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Scale 3499: "Hamel"

Scale 3499: Hamel, 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

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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

Named After Composers
Hamel
Peter Hamel Octatonic
Zeitler
Lythyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,3,5,7,8,10,11}
Forte Number8-22
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2743
Hemitonia4 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections2
Modes7
Prime?no
prime: 1391
Deep Scaleno
Interval Vector465562
Interval Spectrump6m5n5s6d4t2
Distribution Spectra<1> = {1,2}
<2> = {2,3,4}
<3> = {3,4,5,6}
<4> = {5,6,7}
<5> = {6,7,8,9}
<6> = {8,9,10}
<7> = {10,11}
Spectra Variation1.75
Maximally Evenno
Maximal Area Setyes
Interior Area2.732
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicno

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♯{1,5,8}242.1
D♯{3,7,10}242.1
G♯{8,0,3}341.9
Minor Triadscm{0,3,7}242.1
fm{5,8,0}341.9
g♯m{8,11,3}341.9
a♯m{10,1,5}242.3
Augmented TriadsD♯+{3,7,11}341.9
Diminished Triads{5,8,11}242.1
{7,10,1}242.3
Parsimonious Voice Leading Between Common Triads of Scale 3499. Created by Ian Ring ©2019 cm cm D#+ D#+ cm->D#+ G# G# cm->G# C# C# fm fm C#->fm a#m a#m C#->a#m D# D# D#->D#+ D#->g° g#m g#m D#+->g#m f°->fm f°->g#m fm->G# g°->a#m g#m->G#

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
Radius4
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 3499 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3797
Scale 3797: Rocryllic, Ian Ring Music TheoryRocryllic
3rd mode:
Scale 1973
Scale 1973: Zyryllic, Ian Ring Music TheoryZyryllic
4th mode:
Scale 1517
Scale 1517: Sagyllic, Ian Ring Music TheorySagyllic
5th mode:
Scale 1403
Scale 1403: Espla's Scale, Ian Ring Music TheoryEspla's Scale
6th mode:
Scale 2749
Scale 2749: Katagyllic, Ian Ring Music TheoryKatagyllic
7th mode:
Scale 1711
Scale 1711: Adonai Malakh, Ian Ring Music TheoryAdonai Malakh
8th mode:
Scale 2903
Scale 2903: Gothyllic, Ian Ring Music TheoryGothyllic

Prime

The prime form of this scale is Scale 1391

Scale 1391Scale 1391: Aeradyllic, Ian Ring Music TheoryAeradyllic

Complement

The octatonic modal family [3499, 3797, 1973, 1517, 1403, 2749, 1711, 2903] (Forte: 8-22) is the complement of the tetratonic modal family [149, 673, 1061, 1289] (Forte: 4-22)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3499 is 2743

Scale 2743Scale 2743: Staptyllic, Ian Ring Music TheoryStaptyllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3499 is chiral, and its enantiomorph is scale 2743

Scale 2743Scale 2743: Staptyllic, Ian Ring Music TheoryStaptyllic

Transformations:

T0 3499  T0I 2743
T1 2903  T1I 1391
T2 1711  T2I 2782
T3 3422  T3I 1469
T4 2749  T4I 2938
T5 1403  T5I 1781
T6 2806  T6I 3562
T7 1517  T7I 3029
T8 3034  T8I 1963
T9 1973  T9I 3926
T10 3946  T10I 3757
T11 3797  T11I 3419

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 3497Scale 3497: Phrolian, Ian Ring Music TheoryPhrolian
Scale 3501Scale 3501: Maqam Nahawand, Ian Ring Music TheoryMaqam Nahawand
Scale 3503Scale 3503: Zyphygic, Ian Ring Music TheoryZyphygic
Scale 3491Scale 3491: Tharian, Ian Ring Music TheoryTharian
Scale 3495Scale 3495: Banyllic, Ian Ring Music TheoryBanyllic
Scale 3507Scale 3507: Maqam Hijaz, Ian Ring Music TheoryMaqam Hijaz
Scale 3515Scale 3515: Moorish Phrygian, Ian Ring Music TheoryMoorish Phrygian
Scale 3467Scale 3467: Katonian, Ian Ring Music TheoryKatonian
Scale 3483Scale 3483: Mixotharyllic, Ian Ring Music TheoryMixotharyllic
Scale 3531Scale 3531: Neveseri, Ian Ring Music TheoryNeveseri
Scale 3563Scale 3563: Ionoptygic, Ian Ring Music TheoryIonoptygic
Scale 3371Scale 3371: Aeolylian, Ian Ring Music TheoryAeolylian
Scale 3435Scale 3435: Prokofiev, Ian Ring Music TheoryProkofiev
Scale 3243Scale 3243: Mela Rupavati, Ian Ring Music TheoryMela Rupavati
Scale 3755Scale 3755: Phryryllic, Ian Ring Music TheoryPhryryllic
Scale 4011Scale 4011: Styrygic, Ian Ring Music TheoryStyrygic
Scale 2475Scale 2475: Neapolitan Minor, Ian Ring Music TheoryNeapolitan Minor
Scale 2987Scale 2987: Neapolitan Major and Minor Mixed, Ian Ring Music TheoryNeapolitan Major and Minor Mixed
Scale 1451Scale 1451: Phrygian, Ian Ring Music TheoryPhrygian

This scale analysis was created by Ian Ring, Canadian Composer of works for Piano, and total music theory nerd. The software used to generate this analysis is an open source project at GitHub. 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.