Overtone scale - Revision history

Sintel: capit

2026-10-11T13:19:21Z

capit

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	Another way to write this would be 5:6:7:8:9:10, which shows that the tones form both a scale and a chord; indeed, it is a [[9-odd-limit]] [[pentad]] with 5 in the bass. [[Denny Genovese]] would call the above scale "mode 5 of the ~~Harmonic Series~~," or "mode 5" for short. Further examples will be given with a mode number indicated.		Another way to write this would be 5:6:7:8:9:10, which shows that the tones form both a scale and a chord; indeed, it is a [[9-odd-limit]] [[pentad]] with 5 in the bass. [[Denny Genovese]] would call the above scale "mode 5 of the harmonic series," or "mode 5" for short. Further examples will be given with a mode number indicated.

	A [[mode]] in other musical contexts is usually a different rotation of the same intervals. In the case of different harmonic modes, that is not exactly the case. However, in some sense it is a reasonable comparison, because as you slide the subset of harmonics around, you are essentially sampling different segments of integers whose prime factorizations follow simple, constant patterns (every 2nd number has a 2, every 3rd number has a 3, every 5th number has a 5) and therefore the full internal interval set (all dyads, triads, tetrads, etc.) from one mode to the next is more alike than it is different.		A [[mode]] in other musical contexts is usually a different rotation of the same intervals. In the case of different harmonic modes, that is not exactly the case. However, in some sense it is a reasonable comparison, because as you slide the subset of harmonics around, you are essentially sampling different segments of integers whose prime factorizations follow simple, constant patterns (every 2nd number has a 2, every 3rd number has a 3, every 5th number has a 5) and therefore the full internal interval set (all dyads, triads, tetrads, etc.) from one mode to the next is more alike than it is different.

Sintel: Remove primodality section (contains no useful information, and linked already)

2026-10-11T13:18:27Z

Remove primodality section (contains no useful information, and linked already)

← Older revision		Revision as of 13:18, 11 October 2026
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	Mode 30 in particular is interesting because 30 is the product of the first three primes, so it is a fairly good choice if we want a tonic that is not a power of two. It contains modes 6 and 10 as subsets. We have the classic minor triad (from 10), the subminor triad (from 6), two major triads in 30:37:45 and 30:38:45, and the Barbados triad of 30:39:45. Chords not based on the tonic include the harmonic seventh chord (32:40:48:56). A good 13-limit subset with 16 notes in it is 30:32:33:35:36:39:40:42:44:45:48:49:50:54:55:56:60.		Mode 30 in particular is interesting because 30 is the product of the first three primes, so it is a fairly good choice if we want a tonic that is not a power of two. It contains modes 6 and 10 as subsets. We have the classic minor triad (from 10), the subminor triad (from 6), two major triads in 30:37:45 and 30:38:45, and the Barbados triad of 30:39:45. Chords not based on the tonic include the harmonic seventh chord (32:40:48:56). A good 13-limit subset with 16 notes in it is 30:32:33:35:36:39:40:42:44:45:48:49:50:54:55:56:60.

	~~== Primodality ==~~

	[[Primodality]] is a compositional, theoretical and philosophical framework built around the use of large prime modes of the harmonic series. It has its own article, because it is too extensive to do justice here.

	== Solfege systems ==		== Solfege systems ==

Sintel: Categorize modes by divisors, style, reduce solfege tables

2026-10-11T13:17:17Z

Categorize modes by divisors, style, reduce solfege tables

Show changes

Sintel: improve lede, afdo -> harmonics, linking, typos

2026-10-11T01:21:43Z

improve lede, afdo -> harmonics, linking, typos

Show changes

Inthar: /* Over-5 scales */ Remove unsourced claim

2026-04-23T14:37:50Z

Over-5 scales: Remove unsourced claim

← Older revision		Revision as of 14:37, 23 April 2026
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	[[File:Ji-5-6-7-8-9-10-csound-foscil-220hz.mp3\|right\|thumb\|270px\|Mode 5: 5:6:7:8:9:10]]		[[File:Ji-5-6-7-8-9-10-csound-foscil-220hz.mp3\|right\|thumb\|270px\|Mode 5: 5:6:7:8:9:10]]

	; [[5afdo\|Mode 5]]: 5:6:7:8:9:10 – This is essentially a [[7-limit]] fully-diminished seventh chord. [[7/5]] makes a very nice tritone above the bass – the simplest one available in JI – and it is available in all the higher Over-5 modes as well~~. This is the scale used by the Wagogo people of Tanzania~~.		; [[5afdo\|Mode 5]]: 5:6:7:8:9:10 – This is essentially a [[7-limit]] fully-diminished seventh chord. [[7/5]] makes a very nice tritone above the bass – the simplest one available in JI – and it is available in all the higher Over-5 modes as well.

	[[File:Ji-10-11-12-13-14-15-16-17-18-19-20-csound-foscil-220hz.mp3\|right\|thumb\|270px\|Mode 10 scale]]		[[File:Ji-10-11-12-13-14-15-16-17-18-19-20-csound-foscil-220hz.mp3\|right\|thumb\|270px\|Mode 10 scale]]

Sintel: /* See also */ -random self promo

2025-08-10T23:19:41Z

FloraC: Style

2024-12-16T18:59:46Z

Style

Show changes

BudjarnLambeth: /* Next steps */

2024-03-10T10:53:16Z

Next steps

← Older revision		Revision as of 10:53, 10 March 2024
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	* Experiment with using different pitches as the "tonic" of the scale (eg. '''sol lu ta do re mi fu sol''', which could be taken as the 7-note scale starting on '''sol''').		* Experiment with using different pitches as the "tonic" of the scale (eg. '''sol lu ta do re mi fu sol''', which could be taken as the 7-note scale starting on '''sol''').
	* Take subsets of larger scales, which are not strict adjacent overtone scales (eg. '''do re fe sol ta do''').		* Take subsets of larger scales, which are not strict adjacent overtone scales (eg. '''do re fe sol ta do''').
	* Learn the inversions of these scales, which would be [[undertone scales]]. (Undertone scales would have smaller steps at the bottom of the scale, which would get larger as one ascends.)		* Learn the inversions of these scales, which would be [[IFDO\|undertone scales]]. (Undertone scales would have smaller steps at the bottom of the scale, which would get larger as one ascends.)
	* Borrow overtones & undertones from the overtones & undertones of the fundamental -- this process can produce rich fields of interlocking harmonic series, and is often the sort of thing that composers do when they're composing in just intonation. [[Harry Partch]]'s "Monophonic Fabric," which consists of 43 unequal tones per octave, is one famous example.		* Borrow overtones & undertones from the overtones & undertones of the fundamental -- this process can produce rich fields of interlocking harmonic series, and is often the sort of thing that composers do when they're composing in just intonation. [[Harry Partch]]'s "Monophonic Fabric," which consists of 43 unequal tones per octave, is one famous example.

BudjarnLambeth: /* Next steps */

2024-02-19T11:49:30Z

Next steps

← Older revision		Revision as of 11:49, 19 February 2024
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	* Experiment with using different pitches as the "tonic" of the scale (eg. '''sol lu ta do re mi fu sol''', which could be taken as the 7-note scale starting on '''sol''').		* Experiment with using different pitches as the "tonic" of the scale (eg. '''sol lu ta do re mi fu sol''', which could be taken as the 7-note scale starting on '''sol''').
	* Take subsets of larger scales, which are not strict adjacent overtone scales (eg. '''do re fe sol ta do''').		* Take subsets of larger scales, which are not strict adjacent overtone scales (eg. '''do re fe sol ta do''').
	* Learn the inversions of these scales, which would be[[undertone scales]]. (Undertone scales would have smaller steps at the bottom of the scale, which would get larger as one ascends.)		* Learn the inversions of these scales, which would be [[undertone scales]]. (Undertone scales would have smaller steps at the bottom of the scale, which would get larger as one ascends.)
	* Borrow overtones & undertones from the overtones & undertones of the fundamental -- this process can produce rich fields of interlocking harmonic series, and is often the sort of thing that composers do when they're composing in just intonation. [[Harry Partch]]'s "Monophonic Fabric," which consists of 43 unequal tones per octave, is one famous example.		* Borrow overtones & undertones from the overtones & undertones of the fundamental -- this process can produce rich fields of interlocking harmonic series, and is often the sort of thing that composers do when they're composing in just intonation. [[Harry Partch]]'s "Monophonic Fabric," which consists of 43 unequal tones per octave, is one famous example.

BudjarnLambeth: /* Next steps */ removed bold

2024-02-19T11:49:14Z

Next steps: removed bold

← Older revision		Revision as of 11:49, 19 February 2024
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	* Experiment with using different pitches as the "tonic" of the scale (eg. '''sol lu ta do re mi fu sol''', which could be taken as the 7-note scale starting on '''sol''').		* Experiment with using different pitches as the "tonic" of the scale (eg. '''sol lu ta do re mi fu sol''', which could be taken as the 7-note scale starting on '''sol''').
	* Take subsets of larger scales, which are not strict adjacent overtone scales (eg. '''do re fe sol ta do''').		* Take subsets of larger scales, which are not strict adjacent overtone scales (eg. '''do re fe sol ta do''').
	* Learn the inversions of these scales, which would be ~~'''~~[[undertone scales]]~~'''~~. (Undertone scales would have smaller steps at the bottom of the scale, which would get larger as one ascends.)		* Learn the inversions of these scales, which would be[[undertone scales]]. (Undertone scales would have smaller steps at the bottom of the scale, which would get larger as one ascends.)
	* Borrow overtones & undertones from the overtones & undertones of the fundamental -- this process can produce rich fields of interlocking harmonic series, and is often the sort of thing that composers do when they're composing in just intonation. [[Harry Partch]]'s "Monophonic Fabric," which consists of 43 unequal tones per octave, is one famous example.		* Borrow overtones & undertones from the overtones & undertones of the fundamental -- this process can produce rich fields of interlocking harmonic series, and is often the sort of thing that composers do when they're composing in just intonation. [[Harry Partch]]'s "Monophonic Fabric," which consists of 43 unequal tones per octave, is one famous example.

← Older revision		Revision as of 14:37, 23 April 2026
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	[[File:Ji-5-6-7-8-9-10-csound-foscil-220hz.mp3\|right\|thumb\|270px\|Mode 5: 5:6:7:8:9:10]]		[[File:Ji-5-6-7-8-9-10-csound-foscil-220hz.mp3\|right\|thumb\|270px\|Mode 5: 5:6:7:8:9:10]]

	; [[5afdo\|Mode 5]]: 5:6:7:8:9:10 – This is essentially a [[7-limit]] fully-diminished seventh chord. [[7/5]] makes a very nice tritone above the bass – the simplest one available in JI – and it is available in all the higher Over-5 modes as well~~. This is the scale used by the Wagogo people of Tanzania~~.		; [[5afdo\|Mode 5]]: 5:6:7:8:9:10 – This is essentially a [[7-limit]] fully-diminished seventh chord. [[7/5]] makes a very nice tritone above the bass – the simplest one available in JI – and it is available in all the higher Over-5 modes as well.

	[[File:Ji-10-11-12-13-14-15-16-17-18-19-20-csound-foscil-220hz.mp3\|right\|thumb\|270px\|Mode 10 scale]]		[[File:Ji-10-11-12-13-14-15-16-17-18-19-20-csound-foscil-220hz.mp3\|right\|thumb\|270px\|Mode 10 scale]]

← Older revision		Revision as of 23:19, 10 August 2025
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	== See also ==		== See also ==
	* [[Andrew Heathwaite]]: The composer and wiki editor who authored this page and the majority of its contents
	* [[AFDO]]: An alternative framework for describing scales which overlaps substantially with overtone scales		* [[AFDO]]: An alternative framework for describing scales which overlaps substantially with overtone scales
	* [[Mike Sheiman's Very Easy Scale Building From The Harmonic Series Page]]: Another take on the subject of overtone scales		* [[Mike Sheiman's Very Easy Scale Building From The Harmonic Series Page]]: Another take on the subject of overtone scales