**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of Graph Search.

Concept# Interval ratio

Summary

In music, an interval ratio is a ratio of the frequencies of the pitches in a musical interval. For example, a just perfect fifth (for example C to G) is 3:2 (), 1.5, and may be approximated by an equal tempered perfect fifth () which is 27/12 (about 1.498). If the A above middle C is 440 Hz, the perfect fifth above it would be E, at (440*1.5=) 660 Hz, while the equal tempered E5 is 659.255 Hz.
Ratios, rather than direct frequency measurements, allow musicians to work with relative pitch measurements applicable to many instruments in an intuitive manner, whereas one rarely has the frequencies of fixed pitched instruments memorized and rarely has the capabilities to measure the changes of adjustable pitch instruments (electronic tuner). Ratios have an inverse relationship to string length, for example stopping a string at two-thirds (2:3) its length produces a pitch one and one-half (3:2) that of the open string (not to be confused with inversion).
Intervals may be ranked by relative consonance and dissonance. As such ratios with lower integers are generally more consonant than intervals with higher integers. For example, 2:1 (), 4:3 (), 9:8 (), 65536:59049 (), etc.
Consonance and dissonance may more subtly be defined by limit, wherein the ratios whose limit, which includes its integer multiples, is lower are generally more consonant. For example, the 3-limit 128:81 () and the 7-limit 14:9 (). Despite having larger integers 128:81 is less dissonant than 14:9, as according to limit theory.
For ease of comparison intervals may also be measured in cents, a logarithmic measurement. For example, the just perfect fifth is 701.955 cents while the equal tempered perfect fifth is 700 cents.
Frequency ratios are used to describe intervals in both Western and non-Western music. They are most often used to describe intervals between notes tuned with tuning systems such as Pythagorean tuning, just intonation, and meantone temperament, the size of which can be expressed by small-integer ratios.

Official source

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related publications (1)

Related courses (1)

Related concepts (4)

MATH-124: Geometry for architects I

Ce cours entend exposer les fondements de la géométrie à un triple titre :
1/ de technique mathématique essentielle au processus de conception du projet,
2/ d'objet privilégié des logiciels de concept

Related lectures (6)

Major third

In classical music, a third is a musical interval encompassing three staff positions (see Interval number for more details), and the major third () is a third spanning four semitones. Along with the minor third, the major third is one of two commonly occurring thirds. It is qualified as major because it is the larger of the two: the major third spans four semitones, the minor third three. For example, the interval from C to E is a major third, as the note E lies four semitones above C, and there are three staff positions from C to E.

Perfect fifth

In music theory, a perfect fifth is the musical interval corresponding to a pair of pitches with a frequency ratio of 3:2, or very nearly so. In classical music from Western culture, a fifth is the interval from the first to the last of the first five consecutive notes in a diatonic scale. The perfect fifth (often abbreviated P5) spans seven semitones, while the diminished fifth spans six and the augmented fifth spans eight semitones. For example, the interval from C to G is a perfect fifth, as the note G lies seven semitones above C.

Consonance and dissonance

In music, consonance and dissonance are categorizations of simultaneous or successive sounds. Within the Western tradition, some listeners associate consonance with sweetness, pleasantness, and acceptability, and dissonance with harshness, unpleasantness, or unacceptability, although there is broad acknowledgement that this depends also on familiarity and musical expertise. The terms form a structural dichotomy in which they define each other by mutual exclusion: a consonance is what is not dissonant, and a dissonance is what is not consonant.

Harmonic Mean: Music Proportions

Explores the harmonic mean in music proportions and its historical significance in architecture.

Symmetry in Modern Space

Explores the classification and practical applications of symmetries in 3D space, emphasizing user-driven determination of object symmetries.

Geometric Means: Ancient Theories and Modern Applications

Delves into ancient geometric means and their modern applications in geometry.

Rafik Chaabouni, Helger Lipmaa

We show how to express an arbitrary integer interval $I = [0, H]$ as a sumset $I = \sum_{i=1}^\ell G_i * [0, u - 1] + [0, H']$ of smaller integer intervals for some small values $\ell$, $u$, and $H' < u - 1$, where $b * A = \{b a : a \in A\}$ and $A + B = ...