Interval - Ontei (English spelling) interval English

Japanese: 音程 - おんてい（英語表記）interval 英語

This refers to the difference in pitch between two notes. Depending on how it appears, there are harmonic intervals (when they sound simultaneously) and melodic intervals (when they sound sequentially). The Western method of expressing intervals is generally used, which indicates the number of steps on a seven-tone scale based on semitones and whole tones, and uses degrees as the unit of measurement. However, when describing music such as India and West Asia, where intervals narrower than a semitone are important, the term microtone becomes necessary. In the following, we will exclude microtones.

[Miho Minamitani]

Interval display based on the seven-tone scale

Notes that are in the same step as another note are said to be in the same degree or 1st degree relationship, notes that are in two steps are said to be in 2nd degree, notes that are in three steps are said to be in 3rd degree, and so on up to 8th degree (octave). Intervals that exceed an octave (9th, 10th, etc.) are called compound intervals, and intervals that are less than that are called simple intervals, but compound intervals are often reduced to simple intervals by subtracting an octave interval once or several times. Interval notations based on the heptad scale are also used for convenience in music that is not based on the heptad scale, and in the music of non-Western peoples.

(1) Types of intervals Below, we will discuss the range of simple intervals. Intervals with the same degree can differ depending on whether or not a semitone is included, and these are distinguished by the names perfect, major, and minor. All intervals that appear between each harmonic in the natural harmonic series are perfect 1st, major and minor 2nd, major and minor 3rd, perfect 4th, perfect 5th, major and minor 6th, major and minor 7th, and perfect 8th, and are divided into two series: perfect intervals and major and minor intervals. Intervals that add the augmented fourth and diminished fifth that appear in the diatonic scale to these are called diatonic intervals, and augmented and diminished intervals other than augmented fourths and diminished fifths, and double augmented and diminished intervals are called chromatic intervals.

(2) Changes in the names of intervals The names of intervals change based on two series: perfect intervals and major/minor intervals. By increasing or decreasing the interval by a semitone, the intervals change names. In other words, if the interval is widened by a semitone, it becomes an augmented interval, and if it is narrowed, it becomes a diminished interval. In addition, if a major interval is narrowed by a semitone, it becomes a minor interval, and if it is narrowed by another semitone, it becomes a diminished interval.

(3) Inversion of Intervals An interval obtained by shifting one of two tones that make up an interval one octave to the opposite side is called an inversion interval, and the sum of the degrees of this inversion interval and the original interval is always 9.

(4) Consonance of intervals Consonance is when two sounds that sound simultaneously have a good harmony, while a relationship of intervals that is not in harmony is called dissonance. Consonance of intervals is defined as three types: perfect consonant intervals (perfect 1st, perfect 8th, perfect 4th, perfect 5th), imperfect consonant intervals (major and minor 3rd, major and minor 6th), and dissonant intervals (major and minor 2nd, major and minor 7th, and all augmented and diminished intervals).

[Miho Minamitani]

Frequency-based pitch display

(1) By pitch ratio: This is expressed as the simplified fraction ratio (the lower note is the denominator and the higher note is the numerator) of the ratio of the vibration frequencies of two notes that make up one pitch.

(2) Pitch value-based units: The logarithm of pitch ratio is calculated and expressed as a unit (pitch value) ordered by proportionality. The "logarithm value" is calculated by multiplying the logarithm of the pitch ratio by 1000 and expressing it as a three-digit integer. The "Savart value" is expressed based on Savart. 1 Savart is the approximate value of the logarithm of 1 octave = 301.03, which is 1 octave = 300. The "milli-octave value" is calculated by taking the value of the octave as 1000 and calculating the proportions of other pitches to these logarithmic values. The "cent value" was invented by Ellis and is the most widely used today. The semitone of the twelve-tone equal temperament is set to 100. The "Japanese pitch value" is a value in which 1 octave is 6, a whole tone is 1, and a semitone is 0.5, and was invented by acoustician Hisao Tanabe. The "angle value" indicates the pitch value as an angle, with one octave being 360 degrees.

[Miho Minamitani]

[Reference] | Microtone

How to name intervals
©Shogakukan ">

How to name intervals

Diatonic and chromatic intervals
©Shogakukan ">

Diatonic and chromatic intervals

Interval inversions
©Shogakukan ">

Interval inversions

Types of intervals and their relationships
©Shogakukan ">

Types of intervals and their relationships

Source: Shogakukan Encyclopedia Nipponica About Encyclopedia Nipponica Information | Legend

Japanese:

2音間の高さの隔たりをいう。その現れ方によって、和声的音程（同時に響く場合）と旋律的音程（順次に響く場合）がある。音程の表し方として一般的に用いられているのは、半音と全音に基づく七音音階上の段階の数で示す西洋の方法で、単位は度を用いる。ただし、半音より狭い音程が重要な意味をもつインド、西アジアなどの音楽を記述するときには、微分音という用語が必要になる。以下ここでは微分音を除外して述べる。

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七音音階に基づく音程表示

ある音と同一段階にある音は同度、または1度の関係にあるとし、二つの段階にある音は2度、三つの段階ならば3度というように以下8度（オクターブ）まで達する。オクターブを超える音程（9度、10度……）を複合音程、それ以内を単音程というが、複合音程は1回ないし数回オクターブ音程を差し引いて、単音程に還元して考えることが多い。七音音階に基づく音程表示は、七音音階に基づかない音楽、および西洋以外の諸民族の音楽にも便宜的に用いられている。

(1)音程の種類　以下、単音程の範囲で述べる。同じ度数で示される音程でも半音の有無によって違いが生じるが、これを完全、長、短という名称をもって区別する。自然倍音列の各倍音間に現れるすべての音程は、完全1度、長・短2度、長・短3度、完全4度、完全5度、長・短6度、長・短7度、完全8度であり、完全音程と、長・短音程の二つの系列に分けられる。これらに、全音階中に現れる増4度と減5度を加えた音程を全音階的音程といい、増4度と減5度以外の増音程と減音程、重増音程および重減音程を半音階的音程という。

(2)音程の名称の変化　完全音程と長・短音程の2系列を中心とし、そこから半音の幅で増減することによって音程の名称が変化する。すなわち半音広がれば増音程、狭まれば減音程となる。なお、長音程が半音狭まると短音程となり、さらに半音狭まると減音程となる。

(3)音程の転回　音程をなす2音の一つを反対側へ1オクターブ移すことによって得られる音程を転回音程といい、これと原音程との度数の和はつねに9である。

(4)音程の協和　協和とは同時に鳴る音がよく調和して響くような関係にあることをいい、調和しない音程関係を不協和という。音程の協和関係は、完全協和音程（完全1度、完全8度、完全4度、完全5度）、不完全協和音程（長・短3度、長・短6度）、不協和音程（長・短2度、長・短7度と、すべての増・減音程）の3種に定義される。

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振動数に基づく音程表示

(1)音程比によるもの　一つの音程をなす2音の振動数の比を最簡約した分数比（低音が分母、高音が分子）で表すもの。

(2)音程値によるもの　音程比の対数を求めて、それを比例によって秩序づけた単位（音程値）で示すもの。「対数値」は、音程比の対数を1000倍し、3桁(けた)の整数で示すもの。「サバール値」は、サバールを基準として示すもの。1サバールとは、対数値の1オクターブ＝301.03の近似値をとって1オクターブ＝300とした値をいう。「ミリオクターブ値」は、オクターブの値を1000とし、他の音程はこれらと対数値との比例によって算出するもの。「セント値」は、エリスの考案したもので、今日もっとも広く用いられているもの。十二平均律の半音を100とする。「日本式音程値」は、1オクターブを6とし、全音を1、半音を0.5とするもので、音響学者田辺尚雄(ひさお)の考案による。「角度値」は、1オクターブを360度とし、音程の値を角度で示すものである。

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[参照項目] | 微分音

音程の呼び方

全音階的音程と半音階的音程

音程の転回関係

音程の種類と関係

出典　小学館　日本大百科全書(ニッポニカ)日本大百科全書(ニッポニカ)について　情報 | 凡例

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