User:CompactStar/Overtone scale - Revision history

CompactStar at 02:40, 3 June 2024

2024-06-03T02:40:38Z

← Older revision		Revision as of 02:40, 3 June 2024
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	An '''overtone scale''' is an octave-long subset of the [[harmonic series]] repeating at the octave. ~~Alternative terms for overtone scale include~~ '''AFDO''' (arithmetic frequency divisions of the octave) due to an overtone scale being an arithmetically equal division of the octave, and '''ODO''' ([[otonal division]]s of the octave).		An '''overtone scale''' is an octave-long subset of the [[harmonic series]] repeating at the octave. It is also known as an '''AFDO''' (arithmetic frequency divisions of the octave) due to an overtone scale being an arithmetically equal division of the octave, and '''ODO''' ([[otonal division]]s of the octave).

	An overtone scale with n notes maybe referred to as mode n of the [[harmonic series]] or n-AFDO. For example, [[Mode 5]] is a pentatonic scale with the intervals [[1/1]]-[[6/5]]-[[7/5]]-[[8/5]]-[[9/5]]-[[2/1]] or the 5th to 10th harmonics:		An overtone scale with n notes maybe referred to as mode n of the [[harmonic series]] or n-AFDO. For example, [[Mode 5]] is a pentatonic scale with the intervals [[1/1]]-[[6/5]]-[[7/5]]-[[8/5]]-[[9/5]]-[[2/1]] or the 5th to 10th harmonics:

2024-06-03T02:40:23Z

← Older revision		Revision as of 02:40, 3 June 2024
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	An '''overtone scale''' is an octave-long subset of the [[harmonic series]] repeating at the octave. Alternative terms for overtone scale include '''~~ADO~~''' (arithmetic divisions of the octave) due to an overtone scale being an arithmetically equal division of the octave, and '''ODO''' ([[otonal division]]s of the octave).		An '''overtone scale''' is an octave-long subset of the [[harmonic series]] repeating at the octave. Alternative terms for overtone scale include '''AFDO''' (arithmetic frequency divisions of the octave) due to an overtone scale being an arithmetically equal division of the octave, and '''ODO''' ([[otonal division]]s of the octave).

	An overtone scale with n notes maybe referred to as mode n of the [[harmonic series]] or n-~~ADO~~. For example, [[Mode 5]] is a pentatonic scale with the intervals [[1/1]]-[[6/5]]-[[7/5]]-[[8/5]]-[[9/5]]-[[2/1]] or the 5th to 10th harmonics:		An overtone scale with n notes maybe referred to as mode n of the [[harmonic series]] or n-AFDO. For example, [[Mode 5]] is a pentatonic scale with the intervals [[1/1]]-[[6/5]]-[[7/5]]-[[8/5]]-[[9/5]]-[[2/1]] or the 5th to 10th harmonics:

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2023-03-02T04:48:55Z

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	\| '''sol'''		\| '''sol'''
	\|}		\|}
	== ~~List of~~ overtone scales ==		== Individual pages for overtone scales ==
	* [[Mode 2]]		* [[Mode 2]]
	* [[Mode 3]]		* [[Mode 3]]

2023-03-02T04:43:13Z

← Older revision	Revision as of 04:43, 2 March 2023
(No difference)

2023-03-02T04:42:28Z

← Older revision		Revision as of 04:42, 2 March 2023
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	R_n = R_1 + (n-1)d		R_n = R_1 + (n-1)d
	</math>		</math>


			== Over-n scales ==
			Another way to describe Mode 5 is that it is an example of an "Over-5 Scale." As 5 is octave-redundant with 10, 20, 40, 80 etc, any scale with one of those (the form is technically 2<sup>n</sup>*5, where n is any integer greater than or equal to zero) in the denominator of every tone could be called an Over-5 Scale.

	== Lengths ==		== Lengths ==

2023-03-02T04:40:15Z

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 | '''sol'''
 |}
 == See also ==
 * [[Arithmetic temperament]]

2023-03-02T04:38:30Z

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	\|}		\|}
	== See also ==		== See also ==
	* * [[Arithmetic temperament]]		* [[Arithmetic temperament]]
	* [[Arithmetic MOS scale]]		* [[Arithmetic MOS scale]]
	* [http://240edo.googlepages.com/ADO-EDL.XLS Fret position calculator] (excel sheet) based on EDL system and string length		* [http://240edo.googlepages.com/ADO-EDL.XLS Fret position calculator] (excel sheet) based on EDL system and string length

2023-03-02T04:38:17Z

← Older revision		Revision as of 04:38, 2 March 2023
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	\| '''sol'''		\| '''sol'''
	\|}		\|}
			== See also ==
			* * [[Arithmetic temperament]]
			* [[Arithmetic MOS scale]]
			* [http://240edo.googlepages.com/ADO-EDL.XLS Fret position calculator] (excel sheet) based on EDL system and string length
			* How to approximate EDO and ADO systems with each other? [https://sites.google.com/site/240edo/ADOandEDO.xls Download this file]
			* [http://www.soundtransformations.btinternet.co.uk/Danerhudyarthemarmonicseries.htm Magic of Tone and the Art of Music by the late Dane Rhudyar]
			* [[Primodality]]
			* [[8th Octave Overtone Tuning]]

2023-03-02T04:36:44Z

← Older revision		Revision as of 04:36, 2 March 2023
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	</math>		</math>

			== Lengths ==
			If the first division has ratio of R1 and length of L1 and the last, Rn and Ln , we have: Ln = 1/Rn and if Rn >........> R3 > R2 > R1 so :

			L1 > L2 > L3 > …… > Ln

			[[File:ADO-4.jpg\|350px\|center]]

			This lengths are related to reverse of ratios in system.The above picture shows the differences between divisions of length in Mode 12 system . On the contrary , we have equal divisions of length in [https://sites.google.com/site/240edo/equaldivisionsoflength(edl) EDL system]:
			[[File:ADO-5.jpg\|346px\|center]]

	== Relation to superparticular ratios ==		== Relation to superparticular ratios ==

2023-03-02T04:35:52Z

← Older revision		Revision as of 04:35, 2 March 2023
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	An '''overtone scale''' is an octave-long subset of the [[harmonic series]] repeating at the octave. Alternative terms for overtone scale include '''ADO''' (arithmetic divisions of the octave) due to an overtone scale being an arithmetically equal division of the octave, and '''ODO''' ([[otonal division]]s of the octave).		An '''overtone scale''' is an octave-long subset of the [[harmonic series]] repeating at the octave. Alternative terms for overtone scale include '''ADO''' (arithmetic divisions of the octave) due to an overtone scale being an arithmetically equal division of the octave, and '''ODO''' ([[otonal division]]s of the octave).

	An overtone scale with n notes maybe referred to as mode n of the [[harmonic series]] or n-ADO. For example, [[Mode 5]] is a pentatonic scale with the intervals [[1/1]]-[[6/5]]-[[7/5]]-[[8/5]]-[[9/5]]-[[2/1]]:		An overtone scale with n notes maybe referred to as mode n of the [[harmonic series]] or n-ADO. For example, [[Mode 5]] is a pentatonic scale with the intervals [[1/1]]-[[6/5]]-[[7/5]]-[[8/5]]-[[9/5]]-[[2/1]] or the 5th to 10th harmonics:

	{\| class="wikitable"		{\| class="wikitable"