8

The following table lists the first 13 harmonics of the note C

Harmonic   Note   Unique note
-----------------------------
1          C      C
2          C
3          G      G
4          C
5          E      E
6          G
7          A#     A#
8          C
9          D      D
10         E
11         F#     F#
12         G
13         G#     G#

Ordering the unique notes gives:

C - D - E - F# - G - G# - A#

Does this scale have a name? Is it used? What is this scale called?

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  • 4
    Can G# and A# be spelt as Ab and Bb? – Elements in Space Oct 25 '20 at 14:40
  • 1
    Exactly what I was thinking. Certainly the Bb. – Tim Oct 25 '20 at 14:41
  • I would not say that it is a scale; not any series of notes is necessarily a scale. Scales normally repeat in the next octave but the harmonic series has twice as many notes each time that you go up an octave. Also, 7 is rather flatter than the usual A# / Bb. – badjohn Oct 25 '20 at 15:58
  • 1
    Why to the 13th harmonic? – Michael Curtis Oct 26 '20 at 13:48
  • 1
    Because I wanted to limit the scale to 7 notes – Jaap Joris Vens Oct 26 '20 at 15:15
16

There are two different questions that could be read here, which it is not obvious (yet extremely significant) that they are different. One question is "what is the name of the scale consisting of the notes given by the first thirteen harmonics of C", and the other is "what is the name of the scale consisting of the notes C - D - E - F# - G - G# - A#", where the crucial point making these questions different is is that the pitches produced by the harmonics of C are not the same pitches as the ones we usually refer to by the letter names – for example the 'F#' given by the 11th harmonic of is in fact almost equidistant between an F and an F# in equal temperament, and so in my view it's substantially misleading to even give it a note name at all. The seventh and thirteenth harmonics are both also substantially far from the equal-tempered pitch they have been given the name of. So if you sat down at a keyboard and played the notes C - D - E - F# - G - G# - A# (or, as per the Wikipedia article referenced in the answer from Aaron (which does a good job of answering the second sense of the question as I've set out above), the Acoustic Scale C - D - E - F# - G - A - A#), you are not in any real sense playing the scale made up of the first 13 harmonics of C at all.

To do something towards answering the first possible sense of the question, to play this scale or use it in a piece we would have to make clear we are in the world of "microtonal" intonation. The composer Ben Johnston developed a notation which permits writing such notes (see the picture here https://en.wikipedia.org/wiki/Just_intonation#Staff_notation where the "F#" is notated as "up-arrow F") however I am not greatly familiar with his and others' work using these tunings so I don't know if there are any examples of this scale being used; certainly he has composed pieces in which notes tuned to these higher harmonics are used, and I would definitely be interested to know if there is an example where this scale occurs.

A final comment is that, whilst the 7th, 11th and 13th harmonics were signficantly far from any equal-temperament pitch, the D arising as the 9th harmonic is exactly a just perfect fifth above the G arising from the 3rd harmonic, since 9=3x3.

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  • 1
    Amazing. You made me realize that - contrary to what I often heard while studying music theory - the notes of the major scale are not at all based on the harmonic series (well, maybe except the second and the fifth). – Jaap Joris Vens Oct 25 '20 at 18:39
  • 1
    Really helpful that you point out the difference between the "true" acoustic scale and the 12-TET approximation(s). – Aaron Oct 25 '20 at 20:49
  • @hedgie That depends on what you consider "based on". When you write "major scale" you seem to mean the major scale in equal temperament. This temperament has only been the general standard for a little over a century. Earlier temperaments sacrifice some notes to have other notes much closer to "just intonation" (you can't have all notes, cf. syntonic and pythagorean comma). This leads to, for example, not all whole or all half tones being equal sized in early theory books. The notes from the scale are based on the harmonic series, the route they took is just a whole lot longer. – 11684 Oct 26 '20 at 21:27
10

The Musical Scale Search Tool offers four scales whose notes correspond to the OP, with only one -- C Minor Lydian -- containing the pitches in the order specified. The others would be permutations/modes of that scale.

  • G#/Ab leading whole tone G#/Ab; A#/Bb; C; D; E; F#/Gb; G; G#/Ab;
  • C minor lydian C; D; E; F#/Gb; G; G#/Ab; A#/Bb; C;
  • D arabian D; E; F#/Gb; G; G#/Ab; A#/Bb; C; D;
  • G neapolitan major G; G#/Ab; A#/Bb; C; D; E; F#/Gb; G;

Ian Ring's website contains an extensive analysis of the minor lydian scale.

Since the OP scale is constructed in terms of the overtone series, it is in principle the Acoustic scale. However, as given on Wikipedia, the acoustic scale has A natural rather than Ab.

Two songs are reference as using the acoustic scale (A-natural version) in this page from the University of Iowa:

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  • I really hear the whole-tone-ness. – ibonyun Oct 26 '20 at 23:53
  • @ibonyun Indeed, it's a Whole Tone scale with an added note. – helveticat Oct 27 '20 at 21:47
2

Your scale is a mode of the scale that Wikipedia calls Neapolitan major. Unfortunately, Neapolitan major is a minor scale (at least, it harmonizes out to a minor triad at the root, not a major one) and the citations for that name are not very convincing. But you can find references to this scale more easily than yours, so it might be a good search term to know.

Wikipedia duplicates the name Aaron found for your mode: "Lydian minor". Again, this seems to be a name that someone invented and that is reproduced only in a few lists of scales. It seems to be a bad name to me -- shouldn't "Lydian Minor" at least have a b3 in it? But I'm sure that doesn't bother everyone the way it does me.

Names like these usually originated in scale books marketed towards rock guitarists; they represent a kind of folk terminology that hasn't passed into common use (because the scales are rarely used) and usually doesn't have any basis outside that. But all that might not bother you too much -- after all, everything has a name because someone decided to call it that, and names don't have to make logical sense.

It might also be useful to know that your scale is the same as the Carnatic melakata Rishabhapriya. This name connects your scale with real-world music-making rather than obsessive list-making, so it may be more helpful for you. A YouTube search throws up lots of South Indian performances of pieces in Rishabhapriya.

1
  • I gotta agree, "Lydian minor" seems like a misnomer to me. Maybe melodic major #4? – user45266 Oct 26 '20 at 20:13

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