Interval (music)

In music theory, an interval is a difference in pitch between two sounds.
An interval may be described as horizontal, linear, or melodic if it refers to successively sounding tones, such as two adjacent pitches in a melody, and vertical or harmonic if it pertains to simultaneously sounding tones, such as in a chord.
In Western music, intervals are most commonly differences between notes of a diatonic scale. The smallest of these intervals is a semitone. Intervals smaller than a semitone are called microtones. They can be formed using the notes of various kinds of non-diatonic scales. Some of the very smallest ones are called commas, and describe small discrepancies, observed in some tuning systems, between enharmonically equivalent notes such as C and D. Intervals can be arbitrarily small, and even imperceptible to the human ear.
In physical terms, an interval is the ratio between two sonic frequencies. For example, any two notes an octave apart have a frequency ratio of 2:1. This means that successive increments of pitch by the same interval result in an exponential increase of frequency, even though the human ear perceives this as a linear increase in pitch. For this reason, intervals are often measured in cents, a unit derived from the logarithm of the frequency ratio.
In Western music theory, the most common naming scheme for intervals describes two properties of the interval: the quality (perfect, major, minor, augmented, diminished) and number (unison, second, third, etc.). Examples include the minor third or perfect fifth. These names identify not only the difference in semitones between the upper and lower notes but also how the interval is spelled. The importance of spelling stems from the historical practice of differentiating the frequency ratios of enharmonic intervals such as G–G and G–A.
Size.
The size of an interval (also known as its width or height) can be represented using two alternative and equivalently valid methods, each appropriate to a different context: frequency ratios or cents.
Frequency ratios.
The size of an interval between two notes may be measured by the ratio of their frequencies. When a musical instrument is tuned using a just intonation tuning system, the size of the main intervals can be expressed by small-integer ratios, such as 1:1 (unison), 2:1 (octave), 5:3 (major sixth), 3:2 (perfect fifth), 4:3 (perfect fourth), 5:4 (major third), 6:5 (minor third). Intervals with small-integer ratios are often called "just intervals", or "pure intervals".
Most commonly, however, musical instruments are nowadays tuned using a different tuning system, called 12-tone equal temperament. As a consequence, the size of most equal-tempered intervals cannot be expressed by small-integer ratios, although it is very close to the size of the corresponding just intervals. For instance, an equal-tempered fifth has a frequency ratio of 2:1, approximately equal to 1.498:1, or 2.997:2 (very close to 3:2). For a comparison between the size of intervals in different tuning systems, see .
Cents.
The standard system for comparing interval sizes is with cents. The cent is a logarithmic unit of measurement. If frequency is expressed in a logarithmic scale, and along that scale the distance between a given frequency and its double (also called octave) is divided into 1200 equal parts, each of these parts is one cent. In twelve-tone equal temperament (12-TET), a tuning system in which all semitones have the same size, the size of one semitone is exactly 100 cents. Hence, in 12-TET the cent can be also defined as one hundredth of a semitone.
Mathematically, the size in cents of the interval from frequency "f"1 to frequency "f"2 is
Main intervals.
The table shows the most widely used conventional names for the intervals between the notes of a chromatic scale. A perfect unison (also known as perfect prime) is an interval formed by two identical notes. Its size is zero cents. A semitone is any interval between two adjacent notes in a chromatic scale, a whole tone is an interval spanning two semitones (for example, a major second), and a tritone is an interval spanning three tones, or six semitones (for example, an augmented fourth). Rarely, the term ditone is also used to indicate an interval spanning two whole tones (for example, a major third), or more strictly as a synonym of major third.
Intervals with different names may span the same number of semitones, and may even have the same width. For instance, the interval from D to F is a major third, while that from D to G is a diminished fourth. However, they both span 4 semitones. If the instrument is tuned so that the 12 notes of the chromatic scale are equally spaced (as in equal temperament), these intervals also have the same width. Namely, all semitones have a width of 100 cents, and all intervals spanning 4 semitones are 400 cents wide.
The names listed here cannot be determined by counting semitones alone. The rules to determine them are explained below. Other names, determined with different naming conventions, are listed in a separate section. Intervals smaller than one semitone (commas or microtones) and larger than one octave (compound intervals) are introduced below.
Interval number and quality.
In Western music theory, an interval is named according to its "number" (also called "diatonic number") and "quality". For instance, "major third" (or M3) is an interval name, in which the term "major" (M) describes the quality of the interval, and "third" (3) indicates its number.
Number.
The number of an interval is the number of letter names or staff positions (lines and spaces) it encompasses, including the positions of both notes forming the interval. For instance, the interval C–G is a fifth (denoted P5) because the notes from C to the G above it encompass five letter names (C, D, E, F, G) and occupy five consecutive staff positions, including the positions of C and G. The table and the figure above show intervals with numbers ranging from 1 (e.g., P1) to 8 (e.g., P8). Intervals with larger numbers are called compound intervals.
There is a one-to-one correspondence between staff positions and diatonic-scale degrees (the notes of diatonic scale).
This means that interval numbers can be also determined by counting diatonic scale degrees, rather than staff positions, provided that the two notes that form the interval are drawn from a diatonic scale. Namely, C–G is a fifth because in any diatonic scale that contains C and G, the sequence from C to G includes five notes. For instance, in the A-major diatonic scale, the five notes are C–D–E–F–G (see figure). This is not true for all kinds of scales. For instance, in a chromatic scale, the notes from C to G are eight (C–C–D–D–E–F–F–G). This is the reason interval numbers are also called "diatonic numbers", and this convention is called "diatonic numbering".
If one adds any accidentals to the notes that form an interval, by definition the notes do not change their staff positions. As a consequence, any interval has the same interval number as the corresponding natural interval, formed by the same notes without accidentals. For instance, the intervals C–G (spanning 8 semitones) and C–G (spanning 6 semitones) are fifths, like the corresponding natural interval C–G (7 semitones).
Notice that interval numbers represent an inclusive count of encompassed staff positions or note names, not the difference between the endpoints. In other words, one starts counting the lower pitch as one, not zero. For that reason, the interval C–C, a perfect unison, is called a prime (meaning "1"), even though there is no difference between the endpoints. Continuing, the interval C–D is a second, but D is only one staff position, or diatonic-scale degree, above C. Similarly, C–E is a third, but E is only two staff positions above C, and so on. As a consequence, joining two intervals always yields an interval number one less than their sum. For instance, the intervals C–E and E–G are thirds, but joined together they form a fifth (C–G), not a sixth. Similarly, a stack of three thirds, such as C–E, E–G, and G–B, is a seventh (C–B), not a ninth.
This scheme applies to intervals up to an octave (12 semitones). For larger intervals, see below.
Quality.
The name of any interval is further qualified using the terms perfect (P), major (M), minor (m), augmented (A), and diminished (d). This is called its "interval quality". It is possible to have doubly diminished and doubly augmented intervals, but these are quite rare, as they occur only in chromatic contexts. The quality of a compound interval is the quality of the simple interval on which it is based.
Perfect.
Perfect intervals are so-called because they were traditionally considered perfectly consonant,
although in Western classical music the perfect fourth was sometimes regarded as a less than perfect consonance, when its function was contrapuntal. Conversely, minor, major, augmented or diminished intervals are typically considered less consonant, and were traditionally classified as mediocre consonances, imperfect consonances, or dissonances.
Within a diatonic scale all unisons (P1) and octaves (P8) are perfect. Most fourths and fifths are also perfect (P4 and P5), with five and seven semitones respectively. One occurrence of a fourth is augmented (A4) and one fifth is diminished (d5), both spanning six semitones. For instance, in a C-major scale, the A4 is between F and B, and the d5 is between B and F (see table).
By definition, the inversion of a perfect interval is also perfect. Since the inversion does not change the pitch class of the two notes, it hardly affects their level of consonance (matching of their harmonics). Conversely, other kinds of intervals have the opposite quality with respect to their inversion. The inversion of a major interval is a minor interval, the inversion of an augmented interval is a diminished interval.
Major and minor.
As shown in the table, a diatonic scale defines seven intervals for each interval number, each starting from a different note (seven unisons, seven seconds, etc.). The intervals formed by the notes of a diatonic scale are called diatonic. Except for unisons and octaves, the diatonic intervals with a given interval number always occur in two sizes, which differ by one semitone. For example, six of the fifths span seven semitones. The other one spans six semitones. Four of the thirds span three semitones, the others four. If one of the two versions is a perfect interval, the other is called either diminished (i.e. narrowed by one semitone) or augmented (i.e. widened by one semitone). Otherwise, the larger version is called major, the smaller one minor. For instance, since a 7-semitone fifth is a perfect interval (P5), the 6-semitone fifth is called "diminished fifth" (d5). Conversely, since neither kind of third is perfect, the larger one is called "major third" (M3), the smaller one "minor third" (m3).
Within a diatonic scale, unisons and octaves are always qualified as perfect, fourths as either perfect or augmented, fifths as perfect or diminished, and all the other intervals (seconds, thirds, sixths, sevenths) as major or minor.
Augmented and diminished.
Augmented intervals are wider by one semitone than perfect or major intervals, while having the same interval number (i.e., encompassing the same number of staff positions). Diminished intervals, on the other hand, are narrower by one semitone than perfect or minor intervals of the same interval number. For instance, an augmented third such as C–E spans five semitones, exceeding a major third (C–E) by one semitone, while a diminished third such as C–E spans two semitones, falling short of a minor third (C–E) by one semitone.
The augmented fourth (A4) and the diminished fifth (d5) are the only augmented and diminished intervals that appear in diatonic scales (see table).
Example.
Neither the number, nor the quality of an interval can be determined by counting semitones alone. As explained above, the number of staff positions must be taken into account as well.
For example, as shown in the table below, there are four semitones between A and B, between A and C, between A and D, and between A and E, but
Shorthand notation.
Intervals are often abbreviated with a P for perfect, m for minor, M for major, d for diminished, A for augmented, followed by the interval number. The indications M and P are often omitted. The octave is P8, and a unison is usually referred to simply as "a unison" but can be labeled P1. The tritone, an augmented fourth or diminished fifth is often TT. The interval qualities may be also abbreviated with perf, min, maj, dim, aug. Examples:
Inversion.
A simple interval (i.e., an interval smaller than or equal to an octave) may be inverted by raising the lower pitch an octave or lowering the upper pitch an octave. For example, the fourth from a lower C to a higher F may be inverted to make a fifth, from a lower F to a higher C.
\override Score.TimeSignature
\override Score.SpacingSpanner.strict-note-spacing = ##t
\set Score.proportionalNotationDuration = #(ly:make-moment 1/4)
\new Staff «
 \clef treble \time 4/4
 \new Voice \relative c' {
 \stemUp c2 c' c, c' c, c' c, c'
 \new Voice \relative c' {
 \stemDown c2 c d d e e f f
</score>
There are two rules to determine the number and quality of the inversion of any simple interval:
For example, the interval from C to the E above it is a minor third. By the two rules just given, the interval from E to the C above it must be a major sixth.
Since compound intervals are larger than an octave, "the inversion of any compound interval is always the same as the inversion of the simple interval from which it is compounded."
For intervals identified by their ratio, the inversion is determined by reversing the ratio and multiplying the ratio by 2 until it is greater than 1. For example, the inversion of a 5:4 ratio is an 8:5 ratio.
For intervals identified by an integer number of semitones, the inversion is obtained by subtracting that number from 12.
Since an interval class is the lower number selected among the interval integer and its inversion, interval classes cannot be inverted.
Classification.
Intervals can be described, classified, or compared with each other according to various criteria.
Melodic and harmonic.
An interval can be described as
Diatonic and chromatic.
In general,
The table above depicts the 56 diatonic intervals formed by the notes of the C major scale (a diatonic scale). Notice that these intervals, as well as any other diatonic interval, can be also formed by the notes of a chromatic scale.
The distinction between diatonic and chromatic intervals is controversial, as it is based on the definition of diatonic scale, which is variable in the literature. For example, the interval B–E (a diminished fourth, occurring in the harmonic C-minor scale) is considered diatonic if the harmonic minor scales are considered diatonic as well. Otherwise, it is considered chromatic. For further details, see the main article.
By a commonly used definition of diatonic scale (which excludes the harmonic minor and melodic minor scales), all perfect, major and minor intervals are diatonic. Conversely, no augmented or diminished interval is diatonic, except for the augmented fourth and diminished fifth.
The distinction between diatonic and chromatic intervals may be also sensitive to context. The above-mentioned 56 intervals formed by the C-major scale are sometimes called "diatonic to C major". All other intervals are called "chromatic to C major". For instance, the perfect fifth A–E is chromatic to C major, because A and E are not contained in the C major scale. However, it is diatonic to others, such as the A major scale.
Consonant and dissonant.
Consonance and dissonance are relative terms that refer to the stability, or state of repose, of particular musical effects. Dissonant intervals are those that cause tension and desire to be "resolved" to consonant intervals.
These terms are relative to the usage of different compositional styles.
All of the above analyses refer to vertical (simultaneous) intervals.
Simple and compound.
A simple interval is an interval spanning at most one octave (see Main intervals above). Intervals spanning more than one octave are called compound intervals, as they can be obtained by adding one or more octaves to a simple interval (see below for details).
Steps and skips.
Linear (melodic) intervals may be described as "steps" or "skips". A "step", or "conjunct motion",
is a linear interval between two consecutive notes of a scale. Any larger interval is called a "skip" (also called a "leap"), or "disjunct motion". In the diatonic scale, a step is either a minor second (sometimes also called "half step") or major second (sometimes also called "whole step"), with all intervals of a minor third or larger being skips.
For example, C to D (major second) is a step, whereas C to E (major third) is a skip.
More generally, a step is a smaller or narrower interval in a musical line, and a skip is a wider or larger interval, where the categorization of intervals into steps and skips is determined by the tuning system and the pitch space used.
Melodic motion in which the interval between any two consecutive pitches is no more than a step, or, less strictly, where skips are rare, is called "stepwise" or "conjunct" melodic motion, as opposed to "skipwise" or "disjunct" melodic motions, characterized by frequent skips.
Enharmonic intervals.
Two intervals are considered "enharmonic", or "enharmonically equivalent", if they both contain the same pitches spelled in different ways; that is, if the notes in the two intervals are themselves enharmonically equivalent. Enharmonic intervals span the same number of semitones.
For example, the four intervals listed in the table below are all enharmonically equivalent, because the notes F and G indicate the same pitch, and the same is true for A and B. All these intervals span four semitones.
When played as isolated chords on a piano keyboard, these intervals are indistinguishable to the ear, because they are all played with the same two keys. However, in a musical context, the diatonic function of the notes these intervals incorporate is very different.
The discussion above assumes the use of the prevalent tuning system, 12-tone equal temperament ("12-TET"). But in other historic meantone temperaments, the pitches of pairs of notes such as F and G may not necessarily coincide. These two notes are enharmonic in 12-TET, but may not be so in another tuning system. In such cases, the intervals they form would also not be enharmonic. For example, in quarter-comma meantone, all four intervals shown in the example above would be different.
Minute intervals.
There are also a number of minute intervals not found in the chromatic scale or labeled with a diatonic function, which have names of their own. They may be described as microtones, and some of them can be also classified as commas, as they describe small discrepancies, observed in some tuning systems, between enharmonically equivalent notes. In the following list, the interval sizes in cents are approximate.
Compound intervals.
A compound interval is an interval spanning more than one octave. Conversely, intervals spanning at most one octave are called simple intervals (see Main intervals below).
In general, a compound interval may be defined by a sequence or "stack" of two or more simple intervals of any kind. For instance, a major tenth (two staff positions above one octave), also called "compound major third", spans one octave plus one major third.
Any compound interval can be always decomposed into one or more octaves plus one simple interval. For instance, a major seventeenth can be decomposed into two octaves and one major third, and this is the reason why it is called a compound major third, even when it is built by adding up four fifths.
The diatonic number "DN"c of a compound interval formed from "n" simple intervals with diatonic numbers "DN"1, "DN"2, ..., "DN"n, is determined by:
which can also be written as:
The quality of a compound interval is determined by the quality of the simple interval on which it is based. For instance, a compound major third is a major tenth (1+(8−1)+(3−1) = 10), or a major seventeenth (1+(8−1)+(8−1)+(3−1) = 17), and a compound perfect fifth is a perfect twelfth (1+(8−1)+(5−1) = 12) or a perfect nineteenth (1+(8−1)+(8−1)+(5−1) = 19). Notice that two octaves are a fifteenth, not a sixteenth (1+(8−1)+(8−1) = 15). Similarly, three octaves are a twenty-second (1+3×(8−1) = 22), and so on.
Main compound intervals.
It is also worth mentioning here the major seventeenth (28 semitones)—an interval larger than two octaves that can be considered a multiple of a perfect fifth (7 semitones) as it can be decomposed into four perfect fifths (7 × 4 = 28 semitones), or two octaves plus a major third (12 + 12 + 4 = 28 semitones). Intervals larger than a major seventeenth seldom come up, most often being referred to by their compound names, for example "two octaves plus a fifth" rather than "a 19th".
Intervals in chords.
Chords are sets of three or more notes. They are typically defined as the combination of intervals starting from a common note called the root of the chord. For instance a major triad is a chord containing three notes defined by the root and two intervals (major third and perfect fifth). Sometimes even a single interval (dyad) is considered a chord. Chords are classified based on the quality and number of the intervals that define them.
Chord qualities and interval qualities.
The main chord qualities are major, minor, augmented, diminished, half-diminished, and dominant.
The symbols used for chord quality are similar to those used for interval quality (see above). In addition, + or aug is used for augmented, ° or dim for diminished, for half diminished, and dom for dominant (the symbol − alone is not used for diminished).
Deducing component intervals from chord names and symbols.
The main rules to decode chord "names or symbols" are summarized below. Further details are given at Rules to decode chord names and symbols.
The table shows the intervals contained in some of the main chords (component intervals), and some of the symbols used to denote them. The interval qualities or numbers in boldface font can be deduced from chord name or symbol by applying rule 1. In symbol examples, C is used as chord root.
Size of intervals used in different tuning systems.
In this table, the interval widths used in four different tuning systems are compared. To facilitate comparison, just intervals as provided by 5-limit tuning (see symmetric scale n.1) are shown in bold font, and the values in cents are rounded to integers. Notice that in each of the non-equal tuning systems, by definition the width of "each" type of interval (including the semitone) changes depending on the note that starts the interval. This is the art of just intonation. In equal temperament, the intervals are never precisely in tune with each other. This is the price of using equidistant intervals in a 12-tone scale. For simplicity, for some types of interval the table shows only one value (the most often observed one).
In -comma meantone, by definition 11 perfect fifths have a size of approximately 697 cents (700 − "ε" cents, where "ε" ≈ 3.42 cents); since the average size of the 12 fifths must equal exactly 700 cents (as in equal temperament), the other one must have a size of about 738 cents (700 + 11"ε", the wolf fifth or diminished sixth); 8 major thirds have size about 386 cents (400 − 4"ε"), 4 have size about 427 cents (400 + 8"ε", actually diminished fourths), and their average size is 400 cents. In short, similar differences in width are observed for all interval types, except for unisons and octaves, and they are all multiples of ε (the difference between the -comma meantone fifth and the average fifth). A more detailed analysis is provided at -comma meantone Size of intervals. Note that -comma meantone was designed to produce just major thirds, but only 8 of them are just (5:4, about 386 cents).
The Pythagorean tuning is characterized by smaller differences because they are multiples of a smaller "ε" ("ε" ≈ 1.96 cents, the difference between the Pythagorean fifth and the average fifth). Notice that here the fifth is wider than 700 cents, while in most meantone temperaments, including -comma meantone, it is tempered to a size smaller than 700. A more detailed analysis is provided at Pythagorean tuning#Size of intervals.
The 5-limit tuning system uses just tones and semitones as building blocks, rather than a stack of perfect fifths, and this leads to even more varied intervals throughout the scale (each kind of interval has three or four different sizes). A more detailed analysis is provided at 5-limit tuning#Size of intervals. Note that 5-limit tuning was designed to maximize the number of just intervals, but even in this system some intervals are not just (e.g., 3 fifths, 5 major thirds and 6 minor thirds are not just; also, 3 major and 3 minor thirds are wolf intervals).
The above-mentioned symmetric scale 1, defined in the 5-limit tuning system, is not the only method to obtain just intonation. It is possible to construct juster intervals or just intervals closer to the equal-tempered equivalents, but most of the ones listed above have been used historically in equivalent contexts. In particular, the asymmetric version of the 5-limit tuning scale provides a juster value for the minor seventh (9:5, rather than 16:9). Moreover, the tritone (augmented fourth or diminished fifth), could have other just ratios; for instance, 7:5 (about 583 cents) or 17:12 (about 603 cents) are possible alternatives for the augmented fourth (the latter is fairly common, as it is closer to the equal-tempered value of 600 cents). The 7:4 interval (about 969 cents), also known as the harmonic seventh, has been a contentious issue throughout the history of music theory; it is 31 cents flatter than an equal-tempered minor seventh. For further details about reference ratios, see 5-limit tuning#The justest ratios.
In the diatonic system, every interval has one or more "enharmonic equivalents", such as augmented second for minor third.
Interval root.
Although intervals are usually designated in relation to their lower note, David Cope and Hindemith both suggest the concept of interval root. To determine an interval's root, one locates its nearest approximation in the harmonic series. The root of a perfect fourth, then, is its "top" note because it is an octave of the fundamental in the hypothetical harmonic series. The bottom note of every odd diatonically numbered intervals are the roots, as are the tops of all even numbered intervals. The root of a collection of intervals or a chord is thus determined by the interval root of its strongest interval.
As to its usefulness, Cope provides the example of the final tonic chord of some popular music being traditionally analyzable as a "submediant six-five chord" (added sixth chords by popular terminology), or a first inversion seventh chord (possibly the dominant of the mediant V/iii). According to the interval root of the strongest interval of the chord (in first inversion, CEGA), the perfect fifth (C–G), is the bottom C, the tonic.
Interval cycles.
Interval cycles, "unfold [i.e., repeat] a single recurrent interval in a series that closes with a return to the initial pitch class", and are notated by George Perle using the letter "C", for cycle, with an interval-class integer to distinguish the interval. Thus the diminished-seventh chord would be C3 and the augmented triad would be C4. A superscript may be added to distinguish between transpositions, using 0–11 to indicate the lowest pitch class in the cycle.
Alternative interval naming conventions.
As shown below, some of the above-mentioned intervals have alternative names, and some of them take a specific alternative name in Pythagorean tuning, five-limit tuning, or meantone temperament tuning systems such as quarter-comma meantone. All the intervals with prefix "sesqui-" are justly tuned, and their frequency ratio, shown in the table, is a superparticular number (or epimoric ratio). The same is true for the octave.
Typically, a comma is a diminished second, but this is not always true (for more details, see Alternative definitions of comma). For instance, in Pythagorean tuning the diminished second is a descending interval (524288:531441, or about −23.5 cents), and the Pythagorean comma is its opposite (531441:524288, or about 23.5 cents). 5-limit tuning defines four kinds of comma, three of which meet the definition of diminished second, and hence are listed in the table below. The fourth one, called syntonic comma (81:80) can neither be regarded as a diminished second, nor as its opposite. See Diminished seconds in 5-limit tuning for further details.
Additionally, some cultures around the world have their own names for intervals found in their music. For instance, 22 kinds of intervals, called shrutis, are canonically defined in Indian classical music.
Latin nomenclature.
Up to the end of the 18th century, Latin was used as an official language throughout Europe for scientific and music textbooks. In music, many English terms are derived from Latin. For instance, semitone is from Latin "".
The prefix semi- is typically used herein to mean "shorter", rather than "half". Namely, a semitonus, semiditonus, semidiatessaron, semidiapente, semihexachordum, semiheptachordum, or semidiapason, is shorter by one semitone than the corresponding whole interval. For instance, a semiditonus (3 semitones, or about 300 cents) is not half of a ditonus (4 semitones, or about 400 cents), but a ditonus shortened by one semitone. Moreover, in Pythagorean tuning (the most commonly used tuning system up to the 16th century), a semitritonus (d5) is smaller than a tritonus (A4) by one Pythagorean comma (about a quarter of a semitone).
Pitch-class intervals.
In post-tonal or atonal theory, originally developed for equal-tempered European classical music written using the twelve-tone technique or serialism, integer notation is often used, most prominently in musical set theory. In this system, intervals are named according to the number of half steps, from 0 to 11, the largest interval class being 6.
In atonal or musical set theory, there are numerous types of intervals, the first being the ordered pitch interval, the distance between two pitches upward or downward. For instance, the interval from C upward to G is 7, and the interval from G downward to C is −7. One can also measure the distance between two pitches without taking into account direction with the unordered pitch interval, somewhat similar to the interval of tonal theory.
The interval between pitch classes may be measured with ordered and unordered pitch-class intervals. The ordered one, also called directed interval, may be considered the measure upwards, which, since we are dealing with pitch classes, depends on whichever pitch is chosen as 0. For unordered pitch-class intervals, see interval class.
Generic and specific intervals.
In diatonic set theory, specific and generic intervals are distinguished. Specific intervals are the interval class or number of semitones between scale steps or collection members, and generic intervals are the number of diatonic scale steps (or staff positions) between notes of a collection or scale.
Notice that staff positions, when used to determine the conventional interval number (second, third, fourth, etc.), are counted including the position of the lower note of the interval, while generic interval numbers are counted excluding that position. Thus, generic interval numbers are smaller by 1, with respect to the conventional interval numbers.
Generalizations and non-pitch uses.
The term "interval" can also be generalized to other music elements besides pitch. David Lewin's "Generalized Musical Intervals and Transformations" uses interval as a generic measure of distance between time points, timbres, or more abstract musical phenomena.
For example, an interval between two bell-like sounds, which have no pitch salience, is still perceptible. When two tones have similar acoustic spectra (sets of partials), the interval is just the distance of the shift of a tone spectrum along the frequency axis, so linking to pitches as reference points is not necessary. The same principle naturally applies to pitched tones (with similar harmonic spectra), which means that intervals can be perceived "directly" without pitch recognition. This explains in particular the predominance of interval hearing over absolute pitch hearing.


5344 Ryabov


3DMark

3DMark is a computer benchmarking tool created and developed by UL, (formerly Futuremark), to determine the performance of a computer's 3D graphic rendering and CPU workload processing capabilities. Running 3DMark produces a 3DMark score, with higher numbers indicating better performance. The 3DMark measurement unit is intended to give a normalized mean for comparing different PC hardware configurations (mostly graphics processing units and central processing units), which proponents such as gamers and overclocking enthusiasts assert is indicative of end-user performance capabilities.
Many versions of 3DMark have been released since 1998. Scores cannot be compared across versions as each test is based on a specific version of the DirectX API.


3886 Shcherbakovia


Alert Ready

The National Public Alerting System (), branded as Alert Ready (), is the national warning system in Canada. The system consists of infrastructure and standards for the presentation and distribution of public alerts issued by government authorities (including Environment and Climate Change Canada and other provincial public safety agencies), such as weather emergencies, AMBER Alerts, and other emergency notifications, by all broadcasters and last mile distributors in the affected region, including television stations, radio stations, television providers, and mobile networks in the affected region.
The system is based upon the Common Alerting Protocol (CAP), while wireless alerts (Wireless Public Alerting System) use a Canadian variant of the Wireless Emergency Alerts standard adopted in the United States. Alert Ready officially launched on March 31, 2015; under Canadian Radio-television and Telecommunications Commission (CRTC) orders, all terrestrial radio and television broadcasters, digital multichannel television providers are required to relay emergency messages issued through NAAD. Wireless providers were required to implement the system in April 2018. Pelmorex Media (owner of The Weather Network) operates its backend — the "National Alert Aggregation and Dissemination" (NAAD) system — which distributes alerts to broadcasters and other parties. Pelmorex is also responsible for public marketing of the system.
Alert Ready has faced criticism, particularly due to wireless alerts being handled under a blanket category with no opt-outs (as opposed to the severity-based system used by the U.S. WEA system), and criticism over AMBER Alerts (particularly in Ontario) being issued province-wide rather than geographically targeted to relevant regions. In April 2020, the RCMP faced criticism for not cooperating with local officials in use of the system to warn of an active gunman, which had attacked multiple locations in the province of Nova Scotia.
Environment and Climate Change Canada also maintains Weatheradio Canada, which transmits weather information and hazard alerts. Unlike Alert Ready, it utilizes Specific Area Message Encoding (SAME)—the same protocol used by NOAA Weather Radio and the Emergency Alert System in the United States.
History.
Proposals.
Various attempts had been made in the 21st century to establish a public alert system in Canada, by both departments of government and by television broadcasters. In 2001, Pelmorex, owners of The Weather Network and its French language counterpart MétéoMédia, applied to the CRTC for an amendment to their licenses to encompass a mandatory "All Channel Alert" system, requiring all television providers to relay emergency messages on behalf of governments across all of their channels. The service would have used proprietary hardware developed by Pelmorex, and would have been funded primarily by a $0.13 increase in carriage fees for the two channels. However, its initial proposal was denied by the CRTC, citing the need for consultation with broadcasters, television providers, and other parties on how the system would be designed, along with its costs. There were also concerns over the means in which the system was to be implemented technologically, and that the system was not inclusive to the visually impaired because Pelmorex only specified use of a text crawl, without an audio component.
Establishment of such a system in a voluntary form was hampered by CRTC rules at the time, which required television providers to obtain consent from broadcasters before they could overlay emergency notifications onto their programming. In 2005, CRTC called for proposals regarding a national alerting system; Pelmorex and the Canadian Broadcasting Corporation submitted proposals for a national system, while Bell ExpressVu submitted a proposal requesting the removal of the consent requirement. The CBC's proposal would have fed alerts via satellite to decoders installed at local CBC Radio transmitters. It would have allowed television providers to participate on a voluntary basis by installing decoders of their own, if the aforementioned consent requirement were removed. All three applicants promised to adopt the standardized alerting specifications that were developed by the government-backed CANALERT initiative.
While broadcasters and governments supported the proposals for a national alerting system, CTV, Canwest Global and CHUM Limited showed concerns surrounding the Pelmorex proposal, as it would be operated by a for-profit venture that would have the power to override their signals with third-party content, and be redundant to alerts already provided as a public service by some broadcasters. Shaw and Rogers argued that the Pelmorex system was less cost-efficient than the CBC's proposal. It was also disputed whether the CRTC could even order the mandatory distribution of the service, as the CRTC does not regulate alphanumeric content because it is not considered television programming. In 2007, the CRTC removed the consent requirement to ease the adoption of voluntary alerting by broadcast distribution undertakings, but stated that it would reconsider the possibility of a mandatory alert system in the future.
Development.
In 2009, the CRTC approved a proposal by Pelmorex to grant must-carry status to The Weather Network and MétéoMédia on digital television services. As part of the proposal, Pelmorex committed to developing a "national aggregator and distributor" (NAAD) of localized emergency alert messages compliant with the Common Alerting Protocol. Pelmorex established a governance council for the system, including representatives of the broadcasting industry, federal government, members of the Senior Officials Responsible for Emergency Management (SOREM), and the Canadian Association for Public Alerting and Notification, to oversee its operations. NAAD would become operational in 2010.
In a 2011 renewal of the must-carry status, the CRTC praised Pelmorex's work, considering the NAAD system to be "an essential element of a national public alerting system", and expressed an expectation for all broadcasters to voluntarily participate in distributing its alerts. However, as a condition of the renewal, the CRTC ordered Pelmorex to reach agreements with all federal, provincial and territorial emergency management officials to allow them to transmit messages through the system, implement the capability of processing "broadcast intrusive alerts" through the system, and develop a public awareness campaign surrounding the alert system with a budget of at least $1 million per-year. In June of the same year, the province of Alberta launched a new alerting system of its own, Alberta Emergency Alert, which distributes alerts on radio and television, as well as online and via social networking services. This replaced the previous Emergency Public Warning System which had been used since 1992.
Environment Canada, the Canadian Council of Emergency Management Organizations, and the provinces of Manitoba and New Brunswick endorsed the potential use of the NAAD framework as a backend for a mandatory public alerting system. On May 26, 2013, SOREM published a "Common Look and Feel" specification for alerts. Developed with guidance from the broadcasting industry, it describes how and when alerts are to be distributed and presented to the public. As part of a license renewal in May 2013, CBC Radio agreed to implement an alerting system using NAAD by December 31, 2014.
On February 27, 2014, the CRTC issued a proposal to mandate participation in the national alert system by all broadcasters. The commission felt that owing to the importance of the endeavour, broadcasters had displayed an inconsistent level of commitment to implement it voluntarily.
Launch.
On August 29, 2014, the CRTC ruled that all Canadian broadcasters, including over-the-air television broadcasters, radio broadcasters, and broadcast distribution undertakings, must begin participating in the National Public Alerting System by March 31, 2015. Community, campus, and aboriginal broadcasters were given an extended deadline of March 31, 2016 to implement the system. The National Public Alerting System was launched on March 31, 2015 under the public-facing brand Alert Ready (French: En Alerte).
Bell Satellite TV, MTS, Shaw Direct, and Sogetel do not fully participate in the system, as some of their customers utilize legacy set-top boxes that cannot be updated to support the display of public alerts. They were granted a six-month extension for the implementation deadline by the CRTC in order to address these issues, under the condition that they inform customers that they cannot receive public alerts unless they update their hardware, and must present bi-weekly progress reports to the CRTC. CRTC chairman Jean-Pierre Blais criticized the providers for their inability to properly implement the system, stating that the commission "will not hide our disappointment that certain television service providers are not ready, despite having been given more than enough time [to implement it.]"
In December 2015, the CRTC granted an indefinite extension of the exceptions and reporting guidelines to Bell, Shaw Direct, and MTS until they completely phase out hardware that is not compatible with the NPAS. The CRTC felt that the providers had made a good-faith effort in informing customers of their inability to receive public alerts and offering hardware replacements. Bell reported that some customers had declined their offering of a free set-top box replacement as they did not want to participate in receiving alerts. MTS discontinued its legacy "Classic TV" service due to its inability to display alerts, and provided incentives for its remaining customers to upgrade to its current "Ultimate TV" service.
Provincial tests began to improve public awareness of the new system, such as in Manitoba, and Quebec. One of the tests in the province on May 19, 2015, simulating a tornado emergency in the Centre-du-Québec region, surprised many people tuned in to radio or TV in the region, leading some to believe that there was an actual tornado emergency.
Mobile alerting.
On April 6, 2017, the CRTC required all wireless carriers in Canada to begin relaying public alerts over their LTE and post-LTE wireless networks by April 6, 2018, using Cell Broadcast-based standards by ATIS similar to the U.S. Wireless Emergency Alerts system, collaborating with the SOREM Common Look and Feel guidelines. The CRTC required at least half of devices offered by wireless carriers to support wireless public alerts (including at least one device available at no-charge on-contract, and one "accessible" device) by the implementation date. As of April 2019, all devices sold by wireless carriers must support wireless public alerts. The mandate does not apply to networks older than LTE; the CRTC chose to exclude older network technologies (such as 3G) from the mandate, citing wide deployment of LTE networks across the country, and that government funding has been used to support its deployment in underserved areas.
On January 29, 2018, the CRTC informed the Standing Senate Committee on National Security and Defence of concerns surrounding the possibility of false positives (such as a false missile alert in Hawaii earlier that month), and ensuring that the industry meets its goal of at least 50% of devices being capable of receiving mobile alerts by that date.
Operation.
Alert Ready alerts are broadcast to last-mile distributors using the Anik F1R satellite over C-band on virtual channel 206 (with virtual channel 550 as a backup), and prior to September 1, 2019, using the Anik F2 satellite over Ku-band. The Ku-band signals were terminated August 31, 2019 after consultation with the Last Mile Distributors determined that it was underutilized and sufficient alternate services exist. Alerts are also distributed over the internet from web servers based in Oakville and Montreal on TCP port 8080. An RSS feed of past alerts is also available.
The presentation of alerts is dictated by the NPAS Common Look and Feel Guidance. Messages are formatted using the Canadian Profile of the Common Alerting Protocol (CAP-CP), and are provided in at least one of Canada's official languages (either English, French, or both, as determined by local policies and laws). Alerts can contain text and audio components, and contain information designating the region that an alert applies to.
Messages marked with "Broadcast Immediately" flags are used to designate alerts that present "an imminent or unexpected threat to life, that alerting officials wish to be distributed and presented to the public as soon as possible, even if it means disrupting the programming of last mile distributors." On television and radio, relevant alerts marked with this flag are immediately presented to viewers when they are received, interrupting programming to facilitate their display. These alerts are prefaced by the Canadian Alerting Attention Signal. The attention signal is an 8-second sequence of alternating half-second duration complex tones, the first being a combination of tones at frequencies of 932.33 Hz, 1046.5 Hz and 3135.96 Hz, and the second at 440 Hz, 659.26 Hz and 3135.96 Hz (the same signal that is used by Alberta Emergency Alert). The attention signal is followed by the audio of the alert where applicable or supported by hardware (in the absence of audio, the alert may be read using a text to speech system, or a generic message played).
The Common Look and Feel Guidance prescribes that, on television, the text of alerts be displayed on either a crawler, or as a full screen notice that covers programming, in white text on a red background in both cases. Crawlers inserted by television channels are positioned at the centre of the screen out of respect for those inserted by broadcast distribution undertakings at the bottom of the screen. The guidelines note that "automated broadcast interruption need not be used if a person can present the text of an audience alert message verbally and visually mindful of the other guidance found in [the guidelines]."
A separate "Wireless Immediately" flag is used to require Cell Broadcast distribution as well. Wireless alerts on devices specifically supporting Cell Broadcast alerts utilize the same attention signal sound and a specific vibration pattern mimicking this sound. The Common Look and Feel Guidance specifies that the phone's software must display these alerts with a capitalized, bilingual heading reading "EMERGENCY ALERT / ALERTE D'URGENCE", and a limit of 600 characters due to device limitations. Devices may not be configured to allow users to opt out of alerts: they are coded using the same priority level as U.S. presidential alerts—the only U.S. category which may not be disabled. If the device's software is primarily designed for the U.S. implementation of WEA, it will typically identify Canadian wireless emergency alerts as a presidential alert.
Mobile apps are available that distribute alerts as push notifications to mobile devices such as smartphones.
Public awareness testing.
Public awareness tests are held twice per-year, in which a 30-second test message (60 seconds in provinces where bilingual messages are issued) is distributed to radio and television outlets, and a Cell Broadcast message is sent to wireless phones. One is held on a Wednesday in May during Public Safety Canada's Emergency Preparedness Week, and the second is held in November.
Initially, four, quarterly tests were scheduled annually, on the third Wednesday of every third month of the year, along with the Emergency Preparedness Week test. After the introduction of wireless alerts in May 2018, however, SOREM quietly ceased all quarterly tests, citing concerns that tests only directed to broadcast media could cause confusion to the public over the effectiveness and correct operation of the extended system. The CRTC supported this position, officially requiring wireless service providers to participate in two public-visible alerts per year, distributed on all platforms.
There is precedent for alert tests to be postponed or cancelled on a regional basis if there is an ongoing threat of an actual emergency in an area, such as for instance, Spring flooding in parts of Ontario and Quebec in May 2019.
Participating agencies.
Alerts distributed by NAAD originate from specially-designated provincial and federal agencies and ministries, such as Environment and Climate Change Canada, and provincial alerting agencies.
As the system was designed primarily to handle domestic situations such as weather, Environment and Climate Change Canada is currently the only federal agency that is capable of issuing alerts. Following the false alarm in Hawaii in January 2018, discussions began on how the possibility of an actual missile attack threat would be handled, and the Canadian Press reported in December 2018 that they were "finalizing" a protocol for the handling of such events.
Reception.
An activation of the system in Manitoba for a tornado spotting led to criticism over the quality of the text-to-speech system used by Manitoba's implementation of the alert system, with viewers reporting a "garbled" message and mispronunciations of community names.
On March 6, 2016, Alert Ready was used to distribute an AMBER Alert in Ontario relating to an alleged kidnapping of a child in Orillia (the child's father was actually picking up the child after they had run from home). Viewers felt that the frequent notifications (especially as it occurred during the U.S. airing of the series finale of "Downton Abbey", seen via PBS stations carried in Canada) with full-screen messages and alarm sounds as being disruptive, in comparison to the previous, voluntary practice of Canadian broadcasters displaying AMBER Alert messages on tickers. At the same time, the move was praised for providing a higher degree of prominence to the alert; Orillia Ontario Provincial Police commander Patrick Morris defended its use, stating that "while I will apologize for any inconvenience this may have caused, we won't apologize for using all of the tools available to us to find a missing child."
"National Post" columnist Matt Gurney provided similar praise, but noted that the system's operation hindered its ability to disseminate information quickly. He explained that while the purpose of such a system is to "[get] information to the public as rapidly and as clearly as possible", on his television provider's set-top box "the text was arriving on my screen incredibly slowly. Several minutes into the alert, we were just starting to get the description of the child and the suspect vehicle. It was embarrassing — when seconds count, the province needed minutes to deliver incredibly basic, utterly crucial facts about the emergency. The contrast between the urgently screeching buzz of the alarm and the text crawling up the screen in ultra-slow motion seemed designed for comedic effect." He also, similarly, noted the poor quality of the text-to-speech systems.
Wireless alerting.
The first public awareness test to include Cell Broadcast transmission occurred in Ontario and Quebec on May 7, 2018, with the remaining provinces following suit on May 9, in observance of Emergency Preparedness Week. In Quebec, a syntax error in the test message's XML file caused the wireless alert to fail, while users in Ontario reported mixed results. Testing in the remaining provinces and territories, excluding Nunavut, occurred May 9, 2018, again to mixed results, with people reporting having not gotten an alert despite their phones meeting the requirements. Though the test was reported to have worked in Nova Scotia and PEI, reports from Alberta, Manitoba, the Northwest Territories, Newfoundland and Labrador, and Saskatchewan saw people failing to get alerts (although the crown telecom SaskTel deemed it a success). Following the first test, Bell Mobility and Telus acknowledged issues preventing receipt of the messages.
In September 2018, Scott Shortliffe, chief consumer officer of the CRTC, acknowledged that the effectiveness of the system was being affected by technical problems, following a province-wide AMBER Alert in North Battleford, Saskatchewan where the wireless cell broadcast was delayed by several hours (as well as complaints by Manitoba residents over the cross-provincial extension of the alert), and mixed reports during tornadoes in the Ottawa-Gatineau region (including some users not receiving any message, and users in Quebec only receiving an English-language message). On October 3, 2018, CRTC Secretary General Claude Doucet issued a letter ordering service providers to participate in another visible all-channel alert test that was being scheduled in November (scheduled for November 28). SOREM also requested that the CRTC mandate biannual tests of wireless alerts rather than just annual.
Criticism emerged following an AMBER Alert in Ontario on May 14, 2018 for a child allegedly kidnapped in Thunder Bay, Ontario—the first to have included mobile alerts. Three different emergency messages were sent, the first contained only English text, but was resent merely a half hour later in order to add a French-language translation, followed by one more alert message stating that the AMBER Alert had been cancelled, and the child found safe. Criticism was directed primarily towards the intrusive presentation of the message, and that all AMBER Alerts are sent across the entire province rather than regionalized to only cover a vicinity around the city (the alert was received as far as Toronto, which is at least away from Thunder Bay), and the fact that all wireless alerts are mandatory and cannot be disabled (unlike in the U.S., where AMBER Alerts are one of three categories of alerts users may opt out from, while "Presidential" level alerts are mandatory and may not be disabled). There were concerns that such excessive use could result in alarm fatigue and desensitization to actual local emergencies.
In a 2019 follow-up to his previous criticisms of the system, Gurney noted that several instances of AMBER Alerts issued during the early-morning hours in Ontario had prompted residents to call 9-1-1 to complain. He argued that such alerts were only of immediate relevance to recipients that were awake, attentive, and "out-and-about" (who could be targeted via radio and television rather than cell broadcast), but were being given the same intrusive presentation as alerts for imminent threats to public safety that affect a larger population. Gurney thus argued that in such a situation, those who were not awake could learn the details of the alert in the morning instead. He also acknowledged similar opinions presented by Philip Cross in an editorial for its sister publication, the "Financial Post"; Cross felt that AMBER Alerts on phones should be optional as in the U.S., comparing the disruption of sleep caused by late-night alerts to health effects associated with daylight saving time, and noting that the public would be "more likely to arrive at better solutions if we can discuss the issue sanely, rather than have all complaints dismissed as callous disregard for children's safety." In response to an Ontario AMBER Alert that concluded with the victim found murdered, a "Maclean's" editor had deemed all critics of the system to be "horrible" and expressing entitlement for their refusal to participate in the civic duty of locating a missing child in imminent danger.
In October 2019, a 70-year old resident of Hamilton, Ontario was charged with mischief for disrupting emergency services, after repeatedly calling 9-1-1 to complain about an AMBER Alert broadcast.
False alarms.
On January 12, 2020 at 7:24 a.m. ET, an emergency alert was issued for the entire province of Ontario, advising that an incident had been reported at the Pickering Nuclear Generating Station. The alert stated that "there has been no abnormal release of radioactivity from the station", staff was responding to the situation, and that no immediate protective actions were required. Approximately 40 minutes later, Ontario Power Generation issued a statement on its Twitter account indicating that the alert had been sent in error. At around 9:10 a.m., a second emergency alert message was issued, containing a similar retraction. Solicitor General Sylvia Jones stated that the erroneous alert was the result of a mistake during a "routine training exercise" by Ontario's emergency operations centre.
In its aftermath, Dave Ryan and John Tory—the mayors of Pickering and Toronto, made calls for a full investigation into the incident. MPP and Ontario NDP energy and climate change critic Peter Tabuns also responded, stating that "confidence in the accuracy of the [alert] system is essential for public safety." U.S. media outlets drew comparisons between the incident and the 2018 Hawaii false missile alert (coincidentally, the Pickering incident occurred on the eve of the Hawaii incident's second anniversary).
On February 27, 2020, the results of a formal investigation were published. It found that the alert was triggered by a duty officer of Ontario's emergency operations centre at the beginning of his shift, who had accidentally remained logged into the live alert system when performing a regular internal test. It was considered common practice for officers to log into the live system first to ensure it is functioning before switching to a secondary, internal instance of the system designed specifically for testing purposes. The officer had realized his error, but the alert retracting the previous message was delayed due to an inability to receive clear instructions from Emergency Management Ontario supervisors on how to make an alert broadcast-intrusive, or whether the second alert should have been at all.
Testing errors.
On May 12, 2021, Emergency Management British Columbia accidentally re-issued a test alert that had been used for the biannual provincial test one week prior.
Non-usage during the 2020 Nova Scotia attacks.
The Royal Canadian Mounted Police was criticized following the April 19, 2020 killing spree in Nova Scotia, for not having used the alert system to warn of the active gunman at-large. Premier Stephen McNeil stated that he had not formally received any request for the issuance of an emergency alert, and explained that "I can tell you, I'm not going to second-guess why someone or the organization did what they did or didn't do at this moment in time. This was an active environment, I can tell you. Deaths, gunfire. Let's give them an opportunity as an organization to explain that to you." RCMP Chief Superintendent Chris Leather stated that they had primarily relied on Twitter to issue timely updates on the situation due to its fluidity. However, the areas where the shootings occurred had poor internet access, and a large population of seniors (who may not necessarily be active users of social media).
On April 22, Premier McNeil stated that at 10:15 a.m. AT, provincial emergency management officials had attempted to contact RCMP officials "a number of times" for permission and cooperation in issuing an alert. However, the RCMP did not respond; the suspect was shot and killed by police just over an hour later at 11:26 a.m.
The RCMP does not currently have a national strategy or policy for use of emergency alerts during such situations, but some law enforcement agencies began to express interest in evaluating future use of the system as part of their communications strategies.


CTM Festival

The annual CTM Festival is a music and visual arts event held in Berlin, Germany. Founded in 1999, the festival originally focused on electronic music, but has since evolved to cover a wide range of genres under the banner "Festival for Adventurous Music and Art".
Changing through various shapes and formats over the years, the festival currently takes place as a 10-day long event in which the music program is supplemented by an extensive daytime program of workshops, art installations, panel discussions, screenings and presentations that illustrate the latest artistic, technological and economic developments in music and media cultures.
Distinguishing the festival from many others in its field is the fact that CTM spotlights music’s social role in electronic and digital culture. Through the festival, as well as various events curated by CTM throughout the year, the organization reflects the latest musical currents against a backdrop of new technologies, modern art, historical perspective, and social issues.
Books.
GENDERTRONICS – DER KÖRPER IN DER ELEKTRONISCHEN MUSIK
Edited by CTM and Meike Jansen
When, in the early 50s, electronic music appeared on the scene with the promise of abandoning all physical limits of music-making this was – like much besides – a Promethian male fantasy. Indeed, this music subsequently led to everything but disembodiment. From the psychedelic trances of the 60s and Kraftwerk robotics of the 70s, through to Techno ecstasies, gender-political interventions in the 90s and laptop performance – the questions as to how, from whom, to what ends and in which contexts electronics and the human body might be cable-linked have continually had to be addressed anew.
“Gendertronics” is an in-depth study of questions raised by last year’s festival theme, "Performing Sound", edited by CTM and Meike Jansen and published by Edition Suhrkamp Verlag. With contributions from Olaf Arndt, Claudia Basrawi, Jochen Bonz & Thomas Meinecke, Mariola Brillowska, Kurt Dahlke, Diedrich Diederichsen, Harald Fricke, Tom Holert, Miss Kittin, Pinky Rose, Birgit Richard, Terre Thaemlitz, Marc Weiser and 17 black and white drawings by Jan Rohlf. – In German language only.


276 Adelheid

Adelheid (minor planet designation: 276 Adelheid) is a dark Alauda asteroid from the outer region of the asteroid belt, approximately 121 kilometers in diameter. It was discovered by Austrian astronomer Johann Palisa at Vienna Observatory on 17 April 1888. The meaning of the asteroids's name is unknown.
Classification.
"Adelheid" is a member of the Alauda family (), a large family of typically bright carbonaceous asteroids and named after its parent body, 702 Alauda.
Physical characteristics.
Photometric observations in 1992 gave a lightcurve with a period of 6.328 ± 0.012 hours and a brightness variation of 0.10 ± 0.02 in magnitude. The curve is regular with two maxima and minima.
In the Tholen classification, its spectrum has been characterized as that of an X-type asteroid, while polarimetric observations refined its classification to a primitive P-type.
Naming.
Any reference of this minor planet's name to a person or occurrence is unknown.
Unknown meaning.
Among the many thousands of named minor planets, "Adelheid" is one of 120 asteroids, for which no official naming citation has been published. All of these low-numbered asteroids have numbers between and and were discovered between 1876 and the 1930s, predominantly by astronomers Auguste Charlois, Johann Palisa, Max Wolf and Karl Reinmuth "(also see )".


Karate (software)

Karate is an open-source general-purpose test-automation framework that can script calls to HTTP end-points and assert that the JSON or XML responses are as expected. Karate also has support for service-virtualization where it can bring up "mock" (or stub) servers which can substitute for web-services that need to participate in an integration-test. Karate's capabilities include being able to run tests in parallel, HTML reports and compatibility with Continuous Integration tools.
The additional capability to re-use functional tests as performance-tests via integration with the Gatling tool was released in July 2018 The project also added the capability to perform web-UI automation in 2019 which was declared out of RC (release-candidate) status in 2020.
Karate is implemented in Java but test-scripts are written in Gherkin since Karate was originally an extension of the Cucumber framework. It was built within Intuit and released under the MIT license.
History.
Karate was created by Peter Thomas, an Intuit employee.
Basic usage.
This example shows what a simple Karate test script looks like and how it is based on the Gherkin syntax.
Feature: karate 'hello world' example
Scenario: create and retrieve a cat
Given url 'http://myhost.com/v1/cats'
When method post
Then status 201
Given path response.id
When method get
Then status 200
This actually makes two calls, first an HTTP codice_1 to 'http://myhost.com/v1/cats' and then a codice_2 to the same URL but with the value of codice_3 appended as a REST-ful path parameter. The codice_4 keyword is used for asserting that a given payload is as expected. The use of the codice_5 "fuzzy match" token takes care of "ignoring" the actual value since it is dynamic, as it is a server-side auto-generated identifier.
Reception.
Karate was featured as one of the top 5 open-source API testing tools within six months of its release. It was also mentioned as one of the 10 API testing tools to try in 2017.
Karate was first listed in the ThoughtWorks Technology Radar in 2019 with a rating of "Assess". One year later it moved into the "Trial" category in May 2020.


Mono No Aware (organization)

Mono No Aware is a cinema-arts non-profit organization. Founded in 2007, its mission entails the advancement of “connectivity through the cinematic experience.” The organization is named after the Japanese concept mono no aware (物の哀れ), which expresses the impermanence of being and beauty.
Mono No Aware is based in Brooklyn, New York and organizes artist screenings, analog filmmaking workshops, equipment rentals, and film stock distribution. Film artists Bill Brand and Leslie Thornton serve on its Advisory Board. Since its founding, the organization has hosted an annual film festival, exhibiting expanded cinema works from around the world that utilize both analog technologies and live performance. Following the completion of the tenth festival, a month-long series of exhibitions, Mono No Aware undertook the construction of the first non-profit motion picture laboratory to operate in the United States.
Annual film festival.
In 2007, the first Mono No Aware film festival was held in the Galapagos Art Space in Brooklyn. It was free to attend and free to submit and the same holds true today. In 2016, the organization, in celebration of its tenth anniversary, organized MONO X, a 21-event film festival spanning three boroughs in New York City. It presented the work of 150 artists to an audience of 5,000. Works included sculpture, expanded cinema, and installation art incorporating the moving image on film and/or video. Presenting sponsors included Kodak, Brooklyn Brewery, and Technicolor.
Educational Initiatives.
Mono No Aware runs workshops in Brooklyn year-round, and collaborates with institutions throughout North America, to teach students analog filmmaking techniques. Workshops include non-toxic film processing with coffee and beer, hand-making photographic emulsion, 2D and 3D analog animation, optical printing and contact printing, and Super 8mm, 16mm, and 35mm filmmaking.


Sokha (unit)

Sokha (big plow) – a unit of land measure in Russia in 13th-17th centuries. Sokha was used as unit of taxation for worked land owned by someone else or the State. The term originated when Tatars took rent from the actual plows - the land working tool which used 2-3 horses.
At the end of 15th century Novgorod sokha equalled 3 обжs. A Moscow sokha was equal to 10 Novgorod ones and was paid according to the different sizes in various regions of the state.
In 1550 a new land-measure unit was established which kept the old name "sokha". The name was then used for a certain amount of exploited land. A sokha was divided into quarters.
There were several types of sokha:
Here, "government" meant someone who was working in government sectors, and "black" meant an average person ("the masses"), "quarter" or "quart" meant an area of land that is planted with a quarter of rye. The land was planted in such a way that the area of land seeded with two "quarters" was equal to a (an area of land approximately equal to one hectare).
Because of the different types of sokha, land owned by lower classes was worth less towards the tax, and most of the tax was paid by the peasants. Given the same amount of land, they paid twice as much as government officials, and 1.5 times as much as church officials.
In order to find out how many sokhas were in the state, a census measured and counted the rented lands. Quarters of land that were planted for personal use were free from payment. Until the beginning of the 17th century, a peasant who lived and worked on the land owned by a "government" employee, just like a peasant living on their own land or state land, paid equally for each exploited quarter of land. This section of land was called "living". At the beginning of the 17th century, the term "living quarter" was used not for the actual quarter of worked land, but for several whole farms in which more than a single quarter was planted.
This was done in the interest of government officials - their lands were used to establish "living quarters" which constituted 10-16 yards. This means that if every yard was divided into 4 quarters (two desyatinas), then such a "living quarter" was then 40 to 64 quarters of "actual" quarters of utilized land. Therefore, 40 to 64 quarters of government official land paid the same amount of tax as one peasant paid from the single quarter that he lived on (whether self- or state-owned).
In 1678–1679 the sokha was replaced with the "yard count", meaning taxes were to be paid for the number of peasant yards, rather than the area of the land occupied by the yards.
Taxes from small villages was also collected in sokhas. The term sokha remained but now it referred to a certain number of yards/houses. There were several types of sokha again: "best", "average", "lesser", and "worst" villagers. Sokha of the best villages was equal to 40 yards, average - 80, lesser - 160, and worst - 320 yards. Every sokha was charged the same amount of tax. Therefore, best villages paid the same amount for half the number of farms than the average ones. If there were not enough lesser or worst sokhas, then the tax was charged from the people that lived in average or best sokhas.


Just diatonic semitone


2045 Peking


Feddan

A feddan () is a unit of area. It is used in Egypt, Sudan, Syria and the Sultanate of Oman. In Classical Arabic, the word means 'a yoke of oxen': implying the area of ground that could be tilled by them in a certain time. In Egypt the feddan is the only non-metric unit which remained in use following the switch to the metric system. A feddan is divided into 24 kirat (, "qīrāt") in which one kirat equals 175 square metres.
Equivalent units.
1 feddan = 24 kirat = 60 metre × 70 metre = 4200 square metres (m²) = 0.420 hectares = 1.037 acres
In Syria, the feddan ranges from 2295 square metres (m²) to 3443 square metres (m²).


Malagasy units of measurement

A number of units of measurement were used in Madagascar to measure length, mass, capacity, etc. The Metric system was introduced in Madagascar in 1897.
System before metric system.
Several units were used.
Length.
One rahf was equal to 46.46 in (1.18 m) (the value was double in the northern part of Madagascar).
Mass.
For gold and silver.
Units included:
1 vari = 3 nanki
1 sompi = 2 vari = 60 grain.
Capacity.
One bambou was equal to 0.0568 bushel.


Double drop D tuning

Double drop D tuning: DADGBD, also known simply as double drop D, is an alternative guitar tuning: E strings are tuned down ("dropped") one whole step (2 frets) to D rather than E as in standard tuning (EADGBE).
Uses of double dropped D tuning.
The main use for double dropped D is so that guitarists can play intervals of a fifth with one finger on the bass strings, and play the treble side of a barre chord. Some recordings that make effective use of this tuning are "Black Water" by The Doobie Brothers, "The Loner," "Cortez the Killer," "Don't Let It Bring You Down," "Ohio" and "Cinnamon Girl" by Neil Young, "Choctaw Bingo" and "We Can't Make It Here" by James McMurtry, "Find the Cost of Freedom" by Crosby, Stills, Nash, and Young, "Going to California" by Led Zeppelin, "The End" by The Doors, "Devils & Dust" by Bruce Springsteen, "Satellite" by Elliott Smith, "Overkill" by Men At Work, "Bryter Layter" by Nick Drake and "Nobody's Fault but My Own" by Beck.
Examples of chords in dropped D tuning.
Chords in double dropped D tuning are formed as they are in standard tuning, with the exception of the first and sixth strings, which are either omitted or fretted one whole step higher:
Note that these chords are not the power chords commonly played in double drop D tuning. Power chords generally mute the higher notes rather than the lower notes:
For purposes of making the table easier to read, spaces are provided between each number when the fret number becomes a double digit.
Some examples of the simplified barre chords are shown below.
Chords involving the minor third may be more difficult to fret.


Universal testing machine

A universal testing machine (UTM), also known as a universal tester, materials testing machine or materials test frame, is used to test the tensile strength and compressive strength of materials. An earlier name for a tensile testing machine is a tensometer. The "universal" part of the name reflects that it can perform many standard tensile and compression tests on materials, components, and structures (in other words, that it is versatile).
Components.
Several variations are in use. Common components include:
Use.
The set-up and usage are detailed in a test method, often published by a standards organization. This specifies the sample preparation, fixturing, gauge length (the length which is under study or observation), analysis, etc.
The specimen is placed in the machine between the grips and an extensometer if required can automatically record the change in gauge length during the test. If an extensometer is not fitted, the machine itself can record the displacement between its cross heads on which the specimen is held. However, this method not only records the change in length of the specimen but also all other extending / elastic components of the testing machine and its drive systems including any slipping of the specimen in the grips.
Once the machine is started it begins to apply an increasing load on specimen. Throughout the tests the control system and its associated software record the load and extension or compression of the specimen.
Machines range from very small table top systems to ones with over 53 MN (12 million lbf) capacity.


TSE (examination)

The Test of Spoken English (TSE) was an oral test developed by Educational Testing Service which measured the ability of nonnative English speakers to communicate effectively. As of March 2010, the TSE has been superseded by the speaking portion of the TOEFL iBT as well as by the SPEAK test.
Before its retirement, TSE scores were used by academic institutions, corporations, government agencies, health care systems, and other organizations to guide their decisions regarding graduate assistantships in teaching and research, hiring new workers, and licensing and certifying existing employees.
Scoring.
The TSE score consisted of a single score of communicative language ability, which was reported on a scale of 20 to 60. Assigned score levels were averaged across items and raters, and the scores were reported in increments of five (i.e., 20, 25, 30, 35, 40, 45, 50, 55, and 60).


Atom interferometer

An atom interferometer is an interferometer which uses the wave character of atoms. Similar to optical interferometers, atom interferometers measure the difference in phase between atomic matter waves along different paths. Atom interferometers have many uses in fundamental physics including measurements of the gravitational constant, the fine-structure constant, the universality of free fall, and have been proposed as a method to detect gravitational waves. They also have applied uses as accelerometers, rotation sensors, and gravity gradiometers.
Overview.
Interferometry inherently depends on the wave nature of the object. As pointed out by de Broglie in his PhD thesis, particles, including atoms, can behave like waves (the so-called wave–particle duality, according to the general framework of quantum mechanics). More and more high precision experiments now employ atom interferometers due to their short de Broglie wavelength. Some experiments are now even using molecules to obtain even shorter de Broglie wavelengths and to search for the limits of quantum mechanics. In many experiments with atoms, the roles of matter and light are reversed compared to the laser based interferometers, i.e. the beam splitter and mirrors are lasers while the source instead emits matter waves (the atoms).
Interferometer types.
While the use of atoms offers easy access to higher frequencies (and thus accuracies) than light, atoms are affected much more strongly by gravity. In some apparatuses, the atoms are ejected upwards and the interferometry takes place while the atoms are in flight, or while falling in free flight. In other experiments gravitational effects by free acceleration are not negated; additional forces are used to compensate for gravity. While these guided systems in principle can provide arbitrary amounts of measurement time, their quantum coherence is still under discussion. Recent theoretical studies indicate that coherence is indeed preserved in the guided systems, but this has yet to be experimentally confirmed.
The early atom interferometers deployed slits or wires for the beam splitters and mirrors. Later systems, especially the guided ones, used light forces for splitting and reflecting of
the matter wave.
History.
The separation of matter wave packets from complete atoms was first observed by Esterman and Stern in 1930, when a Na beam was diffracted off a surface of NaCl. The first modern atom interferometer reported was a Young's-type double-slit experiment with metastable helium atoms and a microfabricated double slit by Carnal and Mlynek in 1991, and an interferometer using three microfabricated diffraction gratings and Na atoms in the group around Pritchard at MIT. Shortly afterwards, an optical version of a Ramsey spectrometer typically used in atomic clocks was recognized also as an atom interferometer at the PTB in Braunschweig, Germany. The largest physical separation between the partial wave packets of atoms was achieved using laser cooling techniques and stimulated Raman transitions by S. Chu and coworkers in Stanford. More recently atom interferometers have begun moving out of laboratory conditions and have begun to address a variety of applications in real word environments.
Inertial navigation.
The first team to make a working model, Pritchard's, which included D.W. Keith, prompted Keith to leave atomic physics after achieving success, in part because one of the most obvious applications for atom interferometry was in highly accurate gyroscopes for submarines carrying ballistic missiles. AIGs (atomic interferometer gyroscopes) and ASGs (atomic spin gyroscopes) use atomic interferometer to sense rotation or in the latter case, uses atomic spin to sense rotation with both having compact size, high precision, and the possibility of being made on a chip-scale. "AI gyros" may compete, along with ASGs, with the established ring laser gyroscope, fiber optic gyroscope and hemispherical resonator gyroscope in future inertial guidance applications.


Staatsexamen Nederlands als tweede taal

Staatsexamen Nederlands als tweede taal (State Exams Dutch as a Second Language or State Examination of Dutch as a Second Language), often abbreviated as Staatsexamen NT2, is a standardised examination of Dutch language for those who are not native speakers of Dutch. By passing the State Examinations NT2 candidates can show that they have sufficient command of the Dutch language to be able to work or study in the Netherlands.
Organiser.
The Staatsexamen NT2 is organised by Dienst Uitvoering Onderwijs (DUO) (Office of Education) on behalf of the College voor Examens (CvE) (Board of Examinations). CvE is nonetheless still responsible for the organisation, development of the State Examinations NT2, and provision of sample papers.
The actual execution of the examination is done by , a testing and measurement company with international reputation, and Bureau ICE. While Cito is responsible for the listening and speaking exam, Bureau ICE is responsible for the reading and writing exam. Therefore, Cito also provides further training for markers for the speaking exam and facilitates the entire process of grading for this part of the exam.
Level of examinations.
As different levels of language competence are needed for working and for studying, there are two levels of examination, which could be chosen by the candidates. Programme 1 should be taken by candidates who need to work or be under vocational training in a Dutch environment. Programme 2 certifies that the candidates who pass the test have mastered enough Dutch for employment or education in college or university. These exams are set according to the Common European Framework of Reference (CEFR), where Programme 1 corresponds to the B1 level and Programme 2 corresponds to the B2 level.
Structure.
The examination consists of four sections: reading, listening, writing and speaking. A candidate gets the Diploma NT2, only if they pass all four parts.
Candidates complete the listening and speaking tests on a computer, and finish the writing tests partly on the computer and partly on an answer sheet. For the reading test, the reading texts would be printed on a booklet and the candidates should mark their answers on the computer.
Registration.
The exam is registered through the website of DUO. The exam could be taken at Amsterdam, Eindhoven, Delft, Rotterdam, Utrecht and Zwolle almost every week.
Preparation.
Sample papers for the exam are available. Candidates may also decide to enrol in preparation courses offered by various language schools.
Results.
The result for the exam is marked either as "Satisfactory" or "Not satisfactory". The result is announced about five weeks after the exam.
Recognition.
A pass in Programme 2 can fulfil the language requirement for enrolment in college or university in the Netherlands. According to the Dutch nationality law and Integration law for immigrants to the Netherlands, a pass in Programme 1 can exempt candidates from taking the language test in the process of immigration and naturalisation.