Editing Interval (music) (section)

=== Number ===
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[[Image:Staff lines and spaces SVG.svg|right|thumb|350px|[[Staff (music)|Staff]], with [[staff position]]s indicated]]
[[Image:Fifth C to G.png|right|thumb|Fifth from C to G in the A{{music|b}} [[major scale]]]]

The number of an interval is the number of letter names or [[staff position]]s (lines and spaces) it encompasses, including the positions of both notes forming the interval. For instance, the interval B–D is a third (denoted '''m3''') because the notes from B to the D above it encompass three letter names (B, C, D) and occupy three consecutive staff positions, including the positions of B and D. The [[#Main intervals|table]] and the figure above show intervals with numbers ranging from 1 (e.g., '''P1''') to 8 (e.g., '''d8'''). Intervals with larger numbers are called [[#Compound intervals|compound intervals]].

There is a [[one-to-one correspondence]] between staff positions and diatonic-scale [[Degree (music)|degrees]] (the notes of [[diatonic scale]]).{{efn|name=diatonic|
The expression [[diatonic scale]] is herein strictly defined as a [[Heptatonic scale|7-tone scale]], which is either a sequence of successive [[natural note]]s (such as the C-[[major scale]], C–D–E–F–G–A–B, or the A-[[minor scale]], A–B–C–D–E–F–G) or any [[transposition (music)|transposition]] thereof. In other words, a scale that can be written using seven consecutive notes without [[Accidental (music)|accidentals]] on a [[Staff (music)|staff]] with a conventional [[key signature]], or with no signature. This includes, for instance, the [[Major scale|major]] and the [[Natural minor scale|natural minor]] scales, but does not include some other seven-tone scales, such as the [[Melodic minor scale|melodic minor]] and the [[Harmonic minor scale|harmonic minor]] scales (see also [[Diatonic and chromatic]]).}}
This means that interval numbers can also be 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, B–D is a third because in any diatonic scale that contains B and D, the sequence from B to D includes three notes. For instance, in the B-[[natural minor scale|natural minor]] diatonic scale, the three notes are B–C{{music|sharp}}–D. This is not true for all kinds of scales. For instance, in a [[chromatic scale]], there are four notes from B to D: B–C–C{{music|sharp}}–D. This is the reason interval numbers are also called ''diatonic numbers'', and this convention is called ''diatonic numbering''.

If one adds any [[accidental (music)|accidental]]s 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 (music)|natural]] interval, formed by the same notes without accidentals. For instance, the intervals B–D{{music|sharp}} (spanning 4 semitones) and B–D{{music|flat}} (spanning 2 semitones) are thirds, like the corresponding natural interval B–D (3 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 E–E, a perfect unison, is also called a prime (meaning "1"), even though there is no difference between the endpoints. Continuing, the interval E–F{{music|sharp}} is a second, but F{{music|sharp}} is only one staff position, or diatonic-scale degree, above E. Similarly, E–G{{music|sharp}} is a third, but G{{music|sharp}} is only two staff positions above E, and so on. As a consequence, joining two intervals always yields an interval number one less than their sum. For instance, the intervals B–D and D–F{{music|sharp}} are thirds, but joined together they form a fifth (B–F{{music|sharp}}), not a sixth. Similarly, a stack of three thirds, such as B–D, D–F{{music|sharp}}, and F{{music|sharp}}–A, is a seventh (B–A), not a ninth.

This scheme applies to intervals up to an octave (12 semitones). For larger intervals, see {{format link|#Compound intervals}} below.