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Scale 1261: "Modified Blues"

Scale 1261: Modified Blues, Ian Ring Music Theory

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

Jazz and Blues
Modified Blues
Zeitler
Aeodian

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

{0,2,3,5,6,7,10}

Forte Number

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

7-27

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.

none

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.

yes
enantiomorph: 1765

Hemitonia

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

3 (trihemitonic)

Cohemitonia

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

1 (uncohemitonic)

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.

2

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: 695

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, 1, 2, 1, 1, 3, 2] 9

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.

<3, 4, 4, 4, 5, 1>

Interval Spectrum

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

p5m4n4s4d3t

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

Spectra Variation

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

2.286

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.

no

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.

2.549

Polygon Perimeter

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

5.967

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.

none

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".

Improper

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 TriadsD♯{3,7,10}331.43
A♯{10,2,5}142.14
Minor Triadscm{0,3,7}241.86
d♯m{3,6,10}321.29
gm{7,10,2}231.57
Augmented TriadsD+{2,6,10}331.43
Diminished Triads{0,3,6}231.71
Parsimonious Voice Leading Between Common Triads of Scale 1261. Created by Ian Ring ©2019 cm cm c°->cm d#m d#m c°->d#m D# D# cm->D# D+ D+ D+->d#m gm gm D+->gm A# A# D+->A# d#m->D# D#->gm

view full size

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.

Diameter4
Radius2
Self-Centeredno
Central Verticesd♯m
Peripheral Verticescm, A♯

Modes

Modes are the rotational transformation of this scale. Scale 1261 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 1339
Scale 1339: Kycrian, Ian Ring Music TheoryKycrian
3rd mode:
Scale 2717
Scale 2717: Epygian, Ian Ring Music TheoryEpygian
4th mode:
Scale 1703
Scale 1703: Mela Vanaspati, Ian Ring Music TheoryMela Vanaspati
5th mode:
Scale 2899
Scale 2899: Kagian, Ian Ring Music TheoryKagian
6th mode:
Scale 3497
Scale 3497: Phrolian, Ian Ring Music TheoryPhrolian
7th mode:
Scale 949
Scale 949: Mela Mararanjani, Ian Ring Music TheoryMela Mararanjani

Prime

The prime form of this scale is Scale 695

Scale 695Scale 695: Sarian, Ian Ring Music TheorySarian

Complement

The heptatonic modal family [1261, 1339, 2717, 1703, 2899, 3497, 949] (Forte: 7-27) is the complement of the pentatonic modal family [299, 689, 1417, 1573, 2197] (Forte: 5-27)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1261 is 1765

Scale 1765Scale 1765: Lonian, Ian Ring Music TheoryLonian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1261 is chiral, and its enantiomorph is scale 1765

Scale 1765Scale 1765: Lonian, Ian Ring Music TheoryLonian

Transformations:

T0 1261  T0I 1765
T1 2522  T1I 3530
T2 949  T2I 2965
T3 1898  T3I 1835
T4 3796  T4I 3670
T5 3497  T5I 3245
T6 2899  T6I 2395
T7 1703  T7I 695
T8 3406  T8I 1390
T9 2717  T9I 2780
T10 1339  T10I 1465
T11 2678  T11I 2930

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 1263Scale 1263: Stynyllic, Ian Ring Music TheoryStynyllic
Scale 1257Scale 1257: Blues Scale, Ian Ring Music TheoryBlues Scale
Scale 1259Scale 1259: Stadian, Ian Ring Music TheoryStadian
Scale 1253Scale 1253: Zolimic, Ian Ring Music TheoryZolimic
Scale 1269Scale 1269: Katythian, Ian Ring Music TheoryKatythian
Scale 1277Scale 1277: Zadyllic, Ian Ring Music TheoryZadyllic
Scale 1229Scale 1229: Raga Simharava, Ian Ring Music TheoryRaga Simharava
Scale 1245Scale 1245: Lathian, Ian Ring Music TheoryLathian
Scale 1197Scale 1197: Minor Hexatonic, Ian Ring Music TheoryMinor Hexatonic
Scale 1133Scale 1133: Stycrimic, Ian Ring Music TheoryStycrimic
Scale 1389Scale 1389: Minor Locrian, Ian Ring Music TheoryMinor Locrian
Scale 1517Scale 1517: Sagyllic, Ian Ring Music TheorySagyllic
Scale 1773Scale 1773: Blues Scale II, Ian Ring Music TheoryBlues Scale II
Scale 237Scale 237, Ian Ring Music Theory
Scale 749Scale 749: Aeologian, Ian Ring Music TheoryAeologian
Scale 2285Scale 2285: Aerogian, Ian Ring Music TheoryAerogian
Scale 3309Scale 3309: Bycryllic, Ian Ring Music TheoryBycryllic

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.