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Scale 1749: "Acoustic"

Scale 1749: Acoustic, Ian Ring Music Theory

Identical to Lydian but for its lowered seventh; this scale is named Lydian Dominant because its 1-3-5-7 members form a dominant seventh chord. The name "Acoustic" is more common, the name refers to its similarity to the eighth through 14th partials in the harmonic series. For this reason it is also known at the "overtone scale".


Bracelet Diagram

The bracelet shows tones that are in this scale, starting from the top (12 o'clock), going clockwise in ascending semitones. The "i" icon marks imperfect tones that do not have a tone a fifth above. Dotted lines indicate axes of symmetry.

Tonnetz Diagram

41161837294116105072918310504116183
Tonnetz diagrams are popular in Neo-Riemannian theory. Notes are arranged in a lattice where perfect 5th intervals are from left to right, major third are northeast, and major 6th intervals are northwest. Other directions are inverse of their opposite. This diagram helps to visualize common triads (they're triangles) and circle-of-fifth relationships (horizontal lines).

Common Names

Western Modern
Acoustic
Lydian Dominant
Overtone Scale
Western Altered
Mixolydian Sharp 4
Carnatic Mela
Mela Vacaspati
Carnatic Raga
Raga Bhusavati
Unknown / Unsorted
Bhusavali
Overtone
Overtone Dominant
Western Mixed
Lydian-Mixolydian
Lydian-Mixolydian Combo
Named After Composers
Bartok
Zeitler
Lythian

Analysis

Cardinality

Cardinality is the count of how many pitches are in the scale.

7 (heptatonic)

Pitch Class Set

The tones in this scale, expressed as numbers from 0 to 11

{0,2,4,6,7,9,10}

Forte Number

A code assigned by theorist Alan Forte, for this pitch class set and all of its transpositional (rotation) and inversional (reflection) transformations.

7-34

Rotational Symmetry

Some scales have rotational symmetry, sometimes known as "limited transposition". If there are any rotational symmetries, these are the intervals of periodicity.

none

Reflection Axes

If a scale has an axis of reflective symmetry, then it can transform into itself by inversion. It also implies that the scale has Ridge Tones. Notably an axis of reflection can occur directly on a tone or half way between two tones.

[2]

Palindromicity

A palindromic scale has the same pattern of intervals both ascending and descending.

no

Chirality

A chiral scale can not be transformed into its inverse by rotation. If a scale is chiral, then it has an enantiomorph.

no

Hemitonia

A hemitone is two tones separated by a semitone interval. Hemitonia describes how many such hemitones exist.

2 (dihemitonic)

Cohemitonia

A cohemitone is an instance of two adjacent hemitones. Cohemitonia describes how many such cohemitones exist.

0 (ancohemitonic)

Imperfections

An imperfection is a tone which does not have a perfect fifth above it in the scale. This value is the quantity of imperfections in this scale.

3

Modes

Modes are the rotational transformations of this scale. This number does not include the scale itself, so the number is usually one less than its cardinality; unless there are rotational symmetries then there are even fewer modes.

6

Prime Form

Describes if this scale is in prime form, using the Rahn/Ring formula.

no
prime: 1371

Deep Scale

A deep scale is one where the interval vector has 6 different digits.

no

Interval Formula

Defines the scale as the sequence of intervals between one tone and the next.

[2, 2, 2, 1, 2, 1, 2]

Interval Vector

Describes the intervallic content of the scale, read from left to right as the number of occurences of each interval size from semitone, up to six semitones.

<2, 5, 4, 4, 4, 2>

Interval Spectrum

The same as the Interval Vector, but expressed in a syntax used by Howard Hansen.

p4m4n4s5d2t2

Distribution Spectra

Describes the specific interval sizes that exist for each generic interval size. Each generic <g> has a spectrum {n,...}. The Spectrum Width is the difference between the highest and lowest values in each spectrum.

<1> = {1,2}
<2> = {3,4}
<3> = {4,5,6}
<4> = {6,7,8}
<5> = {8,9}
<6> = {10,11}

Spectra Variation

Determined by the Distribution Spectra; this is the sum of all spectrum widths divided by the scale cardinality.

1.143

Maximally Even

A scale is maximally even if the tones are optimally spaced apart from each other.

no

Maximal Area Set

A scale is a maximal area set if a polygon described by vertices dodecimetrically placed around a circle produces the maximal interior area for scales of the same cardinality. All maximally even sets have maximal area, but not all maximal area sets are maximally even.

yes

Interior Area

Area of the polygon described by vertices placed for each tone of the scale dodecimetrically around a unit circle, ie a circle with radius of 1.

2.665

Polygon Perimeter

Perimeter of the polygon described by vertices placed for each tone of the scale dodecimetrically around a unit circle.

6.035

Myhill Property

A scale has Myhill Property if the Interval Spectra has exactly two specific intervals for every generic interval.

no

Balanced

A scale is balanced if the distribution of its tones would satisfy the "centrifuge problem", ie are placed such that it would balance on its centre point.

no

Ridge Tones

Ridge Tones are those that appear in all transpositions of a scale upon the members of that scale. Ridge Tones correspond directly with axes of reflective symmetry.

[4]

Propriety

Also known as Rothenberg Propriety, named after its inventor. Propriety describes whether every specific interval is uniquely mapped to a generic interval. A scale is either "Proper", "Strictly Proper", or "Improper".

Proper

Tertian Harmonic Chords

Tertian chords are made from alternating members of the scale, ie built from "stacked thirds". Not all scales lend themselves well to tertian harmony.

Common Triads

These are the common triads (major, minor, augmented and diminished) that you can create from members of this scale.

* Pitches are shown with C as the root

Triad TypeTriad*Pitch ClassesDegreeEccentricityCloseness Centrality
Major TriadsC{0,4,7}231.71
D{2,6,9}231.71
Minor Triadsgm{7,10,2}231.71
am{9,0,4}231.71
Augmented TriadsD+{2,6,10}231.71
Diminished Triads{4,7,10}231.71
f♯°{6,9,0}231.71
Parsimonious Voice Leading Between Common Triads of Scale 1749. Created by Ian Ring ©2019 C C C->e° am am C->am D D D+ D+ D->D+ f#° f#° D->f#° gm gm D+->gm e°->gm f#°->am

Above is a graph showing opportunities for parsimonious voice leading between triads*. Each line connects two triads that have two common tones, while the third tone changes by one generic scale step.

Diameter3
Radius3
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 1749 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 1461
Scale 1461: Major-Minor, Ian Ring Music TheoryMajor-Minor
3rd mode:
Scale 1389
Scale 1389: Minor Locrian, Ian Ring Music TheoryMinor Locrian
4th mode:
Scale 1371
Scale 1371: Superlocrian, Ian Ring Music TheorySuperlocrianThis is the prime mode
5th mode:
Scale 2733
Scale 2733: Melodic Minor Ascending, Ian Ring Music TheoryMelodic Minor Ascending
6th mode:
Scale 1707
Scale 1707: Dorian Flat 2, Ian Ring Music TheoryDorian Flat 2
7th mode:
Scale 2901
Scale 2901: Lydian Augmented, Ian Ring Music TheoryLydian Augmented

Prime

The prime form of this scale is Scale 1371

Scale 1371Scale 1371: Superlocrian, Ian Ring Music TheorySuperlocrian

Complement

The heptatonic modal family [1749, 1461, 1389, 1371, 2733, 1707, 2901] (Forte: 7-34) is the complement of the pentatonic modal family [597, 681, 1173, 1317, 1353] (Forte: 5-34)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1749 is 1389

Scale 1389Scale 1389: Minor Locrian, Ian Ring Music TheoryMinor Locrian

Transformations:

T0 1749  T0I 1389
T1 3498  T1I 2778
T2 2901  T2I 1461
T3 1707  T3I 2922
T4 3414  T4I 1749
T5 2733  T5I 3498
T6 1371  T6I 2901
T7 2742  T7I 1707
T8 1389  T8I 3414
T9 2778  T9I 2733
T10 1461  T10I 1371
T11 2922  T11I 2742

Nearby Scales:

These are other scales that are similar to this one, created by adding a tone, removing a tone, or moving one note up or down a semitone.

Scale 1751Scale 1751: Aeolyryllic, Ian Ring Music TheoryAeolyryllic
Scale 1745Scale 1745: Raga Vutari, Ian Ring Music TheoryRaga Vutari
Scale 1747Scale 1747: Mela Ramapriya, Ian Ring Music TheoryMela Ramapriya
Scale 1753Scale 1753: Hungarian Major, Ian Ring Music TheoryHungarian Major
Scale 1757Scale 1757, Ian Ring Music Theory
Scale 1733Scale 1733: Raga Sarasvati, Ian Ring Music TheoryRaga Sarasvati
Scale 1741Scale 1741: Lydian Diminished, Ian Ring Music TheoryLydian Diminished
Scale 1765Scale 1765: Lonian, Ian Ring Music TheoryLonian
Scale 1781Scale 1781: Gocryllic, Ian Ring Music TheoryGocryllic
Scale 1685Scale 1685: Zeracrimic, Ian Ring Music TheoryZeracrimic
Scale 1717Scale 1717: Mixolydian, Ian Ring Music TheoryMixolydian
Scale 1621Scale 1621: Scriabin's Prometheus, Ian Ring Music TheoryScriabin's Prometheus
Scale 1877Scale 1877: Aeroptian, Ian Ring Music TheoryAeroptian
Scale 2005Scale 2005: Gygyllic, Ian Ring Music TheoryGygyllic
Scale 1237Scale 1237: Salimic, Ian Ring Music TheorySalimic
Scale 1493Scale 1493: Lydian Minor, Ian Ring Music TheoryLydian Minor
Scale 725Scale 725: Raga Yamuna Kalyani, Ian Ring Music TheoryRaga Yamuna Kalyani
Scale 2773Scale 2773: Lydian, Ian Ring Music TheoryLydian
Scale 3797Scale 3797: Rocryllic, Ian Ring Music TheoryRocryllic

This scale analysis was created by Ian Ring, Canadian Composer of works for Piano, and total music theory nerd. Scale notation generated by VexFlow, graph visualization by Graphviz, and MIDI playback by MIDI.js. Some scale names used on this and other pages are ©2005 William Zeitler (http://allthescales.org) used with permission.

Pitch spelling algorithm employed here is adapted from a method by Uzay Bora, Baris Tekin Tezel, and Alper Vahaplar. (An algorithm for spelling the pitches of any musical scale) Contact authors Patent owner: Dokuz Eylül University, Used with Permission. Contact TTO

Tons of background resources contributed to the production of this summary; for a list of these peruse this Bibliography. Special thanks to Richard Repp for helping with technical accuracy.