# What do you call a scale with 19 notes per octave? Howabout 17 notes per octave?

I know that a 12-note scale (as in the currently ubiquitous 12 equal temperament) is called "chromatic". In a chromatic system, there are sharps and/or flats, but no neighboring sharps and flats.

What is the name of the scale that includes all the following 19 notes? C, C#, D♭, D, D#, E♭, E, E#/F♭, F, F#, G♭, G, G#, A♭, A, A#, B♭, B, B#/C♭

Obviously, this scale can't be done in 12 equal temperament (where the sharps and flats are tempered into the same note). But is there a name for this scale?

On the Wikipedia article for "Chromatic scale", it includes a just tuning section that shows a Pythagorean (3-limit) and 5-limit (Ptolemaic) tuning of all the notes. However, 17 notes are shown for the Pythagorean one, and 19 for the Ptolemy's one. But the same article says that "chromatic" means 12 notes, so I assume it's just showing different options that can be used for the tuning of a chromatic scale. But what do you call a scale that includes all of them?

What is the name of a scale that includes all 19 or 17 of these notes?

Edit: Note that I'm looking for the name of the scale itself, not a temperament that includes approximations of it.

• 19TET does this. A subset of 31TET can do it quite well too. Commented Feb 27, 2018 at 1:45
• Because some of these notes are very close to each other,(e.g. C#/Db) while others are farther apart, (e.g. E/F) the 'tet' or 'edo' bit can't work. The intervals are not constant; the octave isn't divided equally. If it was, the names may well need changing.
– Tim
Commented Feb 27, 2018 at 8:15
• I have indeed seen 19TET labelled with those sharp and flat names. Obviously, some of those notes sound out of tune compared to their 12TET versions. Commented Feb 27, 2018 at 16:06
• Now I am confused. Are you asking for the name of a 17-tone or 19-tone scale in equal temperament? That is, are you asking for the name of the usual 12-tone scale when some enharmonic notes are included?
– user39614
Commented Feb 28, 2018 at 16:16

The Pythagorean chromatic scale uses 3-limit just intonation to get 17 pitches in the octave, with no notes between B and C or between E and F. Ptolemy's intense chromatic scale uses 5-limit just intonation to get 19 pitches in the octave, including B♯/C♭ between B and C, E♯/F♭ between E and F.

You can read a little bit about them at the Wikipedia entry for Chromatic Scale.

• Could you refer or knows of music written using notes on these scales? Commented Feb 27, 2018 at 6:03
• @LoveIsHere -- much music written before about 1500 was using Pythagorean tuning. Here is a page discussing historical tunings. You might listen to recordings of the works of Guillaume de Machaut, for example this, or this.
– user39614
Commented Feb 27, 2018 at 12:01
• Thank you. Although I already read that Wikipedia article, I forgot to mention it when I first posted. So "chromatic" can also mean more than 12 notes? Commented Feb 28, 2018 at 1:44
• @user290527 -- When people talk about the Chromatic scale they usually mean the 12-tone scale you are familiar with. But this was not always so; this Wikipedia article talks about the meaning of chromatic in different contexts. To specify that a scale contains 12, 17, or 19 tones you could use dodecatonic, heptadecatonic, or enneadecatonic, respectively. But the names Pythagorean chromatic scale and Ptolemy's intense chromatic scale refer to more specific types of heptadecatonic and enneadecatonic scales.
– user39614
Commented Feb 28, 2018 at 2:06
• @user290527 -- Pythagorean chromatic scale and Ptolemy's intense chromatic scale are the names of these scales.
– user39614
Commented Feb 28, 2018 at 2:46

19-tet or 19-EDO. 19-tet just attaches the suffix tet to 19 like quintet or octet or other Asian New Years numbers. 19-EDO means 19 equal divisions of the octave.

• I'd caution that the 19TET name only applies if the intervals between adjacent notes are indeed equal. The moment they become unequal, we need to negotiate a new name for your scale--especially one that others will agree to. Commented Feb 27, 2018 at 1:08
• @Dekkadeci the above statement applies for EDO too. and ttw 19TET has nothing to do with -tet, and stands for 19 tone equal temperament. Commented Feb 27, 2018 at 1:42
• Loosely speaking TET = EDO although technically while all nTETs are EDOS, not all EDOS are nTETs. More info here music.stackexchange.com/questions/61742/… Commented Feb 27, 2018 at 1:44
• Actually, the numbers 5,7,12,19,... come from continued fractions representing the number of fifths in multiples of octaves. google.com/… among others. Tet just ended a couple of days ago. One also by the continued fraction method gets tunings of 31 and 53 notes. (And the fret spacing of 18/17 from Galileo Sr).
– ttw
Commented Feb 27, 2018 at 2:21