MIDI tuning standard

Key takeaways

MIDI tuning standard belongs to computer science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect MIDI tuning standard to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of MIDI tuning standard from memory before moving on to harder problems.

Reference excerpt

MIDI Tuning Standard (MTS) is a specification of precise musical pitch agreed to by the MIDI Manufacturers Association in the MIDI protocol. MTS allows for both a bulk tuning dump message, giving a tuning for each of 128 notes, and a tuning message for individual notes as they are played.

Frequency values If f is a frequency in hertz, then the corresponding MIDI note number NMIDI is given by the formula

N M I D I = 69 + 12 ⋅ log 2 ⁡ ( f 440 H z ) = 69 + 12 log ⁡ 2 log ⁡ ( f 440 H z ) , {\displaystyle N_{\mathsf {MIDI}}=69+12\cdot \log _{2}\left({\frac {f}{\ 440\ \mathrm {Hz} \ }}\right)=69+{\frac {12}{\ \log 2\ }}\log \left({\frac {f}{\ 440\ \mathrm {Hz} \ }}\right)\ ,}

where "log" in the second expression is any logarithm (e.g. either the common logarithm log10 , the natural logarithm ln ≡ loge , or any other). The quantity log2( ⁠ f / 440 Hz ⁠ ) is the number of octaves above the 440 Hz concert A, or A4, or a′ . Multiplying it by 12 gives the number of semitones above 440 Hz (the value is negative if the frequency f is lower in pitch than 440 Hz). Adding 69 (decimal, or 0x45 hexadecimal) gives the number of semitones above the C five octaves below middle C. Not only is 440 Hz the standard central pitch for MIDI, it is also widely used as the concert A standard pitch (A4 e.g. USA, UK), and since that is represented in MIDI signals by the integer 69 (nine semitones above middle C (C4, c′), which is 60 decimal or 0x3C hexadecimal), this gives a real number which expresses pitch in a manner consistent with midi and integer notation, known as the MIDI note number, NMIDI . Converting from MIDI note number (NMIDI) to frequency (f) is given by the following formula:

f = 440 H z ⋅ 2 [ ( N M I D I − 69 ) / 12 ] = 440 H z ⋅ exp ⁡ [ ln ⁡ 2 12 ( N M I D I − 69 ) ] . {\displaystyle \ f=440\ {\mathsf {Hz}}\cdot 2^{\left[\ \left(\ N_{\mathsf {MIDI}}\ -\ 69\ \right)/12\ \right]}\ =440\ {\mathsf {Hz}}\cdot \exp \left[\ {\frac {\ \ln 2\ }{12}}\left(\ N_{\mathsf {MIDI}}\ -\ 69\ \right)\ \right]~.}

Frequency Data Format The frequency data format allows for the precise notation of frequencies that differ from equal temperament.

"Frequency data shall be defined in [units] which are fractions of a semitone. The frequency range starts at MIDI note 0, C = 8.1758 Hz, and extends above MIDI note 127, G = 12543.854 Hz. The first byte of the frequency data word specifies the highest equal-tempered semitone not exceeding the frequency. The next two bytes (14 bits) specify the fraction of 100 cents above the semitone at which the frequency lies. Effective resolution = 100 cents / 214 = .0061 cents." This higher resolution allows a logarithmic representation of pitch in which the semitone is divided into 1282 = 214 = 16384 parts, which means the octave is divided into 196608 (logarithmically) equal parts. These parts are exactly ⁠100/16384⁠ cents (approximately 0.0061 cents) in size, which is far below the threshold of human pitch perception and which therefore allows a very accurate representation of pitch.

… excerpt ends here. Continue reading the full article.

Worked examples

Example 1 — a first encounter with MIDI tuning standard

Start with the simplest possible case. Write down what MIDI tuning standard claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In computer science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to MIDI tuning standard before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about MIDI tuning standard ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of MIDI tuning standard

In research: MIDI tuning standard appears in computer science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses MIDI tuning standard in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: MIDI tuning standard is common in secondary-school and first-year university syllabi. It links to neighbouring topics Computer file formats, Electronic music, MIDI standards, so understanding it makes those chapters shorter.
In everyday life: Look for MIDI tuning standard outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

How to study MIDI tuning standard in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what MIDI tuning standard means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain MIDI tuning standard out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is MIDI tuning standard in simple terms?

MIDI Tuning Standard (MTS) is a specification of precise musical pitch agreed to by the MIDI Manufacturers Association in the MIDI protocol. MTS allows for both a bulk tuning dump message, giving a tuning for each of 128 notes, and a tuning message for individual notes as they are played.

Why does MIDI tuning standard matter?

Because it connects several computer science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study MIDI tuning standard?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on MIDI tuning standard.