Naming pitch and interval collections

Question

I have a few questions regarding the correct naming of pitch and interval collections.

1. We call an ordered collection of adjacent pitches a scale. For example, (C D E F G A B) is called C major (or Ionian) scale.

2. But an ordered collection of intervals, without reference to any pitch, is also called a scale. For example, (1 1 1/2 1 1 1 1/2) is called major (or Ionian) scale. Are there more specific terms to distinguish the two?

3. What about a collection of adjacent pitches without one of them being considered special, like the white keys on the piano? That is, is there a generic name that encompasses all of C Ionian, D Dorian, E Phrygian etc.?

4. Finally, is there a word for an unordered collection of intervals? That is, is there a word that encompasses all modes of major contrasted with all modes of melodic minor?

Answer 1

With regard to questions 1 and 2, there isn't any need to distinguish between these; one is just the generic type (eg. Major Scale), the other is a specific instance of it (eg. G Major Scale).

With regard to question 3, these scales you mention are all modes of each other, and so usually you would refer to them as modes of the "most common". So, C Ionian, D Dorian, E Phrygian, F Lydian, G Mixolydian, A Aeolian and B Locrian would normally be referred to as the modes of C Ionian (or the modes of the C Major scale). I would say this is even more likely where the modes are less commonly used than one of the scales; for instance, the 7 modes of the Harmonic Minor are all interesting and useful scales, and do have names of their own (sometimes more than one each!), but it certainly seems easiest to refer to them as being modes of the Harmonic Minor.

With regard to your last question, if you are wishing to describe unordered collections of actual pitches (or generic relationships, which could be in any transposition), you could use Pitch Class Set analysis. I recently linked to information about PC Sets in this question.

Here is information about PC Sets. Here is a PC Set Calculator (great fun!) allowing you to enter collections of pitches and find out what PC Set they are. Here is a table of PC Sets where common names of PC Sets can be found.

Answer 2

1) Not stated as question, but no alternative to scale.

2) may be called a mode. The German wikipedia denotes the formula: mode + base note = key (as in key signature)

3) Not sure what you mean, but I guess it is key (German: Tonart), famous example Bachs d Dorian toccata.

4) This again is mode (German: Tongeschlecht), so modes are major, minor, phrygian, mixolydian...

Answer 3

The major scale consists, as you allude, of a set of intervals: TTSTTTS. This is also known as the Ionian mode: when those notes are played in that particular order,they produce the major scale.This remains the same spacing, wherever you start, for each of the 12 'scales'.C Ionian/D Dorian etc., are all modes of C major. Just as E Dorian/F# Phrygian etc., are all modes of D major.

An unordered (random) collection is as it says.