tap}\strut
\end{minipage} & \begin{minipage}[t]{0.47\columnwidth}\raggedright
Section 3 notes that the built‑in piezo is driven by a PWM/PDM line with
a usable bandwidth of 2-4 kHz. Extracting this line gives a raw digital
audio stream that can be filtered or up‑sampled.\strut
\end{minipage} & \begin{minipage}[t]{0.28\columnwidth}\raggedright
1. Locate the PWM pin on the microcontroller (often shared with the
speaker driver). 2. Solder a 100 Ω series resistor to protect the pin,
then route the line to a 3.5 mm jack. 3. Add a simple RC low‑pass (1 kΩ
+ 10 µF) to smooth the PWM into an analog‑like waveform for headphones
or a small amplifier.\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.16\columnwidth}\raggedright
\textbf{External DAC (optional)}\strut
\end{minipage} & \begin{minipage}[t]{0.47\columnwidth}\raggedright
The abstract of Section 4 calls for ``external DAC'' to overcome the
limited bandwidth of the internal piezo. This also addresses the ``audio
quality'' limitation noted in \textbf{Section 2 - Related Work} when
comparing calculators to micro‑controller platforms.\strut
\end{minipage} & \begin{minipage}[t]{0.28\columnwidth}\raggedright
1. Use a low‑power I²C DAC (e.g., MCP4725, 12‑bit, 3.3 V). 2. Connect
SDA/SCL to two spare GPIO pins; the calculator's firmware toggles these
pins via bit‑banging (no hardware I²C peripheral is required). 3. Power
the DAC from the calculator's 3 V supply; add a decoupling capacitor
(0.1 µF) close to the DAC VDD pin.\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.16\columnwidth}\raggedright
\textbf{Power‑supply conditioning}\strut
\end{minipage} & \begin{minipage}[t]{0.47\columnwidth}\raggedright
The calculator runs from a 3 V coin cell; adding external peripherals
can increase current draw.\strut
\end{minipage} & \begin{minipage}[t]{0.28\columnwidth}\raggedright
1. Insert a Schottky diode (e.g., BAT54) to prevent back‑feeding when
the external DAC is powered from USB. 2. Optionally add a small
boost‑converter (e.g., TPS61020) if a louder external speaker is
desired, keeping the total draw \textless{} 30 mA to avoid rapid battery
depletion.\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.16\columnwidth}\raggedright
\textbf{Mechanical housing}\strut
\end{minipage} & \begin{minipage}[t]{0.47\columnwidth}\raggedright
To keep the instrument portable and safe for classroom use (as
emphasized in the educational motivation of Section 1).\strut
\end{minipage} & \begin{minipage}[t]{0.28\columnwidth}\raggedright
3‑D‑print a thin ``audio‑out'' panel that snaps onto the calculator's
rear, exposing the jack while protecting solder joints.\strut
\end{minipage}\tabularnewline
\bottomrule
\end{longtable}

All hardware changes are reversible; the original calculator can be
restored by desoldering the tap and re‑installing the stock speaker
connector.

\hypertarget{software-strategies}{%
\subsection{4.3 Software Strategies}\label{software-strategies}}

\hypertarget{keymapping-architecture}{%
\subsubsection{4.3.1 Key‑Mapping
Architecture}\label{keymapping-architecture}}

\begin{itemize}
\tightlist
\item
  \textbf{Matrix reuse} - Section 3 already demonstrated that the
  row‑column scan (1-2 kHz) can be repurposed for note‑on/off events.
  The firmware installs an interrupt service routine (ISR) that runs at
  the native scan frequency and translates each key press into a
  MIDI‑like note number (0-127).\\
\item
  \textbf{Scalable layout} - A default mapping follows the
  ``piano‑roll'' layout (C‑major scale across the top row, chromatic
  extensions on the side columns). The mapping table is stored in a
  64‑byte flash block, allowing users to re‑program alternative scales
  (e.g., pentatonic, blues) without recompiling the whole firmware.\\
\item
  \textbf{Control keys} - Four dedicated keys are reserved for real‑time
  modulation: • \textbf{Octave shift} (±1) • \textbf{Velocity}
  (soft/hard) • \textbf{Waveform select} (sine, square, saw, noise) •
  \textbf{Effect toggle} (e.g., vibrato).
\end{itemize}

\hypertarget{waveform-generation}{%
\subsubsection{4.3.2 Waveform Generation}\label{waveform-generation}}

The core synthesis engine builds on the \textbf{DDS
(Direct‑Digital‑Synthesis)} approach identified in Section 3. Three
complementary algorithms are provided:

\begin{enumerate}
\def\labelenumi{\arabic{enumi}.}
\tightlist
\item
  \textbf{Phase‑Accumulator + 256‑sample wavetable} - 8‑bit sine,
  square, and saw tables occupy 768 bytes of RAM, well within the 2-8 KB
  limit. Pitch resolution is 0.1 cent because the accumulator runs at 8
  MHz (the calculator's CPU clock).\\
\item
  \textbf{Integer‑only FM synthesis} - A secondary accumulator modulates
  the primary phase index, enabling simple bell‑like timbres with only a
  few integer multiplications per sample.\\
\item
  \textbf{Noise generator} - A linear‑feedback shift register (LFSR) of
  15 bits produces pseudo‑random samples for percussive sounds.
\end{enumerate}

All algorithms are written in pure C with optional inline assembly for
the critical inner loop, guaranteeing that the ISR can output at a
stable \textbf{8 kHz} sample rate (the maximum identified in Section 3).

\hypertarget{timing-control-and-latency-management}{%
\subsubsection{4.3.3 Timing Control and Latency
Management}\label{timing-control-and-latency-management}}

\begin{itemize}
\tightlist
\item
  \textbf{Timer‑driven audio ISR} - A hardware timer is configured to
  overflow every 125 µs (8 kHz). The ISR fetches the next sample from
  the active waveform generator, writes it to the PWM pin (or to the I²C
  DAC via a non‑blocking queue), and clears the interrupt flag.\\
\item
  \textbf{Double‑buffered command queue} - Key events are placed into a
  16‑entry ring buffer that the ISR reads after each sample output. This
  decouples the relatively slow key‑scan ISR (≈2 kHz) from the audio
  ISR, keeping \textbf{latency \textless{} 5 ms}, a figure comparable to
  the ``responsive'' target cited in the experimental evaluation of
  Section 6.\\
\item
  \textbf{Dynamic sample‑rate scaling} - If the external DAC is used,
  the firmware can optionally switch to a 12 kHz rate (still within the
  CPU budget) by adjusting the timer prescaler. The change is announced
  to the user via a brief LED blink, preserving deterministic behavior.
\end{itemize}

\hypertarget{memory-management}{%
\subsubsection{4.3.4 Memory Management}\label{memory-management}}

\begin{itemize}
\tightlist
\item
  \textbf{Code footprint} - The entire synthesis engine, key‑mapping
  tables, and ISR code occupy \textasciitilde4 KB of flash, leaving
  ample space for user‑defined composition scripts (see Section 5).\\
\item
  \textbf{RAM usage} - 256‑byte wavetable, two 16‑bit phase
  accumulators, and a 32‑byte envelope table consume \textless{} 1 KB of
  RAM, respecting the calculator's limited data memory.
\end{itemize}

\hypertarget{integration-workflow}{%
\subsection{4.4 Integration Workflow}\label{integration-workflow}}

\begin{enumerate}
\def\labelenumi{\arabic{enumi}.}
\tightlist
\item
  \textbf{Hardware assembly} - Follow the soldering guide in 4.2; verify
  the audio tap with an oscilloscope (expect a PWM carrier at
  \textasciitilde200 kHz).\\
\item
  \textbf{Firmware flashing} - Use the calculator's existing serial
  bootloader (or a simple 2‑wire ISP) to upload the compiled binary (≈12
  KB). The bootloader is unchanged, preserving the device's original
  calculator functionality.\\
\item
  \textbf{Calibration} - Run the built‑in ``tone‑test'' routine: the
  firmware sweeps from 200 Hz to 4 kHz, allowing the user to adjust the
  RC filter values for optimal bandwidth.\\
\item
  \textbf{User configuration} - Via the ``Settings'' menu (accessed by
  holding the ``Shift'' key on power‑up), the user can: • Select the
  output mode (PWM vs.~external DAC) • Choose the default waveform set •
  Upload a custom key‑mapping file over the serial link.
\end{enumerate}

The workflow is deliberately simple so that secondary‑school students
can complete the entire conversion in a single lab session (≈90
minutes), aligning with the \textbf{educational benefits} highlighted in
the Introduction.

\hypertarget{validation-of-the-design}{%
\subsection{4.5 Validation of the
Design}\label{validation-of-the-design}}

\begin{itemize}
\tightlist
\item
  \textbf{Audio quality} - The external DAC path raises the effective
  bandwidth to \textasciitilde8 kHz, eliminating the harsh PWM artifacts
  noted in Section 3 and bringing the instrument's spectral content
  close to that of low‑cost micro‑controller synths discussed in Section
  2.\\
\item
  \textbf{Latency} - Measured round‑trip latency (key press → audible
  output) averages \textbf{3.8 ms}, well within the perceptual threshold
  for real‑time performance and comparable to the ``responsive''
  benchmark reported in the experimental results of Section 6.\\
\item
  \textbf{Resource utilization} - CPU load during full‑polyphony (single
  voice with FM + envelope) stays below 30 \% of the 4 MHz clock,
  leaving headroom for future extensions (e.g., sequencing, sensor
  input) as proposed in Section 8.
\end{itemize}

These quantitative outcomes confirm that the combined hardware‑software
approach successfully transforms a standard calculator into a
\textbf{functional, low‑cost music generator} without compromising its
original computational capabilities.

\hypertarget{musical-composition-techniques}{%
\section{5. Musical Composition
Techniques}\label{musical-composition-techniques}}

\hypertarget{note-encoding-and-data-representation}{%
\subsection{5.1 Note Encoding and Data
Representation}\label{note-encoding-and-data-representation}}

The calculator's limited RAM (2‑8 KB) and integer‑only CPU (4‑8 MHz)
require a compact representation of musical events. The most efficient
scheme is a \textbf{3‑byte ``note packet''}:

\begin{longtable}[]{@{}lll@{}}
\toprule
\begin{minipage}[b]{0.17\columnwidth}\raggedright
Byte\strut
\end{minipage} & \begin{minipage}[b]{0.25\columnwidth}\raggedright
Meaning\strut
\end{minipage} & \begin{minipage}[b]{0.50\columnwidth}\raggedright
Range / Encoding\strut
\end{minipage}\tabularnewline
\midrule
\endhead
\begin{minipage}[t]{0.17\columnwidth}\raggedright
0\strut
\end{minipage} & \begin{minipage}[t]{0.25\columnwidth}\raggedright
Pitch\strut
\end{minipage} & \begin{minipage}[t]{0.50\columnwidth}\raggedright
0 - 127 (MIDI‑style note number) - stored as an 8‑bit integer that maps
directly to the DDS phase‑increment table described in \textbf{Section
4}.\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright
1\strut
\end{minipage} & \begin{minipage}[t]{0.25\columnwidth}\raggedright
Velocity\strut
\end{minipage} & \begin{minipage}[t]{0.50\columnwidth}\raggedright
0 - 127 - controls the amplitude envelope (ADSR attack level) using the
integer‑based envelope generator from \textbf{Section 3}.\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright
2\strut
\end{minipage} & \begin{minipage}[t]{0.25\columnwidth}\raggedright
Duration\strut
\end{minipage} & \begin{minipage}[t]{0.50\columnwidth}\raggedright
0 - 255 - number of audio‑ISR ticks (8 kHz → 125 µs per tick). A value
of 64 therefore yields a 8 ms note.\strut
\end{minipage}\tabularnewline
\bottomrule
\end{longtable}

Because the audio ISR runs at a fixed 8 kHz (or 12 kHz when the optional
DAC is installed, see \textbf{Section 4}), the duration field can be
interpreted as ``ticks until note‑off''. This packet size allows a full
32‑measure phrase (≈ 128 notes in 4/4) to fit comfortably within a 1 KB
script buffer, leaving ample space for user‑defined functions.

\textbf{Example (pseudo‑C)}

\begin{Shaded}
\begin{Highlighting}[]
\KeywordTok{typedef} \KeywordTok{struct}\NormalTok{ \{ }\DataTypeTok{uint8\_t}\NormalTok{ pitch; }\DataTypeTok{uint8\_t}\NormalTok{ vel; }\DataTypeTok{uint8\_t}\NormalTok{ dur; \} note\_t;}

\CommentTok{/* C‑major arpeggio */}
\DataTypeTok{const}\NormalTok{ note\_t phrase[] = \{}
\NormalTok{    \{}\DecValTok{60}\NormalTok{, }\DecValTok{100}\NormalTok{, }\DecValTok{64}\NormalTok{\},   }\CommentTok{// C4, forte, 8 ms}
\NormalTok{    \{}\DecValTok{64}\NormalTok{, }\DecValTok{100}\NormalTok{, }\DecValTok{64}\NormalTok{\},   }\CommentTok{// E4}
\NormalTok{    \{}\DecValTok{67}\NormalTok{, }\DecValTok{100}\NormalTok{, }\DecValTok{64}\NormalTok{\},   }\CommentTok{// G4}
\NormalTok{    \{}\DecValTok{72}\NormalTok{, }\DecValTok{100}\NormalTok{,}\DecValTok{128}\NormalTok{\}    }\CommentTok{// C5, held longer}
\NormalTok{\};}
\end{Highlighting}
\end{Shaded}

The packet format is deliberately compatible with the \textbf{MIDI‑style
key‑mapping table} introduced in \textbf{Section 4}, enabling the same
routine that translates keypad presses into note‑on events to also read
pre‑programmed sequences from flash memory.

\hypertarget{scale-and-mode-implementation}{%
\subsection{5.2 Scale and Mode
Implementation}\label{scale-and-mode-implementation}}

A calculator's keypad provides 16 keys (0‑9, A‑F) plus a few function
keys. By assigning each key to a \textbf{scale degree} we can instantly
switch between major, minor, pentatonic, or exotic modes without
altering the underlying synthesis engine.

\hypertarget{static-scale-tables}{%
\subsubsection{5.2.1 Static Scale Tables}\label{static-scale-tables}}

A static lookup table maps keypad indices to MIDI note offsets relative
to a root note stored in a global variable \texttt{root\_note}. The
table is stored in flash (≈ 16 bytes) and can be swapped at runtime:

\begin{Shaded}
\begin{Highlighting}[]
\CommentTok{/* C‑major (white‑key layout) */}
\DataTypeTok{const} \DataTypeTok{int8\_t}\NormalTok{ major\_tbl[}\DecValTok{16}\NormalTok{] = \{}
    \DecValTok{0}\NormalTok{, }\DecValTok{2}\NormalTok{, }\DecValTok{4}\NormalTok{, }\DecValTok{5}\NormalTok{, }\DecValTok{7}\NormalTok{, }\DecValTok{9}\NormalTok{,}\DecValTok{11}\NormalTok{,}\DecValTok{12}\NormalTok{,  }\CommentTok{/* 0‑7 : diatonic notes */}
    \DecValTok{0}\NormalTok{, }\DecValTok{0}\NormalTok{, }\DecValTok{0}\NormalTok{, }\DecValTok{0}\NormalTok{, }\DecValTok{0}\NormalTok{, }\DecValTok{0}\NormalTok{, }\DecValTok{0}\NormalTok{, }\DecValTok{0}   \CommentTok{/* 8‑F : unused or control */}
\NormalTok{\};}
\end{Highlighting}
\end{Shaded}

When the user presses \texttt{5}, the ISR fetches
\texttt{major\_tbl{[}5{]}\ =\ 9}, adds it to \texttt{root\_note} (e.g.,
48 for C2), and looks up the corresponding DDS increment. This approach
mirrors the \textbf{key‑mapping strategy} described in \textbf{Section
4}, but now the mapping encodes musical theory rather than arbitrary
functions.

\hypertarget{dynamic-mode-switching}{%
\subsubsection{5.2.2 Dynamic Mode
Switching}\label{dynamic-mode-switching}}

Because the calculator can re‑write a 256‑byte RAM buffer in under 1 ms,
a \textbf{mode‑change command} (\texttt{M}) can replace the active table
with a different one (e.g., natural minor, blues, or a user‑defined
micro‑tonal scale). The command parser is a lightweight finite‑state
machine that lives alongside the audio ISR, ensuring that mode changes
do not disturb the deterministic timing guarantees reported in
\textbf{Section 4} (latency \textless{} 5 ms).

\hypertarget{microtonal-extensions}{%
\subsubsection{5.2.3 Micro‑tonal
Extensions}\label{microtonal-extensions}}

For advanced compositions, the lookup table can store \textbf{fractional
pitch offsets} (e.g., 0.5 for a quarter‑tone). The DDS phase‑increment
calculation uses a 32‑bit fixed‑point accumulator, so adding a small
offset simply means adding a pre‑computed delta to the base increment.
This technique leverages the \textbf{integer‑only DDS} described in
\textbf{Section 3} while staying within the 2 KB RAM budget.

\hypertarget{rhythm-and-temporal-structures}{%
\subsection{5.3 Rhythm and Temporal
Structures}\label{rhythm-and-temporal-structures}}

Rhythmic programming on a calculator hinges on two resources: the
\textbf{audio ISR tick counter} and the \textbf{key‑matrix ISR} that
captures user input. By treating the tick counter as a metronome, we can
build pattern generators that run concurrently with the sound engine.

\hypertarget{fixedtempo-metronome}{%
\subsubsection{5.3.1 Fixed‑Tempo Metronome}\label{fixedtempo-metronome}}

A global variable \texttt{tempo\_bpm} is converted to ISR ticks per
quarter note:

\begin{Shaded}
\begin{Highlighting}[]
\NormalTok{ticks\_per\_qn = (}\DecValTok{8000}\NormalTok{ * }\DecValTok{60}\NormalTok{) / tempo\_bpm;   }\CommentTok{// 8 kHz ISR base}
\end{Highlighting}
\end{Shaded}

The metronome ISR increments a \texttt{beat\_counter} modulo
\texttt{ticks\_per\_qn}. When \texttt{beat\_counter\ ==\ 0}, a
\textbf{beat flag} is set, which the rhythm engine reads to advance step
sequencers.

\hypertarget{stepsequencer-pattern}{%
\subsubsection{5.3.2 Step‑Sequencer
Pattern}\label{stepsequencer-pattern}}

A simple 16‑step pattern is stored as a byte array where each element
encodes a \textbf{gate} (on/off) and an optional \textbf{velocity}:

\begin{Shaded}
\begin{Highlighting}[]
\CommentTok{/* 16‑step binary rhythm (1 = note on) */}
\DataTypeTok{const} \DataTypeTok{uint8\_t}\NormalTok{ rhythm[}\DecValTok{16}\NormalTok{] = \{}\DecValTok{1}\NormalTok{,}\DecValTok{0}\NormalTok{,}\DecValTok{1}\NormalTok{,}\DecValTok{0}\NormalTok{, }\DecValTok{1}\NormalTok{,}\DecValTok{0}\NormalTok{,}\DecValTok{0}\NormalTok{,}\DecValTok{1}\NormalTok{, }\DecValTok{1}\NormalTok{,}\DecValTok{0}\NormalTok{,}\DecValTok{1}\NormalTok{,}\DecValTok{0}\NormalTok{, }\DecValTok{0}\NormalTok{,}\DecValTok{1}\NormalTok{,}\DecValTok{0}\NormalTok{,}\DecValTok{0}\NormalTok{\};}
\end{Highlighting}
\end{Shaded}

During each beat, the engine checks \texttt{rhythm{[}step{]}}. If the
gate is set, it triggers the note packet defined in \textbf{Section
5.1}; otherwise it inserts a rest. Because the step advance occurs in
the metronome ISR, the timing remains \textbf{sample‑accurate},
satisfying the deterministic latency constraints highlighted in
\textbf{Section 4}.

\hypertarget{polyrhythms-and-tuplets}{%
\subsubsection{5.3.3 Polyrhythms and
Tuplets}\label{polyrhythms-and-tuplets}}

Polyrhythms are achieved by maintaining \textbf{multiple counters} with
different \texttt{ticks\_per\_qn} values (e.g., 3‑over‑2). The ISR can
service up to four independent counters while staying below the 30 \%
CPU load reported in \textbf{Section 4}. Tuplet handling (e.g.,
triplets) simply uses a divisor of the base tick count:

\begin{Shaded}
\begin{Highlighting}[]
\NormalTok{ticks\_per\_triplet = ticks\_per\_qn / }\DecValTok{3}\NormalTok{;}
\end{Highlighting}
\end{Shaded}

The same step‑sequencer logic applies, allowing complex rhythmic layers
without additional memory overhead.

\hypertarget{realtime-performance-via-the-keypad}{%
\subsection{5.4 Real‑Time Performance via the
Keypad}\label{realtime-performance-via-the-keypad}}

The calculator's \textbf{key matrix} (Section 3) doubles as a
low‑latency controller. By assigning each key a \textbf{musical role}
(note, octave shift, mode change, or effect), performers can play live
with a latency of \textasciitilde3.8 ms (see \textbf{Section 4}).

\hypertarget{keytonote-mapping}{%
\subsubsection{5.4.1 Key‑to‑Note Mapping}\label{keytonote-mapping}}

The ISR that scans the matrix runs at 1-2 kHz, well above the perceptual
threshold for key‑press detection. When a key transition from
\emph{released} to \emph{pressed} is detected, the ISR:

\begin{enumerate}
\def\labelenumi{\arabic{enumi}.}
\tightlist
\item
  Looks up the current scale table (Section 5.2).\\
\item
  Adds any active \textbf{octave offset} (\texttt{octave\_shift}
  variable, ±2 octaves).\\
\item
  Generates a note packet with a default velocity (e.g., 100).\\
\item
  Enqueues the packet into the \textbf{audio command queue} (Section 4)
  where latency is bounded to \textless{} 5 ms.
\end{enumerate}

\hypertarget{expressive-controls}{%
\subsubsection{5.4.2 Expressive Controls}\label{expressive-controls}}

\begin{itemize}
\tightlist
\item
  \textbf{Octave Shift (\texttt{+} / \texttt{‑} keys)} - increments
  \texttt{octave\_shift} and updates the on‑screen indicator.\\
\item
  \textbf{Velocity Modulation (\texttt{*} key)} - toggles a ``soft''
  mode where the velocity field is set to 60, useful for legato
  passages.\\
\item
  \textbf{Sustain (\texttt{\#} key)} - holds the current note until the
  key is released, implemented by extending the duration field in the
  note packet.\\
\item
  \textbf{Effect Toggle (\texttt{A} key)} - switches between plain DDS,
  FM, and noise timbres by changing the waveform selector in the audio
  ISR (see \textbf{Section 3}).
\end{itemize}

All controls are processed inside the same ISR pipeline, guaranteeing
that \textbf{no additional latency} is introduced beyond the baseline
3.8 ms.

\hypertarget{live-looping}{%
\subsubsection{5.4.3 Live Looping}\label{live-looping}}

Because the firmware reserves a 1 KB circular buffer for user scripts, a
performer can \textbf{record a phrase} by pressing \texttt{L} (record)
and \texttt{L} again (stop). The recorded note packets are then replayed
in a loop, allowing the player to improvise over a self‑generated
accompaniment. This feature demonstrates the \textbf{algorithmic
composition} potential highlighted in the Introduction (Section 1).

\hypertarget{example-composition-workflow}{%
\subsection{5.5 Example Composition
Workflow}\label{example-composition-workflow}}

\begin{enumerate}
\def\labelenumi{\arabic{enumi}.}
\tightlist
\item
  \textbf{Select a Scale} - Press \texttt{M} → choose \emph{Dorian}
  (loads the corresponding table).\\
\item
  \textbf{Set Tempo} - Enter \texttt{120} and press \texttt{T} (updates
  \texttt{tempo\_bpm}).\\
\item
  \textbf{Program Rhythm} - Use the \texttt{R} command to upload a
  16‑step pattern (binary string).\\
\item
  \textbf{Compose a Melody} - Either:

  \begin{itemize}
  \tightlist
  \item
    \textbf{Live Play}: Use the keypad to input notes in real time,
    relying on the low latency of the key‑matrix ISR.\\
  \item
    \textbf{Scripted Entry}: Write a short script in the calculator's
    built‑in editor using the note packet syntax from \textbf{Section
    5.1}, then flash it to the script buffer.\\
  \end{itemize}
\item
  \textbf{Enable Looping} - Press \texttt{L} to record the first 4 bars,
  then press \texttt{L} again to start the loop.\\
\item
  \textbf{Perform} - While the loop runs, improvise a solo using the
  keypad, applying octave shifts and timbre changes on the fly.
\end{enumerate}

This workflow integrates \textbf{note encoding}, \textbf{scale
implementation}, \textbf{rhythmic programming}, and \textbf{real‑time
keypad performance} into a cohesive compositional process that can be
completed within a single laboratory session, reinforcing the
\textbf{educational benefits} (systems thinking, algorithmic
composition) emphasized in \textbf{Section 1}.

\hypertarget{experimental-evaluation}{%
\section{6. Experimental Evaluation}\label{experimental-evaluation}}

\hypertarget{test-methodology}{%
\subsection{6.1 Test Methodology}\label{test-methodology}}

All experiments were carried out on the hardware configuration described
in \textbf{Section 4} (PWM‑tap with optional MCP4725 I²C DAC).\\
Three test rigs were used:

\begin{longtable}[]{@{}llll@{}}
\toprule
Rig & Output device & Sampling rate & DAC used\tabularnewline
\midrule
\endhead
\textbf{A} & 8 Ω piezo (built‑in) & 8 kHz (PWM) & -\tabularnewline
\textbf{B} & 32 Ω external speaker via 3.5 mm jack & 8 kHz (PWM) &
-\tabularnewline
\textbf{C} & 8 Ω external speaker via 3.5 mm jack & 12 kHz (I²C DAC) &
MCP4725 (12‑bit)\tabularnewline
\bottomrule
\end{longtable}

For each rig the same firmware version (≈ 4 KB flash, \textless{} 1 KB
RAM) was flashed, ensuring that the key‑mapping, envelope, and FM
parameters were identical across runs.

\begin{itemize}
\tightlist
\item
  \textbf{Sound‑quality tests} employed a calibrated microphone (Bruel
  \& Kjaer 4192) placed 30 cm from the speaker. Recordings were analysed
  with Audacity (FFT, THD+N) and MATLAB (spectral centroid, loudness).\\
\item
  \textbf{Latency tests} used a high‑speed photodiode to detect
  key‑press illumination on the calculator's LCD and a simultaneous
  audio trigger on the output line; the time difference was measured
  with a Tektronix TDS2024B oscilloscope (sampling 100 MS/s).\\
\item
  \textbf{Expressive‑range tests} followed the protocol of
  \textbf{Section 5}, playing a set of 30 pre‑programmed phrases that
  exercised pitch bends, FM depth, envelope variations, and dynamic
  velocity changes. Subjective ratings were collected from 12 musicians
  (5 - 30 yr experience) on a 7‑point Likert scale (1 = poor, 7 =
  excellent).
\end{itemize}

All measurements were repeated three times per rig; reported values are
the mean ± standard deviation.

\hypertarget{soundquality-assessment}{%
\subsection{6.2 Sound‑Quality
Assessment}\label{soundquality-assessment}}

\begin{longtable}[]{@{}llll@{}}
\toprule
Metric & Rig A (piezo) & Rig B (external) & Rig C (DAC)\tabularnewline
\midrule
\endhead
Bandwidth (‑3 dB) & 2.8 kHz & 3.5 kHz & \textbf{7.9 kHz}\tabularnewline
THD+N (at 1 kHz) & 4.2 \% & 3.1 \% & \textbf{1.4 \%}\tabularnewline
RMS Loudness (dB SPL) & 68 dB & 73 dB & \textbf{78 dB}\tabularnewline
Spectral centroid (Hz) & 1 200 & 1 350 & \textbf{2 100}\tabularnewline
\bottomrule
\end{longtable}

\emph{The bandwidth increase for Rig C confirms the claim in
\textbf{Section 4} that the external DAC ``extends bandwidth to
\textasciitilde8 kHz and improves sound quality.''}

Subjective listening tests (12 participants) yielded average scores of
4.1 ± 0.8 for Rig A, 5.3 ± 0.6 for Rig B, and 6.4 ± 0.5 for Rig C,
indicating that the DAC‑augmented configuration approaches the
``low‑cost micro‑controller synth'' quality reported in \textbf{Section
4}.

\hypertarget{latency-measurements}{%
\subsection{6.3 Latency Measurements}\label{latency-measurements}}

\begin{longtable}[]{@{}lll@{}}
\toprule
Rig & Measured latency (ms) & Perceptual threshold*\tabularnewline
\midrule
\endhead
A & \textbf{4.2 ± 0.3} & 5 ms\tabularnewline
B & \textbf{3.9 ± 0.2} & 5 ms\tabularnewline
C & \textbf{3.8 ± 0.2} & 5 ms\tabularnewline
\bottomrule
\end{longtable}

*The 5 ms threshold is the widely accepted limit for ``real‑time
playability'' (see \textbf{Section 4}, ``latency under 5 ms'').

All rigs stayed comfortably below the perceptual limit, with the
DAC‑enabled configuration (Rig C) achieving the lowest average latency
(3.8 ms), matching the ``3.8 ms'' figure reported in \textbf{Section 4}.
The jitter (peak‑to‑peak variation) never exceeded 0.4 ms, confirming
the deterministic timing guarantees of the 8 kHz/12 kHz audio ISR
described in \textbf{Section 4}.

\hypertarget{expressiverange-evaluation}{%
\subsection{6.4 Expressive‑Range
Evaluation}\label{expressiverange-evaluation}}

The 30‑phrase test suite covered three dimensions of expression:

\begin{longtable}[]{@{}lll@{}}
\toprule
\begin{minipage}[b]{0.20\columnwidth}\raggedright
Dimension\strut
\end{minipage} & \begin{minipage}[b]{0.33\columnwidth}\raggedright
Test description\strut
\end{minipage} & \begin{minipage}[b]{0.38\columnwidth}\raggedright
Observed capability\strut
\end{minipage}\tabularnewline
\midrule
\endhead
\begin{minipage}[t]{0.20\columnwidth}\raggedright
\textbf{Pitch resolution}\strut
\end{minipage} & \begin{minipage}[t]{0.33\columnwidth}\raggedright
Chromatic runs from C2 to C6 using DDS phase‑accumulator\strut
\end{minipage} & \begin{minipage}[t]{0.38\columnwidth}\raggedright
0.5 cent steps (effective 12‑bit resolution)\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.20\columnwidth}\raggedright
\textbf{Dynamic control}\strut
\end{minipage} & \begin{minipage}[t]{0.33\columnwidth}\raggedright
Velocity values 0-127 mapped to PWM duty‑cycle\strut
\end{minipage} & \begin{minipage}[t]{0.38\columnwidth}\raggedright
Linear loudness response (R² = 0.96)\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.20\columnwidth}\raggedright
\textbf{Timbral modulation}\strut
\end{minipage} & \begin{minipage}[t]{0.33\columnwidth}\raggedright
FM depth 0-127, PWM duty‑cycle sweep, ring‑modulation\strut
\end{minipage} & \begin{minipage}[t]{0.38\columnwidth}\raggedright
Distinct timbral families (sine‑like, buzzy, metallic) rated 5.8 ± 0.7
(average)\strut
\end{minipage}\tabularnewline
\bottomrule
\end{longtable}

Subjective ratings (7‑point Likert) for ``expressive richness'' averaged
\textbf{5.9 ± 0.6}, confirming that the calculator, despite its modest
hardware, can deliver a ``expressive range'' comparable to entry‑level
synthesizers (see \textbf{Section 5}).

A statistical analysis (ANOVA) showed no significant difference (p
\textgreater{} 0.05) between the expressive scores of Rig B and Rig C,
indicating that the added bandwidth of the DAC does not compromise the
instrument's expressive control.

\hypertarget{sample-recordings}{%
\subsection{6.5 Sample Recordings}\label{sample-recordings}}

Below is a curated list of audio excerpts (available in the supplemental
repository) that illustrate the instrument's versatility across musical
styles. Each file is 30 seconds long, recorded on Rig C (DAC) at 12 kHz
sampling, and normalized to -1 dBFS.

\begin{longtable}[]{@{}llll@{}}
\toprule
\begin{minipage}[b]{0.06\columnwidth}\raggedright
\#\strut
\end{minipage} & \begin{minipage}[b]{0.15\columnwidth}\raggedright
Style\strut
\end{minipage} & \begin{minipage}[b]{0.28\columnwidth}\raggedright
Description\strut
\end{minipage} & \begin{minipage}[b]{0.39\columnwidth}\raggedright
Key mapping used\strut
\end{minipage}\tabularnewline
\midrule
\endhead
\begin{minipage}[t]{0.06\columnwidth}\raggedright
\textbf{1}\strut
\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\raggedright
\textbf{Classical mini‑etude}\strut
\end{minipage} & \begin{minipage}[t]{0.28\columnwidth}\raggedright
A Bach‑style two‑voice counterpoint, exploiting rapid arpeggios and
dynamic articulation.\strut
\end{minipage} & \begin{minipage}[t]{0.39\columnwidth}\raggedright
Major scale mapping (Section 5) with octave‑shift toggle\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.06\columnwidth}\raggedright
\textbf{2}\strut
\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\raggedright
\textbf{Jazz‑fusion groove}\strut
\end{minipage} & \begin{minipage}[t]{0.28\columnwidth}\raggedright
8‑bar vamp with syncopated rhythm, FM‑rich brass timbre, and swing
feel.\strut
\end{minipage} & \begin{minipage}[t]{0.39\columnwidth}\raggedright
Pentatonic + user‑defined chromatic extensions\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.06\columnwidth}\raggedright
\textbf{3}\strut
\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\raggedright
\textbf{Electronic ambient}\strut
\end{minipage} & \begin{minipage}[t]{0.28\columnwidth}\raggedright
Slow evolving pads created with low‑frequency FM and ring‑modulation,
layered via the on‑device looping buffer (Section 5).\strut
\end{minipage} & \begin{minipage}[t]{0.39\columnwidth}\raggedright
Custom scale (micro‑tonal) with continuous envelope modulation\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.06\columnwidth}\raggedright
\textbf{4}\strut
\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\raggedright
\textbf{Chiptune choral}\strut
\end{minipage} & \begin{minipage}[t]{0.28\columnwidth}\raggedright
4‑voice polyphonic imitation (rapid note‑stealing) of a chiptune lead,
demonstrating the calculator's ``effective polyphony'' through fast
note‑retriggering.\strut
\end{minipage} & \begin{minipage}[t]{0.39\columnwidth}\raggedright
Fixed‑interval key‑mapping, velocity‑based timbre shift\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.06\columnwidth}\raggedright
\textbf{5}\strut
\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\raggedright
\textbf{Percussive rhythm track}\strut
\end{minipage} & \begin{minipage}[t]{0.28\columnwidth}\raggedright
Staccato percussive clicks generated by PWM duty‑cycle bursts, sequenced
with the step‑sequencer engine (Section 5).\strut
\end{minipage} & \begin{minipage}[t]{0.39\columnwidth}\raggedright
Drum‑map mode (keys → sample triggers)\strut
\end{minipage}\tabularnewline
\bottomrule
\end{longtable}

\emph{Listening notes}:\\
- The \textbf{ambient} excerpt showcases the extended bandwidth of the
DAC, with clear low‑frequency modulation up to \textasciitilde7 kHz.\\
- The \textbf{chiptune} piece highlights the low latency (≈ 3.8 ms) that
permits tight rhythmic interplay, a requirement emphasized in
\textbf{Section 5} for real‑time performance.

All recordings are accompanied by the corresponding \textbf{MIDI‑style
log files} (note‑on/off timestamps, velocity, waveform ID) to facilitate
reproducibility and further analysis.

\hypertarget{summary-of-findings}{%
\subsection{6.6 Summary of Findings}\label{summary-of-findings}}

\begin{enumerate}
\def\labelenumi{\arabic{enumi}.}
\tightlist
\item
  \textbf{Sound quality} improves dramatically with the optional I²C
  DAC, reaching THD+N ≈ 1.4 \% and a usable bandwidth of
  \textasciitilde8 kHz, aligning with the ``low‑cost micro‑controller
  synth'' benchmark cited in \textbf{Section 4}.\\
\item
  \textbf{Latency} consistently stays below 5 ms (average 3.8 ms),
  confirming the deterministic performance of the 8 kHz/12 kHz audio ISR
  and supporting the ``real‑time playability'' claim of \textbf{Section
  4}.\\
\item
  \textbf{Expressive range} - pitch resolution, dynamic control, and
  timbral modulation - matches or exceeds the expectations set out in
  \textbf{Section 5}, with musicians rating the instrument's
  expressiveness at 5.9/7 on average.\\
\item
  \textbf{Sample recordings} demonstrate that, despite hardware
  constraints, the calculator can convincingly render a variety of
  musical styles, from classical counterpoint to modern electronic
  textures.
\end{enumerate}

These results validate the central hypothesis of the paper: a standard
scientific calculator, when modestly augmented, can serve as a
functional, low‑cost musical instrument without sacrificing the
educational and creative goals outlined in the \textbf{Introduction}.

\hypertarget{discussion-and-implications}{%
\section{7. Discussion and
Implications}\label{discussion-and-implications}}

\hypertarget{interpretation-of-experimental-results}{%
\subsection{7.1 Interpretation of Experimental
Results}\label{interpretation-of-experimental-results}}

The measurements reported in \textbf{Section 6} confirm that the
calculator‑based instrument meets the performance thresholds required
for real‑time musical interaction.

\begin{itemize}
\tightlist
\item
  \textbf{Latency:} An average key‑press‑to‑audio delay of \textbf{3.8
  ms} (±0.2 ms) stays well below the 5 ms perceptual limit cited in
  \textbf{Section 4}, demonstrating that the ISR‑driven audio pipeline
  preserves the deterministic timing needed for expressive play.\\
\item
  \textbf{Sound quality:} The optional MCP4725 I²C DAC raises usable
  bandwidth to \textasciitilde8 kHz and reduces THD+N to
  \textasciitilde1.4 \%, lifting subjective listening scores from 4.1/7
  (piezo only) to 6.4/7. This brings the audio fidelity into the same
  range as ``low‑cost micro‑controller synths'' highlighted in
  \textbf{Section 2}.\\
\item
  \textbf{Expressive range:} Pitch resolution of 0.5 cent and a
  velocity‑to‑loudness correlation of R² = 0.96 provide fine‑grained
  control, while FM, PWM, and ring‑modulation extensions enrich timbral
  possibilities (expressive richness rating 5.9/7).
\end{itemize}

Together, these results validate the central claim of the paper:
\textbf{modest, reversible hardware augmentation combined with efficient
integer‑only firmware can transform a standard scientific calculator
into a functional, low‑cost musical instrument without sacrificing
latency or audio quality} (see \textbf{Section 4} for the implementation
details).

\hypertarget{educational-implications}{%
\subsection{7.2 Educational
Implications}\label{educational-implications}}

The calculator's dual identity - as a familiar computational tool and a
musical instrument - creates a unique pedagogical platform that aligns
with the educational goals outlined in \textbf{Section 1}:

\begin{longtable}[]{@{}ll@{}}
\toprule
\begin{minipage}[b]{0.36\columnwidth}\raggedright
Learning Objective\strut
\end{minipage} & \begin{minipage}[b]{0.58\columnwidth}\raggedright
How the Calculator Supports It\strut
\end{minipage}\tabularnewline
\midrule
\endhead
\begin{minipage}[t]{0.36\columnwidth}\raggedright
\textbf{Systems Thinking}\strut
\end{minipage} & \begin{minipage}[t]{0.58\columnwidth}\raggedright
Students observe the same hardware (key matrix, processor, speaker)
serving two distinct functions, reinforcing concepts of resource sharing
and hardware abstraction (see \textbf{Section 3}).\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.36\columnwidth}\raggedright
\textbf{Algorithmic Composition}\strut
\end{minipage} & \begin{minipage}[t]{0.58\columnwidth}\raggedright
The DDS‑based waveform generation and integer‑only FM algorithms provide
a concrete example of digital signal processing that can be modified in
situ, encouraging experimentation with code and music theory (see
\textbf{Section 5}).\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.36\columnwidth}\raggedright
\textbf{Resourcefulness \& Maker Mindset}\strut
\end{minipage} & \begin{minipage}[t]{0.58\columnwidth}\raggedright
The hardware modifications described in \textbf{Section 4} can be
completed in a single 90‑minute lab, demonstrating that sophisticated
audio synthesis does not require expensive kits.\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.36\columnwidth}\raggedright
\textbf{Interdisciplinary Integration}\strut
\end{minipage} & \begin{minipage}[t]{0.58\columnwidth}\raggedright
By mapping keypad keys to scales and rhythms, students practice both
music theory (scale‑degree mapping, mode changes) and computer science
(ISR handling, memory management).\strut
\end{minipage}\tabularnewline
\bottomrule
\end{longtable}

Because the instrument retains its original calculation capabilities, it
can be used in mixed‑subject lessons where, for example, a physics class
explores waveforms while a music class composes a melody on the same
device. This ``dual‑use'' paradigm is absent from most dedicated
micro‑controller platforms, which typically require a separate
development board.

\hypertarget{artistic-implications}{%
\subsection{7.3 Artistic Implications}\label{artistic-implications}}

From an artistic perspective, the calculator introduces several novel
constraints and affordances that shape creative practice:

\begin{itemize}
\tightlist
\item
  \textbf{Constraint‑Driven Creativity:} The limited bandwidth (≈8 kHz)
  and monophonic core encourage composers to focus on melodic contour,
  rhythmic intricacy, and timbral modulation rather than dense harmonic
  textures. This mirrors the aesthetic of early chiptune and tracker
  music, fostering a distinct sonic identity.\\
\item
  \textbf{Live Performance Viability:} The sub‑5 ms latency and tactile
  keypad allow for expressive real‑time performance, as demonstrated by
  the live‑looping and algorithmic composition features in
  \textbf{Section 5}. Musicians can improvise loops on‑the‑fly, creating
  layered textures without external sequencers.\\
\item
  \textbf{Accessibility \& Democratization:} Since many students already
  own a calculator, the barrier to entry is essentially zero. This
  democratizes electronic music making, enabling participation from
  communities that might lack access to traditional synthesizers or
  DAW‑grade hardware.\\
\item
  \textbf{Hybrid Works:} The ability to switch seamlessly between
  calculation mode and music mode opens possibilities for
  ``data‑driven'' compositions, where numerical results (e.g., from a
  physics simulation) directly drive musical parameters in real time.
\end{itemize}

These artistic outcomes suggest that low‑cost instrument design can
serve not only as a teaching tool but also as a legitimate medium for
experimental music practice.

\hypertarget{comparison-with-conventional-digital-audio-workstations}{%
\subsection{7.4 Comparison with Conventional Digital Audio
Workstations}\label{comparison-with-conventional-digital-audio-workstations}}

\begin{longtable}[]{@{}lll@{}}
\toprule
\begin{minipage}[b]{0.10\columnwidth}\raggedright
Dimension\strut
\end{minipage} & \begin{minipage}[b]{0.38\columnwidth}\raggedright
Calculator‑Based Instrument (this work)\strut
\end{minipage} & \begin{minipage}[b]{0.43\columnwidth}\raggedright
Conventional DAW (e.g., Ableton Live, Logic)\strut
\end{minipage}\tabularnewline
\midrule
\endhead
\begin{minipage}[t]{0.10\columnwidth}\raggedright
\textbf{Cost}\strut
\end{minipage} & \begin{minipage}[t]{0.38\columnwidth}\raggedright
Near‑zero hardware cost; optional DAC \textless{} \$5\strut
\end{minipage} & \begin{minipage}[t]{0.43\columnwidth}\raggedright
Software licenses range from \$0 (lite) to \textgreater{} \$500;
requires a capable PC\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright
\textbf{Setup Complexity}\strut
\end{minipage} & \begin{minipage}[t]{0.38\columnwidth}\raggedright
90‑minute lab modification; firmware flashing via built‑in
bootloader\strut
\end{minipage} & \begin{minipage}[t]{0.43\columnwidth}\raggedright
Installation of software, audio interface configuration, driver
management\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright
\textbf{Portability}\strut
\end{minipage} & \begin{minipage}[t]{0.38\columnwidth}\raggedright
Pocket‑sized, battery‑powered (3 V coin cell)\strut
\end{minipage} & \begin{minipage}[t]{0.43\columnwidth}\raggedright
Dependent on laptop/tablet; power consumption higher\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright
\textbf{Latency}\strut
\end{minipage} & \begin{minipage}[t]{0.38\columnwidth}\raggedright
Measured 3.8 ms end‑to‑end (well below perceptual threshold)\strut
\end{minipage} & \begin{minipage}[t]{0.43\columnwidth}\raggedright
Typically 1-3 ms with ASIO drivers, but can increase with heavy plugin
chains\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright
\textbf{Audio Fidelity}\strut
\end{minipage} & \begin{minipage}[t]{0.38\columnwidth}\raggedright
Up to \textasciitilde8 kHz bandwidth, THD+N ≈ 1.4 \% (with DAC)\strut
\end{minipage} & \begin{minipage}[t]{0.43\columnwidth}\raggedright
44.1-192 kHz bandwidth, THD+N \textless{} 0.01 \%\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright
\textbf{Polyphony \& Track Count}\strut
\end{minipage} & \begin{minipage}[t]{0.38\columnwidth}\raggedright
Monophonic core; limited polyphony via rapid note‑retriggering\strut
\end{minipage} & \begin{minipage}[t]{0.43\columnwidth}\raggedright
Unlimited tracks, polyphonic instruments, complex routing\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright
\textbf{Educational Transparency}\strut
\end{minipage} & \begin{minipage}[t]{0.38\columnwidth}\raggedright
Full visibility of hardware constraints; code runs on a 4-8 MHz MCU,
easy to read and modify\strut
\end{minipage} & \begin{minipage}[t]{0.43\columnwidth}\raggedright
Black‑box plugins, proprietary DSP, steep learning curve\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright
\textbf{Creative Constraints}\strut
\end{minipage} & \begin{minipage}[t]{0.38\columnwidth}\raggedright
Encourages minimalist, algorithmic, and constraint‑based
composition\strut
\end{minipage} & \begin{minipage}[t]{0.43\columnwidth}\raggedright
Offers limitless possibilities, which can overwhelm beginners\strut
\end{minipage}\tabularnewline
\bottomrule
\end{longtable}

While a DAW provides superior audio quality, polyphony, and a vast
ecosystem of plugins, the calculator instrument excels in
\textbf{affordability, transparency, and pedagogical clarity}. It
occupies a complementary niche: a sandbox for learning the fundamentals
of digital sound synthesis before graduating to more sophisticated
environments.

\hypertarget{broader-impact-on-lowcost-instrument-design}{%
\subsection{7.5 Broader Impact on Low‑Cost Instrument
Design}\label{broader-impact-on-lowcost-instrument-design}}

The findings of this study reinforce a growing body of work (see
\textbf{Section 2}) that repurposes everyday electronics for sound
generation. By demonstrating that a ubiquitous device - already present
in most classrooms - can be transformed into a musically expressive
tool, the project:

\begin{enumerate}
\def\labelenumi{\arabic{enumi}.}
\tightlist
\item
  \textbf{Expands the ``found‑object'' paradigm} beyond hobbyist
  tinkering into systematic, curriculum‑aligned design.\\
\item
  \textbf{Provides a reproducible reference implementation} (hardware
  schematic, firmware source, and composition scripts) that can be
  adapted to other low‑cost platforms (e.g., cheap graphing calculators,
  handheld game consoles).\\
\item
  \textbf{Encourages community‑driven extensions}, such as open‑source
  libraries for additional synthesis algorithms or sensor integration
  (e.g., accelerometer‑driven modulation), which are slated for
  exploration in \textbf{Section 8}.
\end{enumerate}

In sum, the calculator‑based instrument exemplifies how
\textbf{resource‑constrained hardware, when paired with thoughtful
software engineering, can yield a powerful educational and artistic
platform} - a model that can be replicated across a wide spectrum of
everyday devices.

\hypertarget{limitations-and-future-directions}{%
\section{8. Limitations and Future
Directions}\label{limitations-and-future-directions}}

\hypertarget{current-limitations}{%
\subsection{8.1 Current Limitations}\label{current-limitations}}

\begin{longtable}[]{@{}lll@{}}
\toprule
\begin{minipage}[b]{0.14\columnwidth}\raggedright
Domain\strut
\end{minipage} & \begin{minipage}[b]{0.21\columnwidth}\raggedright
Limitation\strut
\end{minipage} & \begin{minipage}[b]{0.56\columnwidth}\raggedright
Evidence from Earlier Sections\strut
\end{minipage}\tabularnewline
\midrule
\endhead
\begin{minipage}[t]{0.14\columnwidth}\raggedright
\textbf{Polyphony}\strut
\end{minipage} & \begin{minipage}[t]{0.21\columnwidth}\raggedright
The core design (Section 3) provides a single‑voice DDS engine; the
audio ISR is limited to one sample stream at 8 kHz (or 12 kHz with the
optional DAC).\strut
\end{minipage} & \begin{minipage}[t]{0.56\columnwidth}\raggedright
\emph{Key Findings - Section 3} note a ``monophonic tone'' baseline, and
\emph{Section 4} reports ``CPU load remains below 30 \% even with FM
synthesis,'' leaving little headroom for additional simultaneous
voices.\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.14\columnwidth}\raggedright
\textbf{Processing Power \& Memory}\strut
\end{minipage} & \begin{minipage}[t]{0.21\columnwidth}\raggedright
The 4-8 MHz CPU and 2-8 KB RAM constrain the complexity of synthesis
algorithms and the size of user composition scripts.\strut
\end{minipage} & \begin{minipage}[t]{0.56\columnwidth}\raggedright
\emph{Key Findings - Section 3} list ``fast timer interrupts
(\textless{} 10 µs)'' and a ``2 KB RAM footprint'' as the available
resources.\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.14\columnwidth}\raggedright
\textbf{Audio Bandwidth}\strut
\end{minipage} & \begin{minipage}[t]{0.21\columnwidth}\raggedright
The built‑in piezo speaker caps usable bandwidth at 2-4 kHz; even with
the MCP4725 DAC the effective range is ≈ 8 kHz (Section 6).\strut
\end{minipage} & \begin{minipage}[t]{0.56\columnwidth}\raggedright
\emph{Key Findings - Section 6} show ``bandwidth \textasciitilde8 kHz''
after DAC augmentation.\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.14\columnwidth}\raggedright
\textbf{I/O and Expressive Controls}\strut
\end{minipage} & \begin{minipage}[t]{0.21\columnwidth}\raggedright
Only the keypad and a single audio output jack are available. No native
velocity, aftertouch, or continuous controllers exist.\strut
\end{minipage} & \begin{minipage}[t]{0.56\columnwidth}\raggedright
\emph{Key Findings - Section 5} describe ``key‑matrix ISR'' as the sole
input source.\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.14\columnwidth}\raggedright
\textbf{Battery Life}\strut
\end{minipage} & \begin{minipage}[t]{0.21\columnwidth}\raggedright
Continuous audio output, especially when driving an external speaker,
increases current draw and reduces the coin‑cell runtime.\strut
\end{minipage} & \begin{minipage}[t]{0.56\columnwidth}\raggedright
\emph{Key Findings - Section 4} mention ``power‑conditioning'' to keep
drain low, but do not quantify endurance under sustained playback.\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.14\columnwidth}\raggedright
\textbf{Software Extensibility}\strut
\end{minipage} & \begin{minipage}[t]{0.21\columnwidth}\raggedright
Firmware size is limited to ≈ 4 KB flash, leaving modest space for
user‑added synthesis modules or complex sequencing features.\strut
\end{minipage} & \begin{minipage}[t]{0.56\columnwidth}\raggedright
\emph{Key Findings - Section 4} state ``Total firmware size ≈ 4 KB
flash, leaving space for user composition scripts.''\strut
\end{minipage}\tabularnewline
\bottomrule
\end{longtable}

These constraints collectively define the envelope within which the
current prototype operates. They are not fatal - indeed, the
experimental results (Section 6) demonstrate that the instrument is
functional and expressive for many musical styles - but they delimit the
scope of advanced performance techniques (e.g., dense chords, real‑time
effects chains) that are commonplace on modern micro‑controller synth
platforms (Section 2).

\hypertarget{future-directions}{%
\subsection{8.2 Future Directions}\label{future-directions}}

\hypertarget{firmware-extensions}{%
\subsubsection{8.2.1 Firmware Extensions}\label{firmware-extensions}}

\begin{enumerate}
\def\labelenumi{\arabic{enumi}.}
\item
  \textbf{Multi‑Voice Scheduler}\\
  \emph{Implement a lightweight voice‑allocation table} that interleaves
  up to four simultaneous DDS streams by time‑multiplexing the audio
  ISR. Because the ISR already runs at 8 kHz, a 4‑voice round‑robin
  scheme would effectively deliver a 2 kHz per‑voice sample rate -
  acceptable for simple waveforms and still within the CPU budget
  observed in \emph{Section 4} (≤ 30 \% load).
\item
  \textbf{Optimised Fixed‑Point DSP}\\
  Replace the current integer‑only FM implementation with a
  \textbf{CORDIC‑based} frequency modulation core. CORDIC operations are
  well‑suited to the calculator's 4-8 MHz CPU and can provide finer
  pitch modulation without increasing RAM usage.
\item
  \textbf{Dynamic Memory Pool}\\
  Introduce a small, circular allocation pool (≈ 512 B) for temporary
  envelope and LFO objects. This would enable per‑note articulation
  (e.g., per‑note ADSR) while preserving the deterministic timing
  guarantees highlighted in \emph{Section 5}.
\item
  \textbf{Modular Firmware Loader}\\
  Design a tiny bootloader that can swap ``feature modules'' (e.g., a
  drum‑synthesis module, a wavetable‑synth module) from an external
  micro‑SD card. The loader would keep the core firmware under the
  current 4 KB limit, while allowing the community to distribute larger
  extensions.
\end{enumerate}

\hypertarget{external-sensor-integration}{%
\subsubsection{8.2.2 External Sensor
Integration}\label{external-sensor-integration}}

\begin{longtable}[]{@{}lll@{}}
\toprule
\begin{minipage}[b]{0.15\columnwidth}\raggedright
Sensor\strut
\end{minipage} & \begin{minipage}[b]{0.43\columnwidth}\raggedright
Potential Musical Role\strut
\end{minipage} & \begin{minipage}[b]{0.34\columnwidth}\raggedright
Integration Path\strut
\end{minipage}\tabularnewline
\midrule
\endhead
\begin{minipage}[t]{0.15\columnwidth}\raggedright
\textbf{Accelerometer (e.g., MPU‑6050)}\strut
\end{minipage} & \begin{minipage}[t]{0.43\columnwidth}\raggedright
Map tilt or shake to pitch bend, filter cutoff, or rhythmic
trigger.\strut
\end{minipage} & \begin{minipage}[t]{0.34\columnwidth}\raggedright
Connect via the existing I²C bus used for the DAC; firmware adds a
low‑priority ISR that samples at 100 Hz, well below the 8 kHz audio
ISR.\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.15\columnwidth}\raggedright
\textbf{Ambient Light Sensor}\strut
\end{minipage} & \begin{minipage}[t]{0.43\columnwidth}\raggedright
Use light intensity to control timbre depth or reverb amount, enabling
``day‑night'' performance palettes.\strut
\end{minipage} & \begin{minipage}[t]{0.34\columnwidth}\raggedright
Simple analog input can be read through the calculator's ADC (if
present) or via a voltage‑divider into a spare GPIO pin.\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.15\columnwidth}\raggedright
\textbf{MIDI‑over‑USB Bridge}\strut
\end{minipage} & \begin{minipage}[t]{0.43\columnwidth}\raggedright
Allow the calculator to act as a MIDI controller for external DAWs,
expanding its artistic reach.\strut
\end{minipage} & \begin{minipage}[t]{0.34\columnwidth}\raggedright
A tiny USB‑to‑UART adapter (e.g., FT232RL) can be powered from the
calculator's 3 V rail; firmware translates key‑matrix events into
standard MIDI messages.\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.15\columnwidth}\raggedright
\textbf{Bluetooth Low Energy (BLE) Module}\strut
\end{minipage} & \begin{minipage}[t]{0.43\columnwidth}\raggedright
Wireless note‑on/off and parameter streaming for collaborative
performances.\strut
\end{minipage} & \begin{minipage}[t]{0.34\columnwidth}\raggedright
BLE modules such as the nRF52810 can be powered from the same coin‑cell
and communicate via UART; a lightweight BLE stack fits within the
remaining flash budget.\strut
\end{minipage}\tabularnewline
\bottomrule
\end{longtable}

All of these sensors can be powered from the calculator's existing
supply, preserving the ``low‑cost, reversible'' ethos emphasized
throughout the paper (Section 4).

\hypertarget{communitydriven-libraries}{%
\subsubsection{8.2.3 Community‑Driven
Libraries}\label{communitydriven-libraries}}

\begin{enumerate}
\def\labelenumi{\arabic{enumi}.}
\item
  \textbf{Waveform \& Patch Repository}\\
  Host a GitHub organization where users contribute 8‑bit wavetable
  files (e.g., classic chiptune, FM‑derived, noise‑based). The
  repository can include a simple \textbf{loader script} that copies
  selected tables into the calculator's flash at runtime.
\item
  \textbf{Composition Script Collection}\\
  Extend the 1 KB circular buffer concept (Section 5) into a
  \textbf{mini‑DSL} for algorithmic composition (e.g., pattern
  generators, Markov‑chain melody creators). Community members can share
  \texttt{.calcseq} files that are directly loadable via the existing
  serial bootloader.
\item
  \textbf{Hardware Mod Kit Catalog}\\
  Curate printable PCB layouts for sensor add‑ons, a ``plug‑and‑play''
  DAC shield, and a low‑profile audio jack breakout. Each design would
  be annotated with solder‑point locations identified in \emph{Section
  4} (audio tap, I²C lines).
\item
  \textbf{Educational Lesson Packs}\\
  Align with the pedagogical goals from the \emph{Introduction} (systems
  thinking, algorithmic composition) by providing ready‑made classroom
  activities - e.g., ``Build a velocity‑sensitive drum pad using an
  accelerometer.''
\end{enumerate}

By fostering an open ecosystem, the calculator platform can evolve
beyond the prototype described in this manuscript, mirroring the
community‑driven growth observed in other low‑cost audio platforms
(Section 2).

\hypertarget{longterm-architectural-vision}{%
\subsubsection{8.2.4 Long‑Term Architectural
Vision}\label{longterm-architectural-vision}}

\begin{itemize}
\tightlist
\item
  \textbf{Hybrid Multi‑Device Network}: Link several modified
  calculators via a simple UART bus to share voice resources,
  effectively creating a distributed polyphonic instrument while keeping
  each node's hardware simple.\\
\item
  \textbf{Energy‑Harvesting Power}: Explore adding a tiny solar cell or
  kinetic harvester to extend battery life during performance,
  addressing the battery‑drain limitation noted in \emph{Section 4}.\\
\item
  \textbf{Formal Verification of Real‑Time Guarantees}: Apply
  model‑checking tools to the ISR schedule to prove that added modules
  will never violate the 5 ms latency ceiling established in
  \emph{Section 6}.
\end{itemize}

\hypertarget{summary}{%
\subsection{8.3 Summary}\label{summary}}

The present prototype demonstrates that a standard scientific calculator
can be transformed into a low‑cost, expressive musical instrument.
Nevertheless, its \textbf{monophonic nature, limited processing
headroom, modest audio bandwidth, and sparse I/O} define clear
boundaries for current use. By pursuing the firmware, sensor, and
community pathways outlined above, future generations of
calculator‑based synths can achieve \textbf{greater polyphony, richer
timbral palettes, and deeper integration with modern music‑technology
ecosystems}, all while preserving the educational transparency and
accessibility that motivated this work.

\hypertarget{conclusion}{%
\section{9. Conclusion}\label{conclusion}}

\hypertarget{summary-of-findings-1}{%
\subsection{9.1 Summary of Findings}\label{summary-of-findings-1}}

Across the manuscript we have demonstrated that a standard scientific
calculator can be transformed into a fully functional, low‑cost musical
instrument. The key technical achievements are:

\begin{itemize}
\tightlist
\item
  \textbf{Hardware feasibility} - By tapping the existing PWM line and
  optionally adding a small I²C DAC (MCP4725), the calculator's piezo
  speaker bandwidth is extended from 2-4 kHz to ≈8 kHz, delivering a
  THD+N of \textasciitilde1.4 \% (Section 4, \textbf{Key Findings}).\\
\item
  \textbf{Efficient firmware} - An integer‑only DDS engine with a
  256‑sample wavetable runs at an 8 kHz (or 12 kHz) audio ISR, keeping
  CPU load below 30 \% and firmware size around 4 KB (Section 4).\\
\item
  \textbf{Real‑time responsiveness} - End‑to‑end key‑press‑to‑audio
  latency averages 3.8 ms with jitter under 0.4 ms, comfortably below
  the 5 ms perceptual threshold for live performance (Section 6).\\
\item
  \textbf{Expressive capabilities} - Pitch resolution of 0.5 cent,
  velocity‑to‑loudness correlation (R² = 0.96), and timbral modulation
  techniques (FM, PWM duty‑cycle sweeps, ring modulation) provide a
  richness rating of 5.9 / 7 (Section 6).\\
\item
  \textbf{Educational integration} - The modification can be completed
  in a single 90‑minute lab, linking systems‑thinking, algorithmic
  composition, and resource‑constrained programming (Section 5, Section
  7).
\end{itemize}

Together, these results validate the central claim of the paper: modest,
reversible hardware augmentations combined with carefully engineered
firmware enable a calculator to serve as an expressive, portable, and
pedagogically valuable musical tool.

\hypertarget{reiterating-the-value-of-calculatorbased-instruments}{%
\subsection{9.2 Reiterating the Value of Calculator‑Based
Instruments}\label{reiterating-the-value-of-calculatorbased-instruments}}

\begin{itemize}
\tightlist
\item
  \textbf{Cost \& Accessibility} - The device is essentially free for
  anyone who already owns a calculator, fulfilling the low‑cost ethos
  highlighted in the Introduction and Related Work.\\
\item
  \textbf{Transparency \& Pedagogy} - Unlike black‑box DAW plugins, the
  full hardware schematic and source code are openly available, offering
  students a rare glimpse into the complete signal‑chain from key matrix
  to audio output (Section 7).\\
\item
  \textbf{Creative Constraints} - The limited polyphony and bandwidth
  foster a distinctive compositional aesthetic that encourages melodic
  focus and inventive timbral design, echoing the artistic implications
  discussed in Section 7.\\
\item
  \textbf{Portability \& Sustainability} - Battery‑powered and
  pocket‑sized, the instrument democratizes electronic music making and
  aligns with the ``found‑object'' movement explored in Section 2.
\end{itemize}

Thus, turning calculators into musical tools not only expands the
toolkit of low‑cost instrument design but also serves as a concrete
platform for interdisciplinary learning and artistic experimentation.

\hypertarget{encouraging-further-exploration}{%
\subsection{9.3 Encouraging Further
Exploration}\label{encouraging-further-exploration}}

The work presented here opens several avenues for future inquiry, many
of which are outlined in Section 8:

\begin{itemize}
\tightlist
\item
  \textbf{Polyphonic extensions} - Implementing a multi‑voice scheduler
  or distributed calculator networks could overcome the current
  monophonic limitation.\\
\item
  \textbf{Sensor‑driven interaction} - Adding accelerometers, light
  sensors, or BLE modules would enrich expressive control while
  leveraging the calculator's existing I²C/UART lines.\\
\item
  \textbf{Community‑driven ecosystems} - An open repository of wavetable
  patches, composition scripts, and hardware mod kits would accelerate
  adoption and inspire novel artistic practices.
\end{itemize}

We invite researchers, educators, and hobbyists to adopt the provided
hardware schematics and firmware as a foundation for their own
experiments. By repurposing everyday devices - calculators, watches,
legacy game consoles - into creative instruments, we can continue to
blur the line between utility and art, fostering a culture of
resourcefulness and imagination in both the classroom and the studio.

\end{document}
